def pts(S):
shape = deepcopy(S.G['pts'])
C = aff.Center(shape)
shape = aff.Translate(shape, -C[0], -C[1], -C[2])
shape = aff.Rotate(shape, S.P.q)
shape = aff.Translate(shape, S.P.x[0], S.P.x[1], S.P.x[2])
return shape
def WaterBottleScene(G,Gs,t,q,s):
f_ = open(BIGDATA+"WaterBottle.obj",'r')
txt = f_.read()
f_.close()
G_small = ext.OBJ2Graph(txt)
pts = G_small['pts']
C = aff.Center(pts)
pts = aff.Translate(pts,-C[0],-C[1],-C[2],align=False)
G_small['pts'] = pts
# Add special textbook to scene
pts2 = G_sp['pts']
C2 = aff.Center(pts2)
pts2 = aff.Translate(pts2,-C2[0],-C2[1],-C2[2],align=False)
degrees = 90+30
axis = [0,0,1]
q_sp = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2])
pts2 = aff.Rotate(pts2,q_sp,align=False)
t2 = [180.,180.,rec_sp.d/2.]
pts2 = aff.Translate(pts2,t2[0],t2[1],t2[2],align=False)
G_sp['pts'] = pts2
G_small = GraphUnionS(G_small,G_sp)
pts = G_small['pts']
C = aff.Center(pts)
pts = aff.Translate(pts,-C[0],-C[1],-C[2],align=False)
pts = aff.Rotate(pts,q,align=False)
pts = aff.Scale(pts, s[0],s[1],s[2],align=False)
pts = aff.Translate(pts,t[0],t[1],t[2],align=False)
G_small['pts'] = pts
Gs = Append(Gs,G_small)
G = GraphUnionS(G,G_small)
return G,Gs
def TrefoilKnot():
from math import cos,sin,pi
pts = [[0,0,0],[10,0,0],[10,10,0],[0,10,0]]
doc1 = g.Cn(len(pts))
doc1['pts'] = pts
t = 0
dt = .04
path = []
while t <= 2*pi + dt:
# https://en.wikipedia.org/wiki/Trefoil_knot
x = sin(t) + 2*sin(2*t)
y = cos(t) - 2*cos(2*t)
z = -sin(3*t)
pt = [x,y,z]
path.append(pt)
t = t + dt
C = aff.Center(path)
degrees = 30
axis = [0,0,1]
q = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2])
s = [20,20,20] # the same scale as previous for caps
t = [20,0,0]
pts = aff.Translate(path,-C[0],-C[1],-C[2],align=False)
pts = aff.Rotate(pts,q,align=False)
pts = aff.Scale(pts, s[0],s[1],s[2],align=False)
pts = aff.Translate(pts,t[0],t[1],t[2],align=False)
path = pts
#path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]]
H = Extrusion(doc1,path)
return H
def Wire(r, ppath, t, q, s, m=10, n=40):
H = Wire0(r, ppath, m=m, n=n)
pts = H['pts']
C = aff.Center(pts)
pts = aff.Translate(pts, -C[0], -C[1], -C[2], align=False)
pts = aff.Rotate(pts, q, align=False)
pts = aff.Scale(pts, s[0], s[1], s[2], align=False)
pts = aff.Translate(pts, t[0], t[1], t[2], align=False)
H['pts'] = pts
return H
def Torus(r1,r2,t,q,s,m=10,n=40):
