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 inefficient, requiring extensive measurement data or complex modeling, and fail to accurately capture the magnitude of color changes.
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 exponential decay equation to predict BRDF values for various illumination and viewing angles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If extensive measurement data is collected at multiple illumination and viewing geometries, then the accuracy of color prediction is improved, but the measurement time and complexity increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-calculating the BRDF function and storing it in a lookup table before actual color predictions are needed. The BRDF is computed once using a limited set of measurements at specific geometries, then this pre-computed function is reused for predictions at any illumination and viewing angles, eliminating the need for extensive real-time measurements.
Solution Approach 2:
The patent uses copying by creating a mathematical model (BRDF function) that replicates the material's reflectance behavior. Instead of measuring actual light reflection at every possible geometry, the system copies the essential optical properties into a computable function that can be evaluated efficiently for any geometry, significantly reducing measurement requirements.
2Loss of time
If a physical model is developed to calculate color at all angular combinations, then measurement time is reduced, but the complexity of model development and tuning increases
Solution Approach 1:
The patent extracts only the essential optical properties needed for color prediction by measuring at a limited set of critical geometries (including specular and anti-specular angles). Rather than developing a complex physical model that accounts for all possible light interactions, the method extracts the key reflectance characteristics and embeds them in a simplified BRDF function that captures the dominant optical behavior.
Solution Approach 2:
The patent applies parameter changes by transforming the BRDF from a function of illumination and viewing angles into a function of effect flake angle only. This parameter transformation simplifies the model by eliminating illumination angle dependence, reducing the number of parameters that need to be measured and modeled while maintaining prediction accuracy.
3Loss of time
If three-angle measurement data is used with simple interpolation models, then measurement time is reduced, but the ability to predict absolute color accurately deteriorates
Solution Approach 1:
The patent applies preliminary action by pre-computing the BRDF function using a limited set of measurements at specific geometries (including 0°, 45°, and 90° effect flake angles). This pre-computed function captures the absolute color information, and subsequent predictions at other geometries are made by evaluating this pre-established function rather than through simple interpolation, preserving accuracy while reducing measurement time.
Solution Approach 2:
The patent transforms the measurement parameters by converting from standard illumination/viewing angle measurements to effect flake angle measurements. This parameter change allows the use of only three measurements at strategically selected effect flake angles to fully characterize the BRDF, enabling accurate absolute color prediction through a simplified measurement protocol.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for accurate prediction of absolute color across different geometries with a reduced number of measurements, eliminating illumination angle dependence and providing a continuous function for BRDF generation, thus enhancing efficiency and accuracy in color rendering and prediction.
Implementation Method 1
calculating, using Snell's law, a corresponding effect flake angle
Data Source
AI summary
This disclosure is directed to a method for matching color and appearance of an object. The method comprise the step of generating a bidirectional reflectance distribution function (BRDF) of a gonioapparent material containing effect flake pigments in a solid medium using limited measurement data.