def test_triangle_interpolation():
f_list = [
[10.2, 80.3, 80.4],
[80.2, 80.3, 107.4],
[-200.1, -200.2, -200.3],
[-200, -150, -600],
[-100, -40, 10],
[-20, 10, 50],
[10, 30, 50],
[50.1, 50.4, 50.9],
[82.3, 100.5, 200],
[102, 103, 104],
]
for list_ in f_list:
list_ = np.asarray(list_)
amp_py = np.zeros(100)
triangle_interpolation1D(list_, amp_py)
amp_c = np.zeros(100)
clib.triangle_interpolation1D(list_, amp_c)
# plt.plot(amp_py, 'b', label='py')
# plt.plot(amp_c, 'r--', label='c')
# plt.plot(list_-0.5, [0, 2/(list_[2]-list_[0]), 0], 'k*', label='c')
# plt.legend()
# plt.show()
assert np.allclose(amp_py, amp_c, atol=1e-15)
def test_triangle_rasterization5():
# triangles with one or more vertices outside a grid voxel
f_list = [
[[15.0, 15.5, 15.9], [12.0, 12.5, 12.9]], # all in
[[15.0, 15.5, 16.2], [12.0, 12.5, 12.9]], # one out
[[15.0, 15.5, 16.2], [12.0, 12.5, 13.9]], # one out on each dimension
[[15.0, 15.5, 17.2], [12.0, 12.5, 11.9]], # one out on each dimension
[[14.5, 15.5, 18.2], [11.5, 12.0, 11.2]], # one out on each dimension
]
for scl in SCALE:
for i, list_ in enumerate(f_list):
lst1, lst2 = np.asarray(list_) * scl
amp1 = np.zeros((20 * scl, 2 * 20 * scl), dtype=np.float64)
amp2 = np.zeros(2 * 20 * scl, dtype=np.float64)
amp3 = np.zeros(2 * 20 * scl, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst1, amp2)
clib.triangle_interpolation1D(lst2, amp3)
amp1 = amp1[:, ::2] # + 1j * amp1[:, 1::2]
amp2 = amp2[::2] # + 1j * amp2[1::2]
amp3 = amp3[::2] # + 1j * amp3[1::2]
# plot_2d_raster(amp1, lst1, lst2, amp3, amp2, save=f"ras5_{i}", scale=scl)
assert np.allclose(amp2, amp1.sum(axis=1), atol=1e-15)
def test_triangle_rasterization3():
# triangles with one or more vertices outside the 2D grids (left - right)
f_list = [
[[5.5, 8.0, 17.4], [21.5, 12.0, 17.3]], # 1 right
[[5.5, 18.0, 17.4], [21.5, 27.0, 17.3]], # 2 right
[[5.5, 8.0, 17.4], [-14.5, 12.0, 17.3]], # 1 left
[[5.5, 8.0, 17.4], [-14.5, 12.0, -17.3]], # 2 left
[[5.5, 8.0, 17.4], [-4.5, 12.0, 27.3]], # 1 left and 1 right
[[15.5, 8.0, 17.4], [-4.5, 12.0, 27.3]], # 1 left and 1 right
]
for scl in SCALE:
for i, list_ in enumerate(f_list):
lst1, lst2 = np.asarray(list_) * scl
amp1 = np.zeros((20 * scl, 2 * 20 * scl), dtype=np.float64)
amp_x = np.zeros(2 * 20 * scl, dtype=np.float64)
amp_y = np.zeros(2 * 20 * scl, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst2, amp_x)
clib.triangle_interpolation1D(lst1, amp_y)
amp1 = amp1[:, ::2] # + 1j * amp1[:, 1::2]
amp_x = amp_x[::2] # + 1j * amp_x[1::2]
amp_y = amp_y[::2] # + 1j * amp_y[1::2]
