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RandomComplex3.py
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930 lines (866 loc) · 27.7 KB
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## Generate Random Complex K (for circle packing algorithm)
import random
import bpy
import math
## 1rst Generating Random polygon
##
## Starting by generating point maxima and minima.
## In this method, for n>=3, iteratively start by generating 3 points.
## Iterated point procedures randomly chooses an edge, then with minima,
## and maxima constraints picks a point randomly between edge minima and
## maxima, forming a new edge.
## A limit can be placed on subdivisions such that no further subdivision
## of any newly formed edge can take place without the subdivision
## of any older higher Queue priority edges in the randomization process.
## This modification of RandomComplex.py instead uses the computed circumcircle
## of the 3 gon base, and then prescribes boundary points along
## the circumcircle in determining edge subdivisions.
## Alternately one can generate the random circle and then three random points
## given to a distance conformal mapping to the circle's radial arc.
## For instance, one way to do this is in polar coordinates randomly choosing
## an angle and then with a known radius computing x, y coordinates
## from polar ones.
Triangulated = True
MaxSize = 10
PolygonSize = 6 ## must be 3 or higher
MaxScaleIterations = 2
Scale = .5
EarlyRandom = False ## leads to greater probability of less convex polygon,
##more jagged
AllConvex = True ## yields Completely convex polygon with Early Random
## set False, otherwise, is likely to be extremely
## jagged with high JIntensity and high PolygonSize
JIntensity = 0.3 ## scale ranges from 0 to 1 with full intensity at 1
## and zero intensity at zero
def det2(a11,a21,a12,a22):
return a11*a22-a21*a12
def cofactmatrix(matA,element,i,j):
## exclude row and column of element
## where i and j represent the row and column index respectively
matB = []
##print('i: ', i)
##print('j: ', j)
l = 0
for row in matA:
rowvec = []
if l != i:
##print(row)
k = 0
for col in row:
if k != j:
rowvec.append(col)
k += 1
matB.append(rowvec)
l += 1
##print(matB)
return matB
def computedet(matA):
## find the cofactors and determine that the matrix is
## in a given 2x2 base if not repeat the procedure.
## assumed matrix provided is square
i = 0
j = 0
if len(matA) > 2:
cdetsum = 0
for row in matA:
j = 0
if i > 0:
break
for col in matA[i]:
s = i+j % 2
if s == 0:
s = 1
else:
s = -1
matB = cofactmatrix(matA,col,i,j)
det = None
if len(matB) >= 2:
det = computedet(matB)
cdetsum += s*col*det
j += 1
i += 1
return cdetsum
else:
##print(matA)
return det2(matA[0][0],matA[0][1],matA[1][0],matA[1][1])
## sources from http://mathworld.wolfram.com/Circumcircle.html
# x0 = - bx/2a y0 = -by/2a
## r = (bx^2+by^2 - 4ac)^1/2 /2|a|
## a = det([[x1,y1,1],[x2,y2,1],[x3,y3,1]])
## bx = -1* det([[x1^2+y1^2, y1, 1],[x2^2+y2^2,y2,1],[x3^2+y3^2,y3,1]])
## by = det([[x1^2+y1^2, x1, 1],[x2^2+y2^2,x2,1],[x3^2+y3^2,x3,1]])
## c = -1*det([[x1^2+y1^2, x1, y1],[x2^2+y2^2,x2,y2],[x3^2+y3^2,x3,y3]])
def circumcircle(p1,p2,p3):
x1,y1 = p1
x2,y2 = p2
x3,y3 = p3
a = computedet([[x1,y1,1],[x2,y2,1],[x3,y3,1]])
bx = -1* computedet([[abs(x1**2)+abs(y1**2), y1, 1],
[abs(x2**2)+abs(y2**2), y2, 1],
[abs(x3**2)+abs(y3**2), y3, 1]])
by = computedet([[abs(x1**2)+abs(y1**2), x1, 1],
[abs(x2**2)+abs(y2**2), x2, 1],
[abs(x3**2)+abs(y3**2), x3, 1]])
c = -1*computedet([[abs(x1**2)+abs(y1**2), x1, y1],
[abs(x2**2)+abs(y2**2), x2, y2],
[abs(x3**2)+abs(y3**2), x3, y3]])
x0 = -bx/(2*a)
y0 = -by/(2*a)
r = (abs(bx**2)+abs(by**2) - 4*a*c)**.5/ (2*abs(a))
return (x0,y0,r)
def clockwisewalktest(walk):
