Hodographs and normals of rational curves and surfaces
نویسندگان
چکیده
Derivatives and normals of rational Bézier curves and surface patches are discussed. A nonuniformly scaled hodograph of a degree m × n tensor-product rational surface, which provides correct derivative direction but not magnitude, can be written as a degree (2m−2) × 2n or 2m× (2n−2) vector function in polynomial Bézier form. Likewise, the scaled normal direction is degree (3m−2)× (3n−2). Efficient methods are developed for bounding these directions and the derivative magnitude.
منابع مشابه
Pii: S0010-4485(00)00091-9
Applications of rational BeÂzier curves or surfaces often require the computation of derivatives. Even though there are several algorithms or representations for the derivatives of rational BeÂzier curves or surfaces, their advantages and disadvantages have not been explicitly discussed from the viewpoint of computational requirements. This paper presents the representation of the hodographs of...
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ورودعنوان ژورنال:
- Computer Aided Geometric Design
دوره 12 شماره
صفحات -
تاریخ انتشار 1995