From dddc8d7a470da719c0bbec95ee59745a8bc47478 Mon Sep 17 00:00:00 2001
From: Brian Delhaisse <briandelhaisse@gmail.com>
Date: Wed, 1 May 2019 05:50:54 +0200
Subject: [PATCH] update world: update heightmap and terrain generators

---
 .../worlds/utils/heightmap_generator.py       |    434 -
 .../worlds/utils/heightmaps/__init__.py       |      1 +
 .../worlds/utils/heightmaps/diamond_square.py |    223 +
 .../worlds/utils/heightmaps/equation.py       |     56 +
 .../worlds/utils/heightmaps/geospatial.py     |     91 +
 pyrobolearn/worlds/utils/heightmaps/gpr.py    |    109 +
 pyrobolearn/worlds/utils/heightmaps/plot.py   |     77 +
 pyrobolearn/worlds/utils/heightmaps/rbf.py    |     81 +
 pyrobolearn/worlds/utils/obj_generator.py     |    334 +
 .../worlds/utils/pictures/canyon-geo.tif      |    Bin 0 -> 6803623 bytes
 pyrobolearn/worlds/utils/pictures/dem.jpg     |    Bin 0 -> 16854 bytes
 .../worlds/utils/pictures/heightmap.png       |    Bin 0 -> 5897 bytes
 pyrobolearn/worlds/utils/pictures/map.bmp     |    Bin 0 -> 198458 bytes
 pyrobolearn/worlds/utils/terrain_generator.py |    403 -
 .../utils/terrains/terrain_heightmap.obj      |  82181 +++++
 .../worlds/utils/terrains/terrain_map.obj     | 263174 +++++++++++++++
 .../terrains/terrain_smooth_heightmap.obj     |  66054 ++++
 pyrobolearn/worlds/world.py                   |    289 +-
 18 files changed, 412550 insertions(+), 957 deletions(-)
 delete mode 100644 pyrobolearn/worlds/utils/heightmap_generator.py
 create mode 100644 pyrobolearn/worlds/utils/heightmaps/__init__.py
 create mode 100644 pyrobolearn/worlds/utils/heightmaps/diamond_square.py
 create mode 100644 pyrobolearn/worlds/utils/heightmaps/equation.py
 create mode 100644 pyrobolearn/worlds/utils/heightmaps/geospatial.py
 create mode 100644 pyrobolearn/worlds/utils/heightmaps/gpr.py
 create mode 100644 pyrobolearn/worlds/utils/heightmaps/plot.py
 create mode 100644 pyrobolearn/worlds/utils/heightmaps/rbf.py
 create mode 100644 pyrobolearn/worlds/utils/obj_generator.py
 create mode 100755 pyrobolearn/worlds/utils/pictures/canyon-geo.tif
 create mode 100755 pyrobolearn/worlds/utils/pictures/dem.jpg
 create mode 100755 pyrobolearn/worlds/utils/pictures/heightmap.png
 create mode 100644 pyrobolearn/worlds/utils/pictures/map.bmp
 delete mode 100644 pyrobolearn/worlds/utils/terrain_generator.py
 create mode 100644 pyrobolearn/worlds/utils/terrains/terrain_heightmap.obj
 create mode 100644 pyrobolearn/worlds/utils/terrains/terrain_map.obj
 create mode 100644 pyrobolearn/worlds/utils/terrains/terrain_smooth_heightmap.obj

