多曲面反射体的计算机辅助设计及优化

研究了自由曲面反射式照明系统的设计理论和方法.根据反射器的尺寸、位置以及配光要求按点光源设计得到曲面型值点初始坐标后,将双三次B样条曲面引入照明系统的设计,反算出控制顶点.给出了空间任意一条入射光线与反射器区块的交点及其曲面法线向量的求法,为了提高光路追迹的效率,针对多曲面反射体给出了一种快速判断相交区块的算法.探讨了用阻尼最小二乘法对B样条曲面反射器进行优化设计的方法,通过优化运算修正控制顶点Z轴坐标,使得曲面在使用扩展光源时光形分布尽可能满足设计要求.

Automatic Design and Optimization of Segmented Free Form Reflector

The design theory and method for illumination systems with free form reflectors are studied. The coordinates of the initial shape points on the reflector are obtained by raytracing from a point source according to the reflector size,position and illumination requirements. Uniform bicubic B-spline surfaces are used to describe the shape of the reflector,and the control point coordinates are calculated by equation solving. An iterative method is developed to calculate the coordinates of the intersection point of an incident ray with a B-spline surface in 3D space. Formulae are given to calculate the direction cosines of the surface normal at the intersection point. For segmented reflectors,a method is presented to rapidly determine the segment with which the incident ray strikes. The damped-least-squares method is used to optimize the B-spline surface reflector. The Z-coordinates of the control points are adjusted through the optimization,so that the light distribution generated by the reflector with a real (extended) source meets the design requirements.