def frame(self):
"""The local coordinate frame."""
o = self.center
w = self.normal
p = self.points[0]
u = Vector(p, o)
u.normalize()
v = w.cross(u)
return o, u, v, w
def from_point_and_two_vectors(cls, point, v1, v2):
v1 = Vector(*v1)
v2 = Vector(*v2)
n = Vector.cross(v1, v2)
n.unitize()
plane = cls()
plane.point = Point(*point)
plane.normal = n
return plane
def basis(self):
a, b, c = self.normal
u = 1.0, 0.0, -a / c
v = 0.0, 1.0, -b / c
return [
Vector(*vector, unitize=True)
for vector in orthonormalise_vectors([u, v])
]
def from_three_points(cls, p1, p2, p3):
p1 = Point(*p1)
p2 = Point(*p2)
p3 = Point(*p3)
v1 = p2 - p1
v2 = p3 - p1
plane = cls()
plane.point = p1
plane.normal = Vector.cross(v1, v2)
plane.normal.unitize()
return plane
def __sub__(self, other):
"""Create a vector from other to self.
Parameters:
other (sequence, Point): The point to subtract.
Returns:
Vector: A vector from other to self
"""
x = self.x - other[0]
y = self.y - other[1]
z = self.z - other[2]
return Vector(x, y, z)
def normal(self):
"""The (average) normal of the polygon."""
o = self.center
points = self.points
a2 = 0
normals = []
for i in range(-1, len(points) - 1):
p1 = points[i]
p2 = points[i + 1]
u = [p1[_] - o[_] for _ in range(3)]
v = [p2[_] - o[_] for _ in range(3)]
w = cross_vectors(u, v)
a2 += sum(w[_] ** 2 for _ in range(3)) ** 0.5
normals.append(w)
n = [sum(axis) / a2 for axis in zip(*normals)]
n = Vector(n)
return n
plane = (plane.point, plane.normal)
return project_point_plane(self, plane)
# ==============================================================================
# Debugging
# ==============================================================================
if __name__ == '__main__':
# import timeit
# t0 = timeit.timeit('points = [Point(i, i, i) for i in xrange(100000)]', 'from __main__ import Point', number=100)
# t1 = timeit.timeit('points = [[i, i, i] for i in xrange(100000)]', 'from __main__ import Point', number=100)
# print(t0 / t1)
from compas.geometry.objects import Plane
from compas.geometry import projection_matrix
point = Point(0.0, 0.0, 0.0)
normal = Vector(0.0, 0.0, 1.0)
plane = Plane.from_point_and_normal(point, normal)
test = Point(1.0, 2.0, 3.0)
P = projection_matrix()
point.transform(P)
print(point)
def from_point_and_normal(cls, point, normal):
plane = cls()
plane.point = Point(*point)
plane.normal = Vector(*normal)
plane.normal.unitize()
return plane
for vector in orthonormalise_vectors([u, v])
]
# ==============================================================================
# Debugging
# ==============================================================================
if __name__ == '__main__':
from compas.visualization.viewers.viewer import Viewer
from compas.visualization.viewers.core.drawing import xdraw_points
from compas.visualization.viewers.core.drawing import xdraw_lines
base = Point(1.0, 0.0, 0.0)
normal = Vector(1.0, 1.0, 1.0)
plane = Plane.from_point_and_normal(base, normal)
basis = plane.basis()
points = [{'pos': base, 'color': (1.0, 0.0, 0.0), 'size': 10.0}]
lines = []
for vector in basis + [plane.normal]:
lines.append({
'start': base,
'end': base + vector,
'color': (0.0, 0.0, 0.0),
'width': 3.0