Arc-length-based axial deformation and length preserved animation

Abstract

In real life, some objects may deform along axial curves and the lengths of their skeletons usually remain constant during the axial deformation, such as a swimming fish, a swaying tree, etc. This paper presents a practical approach of arc-length-based axial deformation and axial-length-preserved animation. The space spanned by the arc-length parameter and the rotation-minimizing frame on the axis is taken as the embedding space. During animation, the keyframe axial curves are consistently approximated by polylines after sufficient subdivisions and both the edge lengths and the directional vertex angles of the keyframe polylines (or unit edge vectors) are then interpolated to generate the intermediate polylines which are regarded as the discrete expressions of the intermediate axes. Experiments show that our method is very useful, intuitive and easy to control.