def get_orthonormal_frame(u,v):
# Orthogonal frame
a = Vector.cross(u,v)
b = Vector.cross(a,u)
c = Vector.cross(a,b)
# Normalized frame
a.unitize()
b.unitize()
c.unitize()
return (a,b,c)
def arrays_cross(array1, array2):
cross_list = []
for i in range(len(array1)):
u = Vector(array1[i][0], array1[i][1], array1[i][2])
v = Vector(array2[i][0], array2[i][1], array2[i][2])
cross_list.append(u.cross(v))
return cross_list
def ray_mesh_intersect_reflect(ray, mesh, hit, facemap):
base, vector = ray
index = hit[0]
distance = hit[3]
face = facemap[index]
p = base + vector * distance
n = Vector(*mesh.face_normal(face))
n = n.cross(vector.cross(n))
r = base.transformed(Reflection.from_plane((p, n)))
return p, r
front = Plane([0, -1, 0], [0, -1, 0])
back = Plane([0, +1, 0], [0, +1, 0])
halfspaces = array(
[left.abcd, right.abcd, top.abcd, bottom.abcd, front.abcd, back.abcd],
dtype=float)
interior = array([0, 0, 0], dtype=float)
hsi = HalfspaceIntersection(halfspaces, interior)
hull = ConvexHull(hsi.intersections)
mesh = Mesh.from_vertices_and_faces(
[hsi.intersections[i] for i in hull.vertices], hull.simplices)
mesh.unify_cycles()
to_merge = []
for a, b in combinations(mesh.faces(), 2):
na = Vector(*mesh.face_normal(a))
nb = Vector(*mesh.face_normal(b))
if na.dot(nb) >= 1:
if na.cross(nb).length < 1e-6:
to_merge.append([a, b])
for faces in to_merge:
mesh.merge_faces(faces)
viewer = App()
viewer.add(mesh, show_vertices=True, pointsize=10)
viewer.run()
from compas.geometry import Point from compas.geometry import Vector # Point p1 = Point(1, 2, 3) assert p1 ** 3 == [1, 8, 27] assert p1 + [0, 2, 1] == [1, 4, 4] # Vector u = Vector(1, 0, 0) v = Vector(0, 1, 0) assert u + v == [1, 1, 0] assert u.dot(v) == 0.0 assert u.cross(v) == [0, 0, 1] assert (u * 2).unitized() == [1, 0, 0]
from compas.geometry import Vector u = Vector(1.0, 0.0, 0.0) v = Vector(0.0, 1.0, 0.0) uxv = u.cross(v) u_uxv = u.angle(uxv) v_uxv = v.angle(uxv) print(u_uxv) print(v_uxv)
# ============================================================================== Z = Vector(0, 0, 1) controlpoints = [Point(0, 0, 0), Point(4, 2.5, 0), Point(6, -2.5, 0), Point(10, 0, 0)] controlpoly = Polyline(controlpoints) curve = Bezier(controlpoints) poly0 = Polyline(curve.locus()) poly1 = Polyline(offset_polyline(poly0, +0.15)) poly2 = Polyline(offset_polyline(poly0, -0.15)) points0 = [poly0.point(t) for t in linspace(0, 1, 20)] tangents0 = [(c - a).unitized() for a, b, c in window(points0, 3) if a and c] normals0 = [Z.cross(t) for t in tangents0] lines = [[point, point + normal] for point, normal in zip(points0[1:-1], normals0)] points1 = [intersection_line_polyline(line, poly1) for line in lines] points2 = [intersection_line_polyline(line, poly2) for line in lines] # ============================================================================== # Blocks # ============================================================================== frames = [] blocks = [] polygons = [] for (a, b), (a1, b1), (a2, b2) in zip(pairwise(points0[1:-1]), pairwise(points1), pairwise(points2)):
from compas.geometry import Vector u = Vector(1.0, 0.0, 0.0) v = Vector(0.0, 1.0, 0.0) print(u.cross(v)[2] > 0) print(v.cross(u)[2] > 0)
