BRDF Generation for Gonioapparent Materials Using Limited Data
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Solution Overview
Problem
Current methods for predicting the absolute color of gonioapparent materials, such as those with metallic or pearlescent flake pigments, under varying illumination and viewing geometries are inadequate, as they rely on extensive measurement data or complex modeling, which are time-consuming and impractical for accurate color representation.
Innovation Solution
A computer-implemented process that generates a bidirectional reflectance distribution function (BRDF) using limited measurement data by converting photometric data to a linear basis, calculating effect flake angles, and fitting these data with an equation to predict BRDF values for various illumination and viewing angles, thereby eliminating illumination angle dependence and enabling accurate color prediction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If extensive measurement data is collected at many combinations of illumination and viewing angles, then accuracy of BRDF and color prediction is improved, but measurement time and complexity increase significantly
Solution Approach 1:
The patent applies partial action by collecting only a limited subset of measurement data at specific illumination and viewing angles rather than exhaustive measurements. The system determines BRDF parameters from this partial data set, which is sufficient to characterize gonioapparent materials without requiring complete angular coverage, thereby reducing measurement time while maintaining acceptable accuracy
Solution Approach 2:
The patent performs preliminary action by pre-determining BRDF parameters (r, s, t) from a limited set of measurements. These pre-determined parameters are then used to generate the complete BRDF function for any illumination and viewing geometry, eliminating the need for extensive measurements at all possible angle combinations while maintaining prediction accuracy
2Measurement precision
If a physical model is developed and tuned to match actual material behavior, then accuracy of color prediction is improved, but model development complexity and time increase
Solution Approach 1:
The patent changes parameters by representing the BRDF through a simplified parametric model with three parameters (r, s, t) that capture the essential characteristics of gonioapparent materials. This parameter-based approach replaces complex physical models while maintaining prediction accuracy, as the parameters can be directly determined from limited measurements and used to generate accurate color predictions across various geometries
Solution Approach 2:
The patent applies local quality by focusing the measurement and modeling effort on the specific angular dependencies characteristic of gonioapparent materials. Rather than using a universal complex physical model, the system uses a tailored parametric representation that specifically addresses the local behavior of flake-pigmented coatings at different illumination and viewing angles
3Productivity
If simple interpolation models are used with limited measurement data, then measurement time is reduced, but accuracy of BRDF prediction deteriorates
Solution Approach 1:
The patent transforms the problem from direct interpolation of BRDF values to determination of underlying physical parameters (r, s, t) that govern the angular behavior. This parameter-based approach allows simple measurement procedures to yield accurate predictions, as the parameters capture the essential physics of gonioapparent materials and can be used to generate accurate BRDF values for any geometry through the parametric equations
Data Source
AI summary
A computer-implemented process for generating a bidirectional reflectance distribution function (BRDF) of a gonioapparent material containing effect flake pigments in a solid medium using limited measurement data, comprising the following steps: (A) acquiring and inputting into a computing device (1) photometric data and (2) the refractive index of the solid medium of the gonioapparent material; (B) converting any non-linear photometric data from step A) above to linear photometric data; (C) using the illumination angle and the reflective scattering angle associated with the linear photometric data and the refractive index of the medium to calculate corresponding effect flake angles; (D) fitting the linear photometric data and the effect angle data with an equation; (E) calculating the corresponding effect flake angle needed to calculate the BRDF being generated in step (F); and (F) generating the BRDF from the corresponding effect flake angle from step (E) and the equation developed in step (D).