diff --git a/pyrobolearn/worlds/utils/heightmap_generator.py b/pyrobolearn/worlds/utils/heightmap_generator.py
deleted file mode 100644
index c257f06..0000000
--- a/pyrobolearn/worlds/utils/heightmap_generator.py
+++ /dev/null
@@ -1,434 +0,0 @@
-#!/usr/bin/env python
-"""Provide heightmap generators.
-
-The various functions defined here generate
-"""
-
-import numpy as np
-from sklearn.gaussian_process import GaussianProcessRegressor
-from sklearn.gaussian_process.kernels import RBF
-from scipy.interpolate import Rbf
-
-try:
-    import gdal
-except ImportError as e:
-    raise ImportError(repr(e) + '\nTry to install gdal: pip install gdal')
-
-
-__author__ = "Brian Delhaisse"
-__copyright__ = "Copyright 2018, PyRoboLearn"
-__credits__ = ["Brian Delhaisse"]
-__license__ = "MIT"
-__version__ = "1.0.0"
-__maintainer__ = "Brian Delhaisse"
-__email__ = "briandelhaisse@gmail.com"
-__status__ = "Development"
-
-
-def diamond_square_algorithm(n=8, init_values=None, noise=0, lower_bound=0, upper_bound=255, dtype=np.int, seed=None):
-    r"""Diamond-Square Algorithm
-
-    This function implements the diamond-square algorithm [1], to generate random terrains given an initial value
-    for each corner.
-
-    Warnings: the diamond-square algo assumes that the heightmap is a 2D square array.
-
-    Args:
-        n (int): number of points (must be a power of 2). From this, the width and the height will automatically be
-            computed, such that width = height = 2**n + 1.
-        init_values (np.array[4], None): the four initial values for the corners. If None, it will generate 4 values
-            randomly such that they are between the lower_bound and upper_bound.
-        noise (int,float): noise level to add. This corresponds to the standard deviation of the normal distribution.
-        lower_bound (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
-        upper_bound (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
-        dtype (np.int, np.float): type of the returned array for the heightmap
-        seed (int, None): random seed
-
-    Returns:
-        np.array[2**n+1, 2**n+1]: resulting 2D square heightmap
-
-    References:
-        [1] Wikipedia: https://en.wikipedia.org/wiki/Diamond-square_algorithm
-        [2] https://blog.habrador.com/2013/02/how-to-generate-random-terrain.html
-    """
-    # set the seed if given
-    if seed:
-        np.random.seed(seed)
-
-    # create initial heightmap
-    width, height = 2**n + 1, 2**n + 1
-    heightmap = -1 * np.ones((height, width), dtype=dtype)
-    if not init_values:
-        if dtype == np.int:
-            init_values = np.random.randint(low=lower_bound, high=upper_bound+1, size=4)
-        else:
-            init_values = np.random.uniform(low=lower_bound, high=upper_bound, size=4)
-    heightmap[0, 0], heightmap[0, width - 1], heightmap[height - 1, 0], heightmap[height - 1, width - 1] = init_values
-
-    # define diamond-square step function
-    def diamond_square_step(heightmap, square=None, noise=0, lower_bound=0, upper_bound=255):
-        """
-        Diamond-square step which  which performs a diamond step followed by a square step.
-
-        Args:
-            heightmap (np.array[2*N+1,2*N+1]): heightmap (initial square)
-            square (np.array[M,M]): the current square we focus on.
-        """
-        # if no square given
-        if square is None:
-            height, width = heightmap.shape
-            square = np.array([[0, 0], [width - 1, 0], [width - 1, height - 1], [0, height - 1]])
-
-        # check size of square
-        xmin, xmax, ymin, ymax = square[:, 0].min(), square[:, 0].max(), square[:, 1].min(), square[:, 1].max()
-        dx, dy = (xmax - xmin), (ymax - ymin)
-        if dx == 0 or dx == 1 or dy == 0 or dy == 1:
-            return
-
-        # DIAMOND STEP
-        center = np.array([xmin + dx / 2, ymin + dy / 2])
-        yc, xc = center
-        heightmap[xc, yc] = np.mean([heightmap[x, y] for (y, x) in square])  # + np.random.normal(scale=noise)
-        heightmap[xc, yc] = min(max(lower_bound, heightmap[xc, yc]), upper_bound)  # lower and upper bound
-
-        # SQUARE STEP
-        # triangles: a triangle is defined by 3 points
-        triangles = np.array([[c1, c2, center] for c1, c2 in zip(square, list(square[1:]) + [square[0]])])
-
-        squares = []
-        for i, triangle in enumerate(triangles):
-            xmin, xmax, ymin, ymax = triangle[:, 0].min(), triangle[:, 0].max(), triangle[:, 1].min(), triangle[:,
-                                                                                                       1].max()
-
-            if i == 0:  # upper triangle
-                center = np.array([xmin + (xmax - xmin) / 2, ymin])
-                square = np.array([[xmin, ymin], center, [center[0], ymax], [xmin, ymax]])  # left upper square
-            elif i == 1:  # right triangle
-                center = np.array([xmax, ymin + (ymax - ymin) / 2])
-                square = np.array([[xmin, ymin], [xmax, ymin], center, [xmin, center[1]]])  # right upper square
-            elif i == 2:  # lower triangle
-                center = np.array([xmin + (xmax - xmin) / 2, ymax])
-                square = np.array([[center[0], ymin], [xmax, ymin], [xmax, ymax], center])  # right lower square
-            else:  # left triangle
-                center = np.array([xmin, ymin + (ymax - ymin) / 2])
-                square = np.array([center, [xmax, center[1]], [xmax, ymax], [xmin, ymax]])  # left lower square
-
-            yc, xc = center
-            heightmap[xc, yc] = np.mean([heightmap[x, y] for (y, x) in triangle])  # + np.random.normal(scale=noise)
-            heightmap[xc, yc] = min(max(lower_bound, heightmap[xc, yc]), upper_bound)  # lower and upper bound
-
-            # a square is defined by 4 points
-            squares.append(square)
-
-        # for each subsquare in the original square, compute the heightmap recursively
-        for square in squares:
-            diamond_square_step(heightmap, square, noise, lower_bound, upper_bound)
-
-    # start diamond-square algorithm (recursively)
-    diamond_square_step(heightmap, noise=noise, lower_bound=lower_bound, upper_bound=upper_bound)
-    return heightmap
-
-
-def heightmap_gpr(init_values, x, y, kernel=None, alpha=1e-10, lower_bound=0, upper_bound=255, dtype=np.int):
-    r"""
-    Generate a heightmap using gaussian process regression. The advantages of using this method over others to
-    generate terrains lies in the capacity of adding prior knowledge through the kernel and the given initial values.
-    For instance, using a RBF kernel means that we want a smooth terrain instead of a bumpy one.
-    Furthermore, it allows to generate heightmaps which are not necessary square; i.e. they can be rectangular.
-
-    Warnings: this is pretty difficult to exploit if the given data is not consistent. See `heigthmap_rbf` for
-        a better way to generate heightmap.
-
-    Args:
-        init_values (np.array[M,3]): list of `M` 3D points which corresponds to initial values that are used to fit
-            the gaussian process.
-        x (np.array[N], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
-            from the meshgrid is expected. This is used to predict the heightmap at the given points.
-        y (np.array[0], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
-            from the meshgrid is expected. This is used to predict the heightmap at the given points.
-        kernel (None, sklearn.gaussian_process.kernels.Kernel): "The kernel specifying the covariance function of
-            the GP. If None is passed, the kernel '1.0 * RBF(1.0)' is used as default. Note that the kernel's
-            hyperparameters are optimized during fitting" [2]
-        alpha (float, array_like): "Value added to the diagonal of the kernel matrix during fitting. Larger values
-            correspond to increased noise level in the observations. This can also prevent a potential numerical issue
-            during fitting, by ensuring that the calculated values form a positive definite matrix. If an array is
-            passed, it must have the same number of entries as the data used for fitting and is used as
-            datapoint-dependent noise level. Note that this is equivalent to adding a WhiteKernel with c=alpha.
-            Allowing to specify the noise level directly as a parameter is mainly for convenience and for consistency
-            with Ridge." [2]
-        lower_bound (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
-        upper_bound (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
-        dtype (np.int, np.float): type of the returned array for the heightmap
-
-    Returns:
-        np.array[N,O]: resulting 2D heightmap
-
-    References:
-        [1] "Gaussian Processes for Machine Learning", Rasmussen and Williams, 2006
-        [2] Sklearn: https://scikit-learn.org/stable/modules/gaussian_process.html
-    """
-    # check given x and y
-    if len(x.shape) == 1 and len(y.shape) == 1:
-        x, y = np.meshgrid(x, y)
-    if x.shape != y.shape:
-        raise ValueError("Expecting x and y to have the same shape, which should be the case if it is a meshgrid")
-
-    # compute the minimum distance between points
-    N = len(init_values)
-    min_dist = np.inf
-    for i in range(N):
-        for j in range(i+1, N):
-            dist = np.linalg.norm(init_values[i, :2] - init_values[j, :2])
-            if dist < min_dist:
-                min_dist = dist
-    print("Min dist: {}".format(min_dist))
-
-    # check initial values
-    if not isinstance(init_values, np.ndarray):
-        raise TypeError("Expecting init_values to be a numpy array")
-    if init_values.shape[1] != 3:
-        raise ValueError("Expecting a numpy array of 3D points for init_values")
-
-    # create gaussian process and fit on the given initial values
-    kernel = RBF(length_scale=np.sqrt(min_dist))
-    gpr = GaussianProcessRegressor(kernel=kernel, alpha=alpha, normalize_y=True)
-    gpr.fit(init_values[:, :2], init_values[:, 2])
-
-    # predict the heightmap using GPR
-    X = np.dstack((x, y)).reshape(-1, 2)
-    heightmap = gpr.predict(X)
-    heightmap = heightmap.reshape(x.shape)
-
-    print("Params: {}".format(gpr.get_params()))
-
-    # make sure the values of the heightmap are between the bounds (in-place), and is the correct type
-    np.clip(heightmap, lower_bound, upper_bound, heightmap)
-    heightmap.astype(dtype)
-
-    return heightmap
-
-
-def heightmap_rbf(init_values, x, y, function='multiquadric', lower_bound=0, upper_bound=255, dtype=np.int):
-    r"""
-    Generate heightmap by interpolating the given initial points using RBF functions.
-
-    Advantages: fast and easy to use, and the results are pretty good. Heightmaps can also be rectangular.
-
-    Args:
-        init_values (np.array[M,3]): list of `M` 3D points which corresponds to initial values that are used to fit
-            the gaussian process.
-        x (np.array[N], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
-            from the meshgrid is expected. This is used to predict the heightmap at the given points.
-        y (np.array[0], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
-            from the meshgrid is expected. This is used to predict the heightmap at the given points.
-        function (str, callable): "The radial basis function, based on the radius, r, given by the norm
-            (default is Euclidean distance);
-                'multiquadric': sqrt((r/self.epsilon)**2 + 1)
-                'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1)
-                'gaussian': exp(-(r/self.epsilon)**2)
-                'linear': r
-                'cubic': r**3
-                'quintic': r**5
-                'thin_plate': r**2 * log(r)
-            If callable, then it must take 2 arguments (self, r). The epsilon parameter will be available as
-            self.epsilon. Other keyword arguments passed in will be available as well." [1]
-        lower_bound (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
-        upper_bound (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
-        dtype (np.int, np.float): type of the returned array for the heightmap
-
-    Returns:
-        np.array[N,O]: resulting 2D heightmap
-
-    References:
-        [1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.Rbf.html
-    """
-    # check given x and y
-    if len(x.shape) == 1 and len(y.shape) == 1:
-        x, y = np.meshgrid(x, y)
-    if x.shape != y.shape:
-        raise ValueError("Expecting x and y to have the same shape, which should be the case if it is a meshgrid")
-    origin_shape = x.shape
-
-    rbf = Rbf(init_values[:, 0], init_values[:, 1], init_values[:, 2], function=function)
-    heightmap = rbf(x.reshape(-1), y.reshape(-1))
-    heightmap = heightmap.reshape(origin_shape)
-
-    # make sure the values of the heightmap are between the bounds (in-place), and is the correct type
-    np.clip(heightmap, lower_bound, upper_bound, heightmap)
-    heightmap.astype(dtype)
-
-    return heightmap
-
-
-def heightmap_equation(x, y, z, lower_bound=0, upper_bound=255, dtype=np.int):
-    r"""
-    Generate heightmap from 3D equation :math:`z = f(x,y)`.
-
-    Args:
-        x (np.array[N], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
-            from the meshgrid is expected. This is used to predict the heightmap at the given points.
-        y (np.array[0], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
-            from the meshgrid is expected. This is used to predict the heightmap at the given points.
-        z (callable): it must be a function that accepts two arguments `x` and `y` which will be the arrays from the
-            meshgrid.
-        lower_bound (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
-        upper_bound (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
-        dtype (np.int, np.float): type of the returned array for the heightmap
-
-    Examples of 2D surfaces:
-        z = lambda x,y: np.log(y)
-        z = lambda x,y: np.sin(np.pi * x) * np.sin(np.pi * y)
-
-    Returns:
-        np.array[N,O]: resulting 2D heightmap
-    """
-    # check given x and y
-    if len(x.shape) == 1 and len(y.shape) == 1:
-        x, y = np.meshgrid(x, y)
-    if x.shape != y.shape:
-        raise ValueError("Expecting x and y to have the same shape, which should be the case if it is a meshgrid")
-    origin_shape = x.shape
-
-    # call z function: z=f(x,y)
-    heightmap = z(x, y)
-
-    # make sure the values of the heightmap are between the bounds (in-place), and is the correct type
-    np.clip(heightmap, lower_bound, upper_bound, heightmap)
-    heightmap.astype(dtype)
-
-    return heightmap
-
-
-def heightmap_gdal(filename, subsample=None, interpolate_fct='multiquadric', lower_bound=0, upper_bound=255,
-                   dtype=np.int):
-    r"""
-    Heightmap generated using the Geospatial Data Abstraction Library (GDAL), which allows to open Digital Elevation
-    Models (DEM) or Geographic Information System (GIS). It can open a .tiff, .geotiff, ascii grid, or
-     image (jpg, png,...) file.
-
-    Args:
-        filename (str): path to a DEM, GIS, or image file
-        subsample (int, None): if not None, it is the number of points to sub-sample (to smooth the heightmap using
-            the specified function)
-        interpolate_fct (str, callable): "The radial basis function, based on the radius, r, given by the norm
-            (default is Euclidean distance);
-                'multiquadric': sqrt((r/self.epsilon)**2 + 1)
-                'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1)
-                'gaussian': exp(-(r/self.epsilon)**2)
-                'linear': r
-                'cubic': r**3
-                'quintic': r**5
-                'thin_plate': r**2 * log(r)
-            If callable, then it must take 2 arguments (self, r). The epsilon parameter will be available as
-            self.epsilon. Other keyword arguments passed in will be available as well." [1]
-        lower_bound (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
-        upper_bound (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
-        dtype (np.int, np.float): type of the returned array for the heightmap
-
-    Returns:
-        np.array[H,W]: resulting 2D array of size width `W` and height `H`
-
-    References:
-        [1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.Rbf.html
-    """
-    # load data (raster)
-    data = gdal.Open(filename)
-    band = data.GetRasterBand(1)
-    heightmap = band.ReadAsArray()  # elevation values
-
-    if isinstance(subsample, int) and subsample > 0:
-        height, width = heightmap.shape
-        idx_x = np.linspace(0, height-1, subsample, dtype=np.int)
-        idx_y = np.linspace(0, width-1, subsample, dtype=np.int)
-        idx_x, idx_y = np.meshgrid(idx_x, idx_y)
-        x, y = np.arange(width), np.arange(height)
-        x, y = np.meshgrid(x, y)
-        rbf = Rbf(x[idx_x, idx_y], y[idx_x, idx_y], heightmap[idx_x, idx_y], function=interpolate_fct)
-        # Nx, Ny = x.shape[0] / subsample, x.shape[1] / subsample
-        # rbf = Rbf(x[::Nx, ::Ny], y[::Nx, ::Ny], heightmap[::Nx, ::Ny], function=interpolate_fct)
-        heightmap = rbf(x, y)
-
-    # make sure the values of the heightmap are between the bounds (in-place), and is the correct type
-    if lower_bound and upper_bound:
-        np.clip(heightmap, lower_bound, upper_bound, heightmap)
-    elif lower_bound:
-        np.clip(heightmap, lower_bound, heightmap.max(), heightmap)
-    elif upper_bound:
-        np.clip(heightmap, heightmap.min(), upper_bound, heightmap)
-    if dtype:
-        heightmap.astype(dtype)
-
-    return heightmap
-
-
-# alias
-heigtmap_from_image = heightmap_gdal
-
-
-# Tests
-# Conclusion: use `heightmap_rbf` or `heightmap_gdal` as it is pretty good
-if __name__ == '__main__':
-    from mpl_toolkits.mplot3d import Axes3D
-    import matplotlib.pyplot as plt
-
-    # define plot figure for heightmap
-    def plot_figure(heightmap, title='', block=True, z_upper_lim=256):
-        fig = plt.figure()
-        fig.suptitle(title)
-
-        # 1st subplot: 2D heightmap
-        ax = fig.add_subplot(1, 2, 1)
-        ax.set_title('2D heightmap')
-        ax.imshow(heightmap, cmap='gray')
-
-        # 2nd subplot: associated 3D terrain
-        ax = fig.add_subplot(1, 2, 2, projection='3d')
-        ax.set_title('3D terrain')
-        x = np.linspace(0, 1, heightmap.shape[0])
-        y = np.linspace(0, 1, heightmap.shape[1])
-        x, y = np.meshgrid(y, x)
-        ax.plot_surface(x, y, heightmap)
-        ax.set_zlim(0, z_upper_lim)
-        print(x.shape)
-
-        plt.show(block=block)
-
-
-    # # generate heightmap using the diamond-square algorithm
-    # N = 8       # shape of map: 2**N+1, 2**N+1
-    # heightmap = diamond_square_algorithm(N)
-    # plot_figure(heightmap, title='Diamond-Square algorithm')
-
-    # # generate heightmap using gaussian process regression
-    # x = np.array(range(256))
-    # y = np.array(range(256))
-    # N_init = 20
-    # x_init = np.random.randint(low=x.min(), high=x.max(), size=N_init)
-    # y_init = np.random.randint(low=y.min(), high=y.max(), size=N_init)
-    # z_init = np.random.randint(low=0, high=20, size=N_init)
-    # init_values = np.vstack((x_init, y_init, z_init)).T     # shape: Nx3
-    # #init_values = np.array([[163, 73, 0], [13, 15, 1],[69, 102, 2]])
-    # #init_values = np.array([[182, 48, 89], [182, 20, 150], [167, 247, 131]])
-    # heightmap = heightmap_gpr(init_values=init_values, x=x, y=y)
-    # plot_figure(heightmap, title='Gaussian Process Regression')
-
-    # generate heightmap using RBF interpolations
-    x = np.array(range(256))
-    y = np.array(range(256))  # range(128)
-    N_init = 20     # number of bumps
-    x_init = np.random.randint(low=x.min(), high=x.max(), size=N_init)
-    y_init = np.random.randint(low=y.min(), high=y.max(), size=N_init)
-    z_init = np.random.randint(low=0, high=20, size=N_init)
-    init_values = np.vstack((x_init, y_init, z_init)).T     # shape: Nx3
-    # init_values = np.array([[211, 184, 3], [97, 59, 4], [37, 179, 8], [168, 32, 8], [198, 74, 13],
-    #                         [44, 10, 2], [175, 102, 6], [6, 22, 1], [35, 165, 6], [169, 211, 16],
-    #                         [158, 119, 18], [228, 63, 13], [40, 62, 15], [76, 221, 10], [1, 113, 10],
-    #                         [178, 194, 2], [23, 176,10], [231,  88, 7], [247, 209, 6], [72, 94, 2]])
-    heightmap = heightmap_rbf(init_values=init_values, x=x, y=y, function='gaussian') # 'linear', 'multiquadric'
-    plot_figure(heightmap, title='RBF interpolation')
-
-    # # generate heigthmap from an image or tif file
-    # dem = heightmap_gdal('../tests/canyon-geo.tif')
-    # dem = heightmap_gdal('../tests/dem.jpg')
-    dem = heightmap_gdal('../tests/heightmap.png')
-    plot_figure(dem, block=True)
diff --git a/pyrobolearn/worlds/utils/heightmaps/__init__.py b/pyrobolearn/worlds/utils/heightmaps/__init__.py
new file mode 100644
index 0000000..b05b247
--- /dev/null
+++ b/pyrobolearn/worlds/utils/heightmaps/__init__.py
@@ -0,0 +1 @@
+# use `diamond_square`, `rbf`, or `geospatial` as they are pretty good
