关键词: 计算机辅助几何设计, 线性双曲拟Bé, zier曲线, 双曲线, 显式表达, 双线性插值

Abstract: The aim of the paper is to do further study on the geometric properties of linear hyperbolic Bézier-like curves. A given hyperbola with standard equation is changed into the linear hyperbolic Bézier-like form by using geometric and parametric transformations. Comparing the new-form hyperbola with any linear hyperbolic Bézier-like curve, some equations are gotten. By solving the equations, a conclusion that any non-degenerate linear hyperbolic Bézier-like curve is a segment of a hyperbola is drawn. The explicit expressions of the geometric elements of the hyperbola, such as the center, the vertices of the real and imaginary axes, and the foci, in terms of the control points of the linear hyperbolic Bézier-like curve, are also obtained. The theoretical analysis and examples show that all the above-mentioned geometric elements of the hyperbola can be given by the bilinear interpolation forms of the control points of the linear hyperbolic Bézier-like curve.

Key words: computer aided geometric design, linear hyperbolic Bézier-like curve, hyperbola, explicit expression, bilinear interpolation