# plot_2d_raster(amp1, lst1, lst2, amp_x, None, save=f"ras3_{i}", scale=scl)
assert np.allclose(amp_x, amp1.sum(axis=0), atol=1e-2)
def test_triangle_rasterization2():
# triangles with one or more vertices outside the 2D grids (top - down)
f_list = [
[[5.5, -8.0, 17.4], [4.5, 12.0, 17.3]], # 1 down
[[5.5, 8.0, 27.4], [4.5, 12.0, 17.3]], # 1 up
[[25.5, -8.0, 17.4], [4.5, 12.0, 17.3]], # 1 up and down each
[[25.5, -8.0, 27.4], [4.5, 12.0, 17.3]], # 2 up and 1 down
[[-12.5, 28.0, -12.4], [4.5, 12.0, 17.3]], # 2 down and 1 up
[[17.5, -8.0, -27.4], [4.5, 12.0, 3.0]], # 2 down
[[25.5, 8.0, 27.4], [4.5, 12.0, 18.3]], # 2 up
[[-12.5, -8.0, -12.4], [4.5, 12.0, 17.3]], # all out down
[[42.5, 28.0, 32.4], [4.5, 12.0, 17.3]], # all out up
]
for scl in SCALE:
for i, list_ in enumerate(f_list):
lst1, lst2 = np.asarray(list_) * scl
amp1 = np.zeros((20 * scl, 2 * 20 * scl), dtype=np.float64)
amp2 = np.zeros(2 * 20 * scl, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst1, amp2)
amp1 = amp1[:, ::2] # + 1j * amp1[:, 1::2]
amp2 = amp2[::2] # + 1j * amp2[1::2]
# plot_2d_raster(amp1, lst1, lst2, None, amp2, save=f"ras2_{i}", scale=scl)
assert np.allclose(amp2, amp1.sum(axis=1), atol=1e-15)
def test_triangle_rasterization1():
# triangles within the 2D grids
f_list = [
[[6.0, 2.3, 19.0], [15.0, 2.0, 17.9]],
[[10.0, 10.9, 1.0], [15.0, 2.0, 17.9]],
[[10.0, 10.9, 1.0], [15.0, 2.0, 15.9]],
[[10.0, 10.9, 1.0], [15.0, 2.0, 12.0]],
[[1.5, 10.9, 1.0], [16.0, 1.2, 2.4]],
[[1.5, 10.9, 1.6], [15.0, 2.0, 1.0]],
[[1.5, 2.0, 7.4], [1.5, 2.0, 7.3]],
[[1.5, 9.0, 9.4], [1.5, 9.0, 9.4]],
[[1.5, 6.0, 9.4], [1.5, 6.0, 9.4]],
[[1.5, 6.9, 12.1], [1.5, 5.32, 9.0]],
[[1.5, 6.9, 12.1], [1.5, 4.8, 9.0]],
[[1.5, 1.5, 1.5], [1.5, 6.0, 9.4]],
]
for scl in SCALE:
for i, list_ in enumerate(f_list):
lst1, lst2 = np.asarray(list_) * scl
amp1 = np.zeros((20 * scl, 2 * 20 * scl), dtype=np.float64)
amp2 = np.zeros(2 * 20 * scl, dtype=np.float64)
amp3 = np.zeros(2 * 20 * scl, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst1, amp2)
clib.triangle_interpolation1D(lst2, amp3)
amp1 = amp1[:, ::2] # + 1j * amp1[:, 1::2]
amp2 = amp2[::2] # + 1j * amp2[1::2]
amp3 = amp3[::2] # + 1j * amp3[1::2]
# plot_2d_raster(amp1, lst1, lst2, amp3, amp2, save=f"ras1_{i}", scale=scl)
assert np.allclose(amp2, amp1.sum(axis=1), atol=1e-15)
assert np.allclose(amp3, amp1.sum(axis=0), atol=1e-15)
def test_triangle_interpolation():
f_list = [
[-0.91, -4.14, -16.70],
[-0.91, 2.16, -16.70],
[10.2, 80.3, 80.4],
[0.5, 0.7, 50.1],
[10.2, 98.6, 99.2],
[80.2, 80.3, 107.4],
