Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Geometric control of G2-cubic A-splines
Computer Aided Geometric Design
G2 composite cubic Bézier curves
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
The singular point of an algebraic cubic
Applied Numerical Mathematics - Applied and computational mathematics: Selected papers of the third panamerican workshop Trujillo, Peru, 24-28 April 2000
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Let b0, b2,...,b2n be the vertex sequence of a convex polygon and through each b2j choose a line such that b2j-2 and b2j+2 lie on one of its sides, and let b2j+1 be the intersection point of line through b2j and b2j+2. For any choice q2j+1 of an interior point in each triangle b2jb2j+1b2j+2 we construct G2-cubic algebraic splines which interpolate the vertices b0,b2,...,b2n and the points q2j+1. At each b2j the spline is tangent to the prescribed line at this point and it is contained in the union of the triangles b2jb2j+1bj+2. For any j = 0, 1,....,n we show how the choice of q2j+1 limits the range of variation of the curvatures at the vertices b2j and b2j+2. We study the conditions for the curvatures at the specific vertices to vary arbitrarily, hence allowing for the construction of G2-interpolating cubic splines which are as flat or as sharp, as desired at these points. A generalization for nonconvex data sequences is given by breaking the polygon into maximal monotonically convex subsequences. The resulting spline has inflections at user controlled points.