DiagVol: Multi-block Bézier Volume Modeling from Prescribed Diagonal Surface Pairs. (March 2023) - Li, Xiaowei; Hu, Qinghua; Xu, Gang; Qi, Long; Wu, Haiyan; Pang, Yufei
Abstract: In this paper, we present a novel method called DiagVol to construct C 1 continuous multi-block Bézier volumes from N pairs of prescribed diagonal surfaces. The explicit expression of the diagonal surface pair (DSP) is first formulated, and the necessary and sufficient conditions for the pair of diagonal surfaces which can be the DSP of a Bézier volume are derived. The conditions for the DSPs with C 1 continuity of the adjacent blocks are also presented. We can obtain new multi-block volume shapes by modifying the first block and the DSPs of other blocks, and volume morphing and deformation applications are given to show the modeling flexibility of DiagVol. Moreover, an approach to construct energy-minimizing single-block from the prescribed DSP is presented by introducing the Dirichlet energy and strain energy, which is further extended for the construction of multi-block Bézier volumes with C 1 continuity. Experimental results are given to illustrate the modeling flexibility and simulation effects of the presented approach. Highlights: Explicit formulation of the diagonal surface pair of Bézier volume is presented. Necessary and sufficient conditions for two Bézier surfaces being the DSP of a Bézier volume are given. A method to construct a Bézier volume from a prescribed diagonal surface pair is proposed. An approach to construct C 1 continuous multi-block Bézier volumes from given DSPs is presented.