Fix bug in bicubic interpolation and extend test cases to higher orders

skimage/_shared/interpolation.pxd

@@ -159,7 +159,7 @@ cdef inline double cubic_interpolation(double x, double[4] f):
     x : double
         Position in the interval [0, 1].
     f : double[4]
-        Function values at positions [0, 1/3, 2/3, 1].
+        Function values at positions [-1, 0, 1, 2].
 
     Returns
     -------
@@ -206,8 +206,8 @@ cdef inline double bicubic_interpolation(double* image, Py_ssize_t rows,
     if c < 0:
         c0 -= 1
     # scale position to range [0, 1]
-    cdef double xr = (r - r0) / 3
-    cdef double xc = (c - c0) / 3
+    cdef double xr = r - floor(r)
+    cdef double xc = c - floor(c)
 
     cdef double fc[4]
     cdef double fr[4]

skimage/transform/tests/test_warps.py

@@ -117,7 +117,7 @@ def test_fast_homography():
     tform = ProjectiveTransform(H)
     coords = warp_coords(tform.inverse, (img.shape[0], img.shape[1]))
 
-    for order in range(4):
+    for order in range(6):
         for mode in ('constant', 'reflect', 'wrap', 'nearest'):
             p0 = map_coordinates(img, coords, mode=mode, order=order)
             p1 = warp(img, tform, mode=mode, order=order)
@@ -130,8 +130,7 @@ def test_fast_homography():
             # ax3.imshow(np.abs(p0 - p1), cmap=plt.cm.gray)
             # plt.show()
 
-            d = np.mean(np.abs(p0 - p1))
-            assert d < 0.001
+            assert_array_equal(p0, p1)
 
 
 def test_rotate():