## works with nonconvex polygons should be safe
## I believe for the primitive polygon type (3 vertices)
## constructed in this algorithm.
prev = None
samt = 0.0
newwalk = walk[0:len(walk)]
newwalk.append(walk[0])
for vert in newwalk:
if prev == None:
prev = vert
continue
## samt += (vert[0]-prev[0])*(vert[1]+prev[1])
samt += (prev[0]*vert[1]-prev[1]*vert[0])
## if walk.index(vert) == len(walk)-1:
## samt += (walk[0][0] - vert[0])*(walk[0][1]+vert[1])
prev = vert
print('samt: ', samt)
if samt < 0:
print('original walk is clockwise')
return True
else:
print('original walk is counter clockwise')
return False
def polygonwalk(vert,last,target,vedges, walk):
for edge in vedges[vert]:
va, vb = edge
prev = vert
nextv = None
if va == vert:
if vb != last:
walk.append(vb)
if vb != target:
nextv = vb
polygonwalk(nextv,prev,target,vedges,walk)
else:
if va != last:
walk.append(va)
if va != target:
nextv = va
polygonwalk(nextv,prev,target,vedges,walk)
def convextest(v1,v2,v3,v4):
def crossproduct(p1,p2):
return (p1[0]*p2[1] - p1[1]*p2[0])
## assumed v1,v2,v3,v4 are sequentially ordered on the
##polygon walk
## this is cross product comparison
t1 = crossproduct(v1,v2) == crossproduct(v2,v3)
t2 = crossproduct(v3,v4) == crossproduct(v1,v2)
if t1 and t2:
return True
else:
return False
def generateRandomVertex():
return (random.random()*MaxSize, random.random()*MaxSize)
def generateRandomVertexMM(minX,maxX,minY,maxY):
return (random.uniform(minX,maxX),random.uniform(minY,maxY))
def cubicInterpolate (p, x):
return p[1] + 0.5 * x*(p[2] - p[0] + x*(2.0*p[0] - 5.0*p[1] + 4.0*p[2] - p[3] + x*(3.0*(p[1] - p[2]) + p[3] - p[0])))
def distance(a,b):
ax,ay = a
bx,by = b
return ((ax-bx)**2+(ay-by)**2)**.5
def getMinMax(edge):
edgex = edge[0:len(edge)]
edgey = edge[0:len(edge)]
edgex = list(edgex)
edgey = list(edgey)
edgex.sort(key = lambda tup:tup[0])
edgey.sort(key = lambda tup:tup[1])
minx = edgex[0][0]
maxx = edgex[1][0]
miny = edgey[0][1]
maxy = edgey[1][1]
return (minx,maxx,miny,maxy)
def getXScale(minx,maxx):
return 1.0/abs(maxx-minx)
def scale(scale, points):
rpoints = []
for point in points:
rpoints.append((scale*point[0], scale*point[1]))
return rpoints
def translateX(tr, points):
rpoints = []
for point in points:
rpoints.append((tr + point[0], point[1]))
return rpoints
def slope(edge):
a, b = edge
ax,ay = a
bx,by = b
return (by - ay)/(bx - ax)
def angle(slope):
return math.atan(slope)
def rotatecoord(coord, theta):
x,y = coord
return (x*math.cos(theta) - y*math.sin(theta),
x*math.sin(theta) + y*math.cos(theta))
def midpoint(edge):
a,b = edge
return ((a[0]+b[0])/2.0,(a[1]+b[1])/2.0)
def slopenormal(edgeslope):
return - 1/edgeslope
def testdirection(edge1, edge2):
#assumed edge1 = (a,b) and edge2 = (b,c)
# where b intersect edge 1 and 2
a,b = edge1
b,c = edge2
if c > b:
if a > b:
return False
else:
return True
else:
if a > b:
return True
else:
return False
def setRotation(edge, rotheir):
## closest distance to walk pair root determines
## direction of the vector
root = rotheir[edge]
ra, rb = root
rbx, rby = rb
rax, ray = ra
vec = [rbx-rax, rby-ray]
## a,b = edge
## ax,ay = a
## bx,by = b
## ## find which vertex is closest to root a
## dara = distance(a,ra)
## dbra = distance(b,ra)
## if dara < dbra:
## vec = [bx-ax, by-ay]
## else:
## vec = [ax-bx, ay-by]
## 90 degree rotation
print('ab vector: ', vec)
vec = [-vec[1], vec[0]]
