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Rational bi‐cubic G 2 splines for design with basic shapes
Author(s) -
Karčiauskas Kȩstutis,
Peters Jörg
Publication year - 2011
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2011.02013.x
Subject(s) - curvature , geometric design , box spline , computer science , cubic surface , cubic function , cubic form , mathematics , pure mathematics , geometry , algebra over a field , spline interpolation , bilinear interpolation , computer vision
The paper develops a rational bi‐cubic G 2 (curvature continuous) analogue of the non‐uniform polynomial C 2 cubic B‐spline paradigm. These rational splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, in one by default smoothly‐connected structure. The versatility of this new tool for processing exact geometry is illustrated by conceptual design from basic shapes.