Abstract
Skeleton curves and surfaces have many applications in computer aided design and analysis. Construction of skeletons is an active area of research. We consider the inverse problem that of recovering boundary surfaces from given skeleton elements. The skeleton of any 3D object will, in general, consist of curves and surfaces. Therefore, any boundary reconstruction algorithm must systematically process the surfaces generated by the skeletal curves and the skeletal surfaces. In this paper (Part I) we present algorithms for reconstructing boundary surfaces corresponding to skeletal curves. Implemented examples are also included. In a companion paper (Part II) we consider skeletal elements that are surfaces.
The S-λ model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S-λ curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G1 connection of S-λ curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S-λ basis functions, the conditions of G1 geometric continuity between two adjacent S-λ curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S-λ curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system.
Abstract
Skeleton curves and surfaces have many applications in computer aided design and analysis and the construction of skeletons has been an active area of research. We consider the inverse problem that of recovering boundary surfaces from given skeleton elements. The skeleton of any 3D object will, in general, consist of curves and surfaces. Therefore, any boundary reconstruction algorithm must systematically process the surfaces generated by the skeletal curves and the skeletal surfaces. In a companion paper (Part I) we considered the reconstruction of boundaries corresponding to skeletal curves. In this paper (Part II) we consider the reconstruction of boundaries corresponding to skeletal elements that are surfaces. Implemented examples are also included.
This paper is to provide literature review of the Non Uniform Rational B-Splines (NURBS) formulation in the curve and surface constructions. NURBS curves and surfaces have a wide application in Computer Aided Geometry Design (CAGD), Computer Aided Design (CAD), image processing and etc. The formulation of NURBS showing that NURBS curves and surfaces requires three important parameters in controlling the curve and also modifying the shape of the curves and surfaces. Yet, curves and surfaces fitting are still the major problems in the geometrical modeling. With this, the researches that have been conducted in optimizing the parameters in order to construct the intended curves and surfaces are highlighted in this paper.
Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces