基于符号距离函数的无网格Monte Carlo辐射传递方法
Meshless Monte Carlo Radiation Transfer Method for Curved Geometries using Signed Distance Functions
摘要：
意义：蒙特卡罗辐射传输（MCRT）是模拟混浊介质中光传输的黄金标准。典型的MCRT模型使用体素或网格来近似实验几何形状。基于体素的几何形状不允许对平滑弯曲表面进行精确建模，例如可以在生物系统或食品和饮料包装中找到。目的：我们提出了我们的算法，我们长期signedMCRT（sMCRT），一个新的基于几何的方法，它使用有符号的距离函数（SDF）来表示几何模型。SDF能够精确地建模光滑的曲面，同时也能建模复杂的几何形状。方法：我们表明，使用SDF来表示问题的几何形状更准确，并且可以比基于体素的方法更快。sMCRT，可以很容易地结合到现有的基于体素的模型。结果：sMCRT与理论表达式和其他基于体素的MCRT代码进行了验证。我们表明，sMCRT可以准确地模拟任意复杂的几何形状，如微血管血管网络使用SDF。与目前最先进的专门用于曲面的MCRT方法相比，sMCRT的准确度高达45倍。结论：sMCRT是一种高度准确、快速的MCRT方法，由于其能够对平滑曲面进行建模，因此其性能优于可比的基于体素的模型。对于等效场景，sMCRT比体素模型快三倍。sMCRT可在https://github.com/lewisfish/signedMCRT上公开获取
英文摘要：
Significance: Monte Carlo radiation transfer (MCRT) is the gold standard of modeling light transport in turbid media. Typical MCRT models use voxels or meshes to approximate experimental geometry. A voxel based geometry does not allow for the accurate modeling of smooth curved surfaces, such as may be found in biological systems or food and drink packaging. Aim: We present our algorithm which we term signedMCRT (sMCRT), a new geometry-based method which uses signed distance functions (SDF) to represent the geometry of the model. SDFs are capable of modeling smooth curved surfaces accurately whilst also modeling complex geometries. Approach: We show that using SDFs to represent the problem's geometry is more accurate and can be faster than voxel based methods. sMCRT, can easily be incorporated into existing voxel based models. Results: sMCRT is validated against theoretical expressions, and other voxel based MCRT codes. We show that sMCRT can accurately model arbitrary complex geometries such as microvascular vessel network using SDFs. In comparison to the current state-of-the-art in MCRT methods specifically for curved surfaces, sMCRT is up-to forty-five times more accurate. Conclusions: sMCRT is a highly accurate, fast MCRT method that outperforms comparable voxel based models due to its ability to model smooth curved surfaces. sMCRT is up-to three times faster than a voxel model for equivalent scenarios. sMCRT is publicly available at https://github.com/lewisfish/signedMCRT
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