print('rotation edge: ', edge)
print('rotation vector: ', vec)
return vec
def getY(point, slope, x):
return slope*(x - point[0]) + point[1]
def getneighborverts(edge,vedges):
a,b = edge
n1 = None
n2 = None
ne1 = None
ne2 = None
for nedge in vedges[a]:
if edge != nedge:
na,nb = nedge
ne1 = nedge
if na == a:
n1 = nb
else:
n1 = na
for nedge in vedges[b]:
10BC0
if edge != nedge:
na,nb = nedge
ne2 = nedge
if na == b:
n2 = nb
else:
n2 = na
return n1,n2,ne1,ne2
def norm(vec):
##2d norm
vx, vy = vec
d = (abs(vx**2)+abs(vy**2))**.5
vx = vx/d
vy = vy/d
return [vx,vy]
def updateEdges(a,b,edges,dedge,vedges):
edges.append((a,b))
d = distance(a,b)
if d in dedge:
if (a,b) in dedge[d]:
print('duplicate edge FOUND!')
print('dup edge: ', (a,b))
dedge[d].append((a,b))
else:
dedge[d] = [(a,b)]
if a in vedges:
vedges[a].append((a,b))
else:
vedges[a] = [(a,b)]
if b in vedges:
vedges[b].append((a,b))
else:
vedges[b] = [(a,b)]
def updateRotatheir(edge, parent, rotheir):
## assumed under midpoint subdivision a new edge
## will have at least one but not more than one
## matching vertex to the root edge
root = rotheir[parent]
ra, rb = root
a,b = edge
ax,ay = a
bx,by = b
## find which vertex is closest to root a
## dara = distance(a,ra)
## dbra = distance(b,ra)
## if dara < dbra:
## rotheir[edge] = (a,b)
## else:
## rotheir[edge] = (b,a)
if a == ra or a == rb:
if a == rb:
rotheir[edge] = (b,a)
else:
rotheir[edge] = (a,b)
if b == ra or b == rb:
if b == rb:
rotheir[edge] = (a,b)
else:
rotheir[edge] = (b,a)
def deleteEdge(edge,edges,dedge,vedges):
a,b = edge
d = distance(a,b)
edges.remove(edge)
print('removing from dedge: ', dedge[d])
print('edge: ', edge)
dedge[d].remove(edge)
if len(dedge[d]) == 0:
del dedge[d]
## print(edge)
## print(vedges)
vedges[a].remove(edge)
vedges[b].remove(edge)
edgecount = 0
vertices = []
edges = []
dedge = {}
vedges = {}
edged = {}
rotheir = {}
for i in range(0,3):
vertices.append(generateRandomVertex())
if len(vertices) > 0 and len(vertices) != 1:
a = vertices[0]
b = vertices[len(vertices)-1]
updateEdges(a,b,edges,dedge,vedges)
rotheir[(a,b)] = (a,b)
edgecount += 1
a = vertices[2]
b = vertices[1]
c = vertices[0]
centerx,centery,circler = circumcircle(c,b,a)
print('centerx, centery, circler ', (centerx,centery,circler))
updateEdges(a,b,edges,dedge,vedges)
rotheir[(a,b)] = (a,b)
edgecount += 1
## create walk order used in determining rotations
verts = list(vedges.keys())
print(vedges)
a = verts[0]
print('a',a)
tedge = vedges[a][0]
last = None
target = None
walk = [a]
print('walk:', walk)
for vert in tedge:
if vert != a:
target = vert
last = vert
polygonwalk(a,last,target,vedges,walk)
print('original walk: ', walk)
newwalk = []
if not clockwisewalktest(walk):
walk0 = walk[0]
walk1 = walk[1:len(walk)]
walk1 = walk1[::-1] ## reverse the order for clockwise
newwalk.append(walk0)
newwalk += walk1
walk = newwalk
print('rotation order walk: ', walk)
def setrotatheirorder(walk, rotheir):
prev = None
for vert in walk:
if prev == None:
prev = vert
continue
print('vert,prev pair: ', (vert,prev))
if (vert, prev) in rotheir:
print('found rev order rotheir key')
print('vert,prev pair: ', (vert,prev))
rotheir[(vert,prev)] = (prev,vert)
if walk.index(vert) == len(walk)-1:
if (walk[0], vert) in rotheir:
rotheir[(walk[0],vert)] = (vert,walk[0])
prev = vert
def computeNormtoArc(edge, mpoint, norm, r, C):
