Přejít k obsahu


Canal surfaces with rational contour curves and blends bypassing the obstacles

Citace:
BIZZARRI, M., LÁVIČKA, M., VRŠEK, J. Canal surfaces with rational contour curves and blends bypassing the obstacles. COMPUTER-AIDED DESIGN, 2015, roč. 64, č. July, s. 55-67. ISSN: 0010-4485
Druh: ČLÁNEK
Jazyk publikace: eng
Anglický název: Canal surfaces with rational contour curves and blends bypassing the obstacles
Rok vydání: 2015
Autoři: Mgr. Michal Bizzarri Ph.D. , Doc. RNDr. Miroslav Lávička Ph.D. , RNDr. Jan Vršek Ph.D. ,
Abstrakt EN: In this paper, we will present an algebraic condition, see (20), which guarantees that a canal surface, given by its rational medial axis transform (MAT), possesses rational generalized contours (i.e., contour curves with respect to a given viewpoint). The remaining computational problem of this approach is how to find the right viewpoint. The canal surfaces fulfilling this distinguished property are suitable for being taken as modeling primitives when some rational approximations of canal surfaces are required. Mainly, we will focus on the low-degree cases such as quadratic and cubic MATs that are especially useful for applications. To document a practical usefulness of the presented approach, we designed and implemented two simple algorithms for computing rational offset blends between two canal surfaces based on the contour method which do not need any further advanced formalism (as e.g. interpolations with MPH curves). A main advantage of the designed blending technique is its simplicity and also an adaptivity to choose a suitable blend satisfying certain constrains (avoiding obstacles, bypassing other objects, etc.). Compared to other similar methods, our approach requires only one SOS decomposition for the whole family of rational canal surfaces sharing the same silhouette, which significantly simplifies the computational complexity.
Klíčová slova

Zpět

Patička