def french_fries(scale):
def rod():
c = vector3.UnitCube1()
m2 = np.eye(4) * scale
m2[0, 0] = 0.1 * scale
m2[1, 1] = 0.1 * scale
m2[0:3, 3] = [+0.1 / 2.0 * 2 * scale, +0.1 / 2.0 * 2 * scale, + 1.0 / 2.0 * 2 * scale]
m2[3, 3] = 1
iobj = vector3.Transformed(c, m2)
# .move(-0.1/2.0, -0.1/2.0, -1.0/2.0)
iobj \
.move(-0.2 * scale, -0.2 * scale, 0) \
.resize(2) \
.rotate(10, along=make_vector3(1, 1, 0), units="deg") \
.move(0.5 * scale, 0, 0)
return iobj
u = None
for i in range(18):
c = rod().rotate(-30 * i, along=make_vector3(0, 0, 1), units="deg")
if u is None:
u = c
else:
u = vector3.CrispUnion(u, c)
return u
def cube_with_cylinders(scale):
# SCALE = 2. # mm
SCALE = 2.
sz1 = 2.5
radius = 0.5 * SCALE
c_len = 2 * SCALE
A = make_vector4(-c_len/2.0, 0, 0)
# A = make_vector4(0, 0, c_len / 2.0) # bug: aa is wrong
w = make_vector4(1, 0, 0)
w = w / np.linalg.norm(w[0:3])
w[3] = 1
u = make_vector4(0, 1, 0)
cyl = vector3.SimpleCylinder(A, w, u, radius, radius, c_len)
A2 = make_vector4(0, -c_len/2.0, 0)
w2 = make_vector4(1, 0, 0)
w2 = w / np.linalg.norm(w[0:3])
w[3] = 1
u2 = make_vector4(0, 1, 0)
cyl_2 = vector3.SimpleCylinder(A2, u2, w2, radius, radius, c_len)
cube = vector3.UnitCube1(size=sz1)
union = vector3.CrispSubtract(cube, cyl_2)
final_object = vector3.CrispUnion(union, cyl)
# (RANGE_MIN, RANGE_MAX, STEPSIZE) = (-3, +5, 0.2)
return final_object
def cage_rods(rod_r, rod_len, cage_r, N):
import math
un = None
for i in range(N):
th = i / float(N) * np.pi * 2
x, y = cage_r * math.sin(th), cage_r * math.cos(th)
A = make_vector4(x, y, -rod_len / 2.)
w = make_vector4(0, 0, 1)
u = make_vector4(1, 0, 0)
c = vector3.SimpleCylinder(A, w, u, rod_r, rod_r, rod_len)
if un is None:
un = c
else:
un = vector3.CrispUnion(un, c)
return un
def first_csg(scale):
m1 = np.eye(4) * 2 * scale
m1[1, 1] = 0.4 * scale
m1[0:3, 3] = [0, 0, 0]
m1[3, 3] = 1
m2 = np.eye(4) * 1. * scale
rcenter = np.array([0.5, 0, 0]) * scale
m2[0:3, 3] = rcenter[0:3]
m2[3, 3] = 1
m3 = np.eye(4) * 1.2 * scale
m3[0:3, 3] = [1.5 * scale, 0, 0]
m3[3, 3] = 1
iobj = vector3.CrispSubtract(vector3.CrispUnion(vector3.Ellipsoid(m1), vector3.Ellipsoid(m2)), vector3.Ellipsoid(m3))
return iobj
def cyl4(scale):
""" Makes a nice cage with spiral bars. Don't change. """
cage = cage_rods(rod_r=1, rod_len=20, cage_r=10, N=20)
from twist_z import TwistZ
t = TwistZ(cage, 0.02) # cycles per mm
# 0.06 is too much 0.02 is reasonable
base_cyl = vector3.SimpleCylinder(
make_vector4(0, 0, -10), # A
make_vector4(0, 0, -1), # w
make_vector4(1, 0, 0),
11., 11.,
1.)
