TY - JOUR
T1 - A second-order algorithm for curve orthogonal projection onto parametric surface
AU - Xu, Hai-Yin
AU - Fang, Xiongbing
AU - Tam, Hon-Yuen
AU - Wu, Xiaofeng
AU - Hu, Li'an
PY - 2012/1/1
Y1 - 2012/1/1
N2 - Repeated use of point projection to find the projection of a curve on a surface is rather inefficient as the iteration procedures in point projection is typically slow. A novel curve projection scheme is proposed for computing the orthogonal projection of a progenitor curve onto a parametric surface. Under this scheme, the projection curve is parameterized using the parameter of the progenitor curve. Differential geometric characteristics of the projection curve are analysed. A marching method with error adjustment is used to calculate the projection curve. Several examples are presented and comparisons are made to demonstrate the effectiveness of the proposed scheme. © 2012 Copyright Taylor and Francis Group, LLC.
AB - Repeated use of point projection to find the projection of a curve on a surface is rather inefficient as the iteration procedures in point projection is typically slow. A novel curve projection scheme is proposed for computing the orthogonal projection of a progenitor curve onto a parametric surface. Under this scheme, the projection curve is parameterized using the parameter of the progenitor curve. Differential geometric characteristics of the projection curve are analysed. A marching method with error adjustment is used to calculate the projection curve. Several examples are presented and comparisons are made to demonstrate the effectiveness of the proposed scheme. © 2012 Copyright Taylor and Francis Group, LLC.
KW - curve projection
KW - error adjustment
KW - marching
KW - parametric surface
KW - Taylor approximation
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84863125215&origin=recordpage
U2 - 10.1080/00207160.2011.628385
DO - 10.1080/00207160.2011.628385
M3 - 21_Publication in refereed journal
VL - 89
SP - 98
EP - 111
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
SN - 0020-7160
IS - 1
ER -