Two-layer microfacet model with diffraction

Highlights

• Based on the CTD model, we add two coefficients—σ and σ_sd—where σ can be used to adjust brightness and σ_sd to adjust the effect of diffuse diffraction. By adjusting the two coefficients we make a better approximation to the measured data.

• Three techniques are applied in our experiments—precomputation, convolution computation, and the Gauss–Newton method—to reduce the rendering cost and find the best coefficients.

Abstract

The bidirectional scattering distribution function (BSDF) describes how light is scattered on a surface. Microfacet-based BSDF models assume that surfaces are a collection of randomly oriented microfacets, describe the distribution probabilities of these microfacets, and plausibly approximate their reflective properties using parameterized expressions. Traditional analytic microfacet models, such as Cook–Torrance (CT) and the Oren–Nayar (ON), ignore the effects of diffraction. The Cook–Torrance diffraction model (CTD) combines the traditional Cook–Torrance model with diffraction effects to better approximate the measured reflectance. However, the effects of diffuse diffraction are ignored in this two-layer microfacet reflectance model. In this paper, We propose a two-layer microfacet reflectance model that combines the effects of specular diffraction with those of diffuse diffraction. The upper layer of our model is the Cook–Torrance microfacet model with diffraction, while the lower layer is the Oren–Nayar microfacet model that considers the effects of diffuse diffraction. Our model yields a better approximation than the CTD model, especially for plastic-like multi-layer materials. In contrast to previous models where the effects of diffraction cannot be controlled, those of our model can be easily manipulated by the coefficient of diffraction roughness. The proposed OND model is based on three techniques: precomputation, convolution computation, and the Gauss–Newton method.

Introduction

Diffraction is a well-known property of light waves, but is seldom mentioned in physical rendering. Parametric microfacet models, such as Cook–Torrance and Oren–Nayar, create plausible approximations using the corresponding coefficients but do not consider the effects of consideration. A two-scale diffraction model [1] based on Cook–Torrance (CTD) model was proposed that combines reflection with diffraction to fit empirical surfaces, but ignores the lower-layer diffraction effects of dielectrics. To better fit most plastic materials in the MERL database [2], we propose an Oren–Nayar model with diffraction (OND) using a two-layer structure to fit plastic materials. Moreover, we integrate the CTD and OND into plastic-like [3] layered surface fitting (shown in Fig. 1). The remainder of this paper is organized as follows: In Section 2, we review past work on material modeling. Section 3 presents the theories of BSDF, the Cook–Torrance model, and the Cook–Torrance diffraction model. In Section 4, our two-layer reflectance model is detailed. The Gauss–Newton method and convolution computation method are also discussed. Section 5 presents the validation of the proposed OND model, including the classification of plastic materials, comparisons with the CTD model, and the adjustment of coefficients. The Conclusions of this study and directions for the future work are provided in Section 6

The main contributions of this paper are as follows: 1. We add two coefficients to the CTD model, σ and σ_sd. They can adjust the brightness and diffuse diffraction effects respectively. We thus better approximate plastic-like materials than the CTD model. 2. The proposed OND model is established based on three techniques: precomputation and convolution computation to lower rendering cost, and the Gauss–Newton method used to find the regression function and the values of the coefficient to improve the accuracy of the proposed OND model.