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 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 Parabola():
pts = [[0,0,0],[10,0,0],[10,10,0],[0,10,0]]
doc1 = g.Cn(len(pts))
doc1['pts'] = pts
x = 0
dx = .1
path = []
while x <= 10:
pt = [10*x,x**2,0]
path.append(pt)
x = x + dx
#path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]]
H = Extrusion(doc1,path)
return H
def Wire0(r, ppath, m=10, n=40):
assert (len(ppath) >= 2)
C = [0, 0, 0]
H1 = gra.Cn(m)
H1 = gra.CreateCircleGeometry(H1, C[0], C[1], C[2], r)
t = 0
dt = 1. / n
path = []
while t <= 1:
pt = B(t, ppath)
path.append(pt)
t = t + dt
H = ext.Extrusion(H1, path, bcap=True, ecap=True, closed=True)
return H
def Cube(ww,hh,dd,mass=1e8):
G1 = g.Cn(4)
G2 = g.Pn(2)
# graph G
G = g.GraphProduct(G1,G2)
# points to G
pts = [[0,0,0],[0,0,dd],[ww,0,0],[ww,0,dd],
[ww,hh,0],[ww,hh,dd],[0,hh,0],[0,hh,dd]]
G['pts'] = pts
# faces to G sorted by normals x,-x,y,-y,z,-z
F = [[0,1,7,6],[4,5,3,2],[2,3,1,0],
[6,7,5,4],[2,0,6,4],[1,3,5,7]]
G['F'] = F
G['N'] = map(lambda v: FaceNormal(G,v), range(len(F)))
return G
def Torus0(r1,r2,m=10,n=40):
C = [0,0,0]
H1 = gra.Cn(m)
H1 = gra.CreateCircleGeometry(H1,C[0],C[1],C[2],r1)
t = 0
dt = 2*pi/n
path = []
while t <= 2*pi + dt:
x = r2*sin(t)
y = r2*cos(t)
z = 0
pt = [x,y,z]
path.append(pt)
t = t + dt
H = ext.Extrusion(H1,path,bcap=False,ecap=False,closed=True)
return H
def Helix0(r, a, b, m=10, n=40, N=1):
C = [0, 0, 0]
H1 = gra.Cn(m)
H1 = gra.CreateCircleGeometry(H1, C[0], C[1], C[2], r)
t = 0
dt = 2 * pi / n
path = []
while t <= 2 * pi * N + dt:
# https://en.wikipedia.org/wiki/Helix
x = a * sin(t)
y = a * cos(t)
z = b * t
pt = [x, y, z]
path.append(pt)
t = t + dt
H = ext.Extrusion(H1, path, bcap=True, ecap=True, closed=True)
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 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
if event == cv2.EVENT_MOUSEMOVE and (len(pts) > 0):
pt_move = [x,y]
return
return
pts = []
pt_move = [0,0]
print("Select the two points on 2D plane")
cv2.namedWindow("result")
cv2.setMouseCallback("result",getxy)
doc = {}
doc["V"] = list(range(2))
doc["E"] = [[0,1]]
doc["pts"] = [[119, 304],[480, 53]]
doc = graph.Cn(4)
w = 400
h = 400
cx,cy,cz = (w/2,h/2,0)
r = 0.75*w/2
doc = graph.CreateCircleGeometry(doc,cx,cy,cz,r)
doc['_id'] = 1
w = 600
h = 600
gr = racg.Graphics(w=w,h=h)
def PlotGraph(gr,G,color):
black = [0,0,0]
for e in G['E']:
A,B = [G['pts'][v] for v in e]
def Circle(r, k):
G = graph.Cn(k)
C = [0, 0, 0]
G = graph.CreateCircleGeometry(G, C[0], C[1], C[2], r)
return G
