Empirical BRDF model for goniochromatic
materials and soft proofing with reflective inks

Alina Pranovich, Linköping University, Norrköping, Sweden

Jeppe Revall Frisvad, Technical University of Denmark, Kongens Lyngby, Denmark

Sergiy Valyukh, Linköping University, Linköping, Sweden

Sasan Gooran, Linköping University, Norrköping, Sweden

Daniel Nyström, Linköping University, Norrköping, Sweden

Abstract—The commonly used analytic bidirectional reflectance distribution functions (BRDFs) do not model goniochromatism, that is, angle-dependent material color. The material color is usually defined by a diffuse reflectance spectrum or RGB vector and a specular part based on a spectral complex index of refraction inserted in the Fresnel equations for reflection. The angle-dependent specular part of the standard analytic BRDFs mostly affect the intensity of the reflected light and not so much the color. The specular part is thus often modeled using a specular reflectance spectrum or RGB vector and a constant index of refraction. Extension of the commonly used BRDFs based on wave theory can help model goniochromatism, but this comes at the cost of significant added model complexity. We measured the goniochromatism of structual color pigments used for additive color printing and found that we can fit the observed spectral angular dependence of the bidirectional reflectance using a simple modification of the standard microfacet BRDF model. All we need to describe the goniochromatism is an empirically-based spectral parameter, which we use in our model together with a specular reflectance spectrum instead of the spectral complex index of refraction. We demonstrate the ability of our model to fit the measured reflectance of red, green, and blue commercial structural color pigments. Our BRDF model enables straightforward implementation of a shader for interactive preview of 3D objects with printed spatially and angularly varying texture.

Empirical BRDF model for goniochromatic materials and soft proofing with reflective inks Alina Pranovich, Jeppe Revall Frisvad, Sergiy Valyukh, Sasan Gooran, Daniel Nyström IEEE Computer Graphics & Applications 44(5), pp. 143-152. September/October 2024. [abstrac/demo]

Empirical BRDF parameters for RGB reflective inks

Rendering with halftoned reflective inks example

Comparison of fitted model with direct use of sparse measured data

RGB reflective ink photo-render comparison

subdivide coarsen orbit on/off

goniochromatic Schlick for Fresnel sRGB 2 lights

Rotation of sphere (in degrees):