TY - JOUR
T1 - Modeling by composition
AU - Elber, Gershon
AU - Kim, Myung Soo
N1 - Funding Information: The research leading to these results has received partial funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement PIAP-GA-2011-286426 , and was supported in part by the Technion Vice President for Research Fund — Glasberg–Klein research fund , and also in part by NRF Research Grants (No. 2013R1A1A2010085 ).
PY - 2014
Y1 - 2014
N2 - Functional composition can be computed efficiently, robustly, and precisely over polynomials and piecewise polynomials represented in the Bézier and B-spline forms (DeRose et al., 1993) [13], (Elber, 1992) [3], (Liu and Mann, 1997) [14]. Nevertheless, the applications of functional composition in geometric modeling have been quite limited. In this work, as a testimony to the value of functional composition, we first recall simple applications to curve-curve and curve-surface composition, and then more extensively explore the surface-surface composition (SSC) in geometric modeling. We demonstrate the great potential of functional composition using several non-trivial examples of the SSC operator, in geometric modeling applications: blending by composition, untrimming by composition, and surface distance bounds by composition.
AB - Functional composition can be computed efficiently, robustly, and precisely over polynomials and piecewise polynomials represented in the Bézier and B-spline forms (DeRose et al., 1993) [13], (Elber, 1992) [3], (Liu and Mann, 1997) [14]. Nevertheless, the applications of functional composition in geometric modeling have been quite limited. In this work, as a testimony to the value of functional composition, we first recall simple applications to curve-curve and curve-surface composition, and then more extensively explore the surface-surface composition (SSC) in geometric modeling. We demonstrate the great potential of functional composition using several non-trivial examples of the SSC operator, in geometric modeling applications: blending by composition, untrimming by composition, and surface distance bounds by composition.
KW - Blending
KW - Freeform deformations
KW - Hausdorff distance
KW - Rounding
KW - Symbolic computation
UR - http://www.scopus.com/inward/record.url?scp=84887479244&partnerID=8YFLogxK
U2 - 10.1016/j.cad.2013.08.032
DO - 10.1016/j.cad.2013.08.032
M3 - مقالة
SN - 0010-4485
VL - 46
SP - 200
EP - 204
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
IS - 1
ER -