Smooth surface wrapping

A pure geometric optimization problem of a wrapping surface smoothly around a complex object, which in this example is a Stanford bunny.

Author: Armin Geiser

Kratos version: 9.0

Optimization Problem

Objective

• Shape update maximization

Constraints

• No penetration of packaging - bounding mesh (Standford bunny)

  

Optimization settings

• Algorithm type : gradient_projection
• Number of steps : 150
• Step size : 0.001
• Filter radius : 0.015
• Mesh motion : False

Results

Shape Evolution

The below image shows the shape evolution of the wrapping surface during the optimization iterations. The small sphere grows inside the bounding geometry. Using the relatively large filter radius, a smooth local optimum is found. Details smaller than the filter radius (e.g. the ears) are not captured.

Alternative problem setup

The bounding geometry of the Stanford bunny can be approached (wrapped) from the opposite site as well. For such a shrinking optimization we start from a large sphere. Compared to the example described above, the starting geometry is exchanged, the feasible side for the bounding geometry is switched and the objective is swtiched as well - see the setup in the shrink folder for details.