与给定切线多边形相切的3次Bézier样条曲线

Cubic Bézier spline curve with given tangent polygon

讨论了与给定切线多边形相切的 3次Bzier样条曲线 .对于给定的切线多边形 ,在每条边上定义 1个切点及2个Bzier点 ,从而在 2个切点之间构造 2段 3次Bzier曲线 ,通过选取合适的调节参数λi,μi,ρi,3次Bzier曲线段是 2阶几何连续的 .此外 ,证明了该 3次Bzier样条曲线对切线多边形是保形的 。

In this paper, a planar piecewise cubic Bzier curve is discussed which has edges of a given polygons as tangents. For a given tangent polygon, a tangent point and two Bzier points are defined, two cubic Bzier curve segments are constructed. By choosing approarite adjustable parameters λ_i, μ_i, ρ_i, the cubic Bzier spline curve is C2-Continuous, which proves that the cubic Bzier spline curve is shape preserving to the given tangent polygon. The shape preserving spling curve has important role in the computer aided design for the cam.