Abstract: A new subdivision algorithm for the n order uniform B-spline curves is presented, through the relations between the subdivision mask for B-splines and Pascal’ triangle and control vertexes’ geometric position relations in subdividing. Then the other one subdivision scheme for uniform B-splines curves of odd degree with interpolatory restriction is constructed according to the new subdivision algorithm, which can adjust its part shape. It is valid modeling in modifying the local shape through theory and is the example for the subdivision scheme.

Key words: subdivision algorithm, uniform B-spline, interpolatory restriction

摘要： 利用 次均匀B样条细分的掩模与Pascal三角形关系，并借助控制多边形在每次加细过程中新旧控制顶点对应的几何位置关系，给出一种新的 次均匀B样条曲线细分算法，基于该算法构造出带有形状参数的局部插值约束的奇次均匀B样条细分曲线。通过理论和算例说明，该算法几何直观性强、新旧点对应明确、应用灵活且能保持良好的参数连续性。

关键词: 细分算法, 均匀B样条, 插值约束

CLC Number: 

• TP391.72