Name
Abstract | ||
|---|---|---|
We consider the design of parametric curves from geometric constraints such as distance from lines or points and tangency to lines or circles. We solve the Hermite problem with such additional geometric constraints. We use a family of curves with linearly varying normals, LN curves. The nonlinear equations that arise can be of algebraic degree 60. We solve them using the GPU on commodity graphics cards and achieve interactive performance. The family of curves considered has the additional property that the convolution of two curves in the family is again a curve in the family, assuming common Gauss maps, making the class more useful to applications. Further, we consider valid ranges in which the line tangency constraint can be imposed without the curve segment becoming singular. Finally, we remark on the larger class of LN curves and how it relates to Bezier curves. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.cagd.2011.06.009 | Computer Aided Geometric Design |
Keywords | Field | DocType |
hermite problem,constraint-based ln curve,parametric curve,additional property,geometric constraint,curve segment,additional geometric constraint,larger class,bezier curve,line tangency constraint,ln curve,gpu programming,convolution | Applied mathematics,Mathematical optimization,Parametric equation,Family of curves,Nonlinear system,Convolution,Hermite polynomials,Tangent,Bézier curve,Geometric design,Mathematics | Journal |
Volume | Issue | ISSN |
29 | 1 | 0167-8396 |
Citations | PageRank | References |
2 | 0.37 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Young Joon Ahn | 1 | 91 | 11.01 |
| Christoph Hoffmann | 2 | 2 | 0.37 |