diff --git a/pyrobolearn/worlds/utils/heightmaps/diamond_square.py b/pyrobolearn/worlds/utils/heightmaps/diamond_square.py
new file mode 100644
index 0000000..7edc73d
--- /dev/null
+++ b/pyrobolearn/worlds/utils/heightmaps/diamond_square.py
@@ -0,0 +1,223 @@
+#!/usr/bin/env python
+"""Provide the diamond-square heightmap generator.
+
+Generate the heightmap using the diamond-square algorithm [1].
+
+References:
+    [1] Wikipedia: https://en.wikipedia.org/wiki/Diamond-square_algorithm
+"""
+
+import numpy as np
+
+
+__author__ = ["Brian Delhaisse", "Jamie Scollay"]
+__copyright__ = "Copyright 2018, PyRoboLearn"
+__credits__ = ["Brian Delhaisse", "Jamie Scollay"]
+__license__ = "MIT"
+__version__ = "1.0.0"
+__maintainer__ = "Brian Delhaisse"
+__email__ = "briandelhaisse@gmail.com"
+__status__ = "Development"
+
+# the `diamond_square_heightmap_2` was originally written by Jamie Scollay
+# it was then reviewed by Brian Delhaisse, notably with respect to the original code:
+# - it has been cleaned; removed all the ";"
+# - it has been optimized:
+#     - it now uses numpy instead of math and lists, it uses `list.append` instead of adding strings, and then `join`
+#     - it has been simplified.
+# - comments have been added and a better documentation is provided
+
+
+def diamond_square_heightmap(n=8, min_height=0, max_height=255, noise=0, noise_factor=1, init_values=None,
+                             dtype=np.int, seed=None):
+    r"""Diamond-Square Algorithm
+
+    This function implements the diamond-square algorithm [1], to generate random terrains given an initial value
+    for each corner.
+
+    Warnings: the diamond-square algo assumes that the heightmap is a 2D square array.
+
+    Args:
+        n (int): used to create a square array of width and height of 2**n + 1. It also specifies the number of
+            diamond and square steps.
+        min_height (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
+        max_height (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
+        noise (int, float): noise level to add. This corresponds to the standard deviation of the normal distribution.
+        noise_factor (int, float): after each step, the noise is divided by the given factor.
+        init_values (np.array[4], None): the four initial values for the corners. If None, it will generate 4 values
+            randomly such that they are between the min_height and max_height.
+        dtype (np.int, np.float): type of the returned array for the heightmap
+        seed (int, None): random seed
+
+    Returns:
+        np.array[2**n+1, 2**n+1]: resulting 2D square heightmap
+
+    References:
+        [1] Wikipedia: https://en.wikipedia.org/wiki/Diamond-square_algorithm
+        [2] https://blog.habrador.com/2013/02/how-to-generate-random-terrain.html
+    """
+    # set the seed if given
+    if seed:
+        np.random.seed(seed)
+
+    # create initial heightmap
+    width, height = 2**n + 1, 2**n + 1
+    heightmap = -1 * np.ones((height, width), dtype=dtype)
+    if not init_values:
+        if dtype == np.int:
+            init_values = np.random.randint(low=min_height, high=max_height + 1, size=4)
+        else:
+            init_values = np.random.uniform(low=min_height, high=max_height, size=4)
+    heightmap[0, 0], heightmap[0, width - 1], heightmap[height - 1, 0], heightmap[height - 1, width - 1] = init_values
+
+    # define diamond-square step function
+    def diamond_square_step(heightmap, square=None, noise=0, min_height=0, max_height=255):
+        """
+        Diamond-square step which  which performs a diamond step followed by a square step.
+
+        Args:
+            heightmap (np.array[2*N+1,2*N+1]): heightmap (initial square)
+            square (np.array[M,M]): the current square we focus on.
+        """
+        # if no square given
+        if square is None:
+            height, width = heightmap.shape
+            square = np.array([[0, 0], [width - 1, 0], [width - 1, height - 1], [0, height - 1]])
+
+        # check size of square
+        xmin, xmax, ymin, ymax = square[:, 0].min(), square[:, 0].max(), square[:, 1].min(), square[:, 1].max()
+        dx, dy = (xmax - xmin), (ymax - ymin)
+        if dx == 0 or dx == 1 or dy == 0 or dy == 1:
+            return
+
+        # DIAMOND STEP
+        center = np.array([xmin + dx / 2, ymin + dy / 2])
+        yc, xc = center
+        heightmap[xc, yc] = np.mean([heightmap[x, y] for (y, x) in square])  # + np.random.normal(scale=noise)
+        heightmap[xc, yc] = min(max(min_height, heightmap[xc, yc]), max_height)  # lower and upper bound
+
+        # SQUARE STEP
+        # triangles: a triangle is defined by 3 points
+        triangles = np.array([[c1, c2, center] for c1, c2 in zip(square, list(square[1:]) + [square[0]])])
+
+        squares = []
+        for i, triangle in enumerate(triangles):
+            xmin, xmax, ymin, ymax = triangle[:, 0].min(), triangle[:, 0].max(), \
+                                     triangle[:, 1].min(), triangle[:, 1].max()
+
+            if i == 0:  # upper triangle
+                center = np.array([xmin + (xmax - xmin) / 2, ymin])
+                square = np.array([[xmin, ymin], center, [center[0], ymax], [xmin, ymax]])  # left upper square
+            elif i == 1:  # right triangle
+                center = np.array([xmax, ymin + (ymax - ymin) / 2])
+                square = np.array([[xmin, ymin], [xmax, ymin], center, [xmin, center[1]]])  # right upper square
+            elif i == 2:  # lower triangle
+                center = np.array([xmin + (xmax - xmin) / 2, ymax])
+                square = np.array([[center[0], ymin], [xmax, ymin], [xmax, ymax], center])  # right lower square
+            else:  # left triangle
+                center = np.array([xmin, ymin + (ymax - ymin) / 2])
+                square = np.array([center, [xmax, center[1]], [xmax, ymax], [xmin, ymax]])  # left lower square
+
+            yc, xc = center
+            heightmap[xc, yc] = np.mean([heightmap[x, y] for (y, x) in triangle])  # + np.random.normal(scale=noise)
+            heightmap[xc, yc] = min(max(min_height, heightmap[xc, yc]), max_height)  # lower and upper bound
+
+            # a square is defined by 4 points
+            squares.append(square)
+
+        # for each subsquare in the original square, compute the heightmap recursively
+        for square in squares:
+            diamond_square_step(heightmap, square, noise / noise_factor, min_height, max_height)
+
+    # start diamond-square algorithm (recursively)
+    diamond_square_step(heightmap, noise=noise, min_height=min_height, max_height=max_height)
+    return heightmap
+
+
+def diamond_square_heightmap_2(n=8, min_height=0, max_height=255, noise=0, noise_factor=1):
+    """
+    Create a 2D square heightmap using the diamond square algorithm [1]
+
+    Args:
+        n (int): used to create a square array of width and height of 2**n + 1. It also specifies the number of
+            diamond and square steps.
+        min_height (float): minimum height
+        max_height (float): maximum height
+        noise (float): magnitude of the noise added to the computed height.
+        noise_factor (float): after each step, the jitter is divided by the given factor.
+
+    Returns:
+        np.array[size, size]: 2D square heightmap
+
+    References:
+        [1] Wikipedia: https://en.wikipedia.org/wiki/Diamond-square_algorithm
+    """
+    # compute the width and height size (i.e. size of the 2D square array/heightmap)
+    size = int(2 ** n + 1)
+
+    # create initial heightmap of width and height size
+    heightmap = np.zeros((size, size))
+
+    # assign a random height at each corner of the heightmap
+    heightmap[0, 0] = np.random.rand() * max_height
+    heightmap[0, size - 1] = np.random.rand() * max_height
+    heightmap[size - 1, 0] = np.random.rand() * max_height
+    heightmap[size - 1, size - 1] = np.random.rand() * max_height
+
+    # for each diamond and square step
+    for i in range(n):
+        stride = int((size - 1) / 2 ** (i + 1))
+        radius = int((size - 1) / 2 ** i)
+
+        for j in range(2 ** i):
+            for k in range(2 ** i):
+                height = (heightmap[j * radius, k * radius] + heightmap[2 * stride + j * radius, k * radius] +
+                          heightmap[j * radius, 2 * stride + k * radius] +
+                          heightmap[2 * stride + j * radius, 2 * stride + k * radius]) / 4. + (
+                                     np.random.rand() - 0.5) * noise
+                heightmap[stride + j * radius, stride + k * radius] = height
+
+        for j in range(2 ** (i + 1) + 1):
+            for k in range(2 ** i + j % 2):
+                cnt = 0
+                if j == 0:
+                    height1 = 0
+                else:
+                    height1 = heightmap[(j - 1) * stride, stride * ((j + 1) % 2) + k * radius]
+                    cnt += 1
+
+                if k == 0 and j % 2 == 1:
+                    height4 = 0
+                else:
+                    height4 = heightmap[j * stride, stride * (((j + 1) % 2) - 1) + k * radius]
+                    cnt += 1
+
+                if j == 2 ** (i + 1):
+                    height3 = 0
+                else:
+                    height3 = heightmap[(j + 1) * stride, stride * ((j + 1) % 2) + k * radius]
+                    cnt += 1
+
+                if k == (2 ** i + j % 2 - 1) and j % 2 == 1:
+                    height2 = 0
+                else:
+                    height2 = heightmap[j * stride, stride * (((j + 1) % 2) + 1) + k * radius]
+                    cnt += 1
+
+                height = float(height1 + height2 + height3 + height4) / cnt + (np.random.rand() - 0.5) * noise
+                heightmap[j * stride, ((j + 1) % 2) * stride + k * radius] = height
+
+        noise /= noise_factor
+
+    lowest_point = heightmap.min()
+    highest_point = heightmap.max()
+
+    if n > 1:
+        for i in range(size):
+            for j in range(4):
+                heightmap[j, i] = lowest_point + j * 0.25 * (heightmap[j, i] - lowest_point)
+                heightmap[size - j - 1, i] = lowest_point + j * 0.25 * (heightmap[size - j - 1, i] - lowest_point)
+                heightmap[i, j] = lowest_point + j * 0.25 * (heightmap[i, j] - lowest_point)
+                heightmap[i, size - j - 1] = lowest_point + j * 0.25 * (heightmap[i, size - j - 1] - lowest_point)
+
+    return heightmap
diff --git a/pyrobolearn/worlds/utils/heightmaps/equation.py b/pyrobolearn/worlds/utils/heightmaps/equation.py
new file mode 100644
index 0000000..6cdd5d7
--- /dev/null
+++ b/pyrobolearn/worlds/utils/heightmaps/equation.py
@@ -0,0 +1,56 @@
+#!/usr/bin/env python
+r"""Provide the equation heightmap generator.
+
+Generate a heightmap from a 3D equation :math:`z = f(x, y)`.
+"""
+
+import numpy as np
+
+
+__author__ = "Brian Delhaisse"
+__copyright__ = "Copyright 2018, PyRoboLearn"
+__credits__ = ["Brian Delhaisse"]
+__license__ = "MIT"
+__version__ = "1.0.0"
+__maintainer__ = "Brian Delhaisse"
+__email__ = "briandelhaisse@gmail.com"
+__status__ = "Development"
+
+
+def equation_heightmap(x, y, z, min_height=0, max_height=255, dtype=np.int):
+    r"""
+    Generate heightmap from 3D equation :math:`z = f(x,y)`.
+
+    Args:
+        x (np.array[N], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
+            from the meshgrid is expected. This is used to predict the heightmap at the given points.
+        y (np.array[0], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
+            from the meshgrid is expected. This is used to predict the heightmap at the given points.
+        z (callable): it must be a function that accepts two arguments `x` and `y` which will be the arrays from the
+            meshgrid.
+        min_height (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
+        max_height (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
+        dtype (np.int, np.float): type of the returned array for the heightmap
+
+    Examples of 2D surfaces:
+        z = lambda x,y: np.log(y)
+        z = lambda x,y: np.sin(np.pi * x) * np.sin(np.pi * y)
+
+    Returns:
+        np.array[N,O]: resulting 2D heightmap
+    """
+    # check given x and y
+    if len(x.shape) == 1 and len(y.shape) == 1:
+        x, y = np.meshgrid(x, y)
+    if x.shape != y.shape:
+        raise ValueError("Expecting x and y to have the same shape, which should be the case if it is a meshgrid")
+    origin_shape = x.shape
+
+    # call z function: z=f(x,y)
+    heightmap = z(x, y)
+
+    # make sure the values of the heightmap are between the bounds (in-place), and is the correct type
+    np.clip(heightmap, min_height, max_height, heightmap)
+    heightmap.astype(dtype)
+
+    return heightmap
diff --git a/pyrobolearn/worlds/utils/heightmaps/geospatial.py b/pyrobolearn/worlds/utils/heightmaps/geospatial.py
new file mode 100644
index 0000000..a494548
--- /dev/null
+++ b/pyrobolearn/worlds/utils/heightmaps/geospatial.py
@@ -0,0 +1,91 @@
+#!/usr/bin/env python
+"""Provide heightmap generators.
+
+The various functions defined here generate
+"""
+
+import numpy as np
+from scipy.interpolate import Rbf
+
+try:
+    import gdal
+except ImportError as e:
+    raise ImportError(repr(e) + '\nTry to install gdal: pip install gdal')
+
+
+__author__ = "Brian Delhaisse"
+__copyright__ = "Copyright 2018, PyRoboLearn"
+__credits__ = ["Brian Delhaisse"]
+__license__ = "MIT"
+__version__ = "1.0.0"
+__maintainer__ = "Brian Delhaisse"
+__email__ = "briandelhaisse@gmail.com"
+__status__ = "Development"
+
+
+def gdal_heightmap(filename, subsample=None, interpolate_fct='multiquadric', min_height=0, max_height=255,
+                   dtype=np.int):
+    r"""
+    Heightmap generated using the Geospatial Data Abstraction Library (GDAL), which allows to open Digital Elevation
+    Models (DEM) or Geographic Information System (GIS). It can open a .tiff, .geotiff, ascii grid, or
+     image (jpg, png,...) file.
+
+    Args:
+        filename (str): path to a DEM, GIS, or image file (e.g. png)
+        subsample (int, None): if not None, it is the number of points to sub-sample (to smooth the heightmap using
+            the specified function)
+        interpolate_fct (str, callable): "The radial basis function, based on the radius, r, given by the norm
+            (default is Euclidean distance);
+                'multiquadric': sqrt((r/self.epsilon)**2 + 1)
+                'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1)
+                'gaussian': exp(-(r/self.epsilon)**2)
+                'linear': r
+                'cubic': r**3
+                'quintic': r**5
+                'thin_plate': r**2 * log(r)
+            If callable, then it must take 2 arguments (self, r). The epsilon parameter will be available as
+            self.epsilon. Other keyword arguments passed in will be available as well." [1]
+        min_height (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
+        max_height (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
+        dtype (np.int, np.float): type of the returned array for the heightmap
+
+    Returns:
+        np.array[H,W]: resulting 2D array of size width `W` and height `H`
+
+    Examples:
+        >>> # generate heightmap from an image or tif file
+        >>> dem = gdal_heightmap('../pictures/canyon-geo.tif')
+        >>> dem = gdal_heightmap('../pictures/dem.jpg')
+        >>> dem = gdal_heightmap('../pictures/heightmap.png')
+
+    References:
+        [1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.Rbf.html
+    """
+    # load data (raster)
+    data = gdal.Open(filename)
+    band = data.GetRasterBand(1)
+    heightmap = band.ReadAsArray()  # elevation values
+
+    if isinstance(subsample, int) and subsample > 0:
+        height, width = heightmap.shape
+        idx_x = np.linspace(0, height-1, subsample, dtype=np.int)
+        idx_y = np.linspace(0, width-1, subsample, dtype=np.int)
+        idx_x, idx_y = np.meshgrid(idx_x, idx_y)
+        x, y = np.arange(width), np.arange(height)
+        x, y = np.meshgrid(x, y)
+        rbf = Rbf(x[idx_x, idx_y], y[idx_x, idx_y], heightmap[idx_x, idx_y], function=interpolate_fct)
+        # Nx, Ny = x.shape[0] / subsample, x.shape[1] / subsample
+        # rbf = Rbf(x[::Nx, ::Ny], y[::Nx, ::Ny], heightmap[::Nx, ::Ny], function=interpolate_fct)
+        heightmap = rbf(x, y)
+
+    # make sure the values of the heightmap are between the bounds (in-place), and is the correct type
+    if min_height and max_height:
+        np.clip(heightmap, min_height, max_height, heightmap)
+    elif min_height:
+        np.clip(heightmap, min_height, heightmap.max(), heightmap)
+    elif max_height:
+        np.clip(heightmap, heightmap.min(), max_height, heightmap)
+    if dtype:
+        heightmap.astype(dtype)
+
+    return heightmap
diff --git a/pyrobolearn/worlds/utils/heightmaps/gpr.py b/pyrobolearn/worlds/utils/heightmaps/gpr.py
new file mode 100644
index 0000000..43341b3
--- /dev/null
+++ b/pyrobolearn/worlds/utils/heightmaps/gpr.py
@@ -0,0 +1,109 @@
+#!/usr/bin/env python
+"""Provide the gaussian process regression heightmap generator.
+
+Generate a heightmap using gaussian process regression.
+"""
+
+import numpy as np
+from sklearn.gaussian_process import GaussianProcessRegressor
+from sklearn.gaussian_process.kernels import RBF
+
+
+__author__ = "Brian Delhaisse"
+__copyright__ = "Copyright 2018, PyRoboLearn"
+__credits__ = ["Brian Delhaisse"]
+__license__ = "MIT"
+__version__ = "1.0.0"
+__maintainer__ = "Brian Delhaisse"
+__email__ = "briandelhaisse@gmail.com"
+__status__ = "Development"
+
+
+def gpr_heightmap(init_values, x, y, kernel=None, alpha=1e-10, min_height=0, max_height=255, dtype=np.int):
+    r"""
+    Generate a heightmap using gaussian process regression. The advantages of using this method over others to
+    generate terrains lies in the capacity of adding prior knowledge through the kernel and the given initial values.
+    For instance, using a RBF kernel means that we want a smooth terrain instead of a bumpy one.
+    Furthermore, it allows to generate heightmaps which are not necessary square; i.e. they can be rectangular.
+
+    Warnings: this is pretty difficult to exploit if the given data is not consistent. See `heigthmap_rbf` for
+        a better way to generate heightmap.
+
+    Args:
+        init_values (np.array[M,3]): list of `M` 3D points which corresponds to initial values that are used to fit
+            the gaussian process.
+        x (np.array[N], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
+            from the meshgrid is expected. This is used to predict the heightmap at the given points.
+        y (np.array[0], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
+            from the meshgrid is expected. This is used to predict the heightmap at the given points.
+        kernel (None, sklearn.gaussian_process.kernels.Kernel): "The kernel specifying the covariance function of
+            the GP. If None is passed, the kernel '1.0 * RBF(1.0)' is used as default. Note that the kernel's
+            hyperparameters are optimized during fitting" [2]
+        alpha (float, array_like): "Value added to the diagonal of the kernel matrix during fitting. Larger values
+            correspond to increased noise level in the observations. This can also prevent a potential numerical issue
+            during fitting, by ensuring that the calculated values form a positive definite matrix. If an array is
+            passed, it must have the same number of entries as the data used for fitting and is used as
+            datapoint-dependent noise level. Note that this is equivalent to adding a WhiteKernel with c=alpha.
+            Allowing to specify the noise level directly as a parameter is mainly for convenience and for consistency
+            with Ridge." [2]
+        min_height (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
+        max_height (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
+        dtype (np.int, np.float): type of the returned array for the heightmap
+
+    Returns:
+        np.array[N,O]: resulting 2D heightmap
+
+    Examples:
+        >>> # generate heightmap using gaussian process regression
+        >>> x = np.array(range(256))
+        >>> y = np.array(range(256))
+        >>> N_init = 20
+        >>> x_init = np.random.randint(low=x.min(), high=x.max(), size=N_init)
+        >>> y_init = np.random.randint(low=y.min(), high=y.max(), size=N_init)
+        >>> z_init = np.random.randint(low=0, high=20, size=N_init)
+        >>> init_values = np.vstack((x_init, y_init, z_init)).T     # shape: Nx3
+        >>> heightmap = gpr_heightmap(init_values, x, y)
+
+    References:
+        [1] "Gaussian Processes for Machine Learning", Rasmussen and Williams, 2006
+        [2] Sklearn: https://scikit-learn.org/stable/modules/gaussian_process.html
+    """
+    # check given x and y
+    if len(x.shape) == 1 and len(y.shape) == 1:
+        x, y = np.meshgrid(x, y)
+    if x.shape != y.shape:
+        raise ValueError("Expecting x and y to have the same shape, which should be the case if it is a meshgrid")
+
+    # compute the minimum distance between points
+    N = len(init_values)
+    min_dist = np.inf
+    for i in range(N):
+        for j in range(i+1, N):
+            dist = np.linalg.norm(init_values[i, :2] - init_values[j, :2])
