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- W2389072790 abstract "A set of third degree polynomial basis functions with two parameters are presented.They are not only the extension of quadratic Bernstein basis functions,but also the extension of quadratic uniform B-spline basis functions.The quality of the new basis function is analyzed.Then based on the new basis,the cubic polynomial curve with two shape parameters is defined.The new curve holds more abundant geometrical qualities than the cubic Bezier curve and the cubic uniform B-spline curve.Meanwhile,the shape of the new curve can be adjusted.When choosing special shape parameters,a set of open curves approximating to its control polygon can be gained,or a set of closed curves can be gotten.In addition,the new curve can degenerate to a point or a line segment.Thus it expresses three geometric elements uniformly with one expression.The geometrical meaning of the shape parameters is analyzed,and the drawing of the curve in geometry is given.The continuity condition of the curve is also discussed." @default.
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- W2389072790 date "2009-01-01" @default.
- W2389072790 modified "2023-09-28" @default.
- W2389072790 title "Cubic polynomial curve with two shape parameters" @default.
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