## as per wiki using solution indicated.
## s = r - (r*r-l*l)**.5
a,b = edge
l2 = distance(a,b)
l = l2/2.0
s = r - (r*r-l*l)**.5
print('s: ', s)
x,y = mpoint
dnx,dny = [s*norm[0], s*norm[1]]
px,py = [x+dnx,y+dny]
d = distance(mpoint,(px,py))
## check to see that this point relative to norm lies on
## the circle, if not then we recompute the point using -norm
## we then have to find the distance in the direction of the norm
## which is r+ distance(c-mp) where c is the center of the circle,
## and mp is the midpoint.
dist = distance(C,(px,py))
print('radius: ', r)
print('distance between C and px,py: ', distance(C,(px,py)))
if dist < r or dist > r:
normi = [-norm[0],-norm[1]]
dnxi,dnyi = [s*normi[0], s*normi[1]]
pxi,pyi = [x+dnxi,y+dnyi]
dcmp = 2*r-distance(mpoint,(pxi,pyi))
d = dcmp
dnx,dny = [dcmp*norm[0], dcmp*norm[1]]
px,py = [x+dnx,y+dny]
dist = distance(C,(px,py))
print('new distance between C and px,py', dist)
return ((px,py),d)
def computeNormtoArc2(edge, point, norm, r, C):
## generalized solution for any given point on the secant
## different method per wiki
a,b = edge
ax,ay = a
bx,by = b
px, py = point
Cx,Cy = C
## translate point and edge
atrx,atry = [ax-Cx,ay-Cy]
btrx,btry = [bx-Cx,by-Cy]
ptrx,ptry = [px-Cx,py-Cy]
at = (atrx,atry)
bt = (btrx,btry)
##compute angle of secant
sedge = slope((at,bt)) ## invariant under translation
theta = math.atan(sedge)+math.pi/2.0
ptrrtx, ptrrty = rotatecoord((ptrx,ptry), theta)
## also find rotated coordinates of the norm
## since we will compare solution values to the norm
nrtx, nrty = rotatecoord(norm, theta)
## compute y'
yp = ((r*r-ptrrtx*ptrrtx))**.5
## check +/- solution of yp
## this is whether or not the direction of ptrrty to + point on the arc
## is in the desired norm direction. If not then we use the -yp
## solution.
direcyp = yp - ptrrty
##t1 = math.copysign(1,ptrrtx) == math.copysign(1,nrtx)
t2 = math.copysign(1,direcyp) == math.copysign(1,nrty)
if not t2:
yp = -yp
## convert to previous pre rotated coordinate system
strx, stry = rotatecoord((ptrrtx,yp), -theta)
return ((strx+Cx,stry+Cy), distance((strx+Cx,stry+Cy),point))
def Centroid(walk):
## Compute A for a non self intersecting closed polygon
A = 0
i = 0
for vert in walk:
x,y = vert
if i == len(walk)-1:
xp1,yp1 = walk[0]
else:
xp1,yp1 = walk[walk.index(vert)+1]
A += x*yp1-xp1*y
A*=.5
Cx = 0
Cy = 0
for vert in walk:
x,y = vert
if i == len(walk)-1:
xp1,yp1 = walk[0]
else:
xp1,yp1 = walk[walk.index(vert)+1]
Cx += (x+xp1)*(x*yp1-xp1*y)
Cy += (y+yp1)*(x*yp1-xp1*y)
Cx *= 1/(6*A)
Cy *= 1/(6*A)
return Cx,Cy
setrotatheirorder(walk,rotheir)
print('rotheir: ', rotheir)
Q = []
edgec = 0
print(dedge)
qedges = None
pedge = None
parents = []
i = 0
circmax = random.randint(3,12)
if AllConvex:
circmax = PolygonSize+1
while (edgecount < PolygonSize+1):
if len(Q) == 0:
##fill Q
##edgescopy = edges[0:len(edges)]
##random.shuffle(edgescopy)
edgekeys = list(dedge.keys())
edgekeys.sort(reverse = True)
Q = edgekeys[0:1]
## avgQ = sum(Q)/float(len(Q))
## for dist in Q:
## if dist/avgQ < .1:
## Q.remove(dist)
## print('removing dist: ', dist)
print('Q :', Q)
i += 1
if edgec == 0:
print('new qedges: ', dedge[Q[0]])
qedges = dedge[Q[0]][0:len(dedge[Q[0]])]
7440
pedge = dedge[Q[0]][edgec]
else:
pedge = qedges[edgec]
minx,maxx,miny,maxy = getMinMax(pedge)
x = None
y = None
##nvert = generateRandomVertexMM(minx,maxx,miny,maxy)
x = (maxx+minx)/2.0
n1,n2,ne1,ne2 = getneighborverts(pedge,vedges)
## if testdirection(ne1,pedge) and testdirection(pedge,ne2):
if edgecount > circmax:
