def coplanar_points_are_on_same_side_of_line(a, b, p1, p2, atol=1e-8):
"""
Using "same-side technique" from http://blackpawn.com/texts/pointinpoly/default.html
"""
along_line = b - a
return vg.dot(vg.cross(along_line, p1 - a), vg.cross(along_line,
p2 - a)) >= -atol
def test_cross_mixed():
v1 = np.array([[1.0, 0.0, -1.0], [1.0, 2.0, 3.0]])
v2 = np.array([4.0, 5.0, 6.0])
expected = np.array([[5.0, -10.0, 5.0], [-3.0, 6.0, -3.0]])
np.testing.assert_array_almost_equal(vg.cross(v1, v2), expected)
np.testing.assert_array_almost_equal(vg.cross(v2, v1), -expected)
def test_cross_error():
v1 = np.array([[1.0, 0.0, -1.0], [1.0, 2.0, 3.0]])
v2 = np.array([[4.0, 5.0, 6.0]])
with pytest.raises(
ValueError,
match="v2 must be an array with shape \\(2, 3\\); got \\(1, 3\\)"):
vg.cross(v1, v2)
v1 = np.array([[1.0, 0.0, -1.0], [1.0, 2.0, 3.0]])
v2 = np.array([[[4.0, 5.0, 6.0]]])
with pytest.raises(
ValueError,
match="Not sure what to do with 2 dimensions and 3 dimensions"):
vg.cross(v1, v2)
def coplanar_points_are_on_same_side_of_line(a, b, p1, p2):
"""
Test if the given points are on the same side of the given line.
Args:
a (np.arraylike): The first 3D point of interest.
b (np.arraylike): The second 3D point of interest.
p1 (np.arraylike): A first point which lies on the line of interest.
p2 (np.arraylike): A second point which lies on the line of interest.
Returns:
bool: `True` when `a` and `b` are on the same side of the line defined
by `p1` and `p2`.
"""
check_shape_any(a, (3,), (-1, 3), name="a")
vg.shape.check(locals(), "b", a.shape)
vg.shape.check(locals(), "p1", a.shape)
vg.shape.check(locals(), "p2", a.shape)
# Uses "same-side technique" from http://blackpawn.com/texts/pointinpoly/default.html
along_line = b - a
return vg.dot(vg.cross(along_line, p1 - a), vg.cross(along_line, p2 - a)) >= 0
def world_to_view(position, target, up=vg.basis.y, inverse=False):
"""
Create a transform matrix which sends world-space coordinates to
view-space coordinates.
Args:
position (np.ndarray): The camera's position in world coordinates.
target (np.ndarray): The camera's target in world coordinates.
`target - position` is the "look at" vector.
up (np.ndarray): The approximate up direction, in world coordinates.
inverse (bool): When `True`, return the inverse transform instead.
Returns:
np.ndarray: The `4x4` transformation matrix, which can be used with
`polliwog.transform.apply_transform()`.
See also:
https://cseweb.ucsd.edu/classes/wi18/cse167-a/lec4.pdf
http://www.songho.ca/opengl/gl_camera.html
"""
vg.shape.check(locals(), "position", (3, ))
vg.shape.check(locals(), "target", (3, ))
look = vg.normalize(target - position)
left = vg.normalize(vg.cross(look, up))
recomputed_up = vg.cross(left, look)
rotation = transform_matrix_for_rotation(
np.array([left, recomputed_up, look]))
if inverse:
inverse_rotation = rotation.T
inverse_translation = transform_matrix_for_translation(position)
return compose_transforms(inverse_rotation, inverse_translation)
else:
translation = transform_matrix_for_translation(-position)
return compose_transforms(translation, rotation)
def plane_normal_from_points(points):
"""
Given a set of three points, compute the normal of the plane which
passes through them. Also works on stacked inputs (i.e. many sets
of three points).
"""
points, _, transform_result = columnize(points, (-1, 3, 3), name="points")
p1s = points[:, 0]
p2s = points[:, 1]
p3s = points[:, 2]
v1s = p2s - p1s
v2s = p3s - p1s
unit_normals = vg.normalize(vg.cross(v1s, v2s))
return transform_result(unit_normals)
def surface_normals(points, normalize=True):
"""
Compute the surface normal of a triangle. The direction of the normal
follows conventional counter-clockwise winding and the right-hand
rule.
Also works on stacked inputs (i.e. many sets of three points).
"""
points, _, transform_result = columnize(points, (-1, 3, 3), name="points")
p1s = points[:, 0]
p2s = points[:, 1]
p3s = points[:, 2]
v1s = p2s - p1s
v2s = p3s - p1s
normals = vg.cross(v1s, v2s)
if normalize:
normals = vg.normalize(normals)
return transform_result(normals)