+            if dist < min_dist:
+                min_dist = dist
+    print("Min dist: {}".format(min_dist))
+
+    # check initial values
+    if not isinstance(init_values, np.ndarray):
+        raise TypeError("Expecting init_values to be a numpy array")
+    if init_values.shape[1] != 3:
+        raise ValueError("Expecting a numpy array of 3D points for init_values")
+
+    # create gaussian process and fit on the given initial values
+    kernel = RBF(length_scale=np.sqrt(min_dist))
+    gpr = GaussianProcessRegressor(kernel=kernel, alpha=alpha, normalize_y=True)
+    gpr.fit(init_values[:, :2], init_values[:, 2])
+
+    # predict the heightmap using GPR
+    X = np.dstack((x, y)).reshape(-1, 2)
+    heightmap = gpr.predict(X)
+    heightmap = heightmap.reshape(x.shape)
+
+    print("Params: {}".format(gpr.get_params()))
+
+    # make sure the values of the heightmap are between the bounds (in-place), and is the correct type
+    np.clip(heightmap, min_height, max_height, heightmap)
+    heightmap.astype(dtype)
+
+    return heightmap
diff --git a/pyrobolearn/worlds/utils/heightmaps/plot.py b/pyrobolearn/worlds/utils/heightmaps/plot.py
new file mode 100644
index 0000000..b7742dc
--- /dev/null
+++ b/pyrobolearn/worlds/utils/heightmaps/plot.py
@@ -0,0 +1,77 @@
+#!/usr/bin/env python
+"""Plot 2D and 3D heightmap.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from PIL import Image
+
+
+__author__ = "Brian Delhaisse"
+__copyright__ = "Copyright 2018, PyRoboLearn"
+__credits__ = ["Brian Delhaisse"]
+__license__ = "MIT"
+__version__ = "1.0.0"
+__maintainer__ = "Brian Delhaisse"
+__email__ = "briandelhaisse@gmail.com"
+__status__ = "Development"
+
+
+def plot_heightmap(heightmap, title='', block=True, max_height=None):
+    """
+    Plot the given heightmap.
+
+    Args:
+        heightmap (np.array[height, width]): 2D heightmap.
+        title (str): title of the plot.
+        block (bool): if we should block when showing the plot.
+        max_height (None, int, float): max height (z-limit).
+    """
+    fig = plt.figure()
+    fig.suptitle(title)
+
+    # 1st subplot: 2D heightmap
+    ax = fig.add_subplot(1, 2, 1)
+    ax.set_title('2D heightmap')
+    ax.imshow(heightmap, cmap='gray')
+
+    # 2nd subplot: associated 3D terrain
+    ax = fig.add_subplot(1, 2, 2, projection='3d')
+    ax.set_title('3D terrain')
+    x = np.linspace(0, 1, heightmap.shape[0])
+    y = np.linspace(0, 1, heightmap.shape[1])
+    x, y = np.meshgrid(y, x)
+    ax.plot_surface(x, y, heightmap)
+    if max_height is not None:
+        ax.set_zlim(0, max_height)
+
+    plt.show(block=block)
+
+
+def save_heightmap(heightmap, filename='heightmap.bmp'):
+    """
+    Save the heightmap as an image.
+
+    Args:
+        heightmap (np.array[height, width]): 2D heightmap.
+        filename (str): filename to save the image.
+    """
+    min_height = heightmap.min()
+    max_height = heightmap.max()
+    height, width = heightmap.shape
+
+    # create heightmap image
+    img = Image.new('RGB', (height, width), "black")
+    pixels = img.load()
+
+    dist = (max_height - min_height)
+    middle_point = min_height + dist / 2.
+    for i in range(height):
+        for j in range(width):
+            if heightmap[i, j] > middle_point:
+                pixels[i, j] = (0, int(255 * (heightmap[i, j] - middle_point) / (dist / 2.)), 0)
+            else:
+                pixels[i, j] = (10, 10, 200)
+
+    # save image
+    img.save(filename)
diff --git a/pyrobolearn/worlds/utils/heightmaps/rbf.py b/pyrobolearn/worlds/utils/heightmaps/rbf.py
new file mode 100644
index 0000000..cbed550
--- /dev/null
+++ b/pyrobolearn/worlds/utils/heightmaps/rbf.py
@@ -0,0 +1,81 @@
+#!/usr/bin/env python
+"""Provide the radial-basis function heightmap generator.
+
+Generate a heightmap by interpolating the given initial points using RBF functions.
+"""
+
+import numpy as np
+from scipy.interpolate import Rbf
+
+
+__author__ = "Brian Delhaisse"
+__copyright__ = "Copyright 2018, PyRoboLearn"
+__credits__ = ["Brian Delhaisse"]
+__license__ = "MIT"
+__version__ = "1.0.0"
+__maintainer__ = "Brian Delhaisse"
+__email__ = "briandelhaisse@gmail.com"
+__status__ = "Development"
+
+
+def rbf_heightmap(init_values, x, y, function='multiquadric', min_height=0, max_height=255, dtype=np.int):
+    r"""
+    Generate heightmap by interpolating the given initial points using RBF functions.
+
+    Advantages: fast and easy to use, and the results are pretty good. Heightmaps can also be rectangular.
+
+    Args:
+        init_values (np.array[M,3]): list of `M` 3D points which corresponds to initial values that are used to fit
+            the gaussian process.
+        x (np.array[N], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
+            from the meshgrid is expected. This is used to predict the heightmap at the given points.
+        y (np.array[0], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D array
+            from the meshgrid is expected. This is used to predict the heightmap at the given points.
+        function (str, callable): "The radial basis function, based on the radius, r, given by the norm
+            (default is Euclidean distance);
+                'multiquadric': sqrt((r/self.epsilon)**2 + 1)
+                'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1)
+                'gaussian': exp(-(r/self.epsilon)**2)
+                'linear': r
+                'cubic': r**3
+                'quintic': r**5
+                'thin_plate': r**2 * log(r)
+            If callable, then it must take 2 arguments (self, r). The epsilon parameter will be available as
+            self.epsilon. Other keyword arguments passed in will be available as well." [1]
+        min_height (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
+        max_height (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
+        dtype (np.int, np.float): type of the returned array for the heightmap
+
+    Returns:
+        np.array[N,O]: resulting 2D heightmap
+
+    Examples:
+        >>> # generate heightmap using RBF interpolations
+        >>> x = np.array(range(256))
+        >>> y = np.array(range(256))  # range(128)
+        >>> N_init = 20     # number of bumps
+        >>> x_init = np.random.randint(low=x.min(), high=x.max(), size=N_init)
+        >>> y_init = np.random.randint(low=y.min(), high=y.max(), size=N_init)
+        >>> z_init = np.random.randint(low=0, high=20, size=N_init)
+        >>> init_values = np.vstack((x_init, y_init, z_init)).T     # shape: Nx3
+        >>> heightmap = rbf_heightmap(init_values, x, y, function='gaussian')  # 'linear', 'multiquadric'
+
+    References:
+        [1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.Rbf.html
+    """
+    # check given x and y
+    if len(x.shape) == 1 and len(y.shape) == 1:
+        x, y = np.meshgrid(x, y)
+    if x.shape != y.shape:
+        raise ValueError("Expecting x and y to have the same shape, which should be the case if it is a meshgrid")
+    origin_shape = x.shape
+
+    rbf = Rbf(init_values[:, 0], init_values[:, 1], init_values[:, 2], function=function)
+    heightmap = rbf(x.reshape(-1), y.reshape(-1))
+    heightmap = heightmap.reshape(origin_shape)
+
+    # make sure the values of the heightmap are between the bounds (in-place), and is the correct type
+    np.clip(heightmap, min_height, max_height, heightmap)
+    heightmap.astype(dtype)
+
+    return heightmap
diff --git a/pyrobolearn/worlds/utils/obj_generator.py b/pyrobolearn/worlds/utils/obj_generator.py
new file mode 100644
index 0000000..2344ce3
--- /dev/null
+++ b/pyrobolearn/worlds/utils/obj_generator.py
@@ -0,0 +1,334 @@
+#!/usr/bin/env python
+"""OBJ generator.
+
+Create an OBJ file from a heightmap (2D np.array).
+
+References:
+    [1] https://github.com/deltabrot/random-terrain-generator
+"""
+
+import numpy as np
+import time
+
+
+__author__ = ["Jamie Scollay", "Brian Delhaisse"]
+# the code was originally written by Jamie Scollay
+# it was then reviewed by Brian Delhaisse, notably with respect to the original code:
+# - it has been cleaned; removed all the ";"
+# - it has been optimized:
+#     - it now uses numpy instead of math and lists, it uses `list.append` instead of adding strings, and then `join`
+#     - it has been simplified.
+# - comments have been added and a better documentation is provided
+__credits__ = ["Jamie Scollay"]
+__license__ = "MIT"
+__version__ = "1.0.0"
+__maintainer__ = "Brian Delhaisse"
+__email__ = "briandelhaisse@gmail.com"
+__status__ = "Development"
+
+
+def unit_vector(v):
+    """Normalize the given vector.
+
+    Args:
+        v (np.array[3]): vector to normalize.
+
+    Returns:
+        np.array[3]: unit vector
+    """
+    magnitude = np.linalg.norm(v)
+    if magnitude == 0:
+        return v
+    return v / magnitude
+
+
+def unit_normal(v1, v2, v3):
+    """Compute the unit normal between two vectors: (v2-v1) and (v3 - v1).
+
+    Args:
+        v1 (np.array[3]): 3d common point between the two vectors.
+        v2 (np.array[3]): 3d point for 1st vector.
+        v3 (np.array[3]): 3d point for 2nd vector.
+
+    Returns:
+        np.array[3]: unit vector
+    """
+    return unit_vector(np.cross(v2 - v1, v3 - v1))
+
+
+def create_hexagonal_terrain(heightmap, scale=1., tile=True, min_height=0., smooth=True, verbose=True, verbose_rate=1):
+    """
+    Create the terrain with hexagonal tiles from the heightmap, and return the vertices, textures, normals and faces
+    to create an OBJ file.
+
+    Args:
+        heightmap (np.array[height, width]): 2D square heightmap
+        scale (float): scaling factor.
+        tile (bool): if True, it will create a tile texture.
+        min_height (float): minimum height.
+        smooth (bool): if the normals should be smooth.
+        verbose (bool): if True, it will output information about the creation of the terrain.
+        verbose_rate (int): if :attr:`verbose` is True, it will output
+
+    Returns:
+        list: vertices (for OBJ)
+        list: textures (for OBJ)
+        list: (smooth) normals (for OBJ)
+        list: faces (for OBJ)
+
+    References:
+        [1] Wavefront .obj file (Wikipedia): https://en.wikipedia.org/wiki/Wavefront_.obj_file
+    """
+    # The heightmap contains the height for each point on the map. If you have 3 points, then you have two
+    # tiles/segments. Number of segments = number of square tiles in rows or columns.
+    height, width = heightmap.shape
+    num_y_tiles, num_x_tiles = height - 1, width - 1
+
+    scale = float(scale)
+    vertices = []
+    vertices_obj = []
+    textures_obj = []
+    normals_obj = []
+    faces_obj = []
+
+    prevent_output = False
+
+    if tile:
+        textures_obj = [[0, 0], [0, 1], [1, 0], [1, 1]]
+
+    for i in range(num_y_tiles):
+
+        if i == num_y_tiles - 1:
+            tmp_vertices_obj = []
+
+        for j in range(num_x_tiles):
+
+            if not smooth:
+                tmp = 2 * (i * num_x_tiles + j)
+                # add 2 faces each one composed of 3 vertices/textures/normals (with the format: vertex/texture/normal)
+                faces_obj.append(str(i * width + j + 1) + '/' + str(1) + '/' + str(tmp + 1) + ' ' +
+                                 str(i * width + j + 2) + '/' + str(2) + '/' + str(tmp + 1) + ' ' +
+                                 str((i + 1) * width + j + 1) + '/' + str(3) + '/' + str(tmp + 1))
+                faces_obj.append(str((i + 1) * width + j + 1) + '/' + str(3) + '/' + str(tmp + 2) + ' ' +
+                                 str(i * width + j + 2) + '/' + str(2) + '/' + str(tmp + 2) + ' ' +
+                                 str((i + 1) * width + j + 2) + '/' + str(4) + '/' + str(tmp + 2))
+
+            else:
+                # add 2 faces each one composed of 3 vertices/textures/normals (with the format: vertex/texture/normal)
+                faces_obj.append(str(i * width + j + 1) + '/' + str(1) + '/' + str(i * width + j + 1) + ' ' +
+                                 str(i * width + j + 2) + '/' + str(2) + '/' + str(i * width + j + 2) + ' ' +
+                                 str((i + 1) * width + j + 1) + '/' + str(3) + '/' + str((i + 1) * width + j + 1))
+                faces_obj.append(str((i + 1) * width + j + 1) + '/' + str(3) + '/' + str((i + 1)*width + j + 1) + ' ' +
+                                 str(i * width + j + 2) + '/' + str(2) + '/' + str(i * width + j + 2) + ' ' +
+                                 str((i + 1) * width + j + 2) + '/' + str(4) + '/' + str((i + 1) * width + j + 2))
+
+            # T1
+            half_scale = scale / 2.
+            scale_tile = scale / num_x_tiles
+
+            # add vertex [x,y,z] for the obj file
+            vertices_obj.append([-half_scale + i * scale_tile,
+                                 heightmap[i, j],
+                                 -half_scale + j * scale_tile])
+
+            if j == num_x_tiles - 1:
+                vertices_obj.append([-half_scale + i * scale_tile,
+                                     heightmap[i, j+1],
+                                     -half_scale + (j+1) * scale_tile])
+
+            if i == num_y_tiles - 1:
+                tmp_vertices_obj.append([-half_scale + (i+1) * scale_tile,
+                                         heightmap[i+1, j],
+                                         -half_scale + j * scale_tile])
+                if j == num_x_tiles - 1:
+                    tmp_vertices_obj.append([-half_scale + (i+1) * scale_tile,
+                                             heightmap[i+1, j+1],
+                                             -half_scale + (j+1) * scale_tile])
+
+            # T1: add 3 vertices [x,y,z] (that are used to compute the vertex normal)
+            vertices.append(np.array([-half_scale + i * scale_tile,
+                                      heightmap[i, j],
+                                      -half_scale + j * scale_tile]))
+            vertices.append(np.array([-half_scale + i * scale_tile,
+                                      heightmap[i, j + 1],
+                                      -half_scale + (j+1) * scale_tile]))
+            vertices.append(np.array([-half_scale + (i+1) * scale_tile,
+                                      heightmap[i + 1, j],
+                                      -half_scale + j * scale_tile]))
+            #            else:
+            #                textures.append([i/segment, j/segment])
+            #                textures.append([i/segment, (j+1)/segment])
+            #                textures.append([(i+1)/segment, j/segment])
+
+            # compute vertex normal [x,y,z] based on last 3 vertices
+            normal = unit_normal(vertices[-3], vertices[-2], vertices[-1])
+            normals_obj.append(normal)
+
+            # T2: add 3 vertices [x,y,z] (that are used to compute the vertex normal)
+            vertices.append(np.array([-half_scale + (i+1) * scale_tile,
+                                      heightmap[i+1, j],
+                                      -half_scale + j * scale_tile]))
+            vertices.append(np.array([-half_scale + i * scale_tile,
+                                      heightmap[i, j+1],
+                                      -half_scale + (j+1) * scale_tile]))
+            vertices.append(np.array([-half_scale + (i+1) * scale_tile,
+                                      heightmap[i+1, j+1],
+                                      -half_scale + (j+1) * scale_tile]))
+
+            #            else:
+            #                textures.append([(i+1)/segment, j/segment])
+            #                textures.append([i/segment, (j+1)/segment])
+            #                textures.append([(i+1)/segment, (j+1)/segment])
+
+            # compute vertex normal [x,y,z] based on last 3 vertices
+            normal = unit_normal(vertices[-3], vertices[-2], vertices[-1])
+            normals_obj.append(normal)
+
+            # print information if specified
+            if verbose:
+                if (time.time() % verbose_rate) < 0.05 and not prevent_output:
+                    print("{}/{} tiles".format(i * num_x_tiles + j, num_x_tiles * num_y_tiles))
+                    prevent_output = True
+                elif time.time() % verbose_rate > 0.05:
+                    prevent_output = False
+
+    vertices_obj += tmp_vertices_obj
+
+    # if we don't have to smooth the normals
+    if not smooth:
+        return [vertices_obj, textures_obj, normals_obj, faces_obj]
+
+    # smooth the normals using 6 normals
+    smooth_normals = []
+
+    for i in range(num_y_tiles):
+        tmp_smooth_normals = []
+
+        for j in range(num_x_tiles):
+            if j > 0:
+                norm0 = normals_obj[(i * num_x_tiles + (j - 1) * 2)]
+                norm1 = normals_obj[(i * num_x_tiles + (j - 1) * 2) + 1]
+            else:
+                norm0 = np.zeros(3)
+                norm1 = np.zeros(3)
+
+            norm2 = normals_obj[((i * num_x_tiles + j) * 2)]
+
+            if i > 0 and j > 0:
+                norm3 = normals_obj[(((i - 1) * num_x_tiles + (j - 1)) * 2) + 1]
+            else:
+                norm3 = np.zeros(3)
+
+            if i > 0:
+                norm4 = normals_obj[(((i - 1) * num_x_tiles + j) * 2)]
+                norm5 = normals_obj[(((i - 1) * num_x_tiles + j) * 2) + 1]
+            else:
+                norm4 = np.zeros(3)
+                norm5 = np.zeros(3)
+
+            smooth_normals.append(unit_vector(norm0 + norm1 + norm2 + norm3 + norm4 + norm5))
+
+            if j == num_x_tiles - 1:
+                norm0 = normals_obj[((i * num_x_tiles + (j - 1)) * 2)]
+                norm1 = normals_obj[((i * num_x_tiles + (j - 1)) * 2) + 1]
+                if i > 0:
+                    norm2 = normals_obj[(((i - 1) * num_x_tiles + (j - 1)) * 2) + 1]
+                else:
+                    norm2 = np.zeros(3)
+                smooth_normals.append(unit_vector(norm0 + norm1 + norm2))
+
+            if i == num_y_tiles - 1:
+                if j > 0:
+                    norm0 = normals_obj[(((i - 1) * num_x_tiles + (j - 1)) * 2) + 1]
+                else:
+                    norm0 = np.zeros(3)
+
+                norm1 = normals_obj[(((i - 1) * num_x_tiles + j) * 2)]
+                norm2 = normals_obj[(((i - 1) * num_x_tiles + j) * 2) + 1]
+                tmp_smooth_normals.append(unit_vector(norm0 + norm1 + norm2))
+
+                if j == num_x_tiles - 1:
+                    norm0 = normals_obj[(((i - 1) * num_x_tiles + (j - 1)) * 2) + 1]
+                    tmp_smooth_normals.append(norm0)
+
+    smooth_normals += tmp_smooth_normals
+
+    return [vertices_obj, textures_obj, smooth_normals, faces_obj]
+
+
+def create_obj(vertices, textures, normals, faces, filename=None):
+    """
+    Create content of the OBJ file given the vertices, textures, normals, and faces.
+
+    Args:
+        vertices (list): list of vertices (for each corner of a triangular mesh)
+        textures (list): list of textures
+        normals (list): list of normals
+        faces (list): list of faces
+        filename (None, str): if a string is provided, it will save the OBJ file in the given file path.
+
+    Returns:
+        str: content of the OBJ file.
+
+    References:
+        [1] Wavefront .obj file (Wikipedia): https://en.wikipedia.org/wiki/Wavefront_.obj_file
+    """
+
+    # create obj list
+    obj = []
+
+    # add vertices
+    for v in vertices:
+        obj.append("v " + str(v[0]) + " " + str(v[1]) + " " + str(v[2]))
+
+    # add textures
+    for t in textures:
+        obj.append("vt " + str(t[0]) + " " + str(t[1]))
+
+    # add normals
+    for n in normals:
+        obj.append("vn " + str(n[0]) + " " + str(n[1]) + " " + str(n[2]))
+
+    # add faces
+    for f in faces:
+        obj.append("f " + f)
+
+    # create document
+    obj = '\n'.join(obj)
+
+    # create file if specified
+    if filename is not None:
+        with open(filename, "w+") as f:
+            f.write(obj)
+    return obj
+
+
+def create_obj_from_heightmap(heightmap, scale=1., tile=True, min_height=0., smooth=True, verbose=True, verbose_rate=1,
+                              filename=None):
+    """
+    Create an OBJ file from the given 2D heightmap.
+
+    Args:
+        heightmap (np.array[height, width]): 2D square heightmap
+        scale (float): scaling factor.
+        tile (bool): if True, it will create a tile texture.
+        min_height (float): minimum height.
+        smooth (bool): if the normals should be smooth.
+        verbose (bool): if True, it will output information about the creation of the terrain.
+        verbose_rate (int): if :attr:`verbose` is True, it will output
+        filename (None, str): if a string is provided, it will save the OBJ file in the given file path.
+
+    Returns:
+        str: content of the OBJ file.
+
+    References:
+        [1] Wavefront .obj file (Wikipedia): https://en.wikipedia.org/wiki/Wavefront_.obj_file
+    """
+    # create vertices, textures, normals, and faces
+    terrain = create_hexagonal_terrain(heightmap, scale, tile, min_height, smooth, verbose, verbose_rate)
+
+    # create obj based on above information
+    obj = create_obj(vertices=terrain[0], textures=terrain[1], normals=terrain[2], faces=terrain[3],
+                     filename=filename)
+
+    return obj
