Matrix animation and polar decomposition
Ken Shoemake, Tom Duff · 1992
General 3×3 linear or 4×4 homogenous matrices can be formed by composing primitive matrices for translation, rotation, scale, shear, and perspective. Current 3-D computer graphics systems manipulate and interpolate parametric forms of these primitives to generate scenes and motion. For this and other reasons, decomposing a composite matrix in a meaningful way has been a longstanding challenge. This paper presents a theory and method for doing so, proposing that the central issue is rotation extraction, and that the best way to do that is Polar Decomposition. This method also is useful for renormalizing a rotation matrix containing excessive error. Résumé Des matrices correspondant à des transformations linéaires en 3 dimensions, ou bien à des transformations homogènes en 4 dimensions, peuvent être construites en composant des matrices qui décrivent des transformations élémentaires: déplacement, rotation, homothétie, glissement, et perspective. Les systèmes actuels de visualisation grap...