A concise parametrisation of affine transformation

TL;DR

This paper introduces a new parametrisation of affine transformations that improves upon existing methods, enhancing performance in applications like shape analysis and animation, with a practical C++ implementation provided.

Contribution

It proposes a novel affine transformation parametrisation that generalizes and improves existing methods, offering better performance and additional options.

Findings

Shows improved performance in shape and motion applications

Provides a flexible and general affine parametrisation

Includes a ready-to-use C++ implementation

Abstract

Good parametrisations of affine transformations are essential to interpolation, deformation, and analysis of shape, motion, and animation. It has been one of the central research topics in computer graphics. However, there is no single perfect method and each one has both advantages and disadvantages. In this paper, we propose a novel parametrisation of affine transformations, which is a generalisation to or an improvement of existing methods. Our method adds yet another choice to the existing toolbox and shows better performance in some applications. A C++ implementation is available to make our framework ready to use in various applications.