TY - JOUR
T1 - Rational ruled surfaces and their offsets
AU - Pottmann, Helmut
AU - Lü, Wei
AU - Ravani, Bahram
N1 - Funding Information:
This work has been supported in part by the Austrian Science Foundation through Project P09790-MAT. The second author is grateful for a research fellowship by the Austrian Academic Exchange Service and acknowledges support from the Doctoral Science Foundation and National Defense Science Foundation of China.
PY - 1996/11
Y1 - 1996/11
N2 - In this paper, geometric design problems for rational ruled surfaces are studied. We investigate a line geometric control structure and its connection to the standard tensor product B-spline representation, the use of the Klein model of line space, and algorithms for geometry processing. The main part of the paper is devoted to both classical and "circular" offsets of rational ruled surfaces. These surfaces arise in NC milling. Excluding developable surfaces and, for circular offsets, certain conoidal ruled surfaces, we show that both offset types of rational ruled surfaces are rational. In particular, we describe simple tool paths which are rational quartics.
AB - In this paper, geometric design problems for rational ruled surfaces are studied. We investigate a line geometric control structure and its connection to the standard tensor product B-spline representation, the use of the Klein model of line space, and algorithms for geometry processing. The main part of the paper is devoted to both classical and "circular" offsets of rational ruled surfaces. These surfaces arise in NC milling. Excluding developable surfaces and, for circular offsets, certain conoidal ruled surfaces, we show that both offset types of rational ruled surfaces are rational. In particular, we describe simple tool paths which are rational quartics.
UR - http://www.scopus.com/inward/record.url?scp=0030283637&partnerID=8YFLogxK
U2 - 10.1006/gmip.1996.0045
DO - 10.1006/gmip.1996.0045
M3 - Article
AN - SCOPUS:0030283637
SN - 1077-3169
VL - 58
SP - 544
EP - 552
JO - Graphical Models and Image Processing
JF - Graphical Models and Image Processing
IS - 6
ER -