Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Computing the convolution and the Minkowski sum of surfaces
Proceedings of the 21st spring conference on Computer graphics
Convolution surfaces of quadratic triangular Bézier surfaces
Computer Aided Geometric Design
Computer-Aided Design
Proceedings of the 2010 ACM Symposium on Applied Computing
Hermite interpolation by hypocycloids and epicycloids with rational offsets
Computer Aided Geometric Design
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
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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.