# Conversion b/n parameterizations

Hi!

I have the following geometric problem. The parameterisation of a surface is given in the UxV domain. I have another surface in the parameter domain SxT. I have also some (u,v),(s,t) pairs. How may i find a general map form UxV to SxT such that it satisfies f(u,v) = (s,t) for all (most) of the given pairs. (I need to find a point on surface S(SxT) corresonding to the point of surface S(UxV).) Has OCC any function for this task. Or has anyone any tip how and where to start?

Thanks. Hello Ernst,
I am not clear what you are trying to do. Are these surfaces interacting, e.g.intersecting? or are you thinking about some datum (reference) for your mapping? uv data can mean anything in the parametric space of a surface unless you think about some reference for model space I have the U/V space of the surface and i have the S/T space of the texture. I also have some corresponding point b/n surface and texture. (u,v) - (s,t) pairs) I need texture coordinates for the generated triangle vertices. I know there exists such algorithms.

(ex. Bruno L´evy - "Constrained Texture Mapping for Polygonal Meshes"
or "Constrained Minimum Distortion Parameterization" as referenced in Mark Pauly - Point Primitives for Interactive Modeling and Processing of 3D Geometry) Dear Ernest,

in general you have to ask which kind of mapping you want to use.
Some time ago I have seen a publication about this (in german) called patterns on free form surfaces (Muster auf Freiformflächen, Klaus Seifart, Dresden, Techn. Univ., 1995)

If you consider a linear mapping just imagine two parallel planes (e.g. z=1 and z=2) and mark the given point in them (i.e. (u1,v1,1), (s1,t1,2),... ).
A linear mapping would be a central projection (or parallel in some cases).
If you intersect the lines defined by ((u1,v1),(s1,t1)) , ((u2,v2), (s2,t2)),... they should intersect in the center of the projection (or in infinity if parallel).
To get the scaling factor you just have to divide the distances of the center. 