DiagPara: Volumetric parameterization with energy-minimizing pair of diagonal surfaces from given boundaries

Abstract

An efficient approach for constructing volumetric parameterization with internal energy-minimizing pair of diagonal surfaces from given boundaries is presented. The expression for the internal energy of one diagonal surface pair is formulated. Then necessary and sufficient conditions for trivariate tensor-product Bézier volume with minimal internal energy of the diagonal surface pair are derived. From the derived conditions, an efficient construction algorithm for single- and multi-block Bézier volumes with minimal diagonal internal energy by the Lagrange multiplier method is presented. The auxiliary linear system only needs to be solved once. As soon the explicit computation masks are obtained, the interior control points of the volume are then directly calculated. Experimental results are given to illustrate the volumetric parameterization effects of the presented approach.