ifunc = vector3.CrispUnion(base_cyl, t)
# (RANGE_MIN, RANGE_MAX, STEPSIZE) = (-32, +32, 1.92 / 4.0) #15 sec! 2.5 millions voxels
# (RANGE_MIN, RANGE_MAX, STEPSIZE) = (-32 / 2, +32 / 2, 1.92 / 4.0) # 2.5 sec!
return ifunc
def union_of_two_cubes(scale):
c2 = vector3.UnitCube1(1.)
def rotate_scale_(iobj, scale, center, angle=0.):
ns = vector3
import numpy
m = numpy.eye(4)
m[0, 0] = 0.1
iobj = ns.Transformed(iobj, m=m)
iobj \
.resize(scale) \
.move(center[0], center[1], center[2])
if angle != 0.:
iobj.rotate(angle, along=make_vector4(1, 1, 1), units="deg")
return iobj
c2 = rotate_scale_(c2, 2., [1, 1, 1])
iobj = vector3.CrispUnion(rcube_vec(1.), c2)
return iobj
def rods(scale):
# the scale needs to be equal to 2 in order to have a nice object
def rod():
c = vector3.UnitCube1()
m2 = np.eye(4)
m2[0, 0] = 0.1 * scale
m2[1, 1] = 0.1 * scale
m2[2, 2] = scale
iobj = vector3.Transformed(c, m2)
iobj \
.move(-0, -0.3*scale, -1.0*scale) \
.resize(2) \
.rotate(40, along=make_vector3(1, 1, 0), units="deg") \
.move(0.5*scale, 0, 0)
return iobj
u = None
for i in range(17):
c = rod().rotate(-30 * i, along=make_vector3(0, 0, 1), units="deg")
if u is None:
u = c
else:
u = vector3.CrispUnion(u, c)
return u
def cyl2(scale=1.):
SCALE = scale*1. # mm
un = None
M = 5 + 1
for i in range(M):
radius = 0.5 * SCALE
c_len = 2 * SCALE * 1. / (i + 1)
a_x = (i - (M - 1.) / 2.) * 1 * SCALE + -0.5 * c_len
A = make_vector4(a_x, 0, 0)
w = make_vector4(0, 1, 0)
# m = np.eye(4)
center = A # + make_vector4(0, 0, c_len/2.0)
center[3] = 1
R = rotation_matrix(i * 90. / (M - 1.), make_vector4(1, 0, 0), units="deg", around=center)
w = np.dot(R, np.transpose(w))
u = make_vector4(1, 0, 0)
def make_uv(w, u):
w = w / np.linalg.norm(w[0:3])
w[3] = 1
u = u / np.linalg.norm(u[0:3])
u[3] = 1
# print w, "u=",u
assert np.linalg.norm(np.cross(w[:3], u[:3])) > 0.000000001 # cannot be parallel
v3 = np.cross(w[:3], u[:3])
v3 = v3 / np.linalg.norm(v3[:3])
v = make_vector4(v3[0], v3[1], v3[2])
u3 = np.cross(v[:3], w[:3])
u3 = u3 / np.linalg.norm(u3[:3])
u = make_vector4(u3[0], u3[1], u3[2])
# return w, u
return u
u = make_uv(w, u)
print np.linalg.norm(np.cross(w[:3], u[:3]))
print np.linalg.norm(np.cross(w[:3], u[:3])) > 0.000000001
def set4th1(v):
assert v.shape == (4,)
v[3] = 1
return v
# c = SimpleCylinder(A, w, u, radius, radius, c_len)
newlen = c_len * 5
# Long and thin cyliner
c1 = vector3.SimpleCylinder(set4th1(A - 1. * newlen / 2. * w), w, u, radius / 5., radius / 5., newlen)
delta, twist_rate = radius * 0.2, 1./2.
from vector3 import Screw
c2 = Screw(A[:3], w[:3], u[:3], c_len, radius, delta, twist_rate)
c_u = vector3.CrispUnion(c1, c2)
# Fat cylinder
CYL_ONLY = False
if CYL_ONLY:
c = c1
else:
c = c_u
if un is None:
un = c
else:
un = vector3.CrispUnion(un, c)
# (RANGE_MIN, RANGE_MAX, STEPSIZE) = (-32, +32, 1.92 / 4.0 * 1.5 / 1.5)
# return un, (RANGE_MIN, RANGE_MAX, STEPSIZE)
return un