N-sided Surface Generation from Arbitrary Boundary Edges
Abstract
This paper discusses a general theory and an implementation method for generating a surface patch with concave edges, holes, ridges and valleys in CAD/CAM applications. The surface generation method, which has been proposed to create an N-sided patch with holes, is first reviewed. Such surfaces are generally classified as transfinite surfaces, in which a surface is interpolated to span given curves. In the proposed method, each boundary edge defined in a two-dimensional domain has an appropriate blending function. The function is defined so that the derivatives are 0 on the edges, and the function values are 1 on one edge and 0 on the other edges, and each edge in the three-dimensional space is blended smoothly. A revised method is also introduced in this paper. The previously proposed method has some problems in that a surface may not be generated appropriately for concave edges, and the surface has to be manipulated manually if it has holes. This causes distortion and overlap in mapping from a 2D domain into 3D space. In the new method, the blending function is revised, and the boundary edges in the 2D domain are obtained from the edges in the 3D space beforehand. Thus, it is shown that an N-sided patch with concave edges, holes, ridges and valleys can be suitably generated.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2000
- Accession Number
- ADP012027
Entities
People
- Kiyotaka Kato
Organizations
- Mitsubishi Electric