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diff --git a/pyrobolearn/worlds/utils/terrain_generator.py b/pyrobolearn/worlds/utils/terrain_generator.py
deleted file mode 100644
index 9f9b0bc..0000000
--- a/pyrobolearn/worlds/utils/terrain_generator.py
+++ /dev/null
@@ -1,403 +0,0 @@
-#!/usr/bin/env python
-"""Random terrain generator using the Diamond square algorithm.
-
-It generates a random heightmap / terrain using the diamond square algorithm, and outputs an OBJ file.
-
-The code comes from [1], and has been optimized.
-
-References:
-    [1] https://github.com/deltabrot/random-terrain-generator
-"""
-
-import time
-from PIL import Image
-import numpy as np
-
-
-__author__ = ["Jamie Scollay", "Brian Delhaisse"]
-# the code was originally written by Jamie Scollay
-# it was then reviewed by Brian Delhaisse, notably with respect to the original code:
-# - it has been cleaned; removed all the ";"
-# - it has been optimized: it now uses numpy instead of math and lists, it uses list.append instead of adding strings
-# - it is now better documented.
-__credits__ = ["Jamie Scollay"]
-__license__ = "MIT"
-__version__ = "1.0.0"
-__maintainer__ = "Brian Delhaisse"
-__email__ = "briandelhaisse@gmail.com"
-__status__ = "Development"
-
-
-def unit_vector(v):
-    """Normalize the given vector.
-    
-    Args:
-        v (np.float[3]): vector to normalize.
-
-    Returns:
-        np.float[3]: unit vector
-    """
-    magnitude = np.linalg.norm(v)
-    if magnitude == 0:
-        return v
-    return v / magnitude
-
-
-def unit_normal(v1, v2, v3):
-    """Compute the unit normal between two vectors: (v2-v1) and (v3 - v1).
-
-    Args:
-        v1 (np.float[3]): 3d common point between the two vectors.
-        v2 (np.float[3]): 3d point for 1st vector.
-        v3 (np.float[3]): 3d point for 2nd vector.
-
-    Returns:
-        np.float[3]: unit vector
-    """
-    return unit_vector(np.cross(v2 - v1, v3 - v1))
-
-
-def display_loading(count, finish, message):
-    """
-    Display loading message.
-
-    Args:
-        count (int): each row of the surface.
-        finish (int): surface.
-        message (str): message to print.
-    """
-    print(message + ": " + str(count) + "/" + str(finish))
-
-
-def diamond_square_heightmap(n, max_height, jitter, jitter_factor):
-    """
-    Create a 2D square heightmap using the diamond square algorithm [1]
-
-    Args:
-        n (int): used to create a square array of width and height of 2**n + 1. It also specifies the number of
-            diamond and square steps.
-        max_height (float): maximum height
-        jitter (float): magnitude of the noise added to the computed height.
-        jitter_factor (float): after each step, the jitter is divided by the given factor.
-
-    Returns:
-        np.float[size, size]: 2D square heightmap
-
-    References:
-        [1] Wikipedia: https://en.wikipedia.org/wiki/Diamond-square_algorithm
-    """
-    # compute the width and height size (i.e. size of the 2D square array/heightmap)
-    size = int(2**n + 1)
-
-    # create initial heightmap of width and height size
-    heightmap = np.zeros((size, size))
-    
-    # assign a random height at each corner of the heightmap
-    heightmap[0, 0] = np.random.rand() * max_height
-    heightmap[0, size-1] = np.random.rand() * max_height
-    heightmap[size-1, 0] = np.random.rand() * max_height
-    heightmap[size-1, size-1] = np.random.rand() * max_height
-
-    # for each diamond and square step
-    for i in range(n):
-        stride = int((size-1) / 2**(i+1))
-        radius = int((size-1) / 2**i)
-
-        for j in range(2**i):
-            for k in range(2**i):
-                height = (heightmap[j*radius, k*radius] + heightmap[2*stride + j*radius, k*radius] +
-                          heightmap[j*radius, 2*stride + k*radius] +
-                          heightmap[2*stride + j*radius, 2*stride + k*radius]) / 4. + (np.random.rand()-0.5) * jitter
-                heightmap[stride + j*radius, stride + k*radius] = height
-
-        for j in range(2**(i+1) + 1):
-            for k in range(2**i + j%2):
-                cnt = 0
-                if j == 0:
-                    height1 = 0
-                else: 
-                    height1 = heightmap[(j-1) * stride, stride*((j+1)%2) + k*radius]
-                    cnt += 1
-                
-                if k == 0 and j%2 == 1:
-                    height4 = 0
-                else:
-                    height4 = heightmap[j * stride, stride*(((j+1)%2)-1) + k*radius]
-                    cnt += 1
-
-                if  j == 2**(i+1):
-                    height3 = 0
-                else:
-                    height3 = heightmap[(j+1) * stride, stride*((j+1)%2) + k*radius]
-                    cnt += 1
-
-                if k == (2**i + j%2 - 1) and j%2 == 1:
-                    height2 = 0
-                else:
-                    height2 = heightmap[j*stride, stride*(((j+1)%2)+1) + k*radius]
-                    cnt += 1
-
-                height = float(height1 + height2 + height3 + height4) / cnt + (np.random.rand()-0.5) * jitter
-                heightmap[j*stride, ((j+1)%2) * stride + k*radius] = height
-        
-        jitter /= jitter_factor
-
-    lowest_point = heightmap.min()
-    highest_point = heightmap.max()
-            
-    if n > 1:
-        for i in range(size):
-            for j in range(4):
-                heightmap[j, i] = lowest_point + j * 0.25 * (heightmap[j, i] - lowest_point) 
-                heightmap[size-j-1, i] = lowest_point + j * 0.25 * (heightmap[size-j-1, i] - lowest_point)
-                heightmap[i, j] = lowest_point + j * 0.25 * (heightmap[i, j] - lowest_point)
-                heightmap[i, size-j-1] = lowest_point + j * 0.25 * (heightmap[i, size-j-1] - lowest_point)
-    
-    # create heightmap image
-    img = Image.new('RGB', (size, size), "black")
-    pixels = img.load()
-    
-    dist = (highest_point - lowest_point)
-    middle_point = lowest_point + dist/2.
-    for i in range(size):
-        for j in range(size):
-            if heightmap[i, j] > middle_point:
-                pixels[i, j] = (0, int(255 * (heightmap[i, j] - middle_point) / (dist/2.)), 0)
-            else:
-                pixels[i, j] = (10, 10, 200)
-
-    # save image
-    img.save("map.bmp")
-
-    return heightmap
-
-
-def create_hexagonal_terrain(segment, scale, tile, min_height, heightmap, smooth=True, verbose=True, verbose_rate=1):
-    """
-    Create the terrain with hexagonal tiles.
-
-    Args:
-        segment (int): number of segments; number of square tiles in rows or columns.
-        scale (float): scaling factor.
-        tile (bool): if True, it will create a tile texture.
-        min_height (float): minimum height.
-        heightmap (np.float[size, size]): 2D square heightmap
-        smooth (bool): if the normals should be smooth.
-        verbose (bool): if True, it will output information about the creation of the terrain.
-        verbose_rate (int): if :attr:`verbose` is True, it will output
-
-    Returns:
-        list: vertices (for OBJ)
-        list: textures (for OBJ)
-        list: (smooth) normals (for OBJ)
-        list: faces (for OBJ)
-    """
-    scale = float(scale)
-    vertices = []
-    vertices_obj = []
-    textures_obj = []
-    normals_obj = []
-    facesOBJ = []
-    
-    prevent_output = False
-
-    if tile:
-        textures_obj = [[0, 0], [0, 1], [1, 0], [1, 1]]
-    
-    for i in range(segment):
-        if i == segment-1:
-            tmp_vertices_obj = []
-        
-        for j in range(segment):
-            if not smooth:
-                tmp = 2 * (i*segment + j)
-                facesOBJ.append(str(i*(segment+1) + j + 1) + '/' + str(1) + '/' + str(tmp + 1) + ' ' +
-                                str(i*(segment+1) + j + 2) + '/' + str(2) + '/' + str(tmp + 1) + ' ' +
-                                str((i+1)*(segment+1) + j + 1) + '/' + str(3) + '/' + str(tmp + 1))
-                facesOBJ.append(str((i+1)*(segment+1) + j + 1) + '/' + str(3) + '/' + str(tmp + 2) + ' ' +
-                                str(i*(segment+1) + j + 2) + '/' + str(2) + '/' + str(tmp + 2) + ' ' +
-                                str((i+1)*(segment+1) + j + 2) + '/' + str(4) + '/' + str(tmp + 2))
-
-            else:
-                facesOBJ.append(str(i*(segment+1) + j + 1) + '/' + str(1) + '/' + str(i*(segment+1) + j + 1) + ' ' +
-                                str(i*(segment+1) + j + 2) + '/' + str(2) + '/' + str(i*(segment+1) + j + 2) + ' ' +
-                                str((i+1)*(segment+1) + j + 1) + '/' + str(3) + '/' + str((i+1)*(segment+1) + j + 1))
-                facesOBJ.append(str((i+1)*(segment+1) + j + 1) + '/' + str(3) + '/' + str((i+1)*(segment+1) + j + 1) +
-                                ' ' + str(i*(segment+1) + j + 2) + '/' + str(2) + '/' + str(i*(segment+1) + j + 2) +
-                                ' ' + str((i+1)*(segment+1) + j + 2) + '/' + str(4) + '/' +
-                                str((i+1)*(segment+1) + j + 2))
-            
-            # T1
-            half_scale = scale / 2.
-            scale_seg = scale / segment
-            vertices_obj.append([-half_scale + i*scale_seg, heightmap[i, j], -half_scale + j*scale_seg])
-            if j == segment-1:
-                vertices_obj.append([-half_scale + i*scale_seg, heightmap[i, j+1], -half_scale + (j+1)*scale_seg])
-            if i == segment-1:
-                tmp_vertices_obj.append([-half_scale + (i+1)*scale_seg, heightmap[i+1, j], -half_scale + j*scale_seg])
-                if j == segment-1:
-                    tmp_vertices_obj.append([-half_scale + (i+1)*scale_seg, heightmap[i+1, j+1],
-                                             -half_scale + (j+1)*scale_seg])
-
-            vertices.append(np.array([-half_scale + i*scale_seg,
-                                      heightmap[i, j],
-                                      -half_scale + j*scale_seg]))
-            vertices.append(np.array([-half_scale + i*scale_seg,
-                                      heightmap[i, j+1],
-                                      -half_scale + (j+1)*scale_seg]))
-            vertices.append(np.array([-half_scale + (i+1)*scale_seg,
-                                      heightmap[i+1, j],
-                                      -half_scale + j*scale_seg]))
-#            else:
-#                textures.append([i/segment, j/segment])
-#                textures.append([i/segment, (j+1)/segment])
-#                textures.append([(i+1)/segment, j/segment])
-
-            num_vertices = len(vertices)
-            normal = unit_normal(vertices[num_vertices-3], vertices[num_vertices-2], vertices[num_vertices-1])
-            normals_obj.append(normal)
-
-            # T2
-            vertices.append(np.array([-half_scale + (i+1)*scale_seg, heightmap[i+1, j], -half_scale + j*scale_seg]))
-            vertices.append(np.array([-half_scale + i*scale_seg, heightmap[i, j+1], -half_scale + (j+1)*scale_seg]))
-            vertices.append(np.array([-half_scale + (i+1)*scale_seg, heightmap[i+1, j+1], -half_scale + (j+1)*scale_seg]))
-
-#            else:
-#                textures.append([(i+1)/segment, j/segment])
-#                textures.append([i/segment, (j+1)/segment])
-#                textures.append([(i+1)/segment, (j+1)/segment])
-
-            num_vertices = len(vertices)
-            normal = unit_normal(vertices[num_vertices-3], vertices[num_vertices-2], vertices[num_vertices-1])
-            normals_obj.append(normal)
-            
-            if verbose:
-                if (time.time() % verbose_rate) < 0.05 and not prevent_output:
-                    display_loading(i*segment + j, segment*segment, "TER | Segm")
-                    prevent_output = True
-                elif time.time() % verbose_rate > 0.05:
-                    prevent_output = False
-
-    # smooth the normals
-    smooth_normals = []
-    for i in range(segment):
-        tmp_smooth_normals = []
-        for j in range(segment):
-            if j > 0:
-                norm0 = normals_obj[(i*segment + (j-1)*2)]
-                norm1 = normals_obj[(i*segment + (j-1)*2) + 1]
-            else:
-                norm0 = np.zeros(3)
-                norm1 = np.zeros(3)
-            
-            norm2 = normals_obj[((i*segment + j)*2)]
-
-            if i > 0 and j > 0:
-                norm3 = normals_obj[(((i-1)*segment + (j-1))*2) + 1]
-            else:
-                norm3 = np.zeros(3)
-
-            if i > 0:
-                norm4 = normals_obj[(((i-1)*segment + j)*2)]
-                norm5 = normals_obj[(((i-1)*segment + j)*2) + 1]
-            else:
-                norm4 = np.zeros(3)
-                norm5 = np.zeros(3)
-            
-            smooth_normals.append(unit_vector(norm0 + norm1 + norm2 + norm3 + norm4 + norm5))
-
-            if j == segment-1:
-                norm0 = normals_obj[((i*segment + (j-1))*2)]
-                norm1 = normals_obj[((i*segment + (j-1))*2) + 1]
-                if i > 0:
-                    norm2 = normals_obj[(((i-1)*segment + (j-1))*2) + 1]
-                else:
-                    norm2 = np.zeros(3)
-                smooth_normals.append(unit_vector(norm0 + norm1 + norm2))
-
-            if i == segment-1:
-                if j > 0:
-                    norm0 = normals_obj[(((i-1)*segment + (j-1))*2) + 1]
-                else:
-                    norm0 = np.zeros(3)
-
-                norm1 = normals_obj[(((i-1)*segment + j)*2)]
-                norm2 = normals_obj[(((i-1)*segment + j)*2) + 1]
-                tmp_smooth_normals.append(unit_vector(norm0 + norm1 + norm2))
-
-                if j == segment-1:
-                    norm0 = normals_obj[(((i-1)*segment + (j-1))*2) + 1]
-                    tmp_smooth_normals.append(norm0)
-    
-    smooth_normals += tmp_smooth_normals
-
-    vertices_obj += tmp_vertices_obj
-    if smooth:
-        return [vertices_obj, textures_obj, smooth_normals, facesOBJ]
-    return [vertices_obj, textures_obj, normals_obj, facesOBJ]
-
-
-def create_obj(vertices, textures, normals, faces, filename=None):
-    """
-    Create content of the OBJ file.
-
-    Args:
-        vertices (list): list of vertices (for each corner of a triangular mesh)
-        textures (list): list of textures
-        normals (list): list of normals
-        faces (list): list of faces
-        filename (None, str): if a string is provided, it will save the OBJ file in the given file path.
-
-    Returns:
-        str: content of the OBJ file.
-    """
-
-    # create obj list
-    obj = []
-    for v in vertices:
-        obj.append("v " + str(v[0]) + " " + str(v[1]) + " " + str(v[2]))
-    for t in textures:
-        obj.append("vt " + str(t[0]) + " " + str(t[1]))
-    for n in normals:
-        obj.append("vn " + str(n[0]) + " " + str(n[1]) + " " + str(n[2]))
-    for f in faces:
-        obj.append("f " + f)
-
-    # create document
-    obj = '\n'.join(obj)
-
-    # create file if specified
-    if filename is not None:
-        with open(filename, "w+") as f:
-            f.write(obj)
-    return obj
-                
-                
-segments = 8
-scale = 600.
-tile = True
-max_height = 75.
-min_height = 0.
-verbose = True
-verbose_rate = 1
-jitter = 40.
-jitter_factor = 1.5
-smooth = True
-
-# create heightmap, generate terrain from it, and obj mesh
-print("Generating terrain")
-start = time.time()
-
-# create heightmap
-heightmap = diamond_square_heightmap(segments, max_height, jitter, jitter_factor)
-
-# create vertices, textures, normals, and faces
-terrain = create_hexagonal_terrain(2 ** segments, scale, tile, min_height, heightmap, smooth, verbose,
-                                   verbose_rate)
-
-# create obj based on above information
-obj = create_obj(vertices=terrain[0], textures=terrain[1], normals=terrain[2], faces=terrain[3],
-                 filename='terrain.obj')
-
-end = time.time()
-print("Terrain generated in {:.2f} seconds.".format(end - start))
diff --git a/pyrobolearn/worlds/utils/terrains/terrain_heightmap.obj b/pyrobolearn/worlds/utils/terrains/terrain_heightmap.obj
new file mode 100644
index 0000000..1779fdb
--- /dev/null
+++ b/pyrobolearn/worlds/utils/terrains/terrain_heightmap.obj
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+f 16579/3/16579 16451/2/16451 16580/4/16580
+f 16451/1/16451 16452/2/16452 16580/3/16580
+f 16580/3/16580 16452/2/16452 16581/4/16581
+f 16452/1/16452 16453/2/16453 16581/3/16581
+f 16581/3/16581 16453/2/16453 16582/4/16582
+f 16453/1/16453 16454/2/16454 16582/3/16582
+f 16582/3/16582 16454/2/16454 16583/4/16583
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+f 16458/1/16458 16459/2/16459 16587/3/16587
+f 16587/3/16587 16459/2/16459 16588/4/16588
+f 16459/1/16459 16460/2/16460 16588/3/16588
+f 16588/3/16588 16460/2/16460 16589/4/16589
+f 16460/1/16460 16461/2/16461 16589/3/16589
+f 16589/3/16589 16461/2/16461 16590/4/16590
+f 16461/1/16461 16462/2/16462 16590/3/16590
+f 16590/3/16590 16462/2/16462 16591/4/16591
+f 16462/1/16462 16463/2/16463 16591/3/16591
+f 16591/3/16591 16463/2/16463 16592/4/16592
+f 16463/1/16463 16464/2/16464 16592/3/16592
+f 16592/3/16592 16464/2/16464 16593/4/16593
+f 16464/1/16464 16465/2/16465 16593/3/16593
+f 16593/3/16593 16465/2/16465 16594/4/16594
+f 16465/1/16465 16466/2/16466 16594/3/16594
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+f 16595/3/16595 16467/2/16467 16596/4/16596
+f 16467/1/16467 16468/2/16468 16596/3/16596
+f 16596/3/16596 16468/2/16468 16597/4/16597
+f 16468/1/16468 16469/2/16469 16597/3/16597
+f 16597/3/16597 16469/2/16469 16598/4/16598
+f 16469/1/16469 16470/2/16470 16598/3/16598
+f 16598/3/16598 16470/2/16470 16599/4/16599
+f 16470/1/16470 16471/2/16471 16599/3/16599
+f 16599/3/16599 16471/2/16471 16600/4/16600
+f 16471/1/16471 16472/2/16472 16600/3/16600
+f 16600/3/16600 16472/2/16472 16601/4/16601
+f 16472/1/16472 16473/2/16473 16601/3/16601
+f 16601/3/16601 16473/2/16473 16602/4/16602
+f 16473/1/16473 16474/2/16474 16602/3/16602
+f 16602/3/16602 16474/2/16474 16603/4/16603
+f 16474/1/16474 16475/2/16475 16603/3/16603
+f 16603/3/16603 16475/2/16475 16604/4/16604
+f 16475/1/16475 16476/2/16476 16604/3/16604
+f 16604/3/16604 16476/2/16476 16605/4/16605
+f 16476/1/16476 16477/2/16477 16605/3/16605
+f 16605/3/16605 16477/2/16477 16606/4/16606
+f 16477/1/16477 16478/2/16478 16606/3/16606
+f 16606/3/16606 16478/2/16478 16607/4/16607
+f 16478/1/16478 16479/2/16479 16607/3/16607
+f 16607/3/16607 16479/2/16479 16608/4/16608
+f 16479/1/16479 16480/2/16480 16608/3/16608
+f 16608/3/16608 16480/2/16480 16609/4/16609
+f 16480/1/16480 16481/2/16481 16609/3/16609
+f 16609/3/16609 16481/2/16481 16610/4/16610
+f 16481/1/16481 16482/2/16482 16610/3/16610
+f 16610/3/16610 16482/2/16482 16611/4/16611
+f 16482/1/16482 16483/2/16483 16611/3/16611
+f 16611/3/16611 16483/2/16483 16612/4/16612
+f 16483/1/16483 16484/2/16484 16612/3/16612
+f 16612/3/16612 16484/2/16484 16613/4/16613
+f 16484/1/16484 16485/2/16485 16613/3/16613
+f 16613/3/16613 16485/2/16485 16614/4/16614
+f 16485/1/16485 16486/2/16486 16614/3/16614
+f 16614/3/16614 16486/2/16486 16615/4/16615
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+f 16616/3/16616 16488/2/16488 16617/4/16617
+f 16488/1/16488 16489/2/16489 16617/3/16617
+f 16617/3/16617 16489/2/16489 16618/4/16618
+f 16489/1/16489 16490/2/16490 16618/3/16618
+f 16618/3/16618 16490/2/16490 16619/4/16619
+f 16490/1/16490 16491/2/16491 16619/3/16619
+f 16619/3/16619 16491/2/16491 16620/4/16620
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+f 16620/3/16620 16492/2/16492 16621/4/16621
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+f 16622/3/16622 16494/2/16494 16623/4/16623
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+f 16625/3/16625 16497/2/16497 16626/4/16626
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+f 16626/3/16626 16498/2/16498 16627/4/16627
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+f 16627/3/16627 16499/2/16499 16628/4/16628
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+f 16628/3/16628 16500/2/16500 16629/4/16629
+f 16500/1/16500 16501/2/16501 16629/3/16629
+f 16629/3/16629 16501/2/16501 16630/4/16630
+f 16501/1/16501 16502/2/16502 16630/3/16630
+f 16630/3/16630 16502/2/16502 16631/4/16631
+f 16502/1/16502 16503/2/16503 16631/3/16631
+f 16631/3/16631 16503/2/16503 16632/4/16632
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+f 16632/3/16632 16504/2/16504 16633/4/16633
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+f 16634/3/16634 16506/2/16506 16635/4/16635
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+f 16635/3/16635 16507/2/16507 16636/4/16636
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+f 16636/3/16636 16508/2/16508 16637/4/16637
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+f 16637/3/16637 16509/2/16509 16638/4/16638
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+f 16638/3/16638 16510/2/16510 16639/4/16639
+f 16510/1/16510 16511/2/16511 16639/3/16639
+f 16639/3/16639 16511/2/16511 16640/4/16640
+f 16511/1/16511 16512/2/16512 16640/3/16640
+f 16640/3/16640 16512/2/16512 16641/4/16641
\ No newline at end of file
diff --git a/pyrobolearn/worlds/world.py b/pyrobolearn/worlds/world.py
index fdf049a..1a38c69 100644
--- a/pyrobolearn/worlds/world.py
+++ b/pyrobolearn/worlds/world.py
@@ -16,11 +16,14 @@ import time
 
