Paul Borrel

Multi-resolution 3D approximations for rendering complex scenes

We present a simple, effective, and efficient technique for approximating arbitrary polyhedra. It is based on triangulation and vertex-clustering, and produces a series of 3D approximations (also called “levels of detail”) that resemble the original object from all viewpoints, but contain an increasingly smaller number of faces and vertices. The simplification is more efficient than competing techniques because it does not require building and maintaining a topological adjacency graph. Furthermore, it is better suited for mechanical CAD models which often exhibit patterns of small features, because it automatically groups and simplifies features that are geometrically close, but need not be topologically close or even part of a single connected component Using a lower level of detail when displaying small, distant, or background objects improves graphic performance without a significant loss of perceptual information, and thus enables realtime inspection of complex scenes or a convenient environment for animation or walkthrough preview.

Simple constrained deformations for geometric modeling and interactive design

Deformations are a powerful tool for shape modeling and design. We present a new model for producing controlled spatial deformations, which we term Simple Constrained Deformations (Scodef). The user defines a set of constraint points, giving a desired displacement and radius of influence for each. Each constraint point determines a local B-spline basis function centered at the constraint point, falling to zero for points beyond the radius. The deformed image of any point in space is a blend of these basis functions, using a projection matrix computed to satisfy the constraints. The deformation operates on the whole space regardless of the representation of the objects embedded inside the space. The constraints directly influence the final shape of the deformed objects, and this shape can be fine-tuned by adjusting the radius of influence of each constraint point. The computations required by the technique can be done very efficiently, and real-time interactive deformation editing on current workstations is possible.

Deformation of n-dimensional objects

This paper presents deformations that Paul Borrel and Dominique Bechmann Interactive Geometric Modeling IBM Research Division Thomas J. Watson Research Center P.O. Box 704 Yorktown Heights, NY 10598 a new technique for computing space interpolate a set of user-defined constraints. Deformations” are represented by a polynomial mapping from N’ to R“. Constraints are specified by indicating the images of selected points. The deformation is formulated as the product of a polynomial function ~ of 0?” into a higher-dimensional space, Rm, with a linear projection from R“ back to U?”. The projection matrix is computed using a pseudo-inverse technique so as to satisfy all constraints when m is suflicient!y large and to provide a least-square optimal solution when m is too small given the number of specified constraints. For sutlicient m, the additional degrees of freedom may be used to optimize potential functions controlled by attracting and repulsing points of R“. A prototype implementation is presented, whtch demonstrates the application of this technique to the interactive design of free-form shapes (when n = 3) and of deformation processes in space-time domain (when n = 4). For graphic purposes, the deformation is simply applied to the vertices of a triangulation of the object’s faces. Greater control of the deformation is achieved by using a B -spline basis for the imbedding, rather than a power basis. Permission to copy without fee atl or part of this material is granted provided that the copies arc not made or distributed for direct cormnercird advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machine~. To copy otherwise, or to republish, requires a fee and/or specific permission.

DEFORMATION OF N-DIMENSIONAL OBJECTS

This paper presents a new technique for computing space deformations that interpolate a set of user-defined constraints. Constraints are specified by indicating the images of selected points. The deformation is formulated as the product of a polynomial function f of ℝn into a higher-dimensional space, ℝm, with a linear projection from ℝm back to ℝn. The projection matrix is computed using a pseudo-inverse technique. For sufficient m, the degrees of freedom may be used to optimize potential functions controlled by attracting and repulsing points. A prototype implementation is presented, which demonstrates the application of this technique to the interactive design of free-form shapes (when n=3) and of deformation processes in space-time domain (when n=4).

BRUSH as a Walkthrough System for Architectural Models

Brush provides an interactive environment for the real-time visualization and inspection of very large mechanical and architectural CAD databases. It supports immersive and non-immersive virtual reality walkthrough applications (for example, when validating or demonstrating to a customer an architectural concept) and detailed design reviews of complex mechanical assemblies such as engines, plants, airplanes, or ships.