NEW SURFACE REFLECTANCE MODEL WITH THE COMBINATION OF TWO CUBIC FUNCTIONS USAGE

In the article the model of light reflection based on the combination of two cubic bidirectional reflectance distribution functions is developed. The main components of color and the main requirements for reproducing the object`s glares are analyzed. The usage characteristics of Cook-Torrance, Bagher, Oren-Nayar, coupled Shirley reflection models are described. The advantages and disadvantages of the highly productive Blinn-Phong model are considered. The necessity of approximating the Blinn-Phong model by a function of low degree is justified. The characteristics of the cubic polynomial approximation of the Blinn-Phong model are determined. It was established that the main drawback of this approximation is a significant deviation of the function from the reference function in the glare’s attenuation zone. The combined function that combines two cubic functions is proposed. The first cubic function reproduces the glare’s epicenter, and the second replaces the specified function in the attenuation zone. A system of equations for calculating the coefficients of the second function was created. The formula for the connection point of two cubic functions is obtained. A graph of the developed combined model based on cubic functions is obtained. For the combined and original cubic functions a comparison of the maximum relative errors in the glare’s epicenter zone, the maximum absolute errors, and the relative errors at the inflection point was made. A three-dimensional plot of the absolute error of the combined cubic model from the Blinn-Phong model depending on the shininess and the angle value is built. Visualization results based on the combined and the original cubic functions are compared. It is confirmed that the proposed reflection model increases the realism of glare formation in the attenuation zone. The resulting combined reflection model provides a highly accurate approximation of the Blinn-Phong model and is highly efficient because the third power function is used

NOWY MODEL ODBICIA ŚWIATŁA OD POWIERZCHNI WYKORZYSTUJĄCY KOMBINACJĘ DWÓCH FUNKCJI SZEŚCIENNYCH

In the article the model of light reflection based on the combination of two cubic bidirectional reflectance distribution functions is developed. The main components of color and the main requirements for reproducing the object`s glares are analyzed. The usage characteristics of Cook-Torrance, Bagher, Oren-Nayar, coupled Shirley reflection models are described. The advantages and disadvantages of the highly productive Blinn-Phong model are considered. The necessity of approximating the Blinn-Phong model by a function of low degree is justified. The characteristics of the cubic polynomial approximation of the Blinn-Phong model are determined. It was established that the main drawback of this approximation is a significant deviation of the function from the reference function in the glare’s attenuation zone. The combined function that combines two cubic functions is proposed. The first cubic function reproduces the glare’s epicenter, and the second replaces the specified function in the attenuation zone. A system of equations for calculating the coefficients of the second function was created. The formula for the connection point of two cubic functions is obtained. A graph of the developed combined model based on cubic functions is obtained. For the combined and original cubic functions a comparison of the maximum relative errors in the glare’s epicenter zone, the maximum absolute errors, and the relative errors at the inflection point was made. A three-dimensional plot of the absolute error of the combined cubic model from the Blinn-Phong model depending on the shininess and the angle value is built. Visualization results based on the combined and the original cubic functions are compared. It is confirmed that the proposed reflection model increases the realism of glare formation in the attenuation zone. The resulting combined reflection model provides a highly accurate approximation of the Blinn-Phong model and is highly efficient because the third power function is used.W artykule opracowano model odbicia światła oparty na kombinacji dwóch sześciennych dwukierunkowych funkcji rozkładu odbicia. Przeanalizowano główne składniki koloru i główne wymagania dotyczące odtwarzania odblasków obiektu. Opisano charakterystykę użytkowania modeli odbicia Cooka-Torrance'a, Baghera, Orena-Nayara i Shirleya. Rozważono zalety i wady wysoce wydajnego modelu Blinn-Phong. Uzasadniono konieczność aproksymacji modelu Blinna-Phonga funkcją niskiego stopnia. Określono charakterystykę wielomianu sześciennego aproksymującego model Blinna-Phonga. Ustalono, że główną wadą tej aproksymacji jest znaczne odchylenie funkcji od funkcji odniesienia w strefie tłumienia olśnienia. Zaproponowano funkcję kombinowaną, która łączy dwie funkcje sześcienne. Pierwsza funkcja sześcienna odtwarza epicentrum olśnienia, a druga zastępuje określoną funkcję w strefie tłumienia. Stworzono układ równań do obliczania współczynników drugiej funkcji. Uzyskano wzór na punkt połączenia dwóch funkcji sześciennych. Uzyskano wykres opracowanego połączonego modelu opartego na funkcjach sześciennych. Dla połączonych i oryginalnych funkcji sześciennych dokonano porównania maksymalnych błędów względnych w strefie epicentrum olśnienia, maksymalnych błędów bezwzględnych i błędów względnych w punkcie przegięcia. Zbudowano trójwymiarowy wykres błędu bezwzględnego połączonego modelu sześciennego z modelu Blinna-Phonga w zależności od połysku i wartości kąta. Porównano wyniki wizualizacji oparte na połączonych i oryginalnych funkcjach sześciennych. Potwierdzono, że proponowany model odbicia zwiększa realizm powstawania odblasków w strefie tłumienia. Wynikowy połączony model odbicia zapewnia bardzo dokładne przybliżenie modelu Blinna-Phonga i jest bardzo wydajny, ponieważ używana jest funkcja trzeciej potęgi