a,b = pedge
## print('n1:',n1)
## print('n2:', n2)
## print('ne1:', ne1)
## print('ne2:', ne2)
## if testdirection(ne1,pedge) and testdirection(pedge,ne2):
## p = [n1,a,b,n2]
## n1n2slope = slope((n1,n2))
## theta = angle(n1n2slope)
## thetai = -theta
## n1 = rotatecoord(n1, theta)
## a = rotatecoord(a, theta)
## b = rotatecoord(b, theta)
## minx,maxx,miny,maxy = getMinMax((a,b))
## xscale = getXScale(minx,maxx)
## n2 = rotatecoord(n2, theta)
## abslope = slope(pedge)
## midy = getY(pedge[0],abslope,x)
## xr,yr = rotatecoord((x,midy), theta)
## print('xr, yr:', (xr,yr))
## print('x, y: ', (x, midy))
## print('check x, y: ', rotatecoord((xr,yr), thetai))
## p = [n1,a,b,n2]
## ## we need to set up interpolation which means scaling
## ## and translating positions to end up on interval [0,1]
## ## for p1 and p2, will also need to compute position x =-1
## ## for p0 at y.
## p = scale(xscale, p)
## tr = -minx*xscale
## sxt = xscale*xr+tr
## p = translateX(tr, p)
## if p[1][0] != 0.0:
## p = [p[3],p[2],p[1],p[0]]
## ne1 = (p[0],p[1])
## ne2 = (p[2],p[3])
## sne1 = slope(ne1)
## sne2 = slope(ne2)
## ny1 = getY(p[0], sne1, -1)
## ny2 = getY(p[3], sne2, 2)
## print('ny1:', ny1)
## print('ny2:', ny2)
## print('p:',p)
## print('sxt: ', sxt)
## py = [ny1,p[1][1],p[2][1],ny2]
##
## syt = cubicInterpolate (py, sxt)
## ##rescale y back to original coordinate
## ## note: we don't worry about retranslating since this isn't an xcoordinate
## y = syt*1/xscale
## xpt = (sxt-tr)*1/xscale
## x,y = rotatecoord((xpt,y),thetai)
## else:
## a,b = pedge
## xscale = getXScale(minx,maxx)
## ## print('n1:',n1)
## ## print('n2:', n2)
## ## print('ne1:', ne1)
## ## print('ne2:', ne2)
##
## p = [n1,a,b,n2]
## ## we need to set up interpolation which means scaling
## ## and translating positions to end up on interval [0,1]
## ## for p1 and p2, will also need to compute position x =-1
## ## for p0 at y.
## p = scale(xscale, p)
## tr = -minx*xscale
## sxt = xscale*x+tr
## p = translateX(tr, p)
## if p[1][0] != 0.0:
## p = [p[3],p[2],p[1],p[0]]
## ne1 = (p[0],p[1])
## ne2 = (p[2],p[3])
## sne1 = slope(ne1)
## sne2 = slope(ne2)
## ny1 = getY(p[0], sne1, -1)
## ny2 = getY(p[3], sne2, 2)
## print('ny1:', ny1)
## print('ny2:', ny2)
## print('p:',p)
## py = [ny1,p[1][1],p[2][1],ny2]
## syt = cubicInterpolate (py, sxt)
## ##rescale y back to original coordinate
## ## note: we don't worry about retranslating since this isn't an xcoordinate
## y = syt*1/xscale
mpoint = midpoint(pedge)
## pslope = slope(pedge)
## nslope = slopenormal(pslope)
rvec = setRotation(pedge, rotheir)
## y = getY(pedge[0], pslope, x)
x, y = mpoint