 from pyrobolearn.simulators import Simulator
 from pyrobolearn.worlds.world_camera import WorldCamera
-
-# from pyrobolearn.utils.heightmap_generator import *  # TODO: problem with gdal installation
 from pyrobolearn.utils import has_method, has_variable
-
 from pyrobolearn.robots import Body, Robot, robot_names_to_classes
+# TODO: to install the `gdal` library, run the script `pyrobolearn/scripts/install_gdal.sh`, by default do not
+#  import it
+from pyrobolearn.worlds.utils.heightmaps.diamond_square import diamond_square_heightmap, diamond_square_heightmap_2
+from pyrobolearn.worlds.utils.heightmaps.rbf import rbf_heightmap
+from pyrobolearn.worlds.utils.heightmaps.equation import equation_heightmap
+from pyrobolearn.worlds.utils.obj_generator import create_obj_from_heightmap
 
 
 __author__ = "Brian Delhaisse"
@@ -369,6 +372,10 @@ class World(object):
             Robot: instance of the Robot class
         """
         # TODO check the height of the terrain where we wish to load the robot
+        def check_height(position):
+            """check that the position of the robot is in accordance with the height of the terrain for that
+            position."""
+            return position
 
         if isinstance(robot, Robot):  # the robot is already loaded, then add it to the list
             pass
@@ -381,10 +388,13 @@ class World(object):
                 robot = robot_class(self.sim, position=position, orientation=orientation, fixed_base=fixed_base,
                                     *args, **kwargs)
 
