A Survey of Spatial Deformation from a User-Centered Perspective
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A Survey of Spatial Deformation from a User-Centered Perspective James Gain University of Cape Town and Dominique Bechmann LSIIT, University of Strasbourg
The spatial deformation methods are a family of modeling and animation techniques for indirectly reshaping an object by warping the surrounding space, with results that are similar to molding a highly malleable substance. They have the virtue of being computationally efficient (and hence interactive) and applicable to a variety of object representations. In this paper we survey the state of the art in spatial deformation. Since manipulating ambient space directly is infeasible, deformations are controlled by tools of varying dimension - points, curves, surfaces and volumes - and it is on this basis that we classify them. Unlike previous surveys that concentrate on providing a single underlying mathematical formalism, we use the user-centered criteria of versatility, ease of use, efficiency and correctness to compare techniques. Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric Algorithms General Terms: Algorithms, Human factors, Performance Additional Key Words and Phrases: Free-Form Deformation, Spatial Deformation, Warping
1.
INTRODUCTION
Spatial deformations, first introduced by Barr [1984] and Sederberg and Parry [1986], deform an object by warping its ambient space. While this may at first seem convoluted and indirect, it has some considerable advantages: spatial deformations, because they operate on points sampled from an object, are independent of the underlying representation of the embedded object; by controlling the size and shape of the ambient space it is possible to control the scope of the deformation making it local or global, as required; unlike physical simulations (such as mass-spring, finite element and boundary element methods) spatial deformation bypasses complex intra-object interactions with consequent efficiency benefits. In short, spatial deformations are a class of highly interactive, powerful and intuitive modeling techniques. Spatial deformation can be formulated as a mapping F :
