Hybrid Methods for Interactive Shape Manipulation

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Manipulating 2D and 3D shapes interactively is an important task in computer graphics. The challenge is to be able to induce a global change to the shape while preserving its local structure. A deformation tool accepts as an input a source shape as well as some user specified constraints that can be manipulated interactively. The amount of constraints provided by the user should be kept to minimum in order to make the tool intuitive to control. The required output is a shape that satisfies the imposed constraints, yet strives to preserve the character and the fine geometric details of the original shape.</p><p>In this work, we explore several techniques to achieve detail preserving shape deformation. We first provide an algorithm that combines an intrinsic representation of a surface (using differential coordinates) with a data-driven approach. The realism of the deformation is increased by incorporating example shapes that put the deformation into context, demonstrating characteristic deformations of the shape, such as bulging of muscles and appearance of folds for human or animal shapes.</p><p>We then turn over to a different approach which is fundamentally a space deformation technique. Space deformation deforms the ambient space rather than directly deforming the object and any object that is embedded in that space deforms accordingly as a byproduct. The main advantage of space deformation is that it is not limited to a particular geometric representation such as triangle meshes. A popular way to perform space deformation is to use barycentric coordinates, however, deformation with barycentric coordinates essentially destroys fine details of the shape. We extend the notion of barycentric coordinates in two dimensions to complex numbers. This generalization results in a hybrid approach that provides us the ability to obtain shape preservation with a space deformation framework.</p>