k -curves
| Autor: | Zhipei Yan, Gregg D. Wilensky, Stephen N. Schiller, Nathan A. Carr, Scott Schaefer |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
020207 software engineering Center of curvature Geometry 02 engineering and technology Curvature Computer Graphics and Computer-Aided Design 020901 industrial engineering & automation Inflection point Fundamental theorem of curves Torsion of a curve Family of curves 0202 electrical engineering electronic engineering information engineering Vertex (curve) Total curvature Mathematics |
| Zdroj: | ACM Transactions on Graphics. 36:1-7 |
| ISSN: | 1557-7368 0730-0301 |
| DOI: | 10.1145/3072959.3073692 |
| Popis: | We present a method for constructing almost-everywhere curvature-continuous, piecewise-quadratic curves that interpolate a list of control points and have local maxima of curvature only at the control points. Our premise is that salient features of the curve should occur only at control points to avoid the creation of features unintended by the artist. While many artists prefer to use interpolated control points, the creation of artifacts, such as loops and cusps, away from control points has limited the use of these types of curves. By enforcing the maximum curvature property, loops and cusps cannot be created unless the artist intends for them to be. To create such curves, we focus on piecewise quadratic curves, which can have only one maximum curvature point. We provide a simple, iterative optimization that creates quadratic curves, one per interior control point, that meet with G 2 continuity everywhere except at inflection points of the curve where the curves are G 1 . Despite the nonlinear nature of curvature, our curves only obtain local maxima of the absolute value of curvature only at interpolated control points. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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