Polynomial Cauchy Coordinates for Curved Cages
DescriptionBarycentric coordinates are widely used in computer graphics, especially in shape deformation. Traditionally, barycentric coordinates are defined for polygonal domains. In this work, we relax this requirement by representing the boundary of the domain using a Bézier spline and extend the complex-valued Cauchy barycentric coordinates [Weber et al. 2009] to the Bézier case. Compared to the latest polynomial 2D Green coordinates [Michel and Thiery 2023], we obtain equivalent results. We further derive a numerical integration formula for the inverse mapping based on Cauchy's integral formula, enabling deformation between curved cages through an intermediate step. Notably, our approach allows curved cages as input. We also provide expressions for the nth-order derivatives of the coordinates, which facilitate constrained deformations with position constraints. Through extensive experiments, we demonstrate the versatility of our coordinates for interactive deformation.
Event Type
Technical Papers
TimeTuesday, 3 December 20249:00am - 12:00pm JST
LocationHall C, C Block, Level 4
