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Highlights from
Schwarz-Christoffel Toolbox

crrect(w,beta,cr,aff,Q,betar) CRRECT Graphically create a rectified map.
drawpoly(fig,cmd) DRAWPOLY Draw a polygon with the mouse.
modpoly(w,beta) MODPOLY Modify a polygon.
polyedit(varargin) POLYEDIT Polygon editor.
scgui(varargin) SCGUI Create graphical user interface for the SC Toolbox.
scselect(w,beta,m,titl,msg) SCSELECT Select one or more vertices in a polygon.
craffine(w,beta,cr,Q,tol) CRAFFINE Affine transformations for crossratio formulation.
crcdt(w,edge,triedge,edgetri) CRCDT Constrained Delaunay triangulation of a polygon.
crderiv(zp,beta,cr,aff,wcfix,... 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,cr,Q... CRGATHER Convert points into a single embedding in CR formulation.
crimap0(wp,z,beta,aff,qdat,op... CRIMAP0 Single-embedding inverse map in crossratio formulation.
crinvmap(wp,w,beta,cr,aff,wcf... CRINVMAP S-C disk inverse map in crossratio formulation.
crmap(zp,w,beta,cr,aff,wcfix,... 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.
crplot(w,beta,cr,aff,wcfix,Q,... CRPLOT Image of polar grid under disk map in crossratio form.
crqgraph(w,edge,triedge,edget... CRQGRAPH Quadrilateral graph of a triangulation.
crquad(z1,sing1,z,beta,qdat) CRQUAD (not intended for calling directly by the user)
crrderiv(zp,w,beta,wr,betar,c... CRRDERIV Derivative of the crossratio rectified map.
crrmap(zp,w,beta,wr,betar,cr,... CRRMAP Schwarz-Christoffel rectified map in crossratio formulation.
crrplot(w,beta,wr,betar,cr,af... 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.
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,scale,z,... Used by DEINVMAP for solution of an ODE.
deinvmap(wp,w,beta,z,c,qdat,z... 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.
deplot(w,beta,z,c,R,theta,opt... DEPLOT Image of polar grid under Schwarz-Christoffel exterior map.
dequad(z1,z2,sing1,z,beta,qda... 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,z,b... Used by DINVMAP for solution of an ODE.
dinvmap(wp,w,beta,z,c,qdat,z0... 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.
dplot(w,beta,z,c,R,theta,opti... DPLOT Image of polar grid under Schwarz-Christoffel disk map.
dquad(z1,z2,sing1,z,beta,qdat... DQUAD: Numerical quadrature for the disk map.
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.
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,scale,z,... Used by HPINVMAP for solution of an ODE.
hpinvmap(wp,w,beta,z,c,qdat,z... 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.
hpplot(w,beta,z,c,re,im,optio... 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.
moebius(z,w) MOEBIUS Moebius transformation parameters.
plotpoly(w,beta,number) PLOTPOLY Plot a (generalized) polygon.
plotptri(w,Q,lab) PLOTPTRI Plot a polygon triangulation.
ptsource(w,beta,z,c,ws,R,thet... 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,z,b... Used by RINVMAP for solution of an ODE.
rinvmap(wp,w,beta,z,c,L,qdat,... RINVMAP Schwarz-Christoffel rectangle inverse map.
rmap(zp,w,beta,z,c,L,qdat) RMAP Schwarz-Christoffel rectangle map.
rparam(w,beta,cnr,z0,options)... RPARAM Schwarz-Christoffel rectangle parameter problem.
rplot(w,beta,z,c,L,re,im,opti... RPLOT Image of cartesian grid under Schwarz-Christoffel rectangle map.
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,opti... RSPARAM Schwarz-Christoffel Riemann surface parameter problem.
rsplot(w,beta,z,zb,c,R,theta,... 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.
scinvopt(options) SCINVOPT Parameters used by S-C inverse-mapping routines.
scmapopt(varargin) SCMAPOPT Set options for SC maps.
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.
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,scale,z,... Used by STINVMAP for solution of an ODE.
stinvmap(wp,w,beta,z,c,qdat,z... STINVMAP Schwarz-Christoffel strip inverse map.
stmap(zp,w,beta,z,c,qdat) STMAP Schwarz-Christoffel strip map.
stparam(w,beta,ends,z0,option... STPARAM Schwarz-Christoffel strip parameter problem.
stplot(w,beta,z,c,re,im,optio... STPLOT Image of cartesian grid under Schwarz-Christoffel strip map.
stquad(z1,z2,sing1,z,beta,qda... STQUAD (not intended for calling directly by the user)
stquadh(z1,z2,sing1,z,beta,qd... 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.
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Schwarz-Christoffel Toolbox

by Toby Driscoll

12 Feb 2002 (Updated 18 May 2007)

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

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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)

Tags for This File
Everyone's Tags	conformal(2), laplaces equation(2), mapping, polygon
Tags I've Applied
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Comments and Ratings (10)
22 May 2003	Paolo Novati
27 Oct 2004	Francisco Tejo
29 Apr 2007	lv dc	3x, i need test it first.
26 Sep 2008	pepe sanchez	CANT FIND GOOD DOCUMENTATION ABOUT THIS SUBJECT, VERY POOR
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 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.
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.
22 May 2010	Izaak Beekman	Indispensable! Saved so much time using this rather than coding up everything in Fortran!
19 Nov 2010	Ali Afruzi
05 Sep 2011	Charles Nelatury

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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.
18 May 2007	Previous resubmission was missing critical files.

Tag Activity for this File
Tag	Applied By	Date/Time
conformal	Toby Driscoll	22 Oct 2008 06:40:53
mapping	Toby Driscoll	22 Oct 2008 06:40:53
laplaces equation	Toby Driscoll	22 Oct 2008 06:40:53
polygon	Toby Driscoll	22 Oct 2008 06:40:53
laplaces equation	Antonio Fortes	13 Sep 2011 10:20:59
conformal	Faleh Altal	30 Dec 2011 16:57:12

Highlights from Schwarz-Christoffel Toolbox

Schwarz-Christoffel Toolbox

Highlights from
Schwarz-Christoffel Toolbox