PDE-based models for advanced rendering in computer graphics
Swapnali Makdeyswapnali@frcrce.ac.inDepartment of Electronics and Computer ScienceFr. Conceicao Rodrigues College of EngineeringUniversity of MumbaiMumbai, Maharashtra, 400050, IndiaView full profile → , Machindranath B. Diwatediwatemachindra@gmail.comDepartment of MathematicsSinhgad Institute of Technology and Science NarhePune, Maharashtra, 411041, IndiaView full profile → , *Sangram PatilCorresponding authorsangramrpatil@gmail.comDepartment of Mechanical EngineeringBharati Vidyapeeth College of Engineering LavalePune, Maharashtra, 411043, IndiaView full profile → , Avinash B. B. Rautavinash.raut@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Vijaya Sagvekarvijaya.s@xavier.ac.inDepartment of Computer Science and EngineeringXavier Institute of EngineeringUniversity of MumbaiMumbai, Maharashtra, 400016, IndiaView full profile → , Ninad MoreDepartment of Computer Science and EngineeringXavier Institute of EngineeringUniversity of MumbaiMumbai, Maharashtra, 400016, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2809
- Pages:
- 2929–2944
Abstract
To accurately model global illumination, light transport, shadow formation and surface interaction in a complex geometry, mathematically accurate physical models are required for advanced rendering in computer graphics. In this paper, a partial differential equation based rendering framework is proposed which incorporates the radiative transfer, diffusion and geometric evolution models. The framework is solved by the Finite Element Method with an implicit Crank–Nicolson time integration to maintain the numerical stability and convergence. Peak Signal to Noise Ratio, Structural Similarity Index, Mean Squared Error, rendering time and convergence stability are used to evaluate the performance. The result showed that the proposed model can obtain PSNR of 39.8 dB, SSIM of 0.962, MSE of 0.0038, 16.9% reduction in rendering time and 98.4% numerical convergence, which indicates that the proposed model has high visual quality, fast running speed, and physically correct rendering.
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References
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