[-200.1, -200.2, -200.3],
[-200, -150, -600],
[-100, -40, 10],
[-20, 10, 50],
[10, 30, 50],
[0.2, 30, 50],
[-20.2, 0.2, 50],
[-20.2, 0.7, 50],
[-20.2, 1.2, 50],
[50.1, 50.4, 50.9],
[82.3, 100.5, 200],
[102, 103, 104],
[99, 100.1, 100.2],
[98.9, 99.1, 99.5],
[-0.23, -0.02, 0.1],
[98.9, 120, 140],
[0.6, 1.6, 45.5],
[18.35, 18.71, 13.77],
[11.28, 10.97, 6.36],
[60, 99.2, 100.2],
[-0.9, -0.1, 10],
]
for scl in SCALE:
for i, list_ in enumerate(f_list):
list_ = np.sort(list_) * scl
amp_py = np.zeros(100 * scl)
triangle_interpolation1D(list_, amp_py)
amp_c = np.zeros(2 * 100 * scl)
clib.triangle_interpolation1D(list_, amp_c)
amp_c = amp_c[::2] + 1j * amp_c[1::2]
# x = np.arange(100 * scl) / scl
# y = get_height(list_)
# plt.plot(x, amp_py, "b", label="py")
# plt.plot(x, amp_c.real, "r--", label="c")
# plt.plot((list_ - 0.5) / scl, [0, y, 0], "k*--", label="x")
# plt.title("1D interpolation, span(0, 100)")
# plt.legend()
# plt.tight_layout()
# plt.show()
# plt.savefig(f"figs/fig_1D_{i}_{scl}.pdf")
# plt.figure().clear()
assert np.allclose(amp_py, amp_c.real, atol=1e-15)
def test_gaussian_interpolation():
sigma = 1.0 / 4.0
div = 2 * sigma**2
scale = sigma * np.sqrt(2 * np.pi)
f_list = [
5.5,
6.0,
6.2,
6.4,
6.6,
6.8,
7.0,
7.1,
7.5,
7.9,
8.0,
9.23,
10.2,
-0.1,
-0.9,
-1.0,
-1.8,
]
f_list += list(np.arange(20) / 10 + 5)
x = np.arange(20) - 5
for i, item in enumerate(f_list):
list_ = np.asarray([item + 0.5] * 3)
# should be
gauss = np.exp(-((x - item)**2) / div) / scale
gauss /= gauss.sum()
gauss = gauss[5:-5]
# from delta interpolation
amp_c = np.zeros(20)
clib.triangle_interpolation1D(list_, amp_c, type="gaussian")
amp_c = amp_c[::2] + 1j * amp_c[1::2]
# plt.plot(np.arange(10), gauss, label="gauss")
# plt.plot(np.arange(10), amp_c, label="calc")
# plt.legend()
# plt.show()
# plt.bar(np.arange(10), amp_c.real, width=1)
# plt.scatter([item], [1.0], marker="x", color="k", s=50)
# # plt.xticks(np.arange(17) - 3)
# plt.grid(axis="x", which="both")
# plt.title("1D delta interpolation (gaussian), span(0, 10)")
# plt.savefig(f"figs/fig_1D_delta_gaussian{i}.pdf")
# plt.figure().clear()
np.testing.assert_almost_equal(gauss, amp_c, decimal=3)
def get_amps_from_interpolation(list_, scl):
lst1, lst2 = np.asarray(list_) * scl
amp1 = np.zeros((20 * scl, 2 * 20 * scl), dtype=np.float64)
amp2 = np.zeros(2 * 20 * scl, dtype=np.float64)
amp3 = np.zeros(2 * 20 * scl, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst1, amp2)
clib.triangle_interpolation1D(lst2, amp3)
amp1 = amp1[:, ::2] # + 1j * amp1[:, 1::2]
