DiagVol: Multi-block Bézier Volume Modeling from Prescribed Diagonal Surface Pairs

In this paper, we present a novel method called DiagVol to construct C1 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 C1 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 C1 continuity. Experimental results are given to illustrate the modeling flexibility and simulation effects of the presented approach.