Surface Parametrizer

August 17, 2009 by Luigi Giaccari 
Filed under: Computational Geometry 
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Surface Parametrization

CIRCULARPARAMETRIZER:

[uv]=CircularParametrizer(t)

returns a set of 2D coordinates from a 3D triangulated surface. 2D points are disposed inside a circle of unit radius so they represent a parametrization of the initial surface.

The triangulation is represented by the n x 3 t array.

In t are stored the triangles of the initial surface with first point corresponding to index 1.

Triangulation requirements:

The triangulation must be manifold with only one boundary. The boundary of the surface will be the boundary of the parametric space.
With multiple boundaries errors maybe generated.

Algorithm informations:

The parametrization if perfomed using the Springs collapse method.
This ensure no self-intersecant triangles will be in the Output.

For examples see the demo file.

Infos:

Author: Giaccari Luigi, giaccariluigi@msn.com,
Created: 5/4/2009

See also DelaunayTri, voronoi, trimesh, trisurf, triplot, griddata, convhull,
dsearch, tsearch, delaunay3, delaunayn, qhull.

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Surface Parametrizer10.0101

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