H = Torus0(r1,r2,m=m,n=n)
pts = H['pts']
C = aff.Center(pts)
pts = aff.Translate(pts,-C[0],-C[1],-C[2],align=False)
pts = aff.Rotate(pts,q,align=False)
pts = aff.Scale(pts,s[0],s[1],s[2],align=False)
pts = aff.Translate(pts,t[0],t[1],t[2],align=False)
H['pts'] = pts
return H
def Helix(r, a, b, t, q, s, m=10, n=40, N=1):
H = Helix0(r, a, b, m=m, n=n, N=N)
pts = H['pts']
C = aff.Center(pts)
pts = aff.Translate(pts, -C[0], -C[1], -C[2], align=False)
pts = aff.Rotate(pts, q, align=False)
pts = aff.Scale(pts, s[0], s[1], s[2], align=False)
pts = aff.Translate(pts, t[0], t[1], t[2], align=False)
H['pts'] = pts
return H
def ElevationMap(im, w, h, d, t, q, s, m=10):
H = ElevationMap0(im, w, h, d, m=m)
pts = H['pts']
C = aff.Center(pts)
pts = aff.Translate(pts, -C[0], -C[1], -C[2], align=False)
pts = aff.Rotate(pts, q, align=False)
pts = aff.Scale(pts, s[0], s[1], s[2], align=False)
pts = aff.Translate(pts, t[0], t[1], t[2], align=False)
H['pts'] = pts
return H
def RevolveCurve(curve, t, q, s, n=20, bcap=True, ecap=True):
# Assume curve has symmetry y-axis
x0 = curve[0][0]
x_min = min([pt[0] - x0 for pt in curve])
x_max = max([pt[0] - x0 for pt in curve])
y_min = min([pt[1] for pt in curve])
y_max = max([pt[1] for pt in curve])
poly_wb = deepcopy(curve)
pts = [[0, pt[1], 0] for pt in poly_wb]
y_min = min([pt[1] for pt in poly_wb])
y_max = max([pt[1] for pt in poly_wb])
doc = g.Cn(n)
cx, cy, cz = [0, 0, 0]
r0 = 1.
doc1 = CreateCircleGeometry(doc, cx, cy, cz, r0)
spath = []
path = []
pti = poly_wb[0]
xi, yi = pti
yi_last = yi
dx = x_max - x_min
dy = y_max - y_min
epsilon = 1e-4
if abs(dx) > epsilon:
aspect = 1. * dy / dx
else:
aspect = 1. * dx / dy
for i in range(len(poly_wb)):
pti = poly_wb[i]
xi, yi = pti
r = abs(xi - x0)
dy = yi - yi_last
epsilon = .1
if abs(dy) > epsilon:
spath.append(r)
path.append([yi, 0, 0])
yi_last = yi
degrees = 90
axis = [0, 1, 0]
q0 = aff.HH.rotation_quaternion(degrees, axis[0], axis[1], axis[2])
q = q * q0
C = aff.Center(path)
pts = aff.Translate(path, -C[0], -C[1], -C[2], align=False)
pts = aff.Rotate(pts, q, align=False)
pts = aff.Scale(pts, s[0], s[1], s[2], align=False)
pts = aff.Translate(pts, t[0], t[1], t[2], align=False)
path = pts
#path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]]
H = ext.Extrusion0(doc1, path, spath, bcap, ecap)
return H
def Leg(t,q,s):
height = w*(3./5.)
r1 = 8.
r2 = 12.
