TY - JOUR
T1 - Crossing knot lines in composition of freeform B-spline geometry
AU - van Sosin, Boris
AU - Elber, Gershon
N1 - Funding Information: This research was developed with funding from the Defense Advanced Research Projects Agency ( DARPA ), under contract HR0011-17-2-0028 . The views, opinions and/or findings expressed are those of the author and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.
PY - 2018/5
Y1 - 2018/5
N2 - Since the first publications on composition of splines (DeRose et al., 1993; Elber, 1992), it was clear that the composition, T(S), of a tensor product B-spline function S with another B-spline function T is no longer a tensor product B-spline if S crosses a knot line in the domain of T. The reason can be easily explained for the fact that the new function T(S) has a finite continuity that is governed by the knot line of T that is not, in general, an iso-parametric direction of the resulting composition T(S). In this work, we propose two approaches to circumvent this long standing difficulty and reconstruct precise representations for T(S) that are either tensor products or trimmed geometry. We focus our discussion on surface-trivariate compositions, T(S), while we present examples and results, for both reconstruction approaches, for microstructure surfaces and trivariates embedded in surface and trivariate deformation functions.
AB - Since the first publications on composition of splines (DeRose et al., 1993; Elber, 1992), it was clear that the composition, T(S), of a tensor product B-spline function S with another B-spline function T is no longer a tensor product B-spline if S crosses a knot line in the domain of T. The reason can be easily explained for the fact that the new function T(S) has a finite continuity that is governed by the knot line of T that is not, in general, an iso-parametric direction of the resulting composition T(S). In this work, we propose two approaches to circumvent this long standing difficulty and reconstruct precise representations for T(S) that are either tensor products or trimmed geometry. We focus our discussion on surface-trivariate compositions, T(S), while we present examples and results, for both reconstruction approaches, for microstructure surfaces and trivariates embedded in surface and trivariate deformation functions.
KW - B-spline surfaces
KW - B-spline trivariates
KW - Composition
KW - Trimmed surfaces
KW - Untrimming
UR - http://www.scopus.com/inward/record.url?scp=85044945057&partnerID=8YFLogxK
U2 - 10.1016/j.cagd.2018.03.009
DO - 10.1016/j.cagd.2018.03.009
M3 - مقالة
SN - 0167-8396
VL - 62
SP - 217
EP - 227
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
ER -