sc = random.randint(1,8)
print('y at midpoint: ', y)
x = x + rvec[0]/(4*sc ) ##+ i)
y = y + rvec[1]/(4*sc)##+ i)
else:
mpoint = midpoint(pedge)
## pslope = slope(pedge)
## nslope = slopenormal(pslope)
rvec = setRotation(pedge, rotheir)
## y = getY(pedge[0], pslope, x)
## rvec = [mpoint[0]-centerx, mpoint[1]-centery]
x, y = mpoint
print('y at midpoint: ', y)
dmidcent = distance((centerx,centery),mpoint)
## vlen = circler - dmidcent
rvec = norm(rvec)
## rvec = (rvec[0]*vlen, rvec[1]*vlen)
if EarlyRandom:
rval = random.random()
Jshift = 1.0-JIntensity
rval *= JIntensity
rval += Jshift
rvec = (rvec[0]*rval*circler, rvec[1]*rval*circler)
else:
rvec = (rvec[0]*circler, rvec[1]*circler)
## x = x + rvec[0] ##+ i)
## y = y + rvec[1] ##+ i)
print('rvec: ', rvec)
C = [centerx,centery]
## p,d = computeNormtoArc(pedge, mpoint, rvec, circler, C)
## p,d = computeNormtoArc2(pedge, mpoint, rvec, circler, C)
## if EarlyRandom:
## rval = random.random()
## Jshift = 1.0-JIntensity
## rval *= JIntensity
## rval += Jshift
## print('rval: ', rval)
## x,y = [x+rval*d*rvec[0],y+rval*d*rvec[1]]
## else:
## x,y = p
x = centerx + rvec[0]
y = centery + rvec[1]
vertices.append((x,y))
nvert = (x,y)
updateEdges(pedge[0],nvert,edges,dedge,vedges)
updateEdges(pedge[1],nvert,edges,dedge,vedges)
print('new vertex: ', nvert)
deleteEdge(pedge,edges,dedge,vedges)
nedge1 = (pedge[0],nvert)
nedge2 = (pedge[1],nvert)
updateRotatheir(nedge1, pedge, rotheir)
updateRotatheir(nedge2, pedge, rotheir)
del rotheir[pedge]
edgecount += 1
print('pedge: ', pedge)
print('Q[0]', Q[0])
print('qedges', qedges)
print('length qedges - 1: ',len(qedges)-1)
if edgec == len(qedges)-1:
del Q[0]
edgec = 0
else:
edgec += 1
verts = list(vedges.keys())
print(vedges)
a = verts[0]
print('a',a)
tedge = vedges[a][0]
last = None
target = None
walk = [a]
print('walk:', walk)
for vert in tedge:
if vert != a:
target = vert
last = vert
polygonwalk(a,last,target,vedges,walk)
face = []
normneighbors = {}
prevvertices = vertices[0:len(vertices)]
i = 1
bvertices = []
##bvertices += vertices
for vert in vertices:
x,y = vert
bvertices.append((x,y,0.0))
faces = []
height = 0
def addinteriorcycle(cycle,Interior,vertex, order):
##cycle order
## This is specific to the order of face indexing
## in the method given on scaling iterations
## if vertex in Interior:
## Interior[vertex] += cycle
## else:
## Interior[vertex] = [cycle]
if order == 2:
Interior[vertex] = cycle
elif order == 1:
cycle += Interior[vertex]
Interior[vertex] = cycle
## elif order == 4:
## cycle += Interior[vertex]
## Interior[vertex] = cycle
elif order == 5:
Interior[vertex].insert(3,cycle[0])
