On the injectivity of mean value mappings between quadrilaterals

TL;DR

This paper proves that mean value coordinate mappings between quadrilaterals are injective when the target quadrilateral is convex, ensuring reliable and non-overlapping transformations in computer graphics.

Contribution

It establishes the injectivity condition for mean value coordinate mappings specifically between quadrilaterals with convex targets, advancing geometric mapping theory.

Findings

Mean value coordinate mappings are injective for convex quadrilaterals.

The result guarantees non-overlapping mappings in graphics applications.

Provides theoretical foundation for reliable polygon transformations.

Abstract

Mean value coordinates can be used to map one polygon into another, with application to computer graphics and curve and surface modelling. In this paper we show that if the polygons are quadrilaterals, and if the target quadrilateral is convex, then the mapping is injective.