一类带三个形状参数的三角曲面

Triangular surface with three shape parameters

为在控制顶点固定的情况下仍然能够调整三角曲面的外形,将三个形状参数引入多项式基函数中,从而得到一类新的三角曲面。这类三角曲面具有几何不变性、仿射不变性、凸包性、对称性、表示唯一性、角点插值性和角点切平面性等特点,是三角Bézier曲面的扩展。形状参数对曲面外形的影响直观可见,其中一个形状参数更是能够在修改曲面时保持边界不变。通过几个数值实例展示了利用形状参数进行外形调整的方便有效,表明新的表达方式对三角Bézier曲面而言是一种有力的补充。

To adjust the triangular surface with the fixed control points,three shape parameters were introduced into the bivariate polynomial basis functions.Thus,a new class of triangular surface was constructed,which had the features of geometrical invariability,affine invariability,convex hull,symmetry,unique presentation,interpolation at the comers and tangent plane at the endpoints as the extensions of the triangular Bézier surface.The obvious geometric significance of shape parameters was proposed.The new surface could adjust the shape by changing the value of shape parameters,even if when the boundaries were fixed.Several numerical examples showed the efficiency for operation,which indicated that the new surface was a powerful supplement for triangular Bézier surface.