def make_sphere(radius, slices, segments):
profile = [V3.zero() for _ in range(segments)]
dtheta = pi / (segments - 1)
for i in range(segments):
theta = dtheta * i
R = Q.Ru(theta, V3.k())
profile[i] = Q.rotate(R, V3.make(0.0, -radius, 0.0))
return profile_sweep(profile, slices)
def make_capsule(radius, height, slices, segments):
profile = [V3.zero() for _ in range(segments)]
dtheta = pi / (segments - 1)
for i in range(segments):
theta = dtheta * i
R = Q.Ru(theta, V3.k())
dh = -height / 2.0 if i < (segments / 2) else height / 2.0
profile[i] = Q.rotate(R, V3.make(0.0, -radius, 0.0)) + V3.make(
0.0, dh, 0.0)
return profile_sweep(profile, slices)
def concat(B, A):
"""
Concatenate transformations.. First A then B, Hence, C = B*A
:param B:
:param A:
:return:
"""
C = CoordSys()
C.q = Q.unit(Q.prod(B.q, A.q))
C.r = Q.rotate(B.q, A.r) + B.r
return C
def make_coordsys_from_to(A, B):
"""
Assumes that 'A' maps from bf_1 to wcs, and 'B' maps from bf_2 to wcs.
Now compute the transform that maps from bf_1 to bf_2
:param A:
:param B:
:return:
"""
A2B = CoordSys()
A2B.q = Q.unit(Q.prod(Q.conjugate(B.q), A.q))
A2B.r = Q.rotate(Q.conjugate(B.q), A.r - B.r)
return A2B
def rotate(mesh, q):
for vh in mesh.vertices():
p = Q.rotate(q, get_vertex_coords(mesh, vh))
mesh.set_point(vh, OM.TriMesh.Point(p[0], p[1], p[2]))
return mesh
def inverse(X):
C = CoordSys()
C.q = Q.conjugate(X.q)
C.r = Q.rotate(C.q, -X.r)
return C
def xform_vector(X, v):
return Q.rotate(X.q, v)
def xform_point(X, p):
return Q.rotate(X.q, p) + X.r
def profile_sweep(profile, slices):
mesh = OM.TriMesh()
N = len(profile)
J = slices
if N <= 2:
raise RuntimeError(
'profile_sweep(): Profile must have at least 3 points')
if J <= 2:
raise RuntimeError(
'profile_sweep(): Sweep must have at least 3 slices to be a proper volume.'
)
K = (N - 2) * J + 2 # Total number of vertices
bottom = K - 1 # Index to bottom vertex
top = K - 2 # Index to top vertex
H = N - 2 # Number of latitude circles
#F = 2*J*(N-1) # Total number of triangle faces
vhandles = []
# Make a 2D grid of vertices by sweeping profile around y-axis
dtheta = 2.0 * pi / J # The angle of each slice
for j in range(J):
theta = j * dtheta
R = Q.Ru(theta, V3.j())
for i in range(H):
p = Q.rotate(R, profile[i + 1])
vh = mesh.add_vertex(OM.TriMesh.Point(p[0], p[1], p[2]))
vhandles.append(vh)
# Now fill in top and bottom vertices
vh = mesh.add_vertex(
OM.TriMesh.Point(profile[N - 1][0], profile[N - 1][1],
profile[N - 1][2]))
vhandles.append(vh)
vh = mesh.add_vertex(
OM.TriMesh.Point(profile[0][0], profile[0][1], profile[0][2]))
vhandles.append(vh)
# Make faces for bottom-ring
for j in range(J):
#
# V = {c1} {c2} ... {cJ} b t
#
# b c1.0 c2.0 | b c2.0 c3.0| ... | b cJ.0 c1.0
# b 0 (N-2) | b (N-2) 2*(N-2)
#
left = j
right = ((j + 1) % J)
vi = vhandles[bottom]
vj = vhandles[H * right]
vk = vhandles[H * left]
mesh.add_face(vi, vj, vk)
# Make faces for middle-rings
for i in range(H - 1): # ring number
for j in range(J): # slice number
left = j
right = (j + 1) % J
up = i + 1
down = i
vi = vhandles[left * H + down]
vj = vhandles[right * H + down]
vk = vhandles[right * H + up]
vm = vhandles[left * H + up]
mesh.add_face(vi, vj, vk)
mesh.add_face(vi, vk, vm)
# Make faces for top - ring
for j in range(J):
offset = (N - 3)
left = j
right = (j + 1) % J
vi = vhandles[top]
vj = vhandles[left * H + offset]
vk = vhandles[right * H + offset]
mesh.add_face(vi, vj, vk)
mesh.request_face_normals()
mesh.update_face_normals()
return mesh