Meshless Monte Carlo radiation transfer method for curved geometries using signed distance functions

Lewis Thomas McMillan*, Graham David Bruce, Kishan Dholakia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Significance: Monte Carlo radiation transfer (MCRT) is the gold standard for 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 precise modeling of smooth curved surfaces, such as may be found in biological systems or food and drink packaging. Mesh-based geometry allows arbitrary complex shapes with smooth curved surfaces to be modeled. However, mesh-based models also suffer from issues such as the computational cost of generating meshes and inaccuracies in how meshes handle reflections and refractions.

Aim: We present our algorithm, which we term signedMCRT (sMCRT), a geometry-based method that uses signed distance functions (SDF) to represent the geometry of the model. SDFs are capable of modeling smooth curved surfaces precisely while also modeling complex geometries.

Approach: We show that using SDFs to represent the problem’s geometry is more precise than voxel and mesh-based methods.

Results: sMCRT is validated against theoretical expressions, and voxel and mesh-based MCRT codes. We show that sMCRT can precisely model arbitrary complex geometries such as microvascular vessel network using SDFs. In comparison with the current state-of-the-art in MCRT methods specifically for curved surfaces, sMCRT is more precise for cases where the geometry can be defined using combinations of shapes.

Conclusions: We believe that SDF-based MCRT models are a complementary method to voxel and mesh models in terms of being able to model complex geometries and accurately treat curved surfaces, with a focus on precise simulation of reflections and refractions. sMCRT is publicly available at
Original languageEnglish
Article number083003
Number of pages15
JournalJournal of Biomedical Optics
Issue number8
Publication statusPublished - 4 Aug 2022


  • Monte Carlo
  • Light transport
  • Signed distance functions
  • Geometry
  • Meshless


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