Skeleton-based three-dimensional geometric morphing

Morphing Three Dimensional Polyhedral Objects

Three Dimensional Strain Field Morphing

In this paper, we present a new technique for 3D shape morphing using strain fields. Strain is an important geometric quantity used in mechanics to describe the deformation extent of objects. We use it to analyze and control deformation in morphing. Using the position vector field, the strain field between source and target shapes can be obtain. This strain field is then interpolated between ze...

Geometric Details on Skeleton-based Implicit Surfaces

We present a modeling technique to enhance implicit surfaces with procedural geometric details. The details are based on Gabor noise, which enables us to seamlessly handle anisotropy. The orientation of details can be defined with respect to the orientation of the main shape features, which reduces the amount of user input. The method extends to complex details that are tilted with respect to t...

Two-Dimensional Discrete Morphing

In this article we present an algorithm for discrete object deformation. This algorithm is a first step for computing an average shape between two discrete objects and may be used for building a statistical atlas of shapes. The method we develop is based on discrete operators and works only on digital data. We do not compute continuous approximations of objects so that we have neither approxima...

Three-Dimensional Projective Geometry with Geometric Algebra

The line geometric model of 3-D projective geometry has the nice property that the Lie algebra sl(4) of 3-D projective transformations is isomorphic to the bivector algebra of Cl(3, 3), and line geometry is closely related to the classical screw theory for 3-D rigid-body motions. The canonical homomorphism from SL(4) to Spin(3, 3) is not satisfying because it is not surjective, and the projecti...