Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Polynomial/rational approximation of Minkowski sum boundary curves
Graphical Models and Image Processing
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
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
Rational surfaces with linear normals and their convolutions with rational surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
Geometric constraints on quadratic Bézier curves using minimal length and energy
Journal of Computational and Applied Mathematics
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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, over the parameter interval [0, u]. 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. We also remark on the larger class of LN curves and how it relates to Bézier curves.