# Real-Time Far-Field BCSDF Filtering

## TL;DR

This paper introduces a real-time method for rendering complex surfaces like hair and fabric with high accuracy and efficiency.

## Contribution

The novel approach uses vMF distributions to analytically filter BCSDFs without precomputation.

## Key findings

- The method achieves results comparable to 1000 spp Monte Carlo simulations.
- It reduces mean squared error by one to two orders of magnitude over baseline methods.
- Visual fidelity and computational efficiency are confirmed through comparisons and error analysis.

## Abstract

The real-time rendering of large-scale curve-based surfaces (e.g., hair, fabrics) requires efficient handling of bidirectional curve-scattering distribution functions (BCSDFs). While curve-based material models are essential for capturing anisotropic reflectance characteristics, conventional prefiltering techniques encounter challenges in jointly resolving micro-scale BCSDFs variations with tangent distribution functions (TDFs) at pixel-level accuracy. This paper presents a real-time BCSDF filtering framework that achieves high-fidelity rendering without precomputation. Our key insight lies in formulating each pixel’s scattering response as a mixture of von Mises–Fisher (vMF) distributions, enabling analytical convolution between micro-scale BCSDFs and TDFs. Furthermore, we derive closed-form expressions for the integral of TDF-BCSDF products, avoiding the need for numerical approximation and heavy precomputation. Our method demonstrates state-of-the-art performance, achieving results comparable to 1000 spp Monte Carlo simulations under parallax-free conditions, where it improves the mean squared error (MSE) by one to two orders of magnitude over baseline methods. Qualitative comparisons and error analysis confirm both visual fidelity and computational efficiency.