-            else:  # robot is the path to the urdf
+            elif robot[-4:] == 'urdf':  # robot is the path to the urdf
                 robot = Robot(self.sim, urdf=robot, position=position, orientation=orientation, fixed_base=fixed_base,
                               *args, **kwargs)
 
+            else:
+                raise ValueError("The given string does not correspond to any robots or urdfs: {}".format(robot))
+
         elif inspect.isclass(robot):  # robot class
             robot = robot(self.sim, position=position, orientation=orientation, fixed_base=fixed_base, *args, **kwargs)
 
@@ -542,9 +552,6 @@ class World(object):
             object_id (int): object id
             position (float[3]): new position of the object. If None, it will keep the old position.
             orientation (float[4]): new orientation of the object. If None, it will keep the old orientation.
-
-        Returns:
-            None
         """
         if position is None:
             position = self.sim.get_base_pose(object_id)[0]
@@ -568,9 +575,6 @@ class World(object):
                 of the object (or the link if specified)
             frame (int): allows to specify the coordinate system of force/position. sim.LINK_FRAME (=1) for local
                 link frame, and sim.WORLD_FRAME (=2) for world frame. By default, it is the world frame.
-
-        Returns:
-            None
         """
         if position is None:
             if link_id != -1:
@@ -599,9 +603,6 @@ class World(object):
             object_id (int): object id
             color (float[4]): RGBA color
             link_id (int): link id
-
-        Returns:
-            None
         """
         self.sim.change_visual_shape(object_id, link_id, rgba_color=color)
 
@@ -672,9 +673,6 @@ class World(object):
 
         Args:
             object_id (int): object id
-
-        Returns:
-            None
         """
         color = self.get_object_color(object_id)
         color[-1] = 0.
@@ -686,9 +684,6 @@ class World(object):
 
         Args:
             object_id (int): object id
-
-        Returns:
-            None
         """
         color = self.get_object_color(object_id)
         color[-1] = 1.
@@ -739,9 +734,6 @@ class World(object):
         Args:
             object_id (int): object id
             scale (float[3]): scaling factors in each direction
-
-        Returns:
-            None
         """
         # TODO: currently not possible in PyBullet
         pass
@@ -846,18 +838,22 @@ class World(object):
         self.floor_id = self.sim.load_urdf('plane.urdf', use_fixed_base=True, scale=scaling)
         return self.floor_id
 
-    def load_terrain(self, heightmap, position=(0., 0., 0.), scaling=1., replace_floor=True):
+    def load_terrain(self, heightmap, position=(0., 0., 0.), orientation=(.707, 0, 0, .707), scaling=1.,
+                     replace_floor=True, remove_obj=False, texture=None):
         """
-        Load the given terrain/heightmap.
+        Load the given terrain/heightmap into the world.
 
         Args:
-            heightmap (str, np.array[heigth,width]): path to the urdf, sdf, xml, or obj file of the terrain. It can
+            heightmap (str, np.array[heigth, width]): path to the urdf, sdf, xml, or obj file of the terrain. It can
                 also be the path to a heightmap in tif, jpg, or png format. Alternatively, it can represents
                 the heightmap as a 2D numpy array where the values represent the height in meters.
             position (float[3]): position of the terrain. By default, origin of the world.
-            scaling (float): scaling factor of the terrain
+            orientation (tuple of 4 float): orientation of the terrain (expressed as quaternion [x,y,z,w]).
+            scaling (float, tuple of 3 float): scaling factor of the terrain.
             replace_floor (bool): if True, it will replace the existing floor. Be careful, that it can cause
                 problems with collision.
+            remove_obj (bool): if True, it will remove the obj file.
+            texture (str, None): texture to apply.
 
