Parabolic UV Subdivision

import rhinoscriptsyntax as rs

srf = rs.GetObject("Pick Surface",8)

du = rs.SurfaceDomain(srf,0)

dv = rs.SurfaceDomain(srf,1)

dumid =(du[1]-du[0])/2

dvmid =(dv[1]-dv[0])/2

udiv = 20

vdiv = 20

ustep =(du[1]-du[0])/udiv

vstep =(dv[1]-dv[0])/vdiv

print du,dv

rs.EnableRedraw(False)

centroid = rs.SurfaceAreaCentroid(srf)

coordcentroid = centroid[0]

ulist = []

for xu in rs.frange (-dumid,dumid,ustep):

    if xu<0:

        yu = -xu**2

    if xu>=0:

        yu = xu**2

    ulist.append(yu)

#ulist.sort()

umax = ulist[-1]

remapulist = []

for i in ulist:

    remapu = (i/((du[1]-du[0])/2))+((du[1]-du[0])/2)

#    print "i = ", i

#    print "du[1]-du[0] = ", du[1]-du[0]

#    print "remapu = " , remapu

    remapulist.append(remapu)

print remapulist

vlist = []

for xv in rs.frange (-dvmid,dvmid,vstep):

    if xv<0:

        yv = -xv**2

    if xv>=0:

        yv = xv**2

    vlist.append(yv)

vmax = vlist[-1]

remapvlist = []

for i in vlist:

    remapv = (i/((dv[1]-dv[0])/2))+((dv[1]-dv[0])/2)

#    print "i = ", i

#    print "dv[1]-dv[0] = ", dv[1]-dv[0]

#    print "remapv = " , remapv

    remapvlist.append(remapv)

print remapvlist

norlist = []

rowlist = []

for i in remapulist:

    columnlist = []

    colnorlist = []

    for j in remapvlist:

        pt = rs.EvaluateSurface(srf,i,j)

        columnlist.append(pt)

       

        norvect = rs.SurfaceNormal(srf,[i,j])

        norvect = rs.VectorUnitize(norvect)

        norpt = rs.VectorAdd(pt,norvect)

        colnorlist.append(norpt)

       

    rowlist.append(columnlist)

    norlist.append(colnorlist)

for i in range (0,len(rowlist)):

    for j in range (0,len(rowlist[i])):

        pts = rs.AddPoint(rowlist[i][j])

       

       

for i in range (0,len(norlist)):

    for j in range (0,len(norlist[i])):

        norpts = rs.AddPoint(norlist[i][j])

       

attpt = rs.GetPoint ("attractor point",1)

ratio = 0.02

for i in range (0,len(rowlist)-1):

    for j in range (0,len(rowlist[i])-1):

        rs.AddLine(rowlist[i][j],rowlist[i+1][j])

        rs.AddLine(rowlist[i+1][j],rowlist[i+1][j+1])

        rs.AddLine(rowlist[i+1][j+1],rowlist[i][j+1])

        rs.AddLine(rowlist[i][j+1],rowlist[i][j])

       

        vect = rs.VectorCreate(rowlist[i][j],rowlist[i+1][j])*(-1)

        dist = rs.Distance(rowlist[i][j],attpt)

        factor = dist*ratio

        scalevect = rs.VectorScale(vect,factor)

        pt1 = rs.VectorAdd(scalevect,rowlist[i][j])

        pt = rs.AddPoint(pt)

       

        vect = rs.VectorCreate(rowlist[i+1][j],rowlist[i+1][j+1])*(-1)

        dist = rs.Distance(rowlist[i+1][j],attpt)

        factor = dist*ratio

        scalevect = rs.VectorScale(vect,factor)

        pt2 = rs.VectorAdd(scalevect,rowlist[i+1][j])

        pt = rs.AddPoint(pt)

       

        vect = rs.VectorCreate(rowlist[i+1][j+1],rowlist[i][j+1])*(-1)

        dist = rs.Distance(rowlist[i+1][j+1],attpt)

        factor = dist*ratio

        scalevect = rs.VectorScale(vect,factor)

        pt3 = rs.VectorAdd(scalevect,rowlist[i+1][j+1])

        pt = rs.AddPoint(pt)

        

        vect = rs.VectorCreate(rowlist[i][j+1],rowlist[i][j])

        scalevect = rs.VectorScale(vect,0.2)

        pt4 = rs.VectorAdd(scalevect,rowlist[i][j+1])

        pt = rs.AddPoint(pt)

       

        l1 = rs.AddLine(pt1,pt2)

        l2 = rs.AddLine(pt2,pt3)

        l3 = rs.AddLine(pt3,pt4)

        l4 = rs.AddLine(pt4,pt1)

       

        l = rs.JoinCurves([l1,l2,l3,l4],delete_input=True, tolerance=None)

       

        rs.ExtrudeCurvePoint(l,(norlist[i][j]))

       

rs.EnableRedraw(True)