Warping as a modelling tool for CSG/implicit models

Abstract

Free form deformations are useful for describing a class of complex motions within an animation system. Such deformations have been described using a generalization of parametric surfaces and their application to modeling is well documented. In this paper we present a method that can be applied to implicit sulfaces which are dejined as an iso-surjuce around U set of skeletal elements. The resulting surface is approximated by a polygon mesh. Shape distortions, such as "squash and stretch" are applied automatically to models in motion by warping the space in which the models exist. A model will change its shape as the function dejining the warped space can change over time ol; the model will deform as it moves through the warped space. Our system also treats groups of skeletal implicit primitives as CSG primitives. Warping can also be applied to these primitives. Different warp functions, for example bend, taper and twist can be applied locally or globally, the contribution from each primitive is calculated using a set of warp functions associated with that primitive. The interesting shapes, and possibly non-linear motion obtained from space warping, would be dificult to reproduce using other techniques.

Warp-based helical implicit primitives

“…An alternative solution for getting complex analytical implicit primitives, first used in [WO97], is to warp simpler implicit primitives through a transformation such as Barr's bend, twist or taper [Bar84]. As we shall see, these transformations do not preserve the circular quality of the normal cross-section of the primitive (see Figure 10, first row), and thus cannot be applied as is for our purpose.…”

WarpCurves: A tool for explicit manipulation of implicit surfaces

“…Early work adapted the Barr deformations [2] for several implicit representations such as the function-representation (FRep) [21], skeletal implicit surfaces [38], and the BlobTree [37]. The work of Wyvill and van Overveld [38] also presented deformation fields suitable for animation, such as those which squash or stretch implicit models as they pass through the field. A variational warp was applied to implicit surfaces in [24] and this technique was incorporated into a general framework for FRep deformations called extended space mapping [23].…”

“…Furthermore, unlike with point-based surfaces the "reverse" deformation is required [38], and should be very efficient to compute if it is to be used in interactive contexts. Several space warp techniques have been developed for implicit surfaces [21,38,23,28], but these cannot be easily adapted to the task of surface manipulation. Recently Sugihara et al [33] described a space deformer based on a curve handle which can approximate small surface deformations, but no attempt is made to have the surface explicitly track the curve.…”

Generic deformable implicit mesh models for automated reconstruction

“…A popular way to deform implicit surfaces is to twist, bend, and taper the space in which the model lives by choosing a suitable warping function [4,2,34]. However, these deformations are limited to parametric surfaces, such as spheres or cylinders, and there is no way to warp the space in a free form manner.…”