Polyhedral subdivision methods for free-form surfaces
ACM Transactions on Graphics (TOG)
Including shape handles in recursive subdivision surfaces
Computer Aided Geometric Design
Surface interpolation on irregular networks with normal conditions
Computer Aided Geometric Design
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
An introduction to genetic algorithms
An introduction to genetic algorithms
Interpolation over Arbitrary Topology Meshes Using a Two-Phase Subdivision Scheme
IEEE Transactions on Visualization and Computer Graphics
| Hi-index | 0.00 |
This paper considers the problems of how to introduce shape parameters into recursive subdivision schemes for additional shape control and how to find appropriate values of shape parameters to improve the quality of subdivision surface shapes. Following Brunet, we restrict our discussion to the algorithm that constructs a Doo-Sabin subdivision surface to interpolate the vertices of an input polyhedron with arbitrary topology. While Brunet defined one so-called "shape handle" for each vertex of the initial polyhedron, which is used to scale the type-V face obtained after the first step of the subdivision process, we introduce three shape parameters for each vertex: one for the scale and the other two for the orientation of the type-V face. This gives more degrees of freedom to optimize the shape of the result interpolatory surface. We develop a genetic algorithm to compute the optimal set of shape parameters such that a "fairness" measure of the surface is minimized. Examples are provided to demonstrate the effects of the optimal shape parameters on the final interpolatory surfaces.