三维转动的四元数表述

用四元数表达三维的旋转与使用矩阵相比具有两个优点：第一．几何意义明确；第二，计算简单．因此，四元数在数学、物理学和计算机图形学中具有很高的应用价值．本文详细叙述了四元数的这一功能，讨论了四元数的定义、运算、性质、几何意义和它的3种表达形式，给出了使用四元数处理点的各种几何变换的一般结论．

Three dimensional rotation represented by quaternion

Three dimensional rotation represented by quaternion has two advantages over that by matrix: first, the geometric meaning is definitude; second, computation is easy. The application of quaternion to mathematics, physics and computer graphics is significant. The definition, operation, properties, geometric meaning of quaternion and its three expressions are discussed. It is also demonstrated how to use quaternion to transform points.