amp2 = amp2[::2] # + 1j * amp2[1::2]
amp3 = amp3[::2] # + 1j * amp3[1::2]
return amp1, amp2, amp3, lst1, lst2
def test_delta_interpolation_linear():
f_list = [
5.5,
6.0,
6.2,
6.4,
6.6,
6.8,
7.0,
7.1,
7.5,
7.9,
8.0,
-0.1,
-0.9,
-1.0,
-1.8,
9.23,
10.2,
]
f_list += list(np.arange(80) / 40 + 5)
for i, item in enumerate(f_list):
list_ = np.asarray([item + 0.5] * 3)
# should be
amp_ = np.zeros(10)
x1 = int(np.floor(item))
if x1 >= -1 and x1 <= 8:
amp_[x1 + 1] = item - x1
if x1 >= 0 and x1 <= 9:
amp_[x1] = 1 - (item - x1)
# from delta interpolation
amp_c = np.zeros(2 * 10)
clib.triangle_interpolation1D(list_, amp_c, type="linear")
amp_c = amp_c[::2] + 1j * amp_c[1::2]
# plt.bar(np.arange(10), amp_c.real, width=1)
# plt.scatter([item], [1.0], marker="x", color="k", s=50)
# plt.xticks(np.arange(17) - 3)
# plt.grid(axis="x", which="both")
# plt.title("1D delta interpolation (linear), span(0, 10)")
# plt.savefig(f"figs/fig_1D_delta_linear{i}.pdf")
# plt.figure().clear()
assert np.allclose(amp_, amp_c.real, atol=1e-15)
def test_triangle_rasterization4():
# all points outside but intersecting the view
f_list = [
[[-12.5, 18.0, 32.4], [-4.5, 22.0, 27.3]], # all out
[[-12.5, 18.0, -22.4], [-4.5, 22.0, 27.3]], # all out
[[-12.5, 18.0, 22.4], [-4.5, 22.0, -27.3]], # all out
]
for scl in SCALE:
for i, list_ in enumerate(f_list):
lst1, lst2 = np.asarray(list_) * scl
amp1 = np.zeros((20 * scl, 2 * 20 * scl), dtype=np.float64)
amp_x = np.zeros(2 * 20 * scl, dtype=np.float64)
amp_y = np.zeros(2 * 20 * scl, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst2, amp_x)
clib.triangle_interpolation1D(lst1, amp_y)
amp1 = amp1[:, ::2] # + 1j * amp1[:, 1::2]
amp_x = amp_x[::2] # + 1j * amp_x[1::2]
amp_y = amp_y[::2] # + 1j * amp_y[1::2]
def test_delta_interpolation():
f_list = [
5.5,
6.0,
6.2,
6.4,
6.6,
6.8,
7.0,
7.1,
7.5,
7.9,
8.0,
-0.1,
-0.9,
-1.0,
-5.2,
9.23,
10.2,
]
for item in f_list:
list_ = np.asarray([item + 0.5] * 3)
# should be
amp_ = np.zeros(10)
x1 = int(np.floor(item))
if x1 >= -1 and x1 <= 8:
amp_[x1 + 1] = item - x1
if x1 >= 0 and x1 <= 9:
amp_[x1] = 1 - (item - x1)
# from delta interpolarion
amp_c = np.zeros(10)
clib.triangle_interpolation1D(list_, amp_c)
# plt.bar(np.arange(10), amp_c, width=1)
# plt.show()
assert np.allclose(amp_, amp_c, atol=1e-15)
def test_triangle_rasterization():
# triangles within the 2D grids
f_list = [
[[6.0, 2.3, 19.0], [15.0, 2.0, 17.9]],
[[10.0, 10.9, 1.0], [15.0, 2.0, 17.9]],
[[10.0, 10.9, 1.0], [15.0, 2.0, 15.9]],
[[10.0, 10.9, 1.0], [15.0, 2.0, 12.0]],
[[1.5, 10.9, 1.0], [16.0, 1.2, 2.4]],
