Highlights from
Schwarz-Christoffel Toolbox

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  • craffine(w,beta,cr,Q,tol)
    CRAFFINE Affine transformations for crossratio formulation.
  • crcdt(w,edge,triedge,edge...
    CRCDT Constrained Delaunay triangulation of a polygon.
  • crderiv(zp,beta,cr,aff,wc...
    CRDERIV Derivative of the disk map in crossratio formulation.
  • crembed(cr,Q,qnum)
    CREMBED Embed prevertices for given crossratios.
  • crfixwc(w,beta,cr,aff,Q,wc)
    CRFIXWC Fix conformal center in crossratio formulation.
  • crgather(u,uquad,quadnum,...
    CRGATHER Convert points into a single embedding in CR formulation.
  • crimap0(wp,z,beta,aff,qda...
    CRIMAP0 Single-embedding inverse map in crossratio formulation.
  • crinvmap(wp,w,beta,cr,aff...
    CRINVMAP S-C disk inverse map in crossratio formulation.
  • crmap(zp,w,beta,cr,aff,wc...
    CRMAP Schwarz-Christoffel disk map in crossratio formulation.
  • crmap0(zp,z,beta,aff,qdat)
    CRMAP Single-embedding map in crossratio formulation.
  • crossrat(w,Q)
    CROSSRAT Crossratios of a triangulated polygon.
  • crparam(w,beta,cr0,options)
    CRPARAM Crossratio parameter problem.
  • crpfun(x,fdat)
    CRPFUN (not intended for calling directly by the user)
  • crplot(w,beta,cr,aff,wcfi...
    CRPLOT Image of polar grid under disk map in crossratio form.
  • crpsdist(segment,pts)
    CRPSDIST Distance from point(s) to a line segment.
  • crqgraph(w,edge,triedge,e...
    CRQGRAPH Quadrilateral graph of a triangulation.
  • crquad(z1,sing1,z,beta,qd...
    CRQUAD (not intended for calling directly by the user)
  • crrderiv(zp,w,beta,wr,bet...
    CRRDERIV Derivative of the crossratio rectified map.
  • crrect(w,beta,cr,aff,Q,be...
    CRRECT Graphically create a rectified map.
  • crrmap(zp,w,beta,wr,betar...
    CRRMAP Schwarz-Christoffel rectified map in crossratio formulation.
  • crrplot(w,beta,wr,betar,c...
    CRRPLOT Image of cartesian grid under Schwarz-Christoffel rectified map.
  • crsplit(w)
    CRSPLIT Split polygon edges to ensure good crossratios.
  • crspread(u,quadnum,cr,Q)
    CRSPREAD Transform points to every embedding in CR formulation.
  • crtriang(w)
    CRTRIANG Triangulate a polygon.
  • dabsquad(z1,z2,sing1,z,be...
    DABSQUAD (not intended for calling directly by the user)
  • dderiv(zp,z,beta,c)
    DDERIV Derivative of the disk map.
  • ddisp(w,beta,z,c)
    DDISP Display results of Schwarz-Christoffel disk parameter problem.
  • dederiv(zp,z,beta,c)
    DEDERIV Derivative of the exterior map.
  • dedisp(w,beta,z,c)
    DEDISP Display results of Schwarz-Christoffel exterior parameter problem.
  • deimapfun(wp,yp,flag,scal...
    Used by DEINVMAP for solution of an ODE.
  • deinvmap(wp,w,beta,z,c,qd...
    DEINVMAP Schwarz-Christoffel exterior inverse map.
  • demap(zp,w,beta,z,c,qdat)
    DEMAP Schwarz-Christoffel exterior map.
  • deparam(w,beta,z0,options)
    DEPARAM Schwarz-Christoffel exterior parameter problem.
  • depfun(y,fdat)
    Returns residual for solution of nonlinear equations.
  • deplot(w,beta,z,c,R,theta...
    DEPLOT Image of polar grid under Schwarz-Christoffel exterior map.
  • dequad(z1,z2,sing1,z,beta...
    DEQUAD (not intended for calling directly by the user)
  • dfixwc(w,beta,z,c,wc,tol)
    DFIXWC Fix conformal center of disk map.
  • dimapfun(wp,yp,flag,scale...
    Used by DINVMAP for solution of an ODE.
  • dinvmap(wp,w,beta,z,c,qda...
    DINVMAP Schwarz-Christoffel disk inverse map.
  • disk2hp(w,beta,z,c)
    DISK2HP Convert solution from the disk to one from the half-plane.
  • dmap(zp,w,beta,z,c,qdat)
    DMAP Schwarz-Christoffel disk map.
  • dparam(w,beta,z0,options);
    DPARAM Schwarz-Christoffel disk parameter problem.
  • dpfun(y,fdat)
    Returns residual for solution of nonlinear equations.
  • dplot(w,beta,z,c,R,theta,...
