def get_triangulation(self, normal_vector=None):
# Figure out how to triangulate the interior to know
# how to send the points as to the vertex shader.
# First triangles come directly from the points
if normal_vector is None:
normal_vector = self.get_unit_normal()
if not self.needs_new_triangulation:
return self.triangulation
points = self.get_points()
if len(points) <= 1:
self.triangulation = np.zeros(0, dtype="i4")
self.needs_new_triangulation = False
return self.triangulation
if not np.isclose(normal_vector, OUT).all():
# Rotate points such that unit normal vector is OUT
points = np.dot(points, z_to_vector(normal_vector))
indices = np.arange(len(points), dtype=int)
b0s = points[0::3]
b1s = points[1::3]
b2s = points[2::3]
v01s = b1s - b0s
v12s = b2s - b1s
crosses = cross2d(v01s, v12s)
convexities = np.sign(crosses)
atol = self.tolerance_for_point_equality
end_of_loop = np.zeros(len(b0s), dtype=bool)
end_of_loop[:-1] = (np.abs(b2s[:-1] - b0s[1:]) > atol).any(1)
end_of_loop[-1] = True
concave_parts = convexities < 0
# These are the vertices to which we'll apply a polygon triangulation
inner_vert_indices = np.hstack(
[
indices[0::3],
indices[1::3][concave_parts],
indices[2::3][end_of_loop],
]
)
inner_vert_indices.sort()
rings = np.arange(1, len(inner_vert_indices) + 1)[inner_vert_indices % 3 == 2]
# Triangulate
inner_verts = points[inner_vert_indices]
inner_tri_indices = inner_vert_indices[
earclip_triangulation(inner_verts, rings)
]
tri_indices = np.hstack([indices, inner_tri_indices])
self.triangulation = tri_indices
self.needs_new_triangulation = False
return tri_indices
def get_triangulation(self, orientation=None):
# Figure out how to triangulate the interior to know
# how to send the points as to the vertex shader.
# First triangles come directly from the points
if orientation is None:
orientation = self.get_orientation()
if self.triangulation_locked:
return self.saved_triangulation
if len(self.points) <= 1:
return []
points = self.points
indices = np.arange(len(points), dtype=int)
b0s = points[0::3]
b1s = points[1::3]
b2s = points[2::3]
v01s = b1s - b0s
v12s = b2s - b1s
# TODO, account for 3d
crosses = cross2d(v01s, v12s)
convexities = orientation * np.sign(crosses)
atol = self.tolerance_for_point_equality
end_of_loop = np.zeros(len(b0s), dtype=bool)
end_of_loop[:-1] = (np.abs(b2s[:-1] - b0s[1:]) > atol).any(1)
end_of_loop[-1] = True
concave_parts = convexities < 0
# These are the vertices to which we'll apply a polygon triangulation
inner_vert_indices = np.hstack([
indices[0::3],
indices[1::3][concave_parts],
indices[2::3][end_of_loop],
])
inner_vert_indices.sort()
rings = np.arange(1,
len(inner_vert_indices) + 1)[inner_vert_indices %
3 == 2]
# Triangulate
inner_verts = points[inner_vert_indices]
inner_tri_indices = inner_vert_indices[earclip_triangulation(
inner_verts, rings)]
tri_indices = np.hstack([indices, inner_tri_indices])
return tri_indices
def get_quadratic_approximation_of_cubic(a0: npt.ArrayLike, h0: npt.ArrayLike,
h1: npt.ArrayLike,
a1: npt.ArrayLike) -> np.ndarray:
a0 = np.array(a0, ndmin=2)
h0 = np.array(h0, ndmin=2)
h1 = np.array(h1, ndmin=2)
a1 = np.array(a1, ndmin=2)
# Tangent vectors at the start and end.
T0 = h0 - a0
T1 = a1 - h1
# Search for inflection points. If none are found, use the
# midpoint as a cut point.
# Based on http://www.caffeineowl.com/graphics/2d/vectorial/cubic-inflexion.html
has_infl = np.ones(len(a0), dtype=bool)
p = h0 - a0
q = h1 - 2 * h0 + a0
r = a1 - 3 * h1 + 3 * h0 - a0
a = cross2d(q, r)
b = cross2d(p, r)
c = cross2d(p, q)
disc = b * b - 4 * a * c
has_infl &= (disc > 0)
sqrt_disc = np.sqrt(np.abs(disc))
settings = np.seterr(all='ignore')
ti_bounds = []
for sgn in [-1, +1]:
ti = (-b + sgn * sqrt_disc) / (2 * a)
ti[a == 0] = (-c / b)[a == 0]
ti[(a == 0) & (b == 0)] = 0
ti_bounds.append(ti)
ti_min, ti_max = ti_bounds
np.seterr(**settings)
ti_min_in_range = has_infl & (0 < ti_min) & (ti_min < 1)
ti_max_in_range = has_infl & (0 < ti_max) & (ti_max < 1)
# Choose a value of t which starts at 0.5,
# but is updated to one of the inflection points
# if they lie between 0 and 1
t_mid = 0.5 * np.ones(len(a0))
t_mid[ti_min_in_range] = ti_min[ti_min_in_range]
t_mid[ti_max_in_range] = ti_max[ti_max_in_range]
m, n = a0.shape
t_mid = t_mid.repeat(n).reshape((m, n))
# Compute bezier point and tangent at the chosen value of t
mid = bezier([a0, h0, h1, a1])(t_mid)
Tm = bezier([h0 - a0, h1 - h0, a1 - h1])(t_mid)
# Intersection between tangent lines at end points
# and tangent in the middle
i0 = find_intersection(a0, T0, mid, Tm)
i1 = find_intersection(a1, T1, mid, Tm)
m, n = np.shape(a0)
result = np.zeros((6 * m, n))
result[0::6] = a0
result[1::6] = i0
result[2::6] = mid
result[3::6] = mid
result[4::6] = i1
result[5::6] = a1
return result