Blob Metamorphosis based on Minkowski Sums

Abstract

This paper addresses the metamorphosis of soft objects built from skeletons. W e propose a new approach that may be split into three steps. The first step consists in an original splitting of the initial and the final shapes with a view to creating a bijective graph of correspondence. In the second step, we assume that the skeletons are convex polygonal shapes, and thus take advantage of the properties of Minkowski sums to characterize the skeletons of intermediate shapes. Eventually, we characterize the intermediate distance and field functions; we describe a set of interpolation methods and propose to use a restricted class of parametrized distance and field functions so as to preserve coherence and speed-up computations. W e show that we can easily extend those results to achieve a Bézier like metamorphosis where control points are replaced b y control soft objects; in this scope, we have adapted existing accelerated techniques that build a Bézier transformation from a set of convex polyhedra to any kind of convex polygonal shapes. Eventually, we point out that matching all components of the initial and the final shapes generates amorphous intermediate shapes based on an overwhelming number of intermediate sub-components. Thus, we propose heuristics with a view to preserving coherence during the transformation and accelerating computations. W e have implemented and tested our techniques in an experimental ray-tracer.

Interactive surface decomposition for polyhedral morphing

“…Chen et al [9] have produced 3D morphs of cylindrical images. Galin and Akkouche [16] have presented an algorithm for blob metamorphosis based on Minkowski sums. Lazarus and Verroust [28] have proposed a method based on skeletal curves.…”

Procedural Cloudscapes

“…Primitive‐based clouds can be animated using traditional key‐framing and particle systems [SSEH03]. Specific morphing algorithms [JLCLW*05,LJW06,LJWcH07, CMCM11] were proposed to animate clouds by creating a correspondence graph between the initial and final cloud models and generating a generic interpolating model as described in [GA96]. A fundamental problem of these approaches is that the time varying model produces trajectories that linearly interpolate the positions of the initial and final primitives, which yields unrealistic animations.…”

Implicit modeling by metamorphosis of 2d shapes

“…In the process of surface in-betweening the weighting function, in case of the source object, progressively increases from zero to one and, in case of the destination object, decreases from one to zero. The metamorphosis of soft-objects was studied later by Galin and Akkouche [Galin and Akkouche 1996]. Their approach was based on creation of a bijective graph of correspondence between carrier skeletons and then, using Minkowski sum, distance and field functions of intermediate shapes were characterized.…”