    DPLOT Image of polar grid under Schwarz-Christoffel disk map.
  • dquad(z1,z2,sing1,z,beta,...
    DQUAD: Numerical quadrature for the disk map.
  • drawpoly(fig,cmd)
    DRAWPOLY Draw a polygon with the mouse.
  • ellipjc(u,L,flag)
    ELLIPJC Jacobi elliptic functions for complex argument.
  • ellipkkp(L)
    ELLIPKKP Complete elliptic integral of the first kind, with complement.
  • faber(M,m)
    FABER Faber polynomial coefficients for polygonal regions.
  • gaussj(n,alf,bet);
    GAUSSJ Nodes and weights for Gauss-Jacobi integration.
  • hp2disk(w,beta,z,c)
    HP2DISK Convert solution from the half-plane to one from the disk.
  • hpderiv(zp,z,beta,c)
    HPDERIV Derivative of the half-plane map.
  • hpdisp(w,beta,z,c)
    HPDISP Display results of Schwarz-Christoffel half-plane parameter problem.
  • hpimapfun(wp,yp,flag,scal...
    Used by HPINVMAP for solution of an ODE.
  • hpinvmap(wp,w,beta,z,c,qd...
    HPINVMAP Schwarz-Christoffel half-plane inverse map.
  • hpmap(zp,w,beta,z,c,qdat)
    HPMAP Schwarz-Christoffel half-plane map.
  • hpparam(w,beta,z0,options);
    HPPARAM Schwarz-Christoffel half-plane parameter problem.
  • hppfun(y,fdat)
    Returns residual for solution of nonlinear equations.
  • hpplot(w,beta,z,c,re,im,o...
    HPPLOT Image of cartesian grid under Schwarz-Christoffel half-plane map.
  • hpquad(z1,z2,varargin)
    HPQUAD (not intended for calling directly by the user)
  • isinpoly(z,w,beta,tol)
    ISINPOLY Identify points inside a polygon.
  • lapsolve(p,bdata)
    LAPSOLVE Solve Laplace's equation on a polygon.
  • lapsolvegui(varargin)
    LAPSOLVEGUI GUI implemtentation for lapsolvegui.fig.
  • linspace(d1, d2, n)
    LINSPACE Linearly spaced vector.
  • modpoly(w,beta)
    MODPOLY Modify a polygon.
  • moebius(z,w)
    MOEBIUS Moebius transformation parameters.
  • nebroyuf(A,xc,xp,fc,fp,sx...
  • nechdcmp(H,maxoffl)
  • neconest(M,M2)
    % This function is part of the Nonlinear Equations package, see NESOLVE.M.
  • nefdjac(fvec,fc,xc,sx,det...
    % This function is part of the Nonlinear Equations package, see NESOLVE.M.
  • nefn(xplus,SF,fvec,nofun,...
  • neinck(x0,F0,din,scale)
  • nemodel(fc,J,g,sf,sx,glob...
  • neqrdcmp(M)
  • neqrsolv(M,M1,M2,b)
  • nersolv(M,M2,b)
  • nesolve(fvec,x0,details,f...
    FSOLVE Solution to a system of nonlinear equations.
  • nesolvei(fvec,x0,details,...
    FSOLVEI Solution to nonlinear equations with no initial Jacobian.
  • nestop(xc,xp,F,Fnorm,g,sx...
  • parseopt(options)
    Copyright 1998--2001 by Toby Driscoll.
  • plotpoly(w,beta,number)
    PLOTPOLY Plot a (generalized) polygon.
  • plotptri(w,Q,lab)
    PLOTPTRI Plot a polygon triangulation.
  • polyedit(varargin)
    POLYEDIT Polygon editor.
  • ptsource(w,beta,z,c,ws,R,...
    PTSOURCE Field due to point source in a polygon.
  • r2strip(zp,z,L)
    R2STRIP Map from rectangle to strip.
  • rcorners(w,beta,z)
    RCORNERS (not intended for calling directly by the user)
  • rderiv(zp,z,beta,c,L,zs)
    RDERIV Derivative of the rectangle map.
  • rdisp(w,beta,z,c,L)
    RDISP Display results of Schwarz-Christoffel rectangle parameter problem.
  • rimapfun(wp,yp,flag,scale...
    Used by RINVMAP for solution of an ODE.
  • rinvmap(wp,w,beta,z,c,L,q...
    RINVMAP Schwarz-Christoffel rectangle inverse map.
  • rmap(zp,w,beta,z,c,L,qdat)
    RMAP Schwarz-Christoffel rectangle map.
  • rparam(w,beta,cnr,z0,opti...
    RPARAM Schwarz-Christoffel rectangle parameter problem.
  • rpfun(y,fdat)
    Returns residual for solution of nonlinear equations.
  • rplot(w,beta,z,c,L,re,im,...
    RPLOT Image of cartesian grid under Schwarz-Christoffel rectangle map.
  • rptrnsfm(y,cnr)
    RPTRNSFM (not intended for calling directly by the user)
  • rsderiv(zp,z,beta,zb,c)
    RSDERIV Derivative of the Riemann surface map.
  • rsmap(zp,w,beta,z,zb,c,qdat)
    RSMAP Schwarz-Christoffel Riemann surface map.
