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Significance: Monte Carlo radiation transfer (MCRT) is the gold standard ofmodeling light transport in turbid media. Typical MCRT models use voxels ormeshes to approximate experimental geometry. A voxel based geometry does notallow for the accurate modeling of smooth curved surfaces, such as may be foundin biological systems or food and drink packaging.  Aim: We present our algorithm which we term signedMCRT (sMCRT), a newgeometry-based method which uses signed distance functions (SDF) to representthe geometry of the model. SDFs are capable of modeling smooth curved surfacesaccurately whilst also modeling complex geometries.  Approach: We show that using SDFs to represent the problem's geometry is moreaccurate and can be faster than voxel based methods. sMCRT, can easily beincorporated into existing voxel based models.  Results: sMCRT is validated against theoretical expressions, and other voxelbased MCRT codes. We show that sMCRT can accurately model arbitrary complexgeometries such as microvascular vessel network using SDFs. In comparison tothe 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 outperformscomparable voxel based models due to its ability to model smooth curvedsurfaces. sMCRT is up-to three times faster than a voxel model for equivalentscenarios. sMCRT is publicly available athttps://github.com/lewisfish/signedMCRT

Meshless Monte Carlo Radiation Transfer Method for Curved Geometries using Signed Distance Functions