Dynamic surfaces

 
 

Evolution along a surface

Gradient descent, Levenberg-Macquart methods, etc... See Numerical Recipes in C, chap 10 and p. 683-688
 
 

Evolution of a surface

Physics, finite elements.

Equations and forces are defined on each part of the surface.
 

Reference book: John Oprea, Differential Geometry and its applications, Prentice Hall, 1997
 

Euler-Lagrange equations

Two approaches : Lagrange particle-oriented  -vs-  Euler fixed point in space-oriented.

Euler-Lagrange equations (variational principle): p.257

Further reading: Pontryagin Maximum Principle p.297.

Applications : level sets, snakes, physical simulation

Demo: surface Evolver.
 

3D surfaces to get 2D properties : Level Sets methods (transition)
 
 
 

Eric Amram, Feb 1998, MIT 6.838 Advanced Topics in Computer Graphics - Prof. Seth Teller.