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Isometric Piecewise Polynomial Curves
Author(s) -
Fiume Eugene
Publication year - 1995
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 - 10.1111/1467-8659.1410047
Subject(s) - arc length , piecewise , mathematics , polynomial , geometric design , hermite interpolation , family of curves , parametric equation , bézier curve , surface (topology) , hermite polynomials , parametrization (atmospheric modeling) , geometry , arc (geometry) , mathematical analysis , physics , quantum mechanics , radiative transfer
The main preoccupations of research in computer‐aided geometric design have been on shape‐specification techniques for polynomial curves and surfaces, and on the continuity between segments or patches. When modelling with such techniques, curves and surfaces can be compressed or expanded arbitrarily. There has been relatively little work on interacting with direct spatial properties of curves and surfaces, such as their arc length or surface area. As a first step, we derive families of parametric piecewise polynomial curves that satisfy various positional and tangential constraints together with arc‐length constraints. We call these curves isometric curves . A space curve is defined as a sequence of polynomial curve segments, each of which is defined by the familiar Hermite or Bézier constraints for cubic polynomials; as well, each segment is constrained to have a specified arc length. We demonstrate that this class of curves is attractive and stable. We also describe the numerical techniques used that are sufficient for achieving real time interaction with these curves on low‐end workstations.

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