﻿ David Brander - Math Software

## Matlab Functions

Below is a list of some implementations of the DPW method for computing solutions of integrable surfaces. Most of these are given here in two versions: one as a standard Matlab function that should work on any installation of Matlab; and another that uses some C++ mex functions (thanks to Peter Nørtoft), that need to be compiled first (see the readme file). The latter are roughly twice as fast.

The function WdpwB for Willmore surfaces is easy to use, even without any knowledge of the theory. The functions K1surf and ksurf are also quite easy to use to compute solutions directly from the curvature and torsion functions of given space curves.

1. WdpwB- A numerical implementation of the solution of the generalization of Björling's problem for Willmore surfaces. Instructions on how to use it are here: Computing Willmore Surfaces. Code updated 12-11-2014.
Download: WdpwB.zip (for any Matlab installation)
(faster version with c++ mex functions here).
2. K1surf - Computes spherical surfaces (constant Gauss curvature 1 surfaces in Euclidean space) from loop group potentials. Functions for solving the geometric Cauchy problem for these surfaces are included. How to use: Computing CMC and spherical surfaces. Code updated 04-09-2015.
Download: K1surf.zip (for any Matlab installation)
3. ecmch - Computes CMC surfaces using the DPW method. Read this Computing CMC and spherical surfaces for instructions on how to use it. Code updated: 04-09-2015.
Download: ecmch.zip (for any Matlab installation)
(faster version here).
4. ksurf - Computes pseudospherical surfaces from loop group potentials. There is also a function for solving one case of the Geometric Cauchy problem for these surfaces, and functions for constructing surfaces with prescribed singular curves. How to: Computing pseudospherical surfaces. Code updated 17-02-2015.
Download: ksurf.zip (for any Matlab installation)
(faster version here).
5. ksphere - Computes constant curvature surfaces in the 3-sphere using the DPW method. The way to use it is quite similar to ksurf (see above). There is a screenshot here. Code updated 13-11-2014.
Download: ksphere.m (for any Matlab installation)
(faster version here).
6. Elastic curves: some code for designing with elastic curves, developed with collaborators, can be found on GitHub here: DigitalFactory