Shape Editing Research Articles

Blowing Bubbles for Multi-Scale Analysis and Decomposition of Triangle Meshes

Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression and simplification of three-dimensional shapes. Different features, such as flats, limbs, tips, pits and various blending shapes that transition between them, may be characterized in terms of local curvature and other differential properties of the surface or in terms of a global skeletal organization of the volume it encloses. Unfortunately, both solutions are extremely sensitive to small perturbations in surface smoothness and to quantization effects when they operate on triangulated surfaces. Thus, we propose a multi-resolution approach, which not only estimates the curvature of a vertex over neighborhoods of variable size, but also takes into account the topology of the surface in that neighborhood. Our approach is based on blowing a spherical bubble at each vertex and studying how the intersection of that bubble with the surface evolves. We describe an efficient approach for computing these characteristics for a sampled set of bubble radii and for using them to identify features, based on easily formulated filters, that may capture the needs of a particular application.

Approximating digital 3D shapes by rational Gaussian surfaces

A method for approximating spherical topology digital shapes by rational Gaussian (RaG) surfaces is presented. Points in a shape are parametrized by approximating the shape with a triangular mesh, determining parameter coordinates at mesh vertices, and finding parameter coordinates at shape points from interpolation of parameter coordinates at mesh vertices. Knowing the locations and parameter coordinates of the shape points, the control points of a RaG surface are determined to approximate the shape with a required accuracy. The process starts from a small set of control points and gradually increases the control points until the error between the surface and the digital shape reduces to a required tolerance. Both triangulation and surface approximation proceed from coarse to fine. Therefore, the method is particularly suitable for multiresolution creation and transmission of digital shapes over the Internet. Application of the proposed method in editing of 3D shapes is demonstrated.

Rational bicubic simple quadrilateral mesh surfaces

In free-form modeling a closed smooth piecewise surface is highly desirable when the smoothness across the boundaries of patches can be represented within the formulation. Closed, smooth, piecewise bicubic surfaces, defined on simple quadrilateral mesh. (SQM), may be defined as SQM surfaces. We have extended previous work on SQM surfaces and described the surface representation in rational form. The global constraint of the control parameters associated with each control vertex is relaxed. The new local shape-control parameters with their larger range of usability further enhance the power of this free-form surface design scheme. We have also provided more B-spline functions. A complete set of B-spline functions for various topologies of the SQM is now available. Examples demonstrate that editing of shapes for reasonably complex objects can be carried out on an SGI Personal Iris machine at an interactive rate.