CONSTRUCTION AND GEOMETRIC PROPERTIES OF N-QUASI-BEZIER-CURVES WITH MULTIPLE PARAMETERS
Keywords:
Multiple shape parameters, Corner cutting algorithmAbstract
By using novel recurrence relation,we define a Quasi-Bernstein-basis of degree n with multi ple parameters, Next, tased on Quasi-Bernstein-basis, constructs n-Quasi-Bézier-curves (n-QB-curves) and systematically investigates their core geometric properties and computational methods. We propose an angle-cutting algorithm specifically designed for QB-curves, deriving the principles governing local shape adjustments and tension control through parameter manipulation. The length quantization method is established to analyze the curve approximation effect, and the proposed n-Quasi-Bézier-curves have better approximation performance than the traditional method.It is proved that the global or local shape modification of the joining curve can be achieved by adjusting the parameters when the polygon is fixed.The research shows that n-Quasi-Bézier-curves can approximate the control polygon without any degree increase, which has the characteristics of high efficiency and good shape control ability, and provides a new method and idea for the curve design in the field of geometric modeling.References
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