H = TableLeg(height,r1,r2,n=10,m=10)
pts = H['pts']
C = aff.Center(pts)
pts = aff.Translate(pts,-C[0],-C[1],-C[2],align=False)
pts = aff.Rotate(pts,q,align=False)
pts = aff.Scale(pts, s[0],s[1],s[2],align=False)
pts = aff.Translate(pts,t[0],t[1],t[2],align=False)
H['pts'] = pts
return H
def BodyGraph(G, Gs, Gseg, t, q, s):
H = {}
H['V'] = []
H['E'] = []
H['F'] = []
H['N'] = []
H['pts'] = []
degrees = 90
axis = [0, 1, 0]
q0 = aff.HH.rotation_quaternion(degrees, axis[0], axis[1], axis[2])
A = Gseg['pts'][0]
Hf = ext.CubeObj(300, 5, 300, A, q0, s)
H = ext.GraphUnionS(H, Hf)
for e in Gseg['E']:
u, v = e
A, B = [Gseg['pts'][w] for w in e]
v1 = np.array(B) - np.array(A)
v1n = np.linalg.norm(v1)
epsilon = 1e-5
if abs(v1n) < epsilon:
continue
v1 = v1 / np.linalg.norm(v1)
axis1 = [1, 0, 0]
axis2 = list(v1)
q1 = ext.AimAxis(axis1, axis2)
q1 = q1 * q0
r = 10
h = d(A, B)
t0 = list(np.array(A) + h / 2. * v1)
s0 = [1, 1, 1]
He = bs.Cylinder(r, h, t0, q1, s0, n=10, m=10)
H = ext.GraphUnionS(H, He)
Hf = bs.Sphere(40, A, q1, s0, n=10, m=10)
H = ext.GraphUnionS(H, Hf)
#Hf = bs.Cone(60,150,B,q1,s0,n=10,m=10)
#H = ext.GraphUnionS(H,Hf)
degrees = 0 # 180
axis = [0, 0, 1]
q2 = aff.HH.rotation_quaternion(degrees, axis[0], axis[1], axis[2])
q = q * q2
pts = H['pts']
C = Gseg['pts'][0]
pts = aff.Translate(pts, -C[0], -C[1], -C[2])
pts = aff.Rotate(pts, q)
pts = aff.Scale(pts, s[0], s[1], s[2])
pts = aff.Translate(pts, t[0], t[1], t[2])
H['pts'] = pts
return H
def CoffeeCup(n=30):
H = CoffeeCup0(n)
pts = H['pts']
scale = .15
s = [scale,scale,scale] # the same scale as previous for caps
t = [0,0,0]
degrees = 0
axis = [0,1,0]
q = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2])
C = aff.Center(pts)
pts = aff.Translate(pts,-C[0],-C[1],-C[2],align=False)
pts = aff.Rotate(pts,q,align=False)
pts = aff.Scale(pts, s[0],s[1],s[2],align=False)
pts = aff.Translate(pts,t[0],t[1],t[2],align=False)
H['pts'] = pts
return H
def WaterBottle():
global poly_wb
pts = [[0, pt[1], 0] for pt in poly_wb]
y_min = min([pt[1] for pt in poly_wb])
y_max = max([pt[1] for pt in poly_wb])
n = 10
doc = g.Cn(n)
cx, cy, cz = [0, 0, 0]
r = 1.
doc1 = CreateCircleGeometry(doc, cx, cy, cz, r)
spath = []
path = []
pti = poly_wb[0]
xi, yi = pti
yi_last = yi
sy = 33. / (y_max - y_min)
for i in range(len(poly_wb)):
pti = poly_wb[i]
xi, yi = pti
r = abs(xi - x0)
dy = yi - yi_last
epsilon = .1
if abs(dy) > epsilon:
spath.append(r)
path.append([yi * sy, 0, 0])
yi_last = yi
C = aff.Center(path)
degrees = 90
axis = [0, 1, 0]
q = aff.HH.rotation_quaternion(degrees, axis[0], axis[1], axis[2])
s = [20, 20, 20] # the same scale as previous for caps
t = [20, 0, 0]
pts = aff.Translate(path, -C[0], -C[1], -C[2], align=False)
pts = aff.Rotate(pts, q, align=False)
pts = aff.Scale(pts, s[0], s[1], s[2], align=False)
pts = aff.Translate(pts, t[0], t[1], t[2], align=False)
path = pts
#path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]]
H = ext.Extrusion0(doc1, path, spath)
return H
