Abstract
Minkowski Pythagorean hodograph (MPH) curves provide a means for representing domains with rational boundaries via the medial axis transform. Based on the observation that MPH curves are not the only curves that yield rational envelopes, we define and study rational envelope (RE) curves that generalise MPH curves while maintaining the rationality of their associated envelopes.
To demonstrate the utility of RE curves, we design a simple interpolation algorithm using RE curves, which is in turn used to produce rational surface blends between canal surfaces. Additionally, we initiate the study of rational envelope surfaces as a surface analogy to RE curves. (C) 2016 Elsevier B.V. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 92-102 |
| Number of pages | 11 |
| Journal | Computer aided geometric design |
| Volume | 46 |
| DOIs | |
| Publication status | Published - Aug-2016 |
Keywords
- Rational envelope
- Pythagorean hodograph curve
- Medial axis
- MOS surface
- PYTHAGOREAN-HODOGRAPH CURVES
- G(1) HERMITE INTERPOLATION
- CANAL SURFACES
- CONTOUR CURVES
- PARAMETERIZATION
- QUINTICS
- CUBICS
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