Design by optimization of curves and surfaces is a powerful design technique. The mathematical modeling of the design problem often results in a multi-objective optimization (MOO) problem which cannot be handled as such by traditional single objective optimization algorithms. Hence an evolutionary MOO algorithm is used to handle this case. The use of MOO algorithm enhances the design process by...

We present an algorithm for interactive display of trimmed NURBS surfaces. The algorithm converts the NURBS surfaces to B ezier surfaces, tessellates each trimmed B ezier surface into triangles and renders them using the triangle rendering capabilities common in current graphics systems. It makes use of tight bounds for uniform tessellation of B ezier surfaces into cells and traces the trimming...

We describe the structure and use of an interactive modeling and visualization tool used to help students understand various important concepts in curve and surface design. This paper describes those aspects of the tool related to NURBS curves, but Bezier and Hermite curves are also supported as are Bezier and B-Spline surfaces. The focus of this paper is almost exclusively on those features of...

Previous augmented reality displays have rendered crisp virtual walls and virtual objects with finger-surface reactions through haptics feedback devices. The widely used stiffness (or impedance) methods penalize a user’s intrusion into a virtual surface with a force response dependent on the amount of penetration along the contact normal at the virtual proxy location. We present an alternative ...

Extracting the human brain from magnetic resonance head scans is difficult because of its highly convoluted and nonuniform geometry. A technique based on Non-Uniform Rational B-Splines (NURBS) and energy minimising deformable models to extract the brain surface accurately from MR head scans is presented. The weighting parameter that comes with the NURBS definition is explored to attract the sur...

The shape of a NURBS curve or patch is defined by the location of its control points, the weights associated with these points, and the parameter intervals, also called the knot vector. Most of the curve and patch design methods assume that the knot vector is constant and the user is allowed to modify only the control points and the weights. The possibility of controlling the shape through the ...

This article presents a study of the application of Computational Intelligence (CI) methods to the problem of optimal surface reconstruction using triangulations and NURBS (Non-Uniform Rational BSplines) surface approximations on digitized point data. In mechanical engineering surface reconstructions are used to transform physical objects into mathematical representations for computer aided des...

We present algorithms for interactive rendering of largescale NURBS models. The algorithms convert the NURBS surfaces to Bézier surfaces, tessellate each Bézier surface into triangles and render them using the triangle-rendering capabilities common to current graphics systems. This paper presents algorithms for computing tight bounds on surface properties in order to generate high quality tesse...

To fill an N-sided hole on a NURBS surface and to blend a corner formed by NURBS surfaces, we propose a regular N-sided open uniform quadratic subdivision surface derived by applying the open uniform quadratic subdivision scheme to a regular N-sided control mesh which is confined to the hole or to the region of the vertex blend. Boundary conditions such as C and G-continuity required for the ho...

We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, lumenal surfaces are e...