[[1.5, 10.9, 1.6], [15.0, 2.0, 1.0]],
[[1.5, 2.0, 7.4], [1.5, 2.0, 7.3]],
[[1.5, 9.0, 9.4], [1.5, 9.0, 9.4]],
[[1.5, 6.0, 9.4], [1.5, 6.0, 9.4]],
[[1.5, 1.5, 1.5], [1.5, 6.0, 9.4]],
]
for list_ in f_list:
lst1, lst2 = np.asarray(list_)
amp1 = np.zeros((20, 20), dtype=np.float64)
amp2 = np.zeros(20, dtype=np.float64)
amp3 = np.zeros(20, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst1, amp2)
clib.triangle_interpolation1D(lst2, amp3)
# plt.imshow(amp1, origin='lower', cmap='gray', aspect='auto')
# x_t, y_t = np.append(lst2, lst2[0]) - 0.5, np.append(lst1, lst1[0]) - 0.5
# plt.plot(x_t, y_t, 'r', label='vertex')
# plt.scatter(lst2-0.5, lst1-0.5, s=20, color='yellow', label='vertex')
# plt.legend()
# plt.show()
assert np.allclose(amp2, amp1.sum(axis=1), atol=1e-15)
assert np.allclose(amp3, amp1.sum(axis=0), atol=1e-15)
# triangles with one or more vertices outside the 2D grids
f_list2 = [
[[5.5, -8.0, 17.4], [4.5, 12.0, 17.3]], # one point up
[[5.5, 8.0, 27.4], [4.5, 12.0, 17.3]], # one point down
[[25.5, -8.0, 17.4], [4.5, 12.0, 17.3]], # one point up and down each
[[25.5, -8.0, 27.4], [4.5, 12.0, 17.3]], # two points down
[[17.5, -8.0, -27.4], [4.5, 12.0, 3.0]], # two points up
]
for list_ in f_list2:
lst1, lst2 = np.asarray(list_)
amp1 = np.zeros((20, 20), dtype=np.float64)
amp2 = np.zeros(20, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst1, amp2)
# plt.imshow(amp1, origin='lower', cmap='gray', aspect='auto')
# x_t, y_t = np.append(lst2, lst2[0]) - 0.5, np.append(lst1, lst1[0]) - 0.5
# plt.plot(x_t, y_t, 'r', label='vertex')
# plt.scatter(lst2-0.5, lst1-0.5, s=20, color='yellow', label='vertex')
# plt.legend()
# plt.show()
assert np.allclose(amp2, amp1.sum(axis=1), atol=1e-15)
# triangles with one or more vertices outside a grid voxel
f_list2 = [
[[15.0, 15.5, 15.9], [12.0, 12.5, 12.9]], # all in
[[15.0, 15.5, 16.2], [12.0, 12.5, 12.9]], # one out
[[15.0, 15.5, 16.2], [12.0, 12.5, 13.9]], # one out on each dimension
]
for list_ in f_list2:
lst1, lst2 = np.asarray(list_)
amp1 = np.zeros((20, 20), dtype=np.float64)
amp2 = np.zeros(20, dtype=np.float64)
clib.triangle_interpolation2D(lst1, lst2, amp1)
clib.triangle_interpolation1D(lst1, amp2)
# plt.imshow(amp1, origin='lower', cmap='gray', aspect='auto')
# x_t, y_t = np.append(lst2, lst2[0]) - 0.5, np.append(lst1, lst1[0]) - 0.5
# plt.plot(x_t, y_t, 'r', label='vertex')
# plt.scatter(lst2-0.5, lst1-0.5, s=20, color='yellow', label='vertex')
# plt.legend()
# plt.show()
assert np.allclose(amp2, amp1.sum(axis=1), atol=1e-15)