二次均匀TC-B样条曲线的扩展

Extension of uniform quadratic TC-B-spline curves

构造了一种新的三角多项式基函数——带参数的均匀二次TC-B样条基,并由此定义了曲线——带参数的均匀二次TC-B样条曲线。该曲线继承了均匀TC-B样条曲线的优点,有着与其相类似的性质,例如凸包性、几何不变性、变差缩减性等。同时它还能精确表示圆弧、椭圆弧等二次曲线,推广到空间即可以表示旋转曲面。此外,由于引入了形状控制参数,使其在工业设计中具有更大的灵活性和更广的应用范围。

Analogous to the uniform TC-B-spline curves, trigonometric polynomial of the quadratic uniform TC-B basic function and curve with shape parameter are constructed. The curves have the advantages of the uniform TC-B-spline curves. Also the curves can express the circle arc and ellipse arc and can construct rotate surfaces. In addition, because of the shape parameter, the curves have more and more convenience and bigger and bigger using space.