def CubeObj(w,h,d, t,q,s):
G = Cube(w,h,d)
pts = deepcopy(G['pts'])
C = aff.Center(pts)
#pts = aff.Translate(pts,-C[0],-C[1],-C[2])
pts = aff.Rotate(pts,q,align=True)
pts = aff.Scale(pts, s[0],s[1],s[2],align=True)
pts = aff.Translate(pts,t[0],t[1],t[2],align=True)
G['pts'] = pts
#print "C=",C
return G
G['N'] = [] G['pts'] = [] Gs = [] # trefoil knot H0 = ext.TrefoilKnot() degrees = 0 axis = [0,1,0] q = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2]) scale = 1. s = [scale,scale,scale] # the same scale as previous for caps t = [-80,0,50.] pts = H0['pts'] q = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2]) C = aff.Center(pts) pts = aff.Translate(pts,-C[0],-C[1],-C[2],align=False) pts = aff.Rotate(pts,q,align=False) pts = aff.Scale(pts, s[0],s[1],s[2],align=False) pts = aff.Translate(pts,t[0],t[1],t[2],align=False) H0['pts'] = pts Gs = ext.Append(Gs,H0) G = ext.GraphUnionS(G,H0) # square table H1 = SquareTable1() Gs = ext.Append(Gs,H1) G = ext.GraphUnionS(G,H1) # N1 x N2 water bottles N1 = 1 N2 = 1
def Extrusion0(G,path, spath, bcap=True,ecap=True,closed=False):
m = len(G['V'])
n = len(path)
k = n
assert(n>=3)
H = ExtrudeGraph(G,k)
C = aff.Center(G['pts'])
C = np.array(C)
pts = []
F = []
N = []
G0 = deepcopy(G)
G0['F'] = [G['V'][:3]]
N0 = FaceNormal(G0,0)
nn = n-1
if closed:
nn = n
for i in range(n-1):
A = np.array(path[i])
B = np.array(path[(i+1)%n])
vB = B - A
axis1 = N0
axis2 = list(vB)
q_k = AimAxis(axis1,axis2)
s_k = [spath[i],spath[i],spath[i]]
t_k = list(A)
pts_k = deepcopy(G['pts'])
C_k = aff.Center(pts_k)
pts_k = aff.Translate(pts_k,-C_k[0],-C_k[1],-C_k[2],align=False)
pts_k = aff.Rotate(pts_k,q_k,align=False)
pts_k = aff.Scale(pts_k, s_k[0],s_k[1],s_k[2],align=False)
pts_k = aff.Translate(pts_k,t_k[0],t_k[1],t_k[2],align=False)
pts = pts + pts_k
pts_k = deepcopy(G['pts'])
C_k = aff.Center(pts_k)
# use last q_k
s_k = [1,1,1]
# use last B
t_k = list(B)
pts_k = aff.Translate(pts_k,-C_k[0],-C_k[1],-C_k[2],align=False)
pts_k = aff.Rotate(pts_k,q_k,align=False)
pts_k = aff.Scale(pts_k, s_k[0],s_k[1],s_k[2],align=False)
pts_k = aff.Translate(pts_k,t_k[0],t_k[1],t_k[2],align=False)
pts = pts + pts_k
for i in range(n-1):
for e in G['E']:
u1,v1 = map(lambda u: u + m*i,e)
u2,v2 = map(lambda u: u + m*(i+1),e)
f = [u1,u2,v2,v1]
f1 = [u1,u2,v1]
f2 = [v1,u2,v2]
for fi in [f1,f2]:
G_f = ExtrudeGraph(G,2)
f2i = map(lambda u: u - m*i, fi)
G_f['F'] = [deepcopy(f2i)]
G_f['pts'] = deepcopy(pts[i*m:(i+2)*m])
N_fi = FaceNormal(G_f,0)
F.append(fi)
N.append(N_fi)
# add caps onto ends
flag_a = bcap # begin cap
flag_b = ecap # end cap
if flag_a and use_tripy:
pts_0 = pts[:m]
C_k = aff.Center(pts_0)
axis1 = N0
axis2 = list(vB)
q_k = AimAxis(axis1,axis2)
s_k = [1,1,1] # the same scale as previous for caps
pts_k = aff.Translate(pts_0,-C_k[0],-C_k[1],-C_k[2],align=False)
pts_k = aff.Rotate(pts_k,q_k,align=False)
pts_k = aff.Scale(pts_k, s_k[0],s_k[1],s_k[2],align=False)
pts_k = aff.Translate(pts_k,C_k[0],C_k[1],C_k[2],align=False)
