Jacobians and Hessians of Mean Value Coordinates for Closed Triangular Meshes

TL;DR

This paper derives formulas for the derivatives of Mean Value Coordinates transformations, enabling precise deformation control of interior objects within a closed triangular mesh cage.

Contribution

It provides explicit derivative formulas for Mean Value Coordinates, enhancing deformation accuracy and computational understanding for mesh-based modeling.

Findings

Derived explicit formulas for derivatives of Mean Value Coordinates.

Improved understanding of deformation behavior in mesh-based models.

Facilitated more precise and controllable mesh deformations.

Abstract

In this technical note, we present the formulae of the derivatives of the Mean Value Coordinates based transformations, using an enclosing triangle mesh, acting as a cage for the deformation of an interior object.