Efficient ray-tracing for free-form reflectors

Efficient ray-tracing is the basis for computer-aided design and analysis of illumination optical systems, which requires the sampling of hundreds of thousands of rays to achieve accurate results of illumination analysis. One type of most widely used illumination systems is free-form segmented reflectors with B-spline surfaces. An iterative method is used 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, so that the direction cosines of the reflected ray can be obtained. For segmented reflectors, a method is presented to rapidly determine the segment with which the incident ray strikes. Experimental results show that the scheme proposed in this paper can perform ray-tracing through free-form reflectors with excellent efficiency, and is suitable for use in CAD software for vehicle headlights, for example.