z_k = pts_k[0][2]
pts_k = map(lambda pt: pt[:2], pts_k)
tris = Triangulate(pts_k)
for tri in tris:
f = map(lambda u: u + 0*m, tri)
F.append(f)
A,B,C = map(lambda u: pts_k[u], tri)
Nk = FaceNormalABC(A,B,C)
N.append(Nk) # some normal N0
a,b,c = f
e1 = [a,b]
e2 = [b,c]
e3 = [c,a]
if e1 not in H['E']:
H['E'].append(e1)
if e2 not in H['E']:
H['E'].append(e2)
if e3 not in H['E']:
H['E'].append(e3)
if flag_b and use_tripy:
pts_0 = pts[-m:]
C_k = aff.Center(pts_0)
s_k = [1,1,1] # the same scale as previous for caps
t_k = list(B)
pts_k = aff.Translate(pts_0,-C_k[0],-C_k[1],-C_k[2],align=False)
pts_k = aff.Scale(pts_k, s_k[0],s_k[1],s_k[2],align=False)
pts_k = aff.Translate(pts_k,C_k[0],C_k[1],C_k[2],align=False)
z_k = pts_k[0][2]
pts_k = map(lambda pt: pt[:2], pts_k)
tris = Triangulate(pts_k)
for tri in tris:
f = map(lambda u: u + (n-1)*m, tri)
F.append(f)
A,B,C = map(lambda u: pts_k[u], tri)
Nk = FaceNormalABC(A,B,C)
N.append(Nk) # some normal N0
a,b,c = f
e1 = [a,b]
e2 = [b,c]
e3 = [c,a]
if e1 not in H['E']:
H['E'].append(e1)
if e2 not in H['E']:
H['E'].append(e2)
if e3 not in H['E']:
H['E'].append(e3)
H['pts'] = pts
H['F'] = F
H['N'] = N
return H
def TableLeg(height,radius1,radius2,n=10,m=10):
h = height
r1 = radius1
r2 = radius2
curve = []
x0 = 0
for i in range(1,m-1):
r = mapto.MapTo(0,r1,m-1,r2,i)
xi = r
yi = mapto.MapTo(0,0,m-1,h,i)
pt = [xi,yi]
curve.append(pt)
yi = mapto.MapTo(0,0,m-1,h,.1)
curve = [[0,yi]]+curve+[[0,height]]
# Assume curve has symmetry y-axis
x0 = curve[0][0]
x_min = min(map(lambda pt: pt[0]-x0,curve))
x_max = max(map(lambda pt: pt[0]-x0,curve))
y_min = min(map(lambda pt: pt[1],curve))
y_max = max(map(lambda pt: pt[1],curve))
poly_wb = deepcopy(curve)
pts = map(lambda pt: [0,pt[1],0], poly_wb)
y_min = min(map(lambda pt: pt[1],poly_wb))
y_max = max(map(lambda pt: pt[1],poly_wb))
doc = g.Cn(n)
cx,cy,cz = [0,0,0]
r0 = 1.
doc1 = rc.CreateCircleGeometry(doc,cx,cy,cz,r0)
spath = []
path = []
pti = poly_wb[0]
xi,yi = pti
yi_last = yi
dx = x_max-x_min
dy = y_max-y_min
epsilon = 1e-4
if abs(dx) > epsilon:
aspect = 1.*dy/dx
else:
aspect = 1.*dx/dy
for i in range(len(poly_wb)):
pti = poly_wb[i]
xi,yi = pti
r = abs(xi - x0)
dy = yi-yi_last
epsilon = .1
if abs(dy) > epsilon:
spath.append(r)
path.append([yi,0,0])
yi_last = yi
degrees = 90+180
axis = [0,1,0]
q0 = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2])
q = q0
t = [0,0,-height*.4]
s = [1,1,1]
C = aff.Center(path)
pts = aff.Translate(path,-C[0],-C[1],-C[2],align=False)
pts = aff.Rotate(pts,q,align=False)
pts = aff.Scale(pts, s[0],s[1],s[2],align=False)
pts = aff.Translate(pts,t[0],t[1],t[2],align=False)
path = pts
#path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]]
H = ext.Extrusion0(doc1,path,spath)
return H
def CoffeeCup0(n=30,m=20,r0=20.):
flag_cup = True
flag_handle = True
H1 = {}
H1['V'] = []
H1['E'] = []
H1['pts'] = []
H1['F'] = []
H1['N'] = []
H2 = {}
H2['V'] = []
H2['E'] = []
H2['pts'] = []
H2['F'] = []
H2['N'] = []
if flag_cup:
