Continuous-resolution-level constraints in variational design of multiresolution shapes

• Published in: The Visual Computer Vol. 14; no. 4; pp. 177 - 192
• Main Authors: Takahashi, Shigeo, Shinagawa, Yoshihisa, Kunii, Tosiyasu L.
• Format: Journal Article
• Language: English; Japanese
• Published: Heidelberg Springer Science and Business Media LLC 09.10.1998; Springer Nature B.V
• ISSN: 0178-2789; 1432-2315
• DOI: 10.1007/s003710050133

This paper introduces continuous-resolution-level constraints to hierarchical editing of curves and surfaces based on B-spline wavelets. The constraints specify the shape at a continuous-resolution level by interpolating those at integer-resolution levels. Energy functions subject to the shape deformations are used to control the smoothness of the curves and surfaces. This paper proposes two interpolation schemes for the continuous-level shapes: linear interpolation and cardinal-spline interpolation. The continuous-level shape is obtained as a transformation of that at an integer-resolution level, and the continuous-level constraints are reduced to those at integer-resolution levels. Experimental results are presented to show that the continuous-level constraints effectively control the multiresolution curves and surfaces.