Deforming 3D Shapes by Bending and Twisting a Virtual Ribbon with Both Hands

Abstract

Bender is an interactive tool for bending and warping triangulated surfaces. The designer uses a virtual ribbon to grab a portion of the shape and to deform it through direct manipulation. The ribbon is defined by its centerline-a wire made of two smoothly joined circular arcs-and by its twist-the continuous field of normal directions along the wire. The wire and the twist are controlled by a Polhemus tracker in each hand. The deformation model is based on a new formulation of a 3D space warp that uses screw-motions to map coordinate systems aligned with the initial ribbon to corresponding coordinate systems aligned with the final ribbon. Circular biarcs are easy to control and permit the correct handling of situations where a vertex is influenced by different sections of the wire. Screw-motions define smoother and more intuitive warps than other formulations. The combination significantly extends the editing capabilities of previously proposed shape deformation tools and produces smooth and predictable results for configurations where the radius of the tubular region of influence around the ribbon does not exceed the radii of the arcs.