车灯光源优化问题的探讨

本文讨论了在一定的光源设计前提下,光照强度及其分布所满足的规律,并在此基础上,分析了车灯线光源的优 化设计的途径。在分析的方法上,我们侧重于计算机数值模拟辅以理论推导,提出了一系列创新的技术,用以克 服离散途径解决连续问题时所遇到的困难。在基本的方法上,我们将线光源用离散的点光源逼近,将抛物面离 散为网格。这里我们从法向量变化率出发。提出按曲率划分而非单纯尺寸长度划分,大大提高了模拟精度。在 处理离散条件下点线相交时,我们引入了连通集这一重要概念,以克服(屏上点,光源)1—>(抛面面上点)映射 时的多值性,解决了因细分抛物面而产生的多重光路的问题。在实现过程中,我们应用了广度优先的线性复杂 度算法,使计算效率一跃提升了近5000倍。在解决多点采样问题时,我们又开发了并行连通集算法,减少了串行 算法的重复计算,使计算速度加快了近2000倍。在验证模型合理性和进行数据分析时,在第一题中我们着重于 收敛的程度问题,并证明我们的模型是稳定的,能克服误差的影响;第二小题中,我们着重分析光强分布的合理 性问题,并结合第三小题的要求,对图象进行分析,最终得出题目中的设计规范是符合实际应用需要的,并且光 源消耗很优化,光强分布合理。

Computational Analysis and Optimization of the Integrity Distribution

In this paper, we presented our algorithms and techniques to derive the intensity distribution of the light source. Our basic method is numeric simulation, with the help of theoretical derivation. We devised several innovations to approach the originally continuous problem by discrete computation. We first divide the linear light source into minute segments, which are modeled as independent point light sources. We then set up a Cartesian coordination on the paraboloid. Different from the traditional uniform-sized grid, we use a grid according to the solid angle > getting a more accurate modeling of the paraboloid. Our major innovation lies in the motivation and implementation of the "connected-set" idea. There may exits multiple points in the paraboloid that acts as the reflection point. Which is worse, one such point may be several (nominated) coordinates in our approximation. So we have to group these consecutive coordinates back into one "reflection point'. Put another way, we should divide nominated coordinates into several connected-sets, where each connected-set represents on "reflection point" . To implement this idea, we use the Bread-First Search, which is linear to the number of nominated coordinates. To scale up to problem 2, we further developed a parallel algorithm to compute the connected-sets for each sampling point in the screen simultaneously. This is substantially faster than the obvious serial algorithm that runs sequentially for each sampling point. We have also proved the correctness of this parallel algorithm. Our experimental results showed that our model is reasonable, accurate and efficient .