Nadler. E., Nonnegativity of bivariate quadratic functions on a triangle. Computer Aided Geometric Design 9 (1992) 19.5-205. A necessary and sufficient condition for the nonnegativity of a bivariate quadratic defined on a triangle is presented in terms of the Bernstein-Bkzier form of the function. Keywfords. Nonnegativity, bivariate quadratic function, Bernstein-BCzier form, positiviry preservi...

Engineering designs are often determined by functional considerations, yet modeled with purely geometric parameters. Because of this, a difficult part of a design engineer’s job is tracking how changes to the geometric model might alter the functional performance of the design. This paper proposes a design interface that uses temporary functional views of geometric models to augment design engi...

This paper shows how to construct a rational Bezier model of a swept surface that interpolates N frames (i.e., N position/orientation pairs) of a fixed rational space curve c(s) and maintains the shape of the curve at all intermediate points of the sweep. Thus, the surface models an exact sweep of the curve, consistent with the given data. The primary novelty of the method is that this exact mo...

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and th...

nalyzing and interrogating designed surfaces remains an important and widely researched issue in computer-aided geometric design (CAGD). Treating families of characteristic curves— such as contour lines, lines of curvature, asymptotic lines, isophotes, and reflection lines—on the surface proves a popular method of doing this. All these curves have something in common: s They reflect the surface...

A method for subdividing polygonal complexes and identifying conditions to control their limit curves is presented. A polygonal complex is a sequence of panels where every two adjacent panels share one edge only. We formulate this problem and establish a general theory which has a number of applications in CAGD such as the generation of subdivision surfaces through predefined arbitrary network ...

In this paper we introduce an intermediate representation of surfaces that we call semi-implicit. We give a general definition in the language of projective complex algebraic geometry, and we begin its systematic study with an effective view point. Our last section will apply this representation to investigate the intersection of two bi-cubic surfaces, these surfaces are widely used in Computer...

An information model is presented that supports sharing of design definition data between the designs of completely configured variants within a product family. Design data sharing is supported across many levels of a design’s product structure hierarchy: A change in one subassembly component does not force the whole subassembly to be duplicated. This is achieved for completely configured model...

This is the manuscript for talks given in a seminar on computer aided geometric design at the University of Saarland. The aim of the talks was to introduce the basic concepts of algebraic geometry, the computational tools, i.e. resultants and Groebner bases, and their geometric applications.