  • rsparam(w,beta,branch,z0,...
    RSPARAM Schwarz-Christoffel Riemann surface parameter problem.
  • rsplot(w,beta,z,zb,c,R,th...
    RSPLOT Image of polar grid under Schwarz-Christoffel RS map.
  • rsquad(z1,z2,varargin)
    RSQUAD (not intended for calling directly by the user)
  • scaddvtx(w,beta,pos,window)
    SCADDVTX Add a vertex to a polygon.
  • scangle(w)
    SCANGLE Turning angles of a polygon.
  • sccheck(type,w,beta,aux)
    SCCHECK Check polygon inputs to Schwarz-Christoffel functions.
  • scdemo
    SCDEMO Demonstrate the Schwarz-Christoffel Toolbox.
  • scfix(type,w,beta,aux)
    SCFIX Fix polygon to meet Schwarz-Christoffel toolbox constraints.
  • scgexprt(data)
    Export data to base workspace.
  • scgimprt(data)
    Import data from base workspace.
  • scgui(varargin)
    SCGUI Create graphical user interface for the SC Toolbox.
  • scimapz0(prefix,wp,w,beta...
    SCIMAPZ0 (not intended for calling directly by the user)
  • scinvopt(options)
    SCINVOPT Parameters used by S-C inverse-mapping routines.
  • scmapopt(varargin)
    SCMAPOPT Set options for SC maps.
  • scpadapt(zp,wp,minlen,max...
    SCPADAPT (not intended for calling directly by the user)
  • scparopt(varargin)
    SCPAROPT is defunct. Use SCMAPOPT instead.
  • scpltopt(options)
    SCPLTOPT Parameters used by S-C plotting routines.
  • scqdata(beta,nqpts);
    SCQDATA Gauss-Jacobi quadrature data for SC Toolbox.
  • scselect(w,beta,m,titl,msg)
    SCSELECT Select one or more vertices in a polygon.
  • slide=scdfaber
    This is a slideshow file for use with playshow.m and makeshow.m
  • slide=scdinf
    This is a slideshow file for use with playshow.m and makeshow.m
  • slide=scdlong
    This is a slideshow file for use with playshow.m and makeshow.m
  • slide=scdtutor
    This is a slideshow file for use with playshow.m and makeshow.m
  • stderiv(zp,z,beta,c,j)
    STDERIV Derivative of the strip map.
  • stdisp(w,beta,z,c)
    STDISP Display results of Schwarz-Christoffel strip parameter problem.
  • stimapfun(wp,yp,flag,scal...
    Used by STINVMAP for solution of an ODE.
  • stinvmap(wp,w,beta,z,c,qd...
    STINVMAP Schwarz-Christoffel strip inverse map.
  • stmap(zp,w,beta,z,c,qdat)
    STMAP Schwarz-Christoffel strip map.
  • stparam(w,beta,ends,z0,op...
    STPARAM Schwarz-Christoffel strip parameter problem.
  • stpfun(y,fdat)
    Returns residual for solution of nonlinear equations.
  • stplot(w,beta,z,c,re,im,o...
    STPLOT Image of cartesian grid under Schwarz-Christoffel strip map.
  • stquad(z1,z2,sing1,z,beta...
    STQUAD (not intended for calling directly by the user)
  • stquadh(z1,z2,sing1,z,bet...
    Copyright 1998 by Toby Driscoll.
  • composite(varargin)
    COMPOSITE Form a composition of maps.
  • crdiskmap(poly,varargin)
    CRDISKMAP Schwarz-Christoffel cross-ratio disk map object.
  • crrectmap(poly,varargin)
    CRRECTMAP Schwarz-Christoffel cross-ratio disk map object.
  • diskmap(varargin)
    DISKMAP Schwarz-Christoffel disk map object.
  • extermap(varargin)
    EXTERMAP Schwarz-Christoffel exterior map object.
  • hplmap(varargin)
    HPLMAP Schwarz-Christoffel half-plane map object.
  • moebius(varargin)
    MOEBIUS Moebius transformation.
  • polygon(x,y,alpha)
    POLYGON Contruct polygon object.
  • rectmap(poly,varargin)
    RECTMAP Schwarz-Christoffel rectangle map object.
  • riesurfmap(varargin)
    RIESURFMAP Schwarz-Christoffel map to Riemann surface.
  • scmap(poly,opt)
    SCMAP Construct generic Schwarz-Christoffel map object.
  • scmapdiff(f)
    SCMAPDIFF Derivative of a Schwarz-Christoffel map.
  • scmapinv(M)
    SCMAPINV Inverse of a Schwarz-Christoffel map.
  • stripmap(poly,varargin)
    STRIPMAP Schwarz-Christoffel strip map object.
  • Contents.m
    Schwarz-Christoffel Toolbox
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Schwarz-Christoffel Toolbox