Approximation of Bidirectional Reflectance Distribution Function with 3-Degree Polynomial

The purpose of this article is approximation of BRDF with functions of argument cos(x). The described approach proposes usage of two functions for BRDF approximation. One of them is a cubic polynomial (with argument cos(x)) and the second one is the function, that assures monotonous falling of the function. Usage of this approach leads to considerable reduce of the approximation error and increases accuracy of the object's highlights representation

Design principles of hardware-based phong shading and bump-mapping

The VISA+ hardware architecture is the first of a new generation of graphics accelerators designed primarily to render bump-, texture-, environment- and environment-bump-mapped polygons. This paper presents examples of the main graphical capabilities and discusses methods and simplifications used to create high quality images. One of the key concepts in the VISA+ design, the use of reflectance cubes, is predestined for environment mapping. In combination with bump- and texture-mapping it shows the strength of our new architecture. Furthermore it justifies some of the decisions made during simulation and development of the complex VISA+ architecture

Effective Models for the Specular Color Constituent Computing

This paper describes the alternative BRDF (Bidirection reflectance distribution function) models. Main emphasis was done on the models development with simple hardware implementation, based on formulas with low computation complexity. The results, achieved by authors, testify the increase of BRDF approximation accuracy in more than 22 times in comparison with most widespread solution

A Precomputed Polynomial Representation for Interactive BRDF Editing with Global Illumination

The ability to interactively edit BRDFs in their final placement within a computer graphics scene is vital to making informed choices for material properties. We significantly extend previous work on BRDF editing for static scenes (with fixed lighting and view), by developing a precomputed polynomial representation that enables interactive BRDF editing with global illumination. Unlike previous recomputation based rendering techniques, the image is not linear in the BRDF when considering interreflections. We introduce a framework for precomputing a multi-bounce tensor of polynomial coefficients, that encapsulates the nonlinear nature of the task. Significant reductions in complexity are achieved by leveraging the low-frequency nature of indirect light. We use a high-quality representation for the BRDFs at the first bounce from the eye, and lower-frequency (often diffuse) versions for further bounces. This approximation correctly captures the general global illumination in a scene, including color-bleeding, near-field object reflections, and even caustics. We adapt Monte Carlo path tracing for precomputing the tensor of coefficients for BRDF basis functions. At runtime, the high-dimensional tensors can be reduced to a simple dot product at each pixel for rendering. We present a number of examples of editing BRDFs in complex scenes, with interactive feedback rendered with global illumination

Efficient Methods for Fast Shading

On devices without battery consuming and specialized hardware for rendering, it is important to improve the speed and quality so that these methods are suitable for real-time rendering. Furthermore such algorithms are needed on the coming multicore architectures. We show how the methods by Gouraud and Phong, the commonly most used methods for shading, can be improved and made faster for both software rendering as well as simple low energy consuming hardware implementations. Moreover, this paper summarizes the authors’ achievements in increasing shading speed and performance and a Bidirectional Reflectance Distribution Function is simplified for faster computing and hardware implementatio

Analysis of Human Faces Using a Measurement-Based Skin Reflectance Model

We have measured 3D face geometry, skin reflectance, and subsurface scattering using custom-built devices for 149 subjects of varying age, gender, and race. We developed a novel skin reflectance model whose parameters can be estimated from measurements. The model decomposes the large amount of measured skin data into a spatially-varying analytic BRDF, a diffuse albedo map, and diffuse subsurface scattering. Our model is intuitive, physically plausible, and -- since we do not use the original measured data -- easy to edit as well. High-quality renderings come close to reproducing real photographs. The analysis of the model parameters for our sample population reveals variations according to subject age, gender, skin type, and external factors (e.g., sweat, cold, or makeup). Using our statistics, a user can edit the overall appearance of a face (e.g., changing skin type and age) or change small-scale features using texture synthesis (e.g., adding moles and freckles). We are making the collected statistics publicly available to the research community for applications in face synthesis and analysis.Engineering and Applied Science