## only to be found on scaled walk 1 time for exception.
## this is where 4th cycle is populated before the first.
## elif order == 6:
## cycle += Interior[vertex]
## Interior[vertex] = cycle
elif order == 7:
Interior[vertex] += cycle
Exterior = {}
for vert in walk:
verti = vertices.index(vert)
Exterior[verti] = .1##random.random()
Interior ={}
while i < MaxScaleIterations:
index = len(walk)*i
indexmn1 = len(walk)*(i-1)
nvertices = []
nvertices2 = []
height += random.random()*.1
for vert in walk:
verti = vertices.index(vert)
vert1 = verti+indexmn1
vert2 = verti+index
vindex = walk.index(vert)
vindexn = None
if vindex == 0:
vindexn = len(walk)-1
else:
vindexn = vindex-1
vnc = walk[vindexn]
vni = vertices.index(vnc)
vert3 = vni + index
vert4 = vni + indexmn1
if Triangulated:
face = (vert1,vert2,vert4)
faces.append(face)
face = (vert4,vert2,vert3)
faces.append(face)
## order of operations for a given vertex
## A vertex is first encountered in the 2nd
## configuration, followed by the 3rd, followed
## by the 1rst, followed by the 4th normally
## 3rd configuration is not recorded (repetition of writing
## vertices). There should normally by 6 vertices
## recorded over the entire sequence for 1 vertex forming a cycle.
cycle4 = [vert1,vert2,vert3]
## cycle3 = [vert2]
cycle1 = [vert4]
cycle2 = [vert4,vert1]
if i == 1:
addinteriorcycle(cycle2,Interior,vert2,2)
elif i == MaxScaleIterations-1:
cycle2 = [vert3,vert4,vert1]
cycle3 = [vert2]
addinteriorcycle(cycle4,Interior,vert4,1)
if walk.index(vert) == len(walk)-1:
addinteriorcycle(cycle1,Interior,vert1,5)
addinteriorcycle(cycle2,Interior,vert2,7)
addinteriorcycle(cycle3,Interior,vert3,1)
elif walk.index(vert) == 0:
addinteriorcycle(cycle3,Interior,vert3,2)
addinteriorcycle(cycle2,Interior,vert2,2)
addinteriorcycle(cycle1,Interior,vert1,1)
else:
addinteriorcycle(cycle1,Interior,vert1,1)
addinteriorcycle(cycle3,Interior,vert3,1)
addinteriorcycle(cycle2,Interior,vert2,2)
else:
addinteriorcycle(cycle2,Interior,vert2,2)
addinteriorcycle(cycle4,Interior,vert4,1)
if walk.index(vert) == len(walk)-1:
addinteriorcycle(cycle1,Interior,vert1,5)
else:
addinteriorcycle(cycle1,Interior,vert1,1)
else:
face = (vert1,vert2,vert3,vert4)
faces.append(face)
for vert in prevvertices:
x,y = vert
## translate coordinates
xtr = x - centerx
ytr = y - centery
xs = xtr*Scale
ys = ytr*Scale
xs += centerx
ys += centery
nvertices2.append((xs,ys))
nvertices.append((xs, ys, height))
prevvertices = nvertices2[0:len(nvertices2)]
bvertices += nvertices
i+= 1
height += random.random()*.1
bvertices.append((centerx,centery,height))
## Final face/vertex pass
vert3 = len(bvertices)-1
Interior[vert3] = []
for vert in walk:
cycle = [vert3]
verti = vertices.index(vert)
vert1 = verti+index
Interior[vert3].append(vert1)
cycle += Interior[vert1]
Interior[vert1] = cycle
vindex = walk.index(vert)
vindexn = None
if vindex == 0:
vindexn = len(walk)-1
else:
vindexn = vindex-1
vnc = walk[vindexn]
vni = vertices.index(vnc)
vert2 = vni + index
face = (vert1,vert3,vert2)
faces.append(face)
## to solve the problem of nested scaling of a polygon to a common
## centroid, one need translate coordinates of the original polygon
## so that the centroid is the origin, scale all vertices, then
## retranslate these coordinates back to the original coordinate
## system.
##for vert in walk:
## face.append(vertices.index(vert))
##bvertices = []
##for vert in vertices:
## x,y = vert
## bvertices.append((x,y,0.0))
##faces = []
##faces.append(tuple(face))
meshName = "Polygon"
obName = "PolygonObj"
me = bpy.data.meshes.new(meshName)
ob = bpy.data.objects.new(obName, me)
ob.location = bpy.context.scene.cursor_location
bpy.context.scene.objects.link(ob)
me.from_pydata(bvertices,[],faces)
me.update(calc_edges=True)