Multi-sided surfaces are important in several areas of Computer-Aided Geometric Design, including curve network based design, approximation of triangular meshes, hole filling, and so on. In the majority of surface representations, the boundary constraints entirely determine the interior of these patches, however, frequently there is a need to have additional design freedom for shaping the surfa...

We consider, from an algebro-geometric perspective, the problem of determining the dimension of the space of bivariate and trivariate piecewise polynomial functions (or splines) defined on triangular and tetrahedral partitions. Classical splines on planar rectangular grids play an important role in Computer Aided Geometric Design, and splines spaces over arbitrary subdivisions of planar domains...

Biirger, H. and R. Schaback, A parallel multistage method for surface/surface intersection, Computer Aided Geometric Design 10 (1993) 277-291. A global divide-and-conquer method and a local marching method are combined into a massively parallel algorithm for surface/surface intersection. Special attention is given to the comparison of bounding boxes and to the safe and efficient calculation of ...

In the nineties, several methods for dealing in a more efficient way with the implicitization of rational parametrizations were explored in the Computer Aided Geometric Design Community. The analysis of the validity of these techniques has been a fruitful ground for Commutative Algebraists and Algebraic Geometers, and several results have been obtained so far. Yet, a lot of research is still be...

Constructing N -sided surface patches to fill holes plays an important role in Computer Aided Geometric Design. In this paper, we present a method to construct a single toric surface patch interpolating N -sided boundary curves. The control points of the patch are determined by the given boundary curves and energy optimization. The main advantage of the method is that the toric surface patch ca...

We study the Plateau problem restricted to polynomial surfaces using techniques coming from the theory of Computer Aided Geometric Design. The results can be used to obtain polynomial approximations to minimal surfaces. The relationship between harmonic Bézier surfaces and minimal surfaces with free boundaries is shown.

Shaded display is popular for displaying curved surfaces because of the realistic appearance of the images produced. In the eld of computer aided geometric design, however, line drawings are more commonly used. For accurate evaluation of the curved surfaces in these designs, the conventional method of approximating curved surfaces with polygons is insu cient. In this paper we will present a met...

In this work, we develop a framework based on piecewise Bézier curves to plane shapes deformation and we apply it to shape optimization problems. We describe a general setting and some general result to reduce the study of a shape optimization problem to a finite dimensional problem of integration of a special type of vector field. We show a practical problem where this approach leads to effici...

SMART, Solid Modeling Aerospace Research Tool, isthe Vehicle AnalysisBranch of NASA Langley Research Center's computer-aided design tool used in aerospace vehicledesign. Modeling of structuralcomponents using SMART includes the representationof the transverseor cross-wiseelements of a vehicle'sfuselage,ringframes and bulkheads. Ringframes are placed along a vehicle'sfuselage to provide structur...

Aimed at an audience of researchers and graduate students in computational geometry and algorithm design, this book uses the Geometric Spanner Network Problem to showcase a number of useful algorithmic techniques, data structure strategies, and geometric analysis techniques with many applications, practical and theoretical. The authors present rigorous descriptions of the main algorithms and th...