Many textiles do not noticeably stretch under their own weight. Unfortunately, for better performance many cloth solvers disregard this fact. We propose a method to obtain very low strain along the warp and weft direction using Constrained Lagrangian Mechanics and a novel fast projection method. The resulting algorithm acts as a velocity filter that easily integrates into existing simulation code.

This paper presents a method for constructing composite surfaces based on a collection of quadrilateral patches. A global parameterization using bilinear quadrilateral meshes and FEM like minimization procedure are introduced. Smoothing conditions such as C1 and G1 are handled by constraint equation and a related duality argument is implemented. The surfaces that can be constructed in this way include conforming and non‐conforming connections (3 n 6, T‐nodes) between elementary patches. Non‐manifold surfaces are automatically treated also by this data structure. The underlying quadratic programming with linear constraints is solved by duality methods. Hierarchical data structure with bordering matrices methods are implemented to deal with local refinement (subdivision). The present work details the actual implementation for the case of Bézier patches.

The theory of optimal control is introduced as a new approach for handling curve fitting and design problems. Optimal control provides a uniform formal framework for stating and solving multiple problems in computer-aided geometric design (CAGD). As a result, new classes of curves are defined and known problems are analyzed from a new viewpoint. Often, families of curves which are defined by a minimization problem rely on parameters. Such problems are an appropriate base for handling curve fitting and design by optimal control methods. The methods suit a wide variety of problems. They are demonstrated on three applications of curve fitting and design: smoothing /spl nu/-splines, smoothing interpolating splines and approximating curves. All the applications are treated and solved using the uniform framework. The solution technique is based on the relaxation method.

A new method for surface reconstruction from an initial triangular mesh is introduced. The method transforms the mesh to a quadrilateral one and then builds a smooth surface on top of it. This approach is efficient for large collections of triangular patches, including difficult situations such as sharp junctions and n-patch vertices. During the reconstruction process, the number of mesh elements is considerably reduced. The possibility of parallel computation makes the method efficient in practice. The method is illustrated by building several free-form surfaces from a triangular mesh.

In this work, a new method for mesh simplification and surface reconstruction specifically designed for the needs of CAD/CAM engineering design and analysis is introduced. The method simplifies the original free-form face model by first constructing restricted curvature deviation regions, generating a boundary conforming finite element quadrilateral mesh of the regions, and then fitting a smooth surface over the quadrilateral mesh using the plate energy method. It is more general in scope than existing methods because it handles models with free-form faces and non-manifold geometry, not just triangular or polygonal faces. It produces a high-quality quadrilateral mesh which is suited for both finite element analysis and CAD/CAM. The smooth surface obtained by energy functional stabilization over limited curvature regions preserves the number of quadrilateral elements, and is best suited for surface modeling. The method is illustrated by building of several free-form surfaces from an arbitrary topology mesh.

Abstract Piecewise Bézier Curves are constructed using a minimization principle. Ck and GCk continuity is imposed by linear constraints. The corresponding quadratic programming with linear constraints problem is introduced and solved by duality methods. Bordering matrices methods are implemented to deal with local refinement (subdivision). The result is a versatile tool for defining/editing contours made of piecewise Bézier curves.

Some important trends in geometric modeling are the reliance on solid models rather than surface-based models and the enhancement of the expressive power of models, by using free-form objects in addition to the usual geometric primitives and by incorporating physical principles. An additional trend is the emphasis on interactive performance. In this paper, we integrate all of these requirements into a single geometric primitive by endowing the tri-variate tensor-product free-form solid with several important physical properties, including volume and internal deformation energy. Volume preservation is of benefit in several application areas of geometric modeling, including computer animation, industrial design and mechanical engineering. However, previous physics-based methods, which have usually used some form of "energy", have neglected the issue of volume (or area) preservation. We present a novel method for modeling an object composed of several tensor-product solids while preserving the desired volume of each primitive and ensuring high-order continuity constraints between the primitives. The method utilizes the Uzawa algorithm for non-linear optimization, with objective functions based on deformation energy or least squares. We show how the algorithm can be used in an interactive environment by relaxing exactness requirements while the user interactively manipulates free-form solid primitives. On current workstations, the algorithm runs in real-time for tri-quadratic volumes and close to real-time for tri-cubic volumes.