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12 Feb 2002 (Updated )

Computes conformal maps to polygons, allowing easy solution of Laplace's equation.

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File Information
Description

The Schwarz-Christoffel transformation is a recipe for a conformal map to a region bounded by a polygon. They can be computed to very high accuracy in little time. These maps can make certain Laplace boundary value problems trivial to solve on such domains.
Example:
p = polygon([0 i -1+i -1-i 1-i 1]); % L-shaped region
f = diskmap(p); % find map
plot(f) % visualize it
phi = lapsolve(p,[1 nan 4 3 nan 2]); % solve a BVP
[t,x,y] = triangulate(p);
trisurf(t,x,y,phi(x+i*y)); % see it

MATLAB release MATLAB 7.4 (R2007a)
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Comments and Ratings (13)
12 Jul 2014 Boughrara kamel

there are not many documentation

14 Mar 2012 Samina Kosar

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i am interested to draw like this in SC-Toolbox, can anyone help me in this regards, the example explained about is for bounded polygon, could you please describe the same map for my figer. please dont take it as dashes, its line two lines having angle 90 degree.

03 Mar 2012 Anton Semechko

This implementation saved me a bunch of time. Thanks a lot!

P.S. - Any one who needs documentation for this toolbox can find it on Toby's website (http://www.math.udel.edu/~driscoll/software/SC/guide.pdf)

05 Sep 2011 Charles Nelatury  
19 Nov 2010 Ali Afruzi  
22 May 2010 Izaak Beekman

Indispensable! Saved so much time using this rather than coding up everything in Fortran!

02 Feb 2009 Boughrara kamel

I have sent to you an example to the polygone where i have severe crowding. Could you give me answer and your opignon.

26 Jan 2009 Boughrara kamel

I have used the toolbox and it is excellent.
I have some problems with crowding for some polygon.
I will send you the polygon where i have the problem.

08 Oct 2008 Al van Deursen

I used the software on many instances and found its results in excellent agreement with practical experiments. Wrote a few scientific papers using the results.
Documentation on Driscoll's personal webpage was more than sufficient for somebody with knowledge in basic calculus and Schwarz - Christoffel analysis.

26 Sep 2008 pepe sanchez

CANT FIND GOOD DOCUMENTATION ABOUT THIS SUBJECT, VERY POOR

29 Apr 2007 lv dc

3x, i need test it first.

27 Oct 2004 Francisco Tejo  
22 May 2003 Paolo Novati  
Updates
29 May 2002

Minor bug fixes. No enhancements.

09 Dec 2002

Changes for compatability with MATLAB 6.5.

New routine for solving Laplace's equation.

09 May 2003

Changes for compatability with MATLAB 6.5.

New routine for solving Laplace's equation.

16 May 2007

Fixes an incompatibility (bug?) with matlab release 2007a.

28 May 2014

Now accessing the Github repository.

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