【摘要】 把Bézier曲线的离散公式推广到区间Bézier曲线,并提出区间控制多边形的概念,证明了离散不断进行时,区间控制多边形收敛到原区间Bézier曲线.这里的离散公式可以增加控制顶点的数目,便于更加灵活地对这些区间曲线作形状控制.由离散公式和离散的收敛性可得到一种简洁有效的区间Bézier曲线的几何作图方法.更多还原

【Abstract】 The subdivision formula for Bézier curves is generalized to interval Bézier curves. The definition of interval control polygon is given and it is proved that the interval control polygon converges to the original interval Bézier curve as the curve subdivides incessantly. By subdivision a new control polygon can be obtained which has more interval control points and more flexibility in controlling its shape. Also an efficient geometric method is provided to generate an interval Bézier curve.更多还原