摘要
本文提出“积分曲线法”,即用常微分方程初值问题数值解法中的预报-校正技术来绘制平面曲线和各类空间曲线,其中包括: 1.函数曲面与自由曲面的交线; 2.函数曲面与函数曲面的交线; 3.自由曲面与自由曲面的交线。 无论是平面曲线还是上述各类空间曲线,求曲线上的一个点,用积分曲线法都仅需计算预报点和校正点两点的雅可比行列式,达到二阶或四阶精度(更高阶的精度也能达到),从而不仅解决了各类曲面的求交问题,而且统一了平面曲线和各类空间曲线的算法。具有简便、高效、精确和节约内存等优点。
In this paper, INTEGRAL CURVE METHOD is presented, i.e. drawing both plane curve and space curve by applying 'PREDICTOR-CORRCTOR' technique which is often used in numerical solution for initial value problems of ordinary differential equations, which includes.1. the intsection between a free-form surface and a function surface;2. the intersection between two function surfaces;3. the intersection between two free-form surfaces.whether plane curve or space curve, to find a point on the curve only needs to calculate the JACOBI determinant of PREDICTOR point and CORRECTOR point, reaching the second order precision or the forth precision (the precision more than the second order or the forth order can be reached also ) . Thus, not only the problem of finding the intersection between various surfaces is resolved, but also the algorithms for drawing both plane curve and space curve are unified.It has been proved that the algorithm has many advantages, for instance, convenient, efficient, accurate, and mermory is greatly saved.
关键词
计算机图形学
曲线
绘制
曲面
求交
Computer graphice, Drawing curve, Finging the intersection between two surfaces, Predictor-Corrector.
