import openGJKpy as opengjk from scipy.spatial.transform import Rotation as R import numpy as np import pytest def distance_point_to_line_3D(P1, P2, point): """ distance from point to line """ return np.linalg.norm(np.cross(P2-P1, P1-point))/np.linalg.norm(P2-P1) def distance_point_to_plane_3D(P1, P2, P3, point): """ Distance from point to plane """ return np.abs(np.dot(np.cross(P2-P1, P3-P1) / np.linalg.norm(np.cross(P2-P1, P3-P1)), point-P2)) @pytest.mark.parametrize("delta", [0.1, 1e-12, 0, -2]) def test_line_point_distance(delta): line = np.array([[0.1, 0.2, 0.3], [0.5, 0.8, 0.7]], dtype=np.float64) # point_on_line = line[0] + 0.27*(line[1]-line[0]) normal = np.cross(line[0], line[1]) point = point_on_line + delta * normal distance = opengjk.pygjk(line, point) actual_distance = distance_point_to_line_3D( line[0], line[1], point) print(distance, actual_distance) assert(np.isclose(distance, actual_distance, atol=1e-15)) @pytest.mark.parametrize("delta", [0.1, 1e-12, 0]) def test_line_line_distance(delta): line = np.array([[-0.5, -0.7, -0.3], [1, 2, 3]], dtype=np.float64) point_on_line = line[0] + 0.38*(line[1]-line[0]) normal = np.cross(line[0], line[1]) point = point_on_line + delta * normal line_2 = np.array([point, [2, 5, 6]], dtype=np.float64) distance = opengjk.pygjk(line, line_2) actual_distance = distance_point_to_line_3D( line[0], line[1], line_2[0]) print(distance, actual_distance) assert(np.isclose(distance, actual_distance, atol=1e-15)) @pytest.mark.parametrize("delta", [0.1**(3*i) for i in range(6)]) def test_tri_distance(delta): tri_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0]], dtype=np.float64) tri_2 = np.array([[1, delta, 0], [3, 1.2, 0], [1, 1, 0]], dtype=np.float64) P1 = tri_1[2] P2 = tri_1[1] point = tri_2[0] actual_distance = distance_point_to_line_3D(P1, P2, point) distance = opengjk.pygjk(tri_1, tri_2) print("Computed distance ", distance, "Actual distance ", actual_distance) assert(np.isclose(distance, actual_distance, atol=1e-15)) @pytest.mark.parametrize("delta", [0.1*0.1**(3*i) for i in range(6)]) def test_quad_distance2d(delta): quad_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0]], dtype=np.float64) quad_2 = np.array([[0, 1+delta, 0], [2, 2, 0], [2, 4, 0], [4, 4, 0]], dtype=np.float64) P1 = quad_1[2] P2 = quad_1[3] point = quad_2[0] actual_distance = distance_point_to_line_3D(P1, P2, point) distance = opengjk.pygjk(quad_1, quad_2) print("Computed distance ", distance, "Actual distance ", actual_distance) assert(np.isclose(distance, actual_distance, atol=1e-15)) @pytest.mark.parametrize("delta", [1*0.5**(3*i) for i in range(7)]) def test_tetra_distance_3d(delta): tetra_1 = np.array([[0, 0, 0.2], [1, 0, 0.1], [0, 1, 0.3], [0, 0, 1]], dtype=np.float64) tetra_2 = np.array([[0, 0, -3], [1, 0, -3], [0, 1, -3], [0.5, 0.3, -delta]], dtype=np.float64) actual_distance = distance_point_to_plane_3D(tetra_1[0], tetra_1[1], tetra_1[2], tetra_2[3]) distance = opengjk.pygjk(tetra_1, tetra_2) print("Computed distance ", distance, "Actual distance ", actual_distance) assert(np.isclose(distance, actual_distance, atol=1e-15)) @pytest.mark.parametrize("delta", [(-1)**i*np.sqrt(2)*0.1**(3*i) for i in range(6)]) def test_tetra_collision_3d(delta): tetra_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=np.float64) tetra_2 = np.array([[0, 0, -3], [1, 0, -3], [0, 1, -3], [0.5, 0.3, -delta]], dtype=np.float64) actual_distance = distance_point_to_plane_3D(tetra_1[0], tetra_1[1], tetra_1[2], tetra_2[3]) distance = opengjk.pygjk(tetra_1, tetra_2) if delta < 0: assert(np.isclose(distance, 0, atol=1e-15)) else: print("Computed distance ", distance, "Actual distance ", actual_distance) assert(np.isclose(distance, actual_distance, atol=1e-15)) @pytest.mark.parametrize("delta", [0, -0.1, -0.49, -0.51]) def test_hex_collision_3d(delta): hex_1 = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]], dtype=np.float64) P0 = np.array([1.5+delta, 1.5+delta, 0.5], dtype=np.float64) P1 = np.array([2, 2, 1], dtype=np.float64) P2 = np.array([2, 1.25, 0.25], dtype=np.float64) P3 = P1 + P2 - P0 quad_1 = np.array([P0, P1, P2, P3], dtype=np.float64) n = (np.cross(quad_1[1]-quad_1[0], quad_1[2]-quad_1[0]) / np.linalg.norm( np.cross(quad_1[1]-quad_1[0], quad_1[2]-quad_1[0]))) quad_2 = quad_1 + n hex_2 = np.zeros((8, 3), dtype=np.float64) hex_2[:4, :] = quad_1 hex_2[4:, :] = quad_2 actual_distance = np.linalg.norm( np.array([1, 1, P0[2]], dtype=np.float64)-hex_2[0]) distance = opengjk.pygjk(hex_1, hex_2) if P0[0] < 1: assert(np.isclose(distance, 0, atol=1e-15)) else: print("Computed distance ", distance, "Actual distance ", actual_distance) assert(np.isclose(distance, actual_distance, atol=1e-15)) @pytest.mark.parametrize("c0", [0, 1, 2, 3]) @pytest.mark.parametrize("c1", [0, 1, 2, 3]) def test_cube_distance(c0, c1): cubes = [np.array([[-1, -1, -1], [1, -1, -1], [-1, 1, -1], [1, 1, -1], [-1, -1, 1], [1, -1, 1], [-1, 1, 1], [1, 1, 1]], dtype=np.float64)] r = R.from_euler('z', 45, degrees=True) cubes.append(r.apply(cubes[0])) r = R.from_euler('y', np.arctan2(1.0, np.sqrt(2))) cubes.append(r.apply(cubes[1])) r = R.from_euler('y', 45, degrees=True) cubes.append(r.apply(cubes[0])) dx = cubes[c0][:,0].max() - cubes[c1][:,0].min() cube0 = cubes[c0] for delta in [1e8, 1.0, 1e-4, 1e-8, 1e-12]: cube1 = cubes[c1] + np.array([dx + delta, 0, 0]) distance = opengjk.pygjk(cube0, cube1) print(distance, delta) assert(np.isclose(distance, delta)) def test_random_objects(): for i in range(1, 8): for j in range(1, 8): for k in range(1000): arr1 = np.random.rand(i, 3) arr2 = np.random.rand(j, 3) opengjk.pygjk(arr1, arr2) def test_large_random_objects(): for i in range(1, 8): for j in range(1, 8): for k in range(1000): arr1 = 10000.0*np.random.rand(i, 3) arr2 = 10000.0*np.random.rand(j, 3) opengjk.pygjk(arr1, arr2)