# polygon curve of surface of revolution
# Create Cup. At present, its imperfect recreating
# a cover to coffee cup.
curve1a = [[406, 388], [441, 384], [469, 378], [489, 363], [506, 347],
[518, 330], [520, 314], [522, 297], [525, 276], [528, 258],
[530, 228], [528, 182], [528, 150], [527, 113], [527, 91],
[532, 73], [540, 68]]
curve1b = [[554, 70], [554, 86], [549, 108],
[550, 136], [546, 181], [547, 214], [544, 249], [544, 268],
[538, 281], [540, 288], [539, 300], [531, 312], [532, 329],
[526, 350], [513, 362], [502, 378], [482, 393], [446, 406],
[417, 409]]
curve1 = curve1a + curve1b
x0 = curve1[0][0]
x_min = min(map(lambda pt: pt[0]-x0,curve1))
x_max = max(map(lambda pt: pt[0]-x0,curve1))
y_min = min(map(lambda pt: pt[1],curve1))
y_max = max(map(lambda pt: pt[1],curve1))
degrees = 0
axis = [0,1,0]
q = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2])
scale = 1.
s = [scale,scale,scale] # the same scale as previous for caps
t = [0,0,0]
H1 = rc.RevolveCurve(curve1,t,q,s, n, bcap=False, ecap=False)
if flag_handle:
# Create Handle
curve2 = [[203, 130], [189, 114], [165, 102], [149, 100], [132, 101],
[116, 106], [106, 113], [107, 128], [112, 152], [118, 169],
[127, 184], [138, 201], [149, 208], [165, 209], [186, 214],
[207, 213]]
# Assume curve has symmetry y-axis
x0 = curve2[0][0]
x_min = min(map(lambda pt: pt[0]-x0,curve2))
x_max = max(map(lambda pt: pt[0]-x0,curve2))
y_min = min(map(lambda pt: pt[1],curve2))
y_max = max(map(lambda pt: pt[1],curve2))
poly_wb = deepcopy(curve2)
pts = map(lambda pt: [0,pt[1],0], poly_wb)
y_min = min(map(lambda pt: pt[1],poly_wb))
y_max = max(map(lambda pt: pt[1],poly_wb))
doc = g.Cn(m)
cx,cy,cz = [0,0,0]
doc1 = rc.CreateCircleGeometry(doc,cx,cy,cz,r0)
spath = []
path = []
pti = poly_wb[0]
xi,yi = pti
yi_last = yi
dx = x_max-x_min
dy = y_max-y_min
for i in range(len(poly_wb)):
pti = poly_wb[i]
xi,yi = pti
r = abs(xi - x0)
dy = yi-yi_last
epsilon = .1
if abs(dy) > epsilon:
spath.append(1.)
path.append([xi,yi,0])
degrees = 90+180
axis = [1,0,0]
q0 = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2])
q = q0
t = [-184,0,100]
s = [1,1,1]
C = aff.Center(path)
pts = aff.Translate(path,-C[0],-C[1],-C[2],align=False)
pts = aff.Rotate(pts,q,align=False)
pts = aff.Scale(pts, s[0],s[1],s[2],align=False)
pts = aff.Translate(pts,t[0],t[1],t[2],align=False)
path = pts
H2 = ext.Extrusion0(doc1,path,spath)
H = ext.GraphUnionS(H1,H2)
return H
