Surface approximation of point clouds by using multiquadric functions

The following literature provides the easiest way to generate a surface that approximates a given point set.

Only the limitation found in this approach is that the generated surface becomes a height field, i.e. it is always of the form z=f(x,y).

[1] R. L. Hardy, “Multiquadric equations of topography and other irregular surfaces,” J. Geophys. Res., vol. 76, no. 8, pp. 1905–1915, Mar. 1971.

import rhinoscriptsyntax as rs import Rhino.Geometry as rg import math func=lambda xi,xj,yi,yj:math.sqrt(((xj-xi)**2)+((yj-yi)**2)+x) A=rg.Matrix(len(pnts),len(pnts)) z=rg.Matrix(len(pnts),1) for i in range(len(pnts)): for j in range(len(pnts)): pi=pnts[i] pj=pnts[j] A[i,j]=func(pi.X,pj.X,pi.Y,pj.Y) z[i,0]=pi.Z A.Invert(0.0) #this parameter should be 0.0 c=A*z a=list() for srf in srfs: domU=srf.Domain(0) domV=srf.Domain(1) for i in rs.frange(0,1,0.05): for j in rs.frange(0,1,0.05): u=domU[0]+i*(domU[1]-domU[0]) v=domV[0]+j*(domV[1]-domV[0]) (b,P,A)=srf.Evaluate(u,v,0) z=0 for j in range(len(pnts)): z=z+c[j,0]*func(P.X,pnts[j].X,P.Y,pnts[j].Y) newP=rg.Point3d(P.X,P.Y,z) a.append(newP) newSrf=rs.AddSrfPtGrid((20,20),a) newSrf = rg.NurbsSurface.CreateFromPoints(a, 20, 20, 3, 3) a=list() a.append(newSrf)

page revision: 5, last edited: 23 Nov 2014 10:05