         Returns:
             int: unique id of the terrain.
@@ -867,111 +863,101 @@ class World(object):
         - `openmesh`: https://www.openmesh.org/media/Documentations/OpenMesh-6.2-Documentation/a00036.html
         - `bpy`: Blender python API - https://docs.blender.org/api/current/
         """
-        if self.floor_id > -1:  # there is already a floor defined
+        # if there is already a floor, remove it if specified
+        if self.floor_id > -1:
             if replace_floor:
                 self.sim.remove_body(self.floor_id)
 
-        if heightmap[-4:] == 'obj':  # obj (mesh)
-            self.floor_id = self.load_mesh(heightmap, position, mass=0., scale=[scaling] * 3, flags=1,
-                                           object_type='terrain')
-        elif heightmap[-4:] == '.sdf':  # SDF
-            self.floor_id = self.load_sdf(filename=heightmap, scaling=scaling)
-        elif heightmap[-4:] == '.xml':  # MJCF
-            self.floor_id = self.load_mjcf(filename=heightmap, scaling=scaling)
-        elif heightmap[-5:] == '.urdf':  # URDF
-            self.floor_id = self.sim.load_urdf(heightmap, position, use_fixed_base=True, scale=scaling)
-        else:  # heightmap (.tif, .jpg, .png, etc)
-            def create_mesh(heightmap):
-                # create 3D mesh
-                # create3DMesh(heightmap, filename=, subsample=, interpolate_fct=)
-                pass
+        # if heightmap is a 2D array
+        if isinstance(heightmap, np.ndarray):
+            self.generate_terrain(heightmap, filename='heightmap.obj')
+            heightmap = 'heightmap.obj'
 
-            # create process to create the 3D mesh
-            process = multiprocessing.Process(target=create_mesh, args=(heightmap,))
-            process.start()
-            process.join()
+        filename = heightmap
 
+        # if heightmap is a string, it is the path to the 3d terrain or image
+        if isinstance(filename, str):
+
+            if filename[-3:] == 'obj':  # obj (mesh)
+                if not isinstance(scaling, (list, tuple)):
+                    scaling = [scaling] * 3
+                self.floor_id = self.load_mesh(filename, position, orientation, mass=0., scale=scaling, flags=1,
+                                               object_type='terrain')
+
+            elif filename[-3:] == 'sdf':  # SDF
+                self.floor_id = self.load_sdf(filename=filename, scaling=scaling)
+
+            elif filename[-3:] == 'xml':  # MJCF
+                self.floor_id = self.load_mjcf(filename=filename, scaling=scaling)
+
+            elif filename[-4:] == 'urdf':  # URDF
+                self.floor_id = self.sim.load_urdf(filename, position, use_fixed_base=True, scale=scaling)
+
+            else:  # heightmap (.tif, .jpg, .png, etc)
+                # if extension is jpg or png
+                if filename[-3:] == 'png' or filename[-3:] == 'jpg':
+                    heightmap = cv2.imread(filename, cv2.IMREAD_GRAYSCALE)
+                else:  # use gdal to open the heightmap
+                    heightmap = self.generate_heightmap(algo=6, filename=filename)
+
+                self.generate_terrain(heightmap, filename=filename)
+
+                # load the obj
+                if not isinstance(scaling, (list, tuple)):
+                    scaling = [scaling] * 3
+                self.floor_id = self.load_mesh(filename, position, orientation, mass=0., scale=scaling, flags=1,
+                                               object_type='terrain')
+        else:
+            raise TypeError("Expecting the given 'heightmap' to be a string or a numpy array, instead got: "
+                            "{}".format(type(heightmap)))
+
+        if filename[-3:] == 'obj' and remove_obj:
             # remove mesh from memory
             os.remove(filename + '.obj')  # remove mesh from memory
             # os.remove(filename + '.mtl')
 
-            # apply the given texture if provided
-            if isinstance(texture, str):
-                texture = self.sim.load_texture(texture)
-                self.sim.change_visual_shape(heightmap, -1, texture_id=texture)
+        # apply the given texture if provided
+        if isinstance(texture, str):
+            texture = self.sim.load_texture(texture)
+            self.sim.change_visual_shape(object_id=self.floor_id, link_id=-1, texture_id=texture)
 
+        # return the floor id
         return self.floor_id
 
-    def load_heightmap(self, heightmap, texture=None, position=(0., 0., 0.), scale=1.):
+    def load_heightmap(self, filename):
         """
-        Load a heightmap for the terrain.
+        Load a heightmap from an image.
 
         Args:
-            heightmap (str, np.ndarray[M,M]): if string, filename containing the heightmap in  the png, jpg, obj format
-                if a 2D numpy arrays, the values represent the height in meters.
-            texture: texture to apply
-            position (float[3]): position of the terrain
-            scale (float): scaling factor
+            filename (str): filename containing the heightmap in the png, jpg, tif, bmp format
 
         Returns:
-            int: unique id of the floor
+            np.array[H,W]: heightmap (height, width)
 
         Modules to create mesh files (.obj):
         - `mayavi`: https://docs.enthought.com/mayavi/mayavi/
         - `openmesh`: https://www.openmesh.org/media/Documentations/OpenMesh-6.2-Documentation/a00036.html
         - `bpy`: Blender python API - https://docs.blender.org/api/current/
         """
+        if not isinstance(filename, str):
+            raise TypeError("Expecting the given 'filename' to be a string (i.e. the path to the heightmap image), "
+                            "instead got: {}".format(type(filename)))
 
-        extension, filename = None, 'generated_file'
+        # load heightmap
+        if filename[-3:] == 'png' or filename[-3:] == 'jpg':
+            heightmap = cv2.imread(filename, cv2.IMREAD_GRAYSCALE)
+        else:  # use gdal to open the heightmap
+            heightmap = self.generate_heightmap(algo=6, filename=filename)
 
-        # if string, get the extension and name of the file
-        if isinstance(heightmap, str):
-            extension = heightmap.split('.')[-1]
-            filename = heightmap[:-4]
-
-            # if picture (png/jpg), load 2D array (grayscale values)
-            if extension == 'png' or extension == 'jpg':
-                heightmap = cv2.imread(filename, cv2.IMREAD_GRAYSCALE)
-
-        # if 2D numpy array, create the mesh (in the .obj format)
-        if isinstance(heightmap, np.ndarray):
-            heightmap = heightmap.astype(np.float)
-            mlab.surf(heightmap)
-            mlab.savefig(filename + '.obj')
-            mlab.close()
-            # TODO: set the map of the world
-
-        elif extension != 'obj':
-            raise ValueError("Expecting heightmap in a png/jpg/obj format")
-
-        # load the mesh of the terrain
-        heightmap = self.load_terrain(filename, position=position, scaling=scale)
-
-        # change the dynamic properties of the terrain based on the given type (grass, mud, bumpy
-        # WARNING: only 1 type can be specified. Currently, it is not possible to have different dynamic properties
-        # for different parts of the terrain. Loading multiple terrains is currently not supported (there is only
-        # 1 unique id for the floor).
-
-        # apply the given texture if provided
-        if isinstance(texture, str):
-            texture = self.sim.load_texture(texture)
-            self.sim.change_visual_shape(heightmap, -1, texture_id=texture)
-
-        # remove mesh from memory
-        os.remove(filename + '.obj')  # remove mesh from memory
-        os.remove(filename + '.mtl')
-
-        # replace the floor if there is already one present
-        if self.floor_id > -1:
-            self.sim.remove_body(self.floor_id)
-        self.floor_id = heightmap
-
-        return self.floor_id
+        return heightmap
 
     # aliases
     loadDEM = load_heightmap
 
-    def generate_heightmap(self, filename=None, algo=None):
+    @staticmethod
+    def generate_heightmap(algo=2, filename=None, width=256, height=256, n=8, min_height=0, max_height=255, noise=0,
+                           noise_factor=1, init_values=None, x=None, y=None, z=None, function='multiquadric',
+                           dtype=np.int):
         """
         Generate a heightmap (png) using the specified algorithm. We provide 4 algorithms to generate this last one:
         1. by generating it randomly (not advised)
@@ -987,23 +973,85 @@ class World(object):
         approaches.
 
         Args:
-            filename (None, str): if not None, it will save the heightmap in the format specified by the filename.
-                The format is inferred from the filename. Supported ones include '.png', '.jpg', and '.obj'.
+            algo (int): specifies which algorithm to use to generate the heightmap.
+                1. randomly
+                2. diamond-square algorithm
+                3. diamond-square algorithm (version 2)
+                4. RBF interpolation
+                5. 3d equation
+                6. geospatial
+            filename (str, None): if algo=6, path to a DEM, GIS, or image file (e.g. png) to open.
+            n (int): used to create a square array of width and height of 2**n + 1. It also specifies the number of
+                diamond and square steps.
+            min_height (int,float): lower bound; each value in the heightmap will be higher than or equal to this bound
+            max_height (int,float): upper bound; each value in the heightmap will be lower than or equal to this bound
+            noise (float): magnitude of the noise added to the computed height.
+            noise_factor (float): after each step, the jitter is divided by the given factor.
+            init_values (np.array[M,3]): list of `M` 3D points which corresponds to initial values that are used to fit
+                the gaussian process.
+            x (np.array[N], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D
+                array from the meshgrid is expected. This is used to predict the heightmap at the given points.
+            y (np.array[0], np.array[N,O]): If 1d array, it will compute the meshgrid. Otherwise, the resulting 2D
+                array from the meshgrid is expected. This is used to predict the heightmap at the given points.
+            z (callable): it must be a function that accepts two arguments `x` and `y` which will be the arrays from
+                the meshgrid.
+            function (str, callable): "The radial basis function, based on the radius, r, given by the norm
+                (default is Euclidean distance);
+                    'multiquadric': sqrt((r/self.epsilon)**2 + 1)
+                    'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1)
+                    'gaussian': exp(-(r/self.epsilon)**2)
+                    'linear': r
+                    'cubic': r**3
+                    'quintic': r**5
+                    'thin_plate': r**2 * log(r)
+                If callable, then it must take 2 arguments (self, r). The epsilon parameter will be available as
+                self.epsilon. Other keyword arguments passed in will be available as well."
+            dtype (np.int, np.float): type of the returned array for the heightmap
 
         Returns:
-            np.array[W,H]: heightmap (with, height)
+            np.array[H,W]: heightmap (height, width)
         """
-        pass
+        if algo == 1:  # random
+            heightmap = np.random.randint(min_height, max_height)
+        elif algo == 2:  # diamond-square
+            heightmap = diamond_square_heightmap(n=n, min_height=min_height, max_height=max_height, noise=noise,
+                                                 noise_factor=noise_factor)
+        elif algo == 3:  # diamond-square (version 2)
+            heightmap = diamond_square_heightmap_2(n=n, min_height=min_height, max_height=max_height, noise=noise,
+                                                   noise_factor=noise_factor)
+        elif algo == 4:  # RBF interpolation
+            heightmap = rbf_heightmap(init_values=init_values, x=x, y=y, function=function, min_height=min_height,
+                                      max_height=max_height, dtype=dtype)
+        elif algo == 5:  # 3D equation
+            heightmap = equation_heightmap(x=x, y=y, z=z, min_height=min_height, max_height=max_height, dtype=dtype)
+        elif algo == 6:  # geospatial
+            from pyrobolearn.worlds.utils.heightmaps.geospatial import gdal_heightmap
+            heightmap = gdal_heightmap(filename=filename)
+        else:
+            raise NotImplementedError("The algo should be between 1 and 6 (see documentation).")
+        return heightmap
 
-    def generate_terrain(self, heightmap, filename):
+    @staticmethod
+    def generate_terrain(heightmap, filename, scale=600, smooth=True, verbose=True):
         """
-        Generate the terrain (obj) file and load it in the world.
+        Generate the terrain (obj) file; that is, create the OBJ file from the heightmap.
 
         Args:
             heightmap (np.array[W,H]): 2D heightmap.
             filename (str): filename.
+            scale (float): scaling factor.
+            smooth (bool): if the normals should be smooth.
+            verbose (bool): if True, it will output information about the creation of the terrain.
+
+        Returns:
+            str: content of the OBJ file.
+
+        References:
+            [1] Wavefront .obj file (Wikipedia): https://en.wikipedia.org/wiki/Wavefront_.obj_file
         """
-        pass
+        obj = create_obj_from_heightmap(heightmap=heightmap, scale=scale, smooth=smooth, verbose=verbose,
+                                        filename=filename)
+        return obj
 
     def load_stadium(self, scaling=1.):
         """
@@ -1065,7 +1113,7 @@ class World(object):
         Returns:
             int: unique id of the table
         """
-        table = self.sim.load_urdf('table/table.urdf', scale=scaling)
+        table = self.sim.load_urdf('table/table.urdf', position=position, scale=scaling)
         self.movable_bodies[table] = 'table'
         return table
 
@@ -1618,18 +1666,19 @@ if __name__ == '__main__':
     sim = BulletSim()
 
     # create world
-    world = BasicWorld(sim)
-    # world = World(sim)
+    # world = BasicWorld(sim)
+    world = World(sim)
     # world.load_bot_lab()
 
-    # # load meshes
-    # world.load_mesh('meshes/terrain.obj',
-    #                position=[0, 0, -2],
-    #                orientation=[.707, 0, 0, .707],
-    #                mass=0.,
-    #                scale=(.1, .1, .1),
-    #                # color=[1, 0, 0, 1],
-    #                flags=1)
+    # load meshes
+    world.load_mesh('utils/terrains/terrain_map.obj',
+                    position=[0, 0, -2],
+                    orientation=[.707, 0, 0, .707],
+                    mass=0.,
+                    scale=(.1, .1, .1),
+                    # color=[1, 0, 0, 1],
+                    flags=1)
+    # world.load_visual_mesh('meshes/cube_color.dae', position=[0, 0, 1])
     # world.load_mesh('bedroom.obj', [0, 0, 0], mass=0., color=[0.4, 0.4, 0.4, 1], flags=1) #, scale=(0.01, 0.01, 0.01))
     # world.load_mesh('mtsthelens.obj', [0, 0, -8], mass=0., color=[0.2, 0.5, 0.2, 1], flags=1, scale=(0.01,0.01,0.01))
     # world.load_mesh('meshes/terrain.obj', [0,0,0], mass=0., color=[1,1,1,1], flags=1)