带参数的二次三角样条曲线扩展

Quadratic Trigonometric Polynomial Spline Curves with Shape Parameters

为获得精确的二次曲线和二次曲面,构造新的三角多项式基函数—带双参数的二次三角多项式样条基,并由此定义带双参数二次三角多项式样条曲线。该曲线继承均匀TC-B样条曲线的优点,具有与其相类似的性质,能精确表示圆弧和椭圆弧等二次曲线,可扩展应用于空间的旋转曲面。此外,形状控制参数的引入会使其在工业设计中具有更大的灵活性和更广的应用范围。

To obtain precise quadratic curves and quadratic surfaces, we build the new trigonometric polynomial base function with two shape parameters and then define its quadratic trigonometric polynomial spline curves. The curves have the advantages and similar properties of the uniform TC-B-spline curves, can express the circle arc and the ellipse arc exactly and can be extended to construct the rotational surfaces in space. In addition, the introduction of shape parameters makes the curves have more agility and wider application to industrial design.