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Spherical Harmonic Lighting
Spherical harmonic (SH) lighting is a family of real-time rendering techniques that can produce highly realistic shading and shadowing with comparatively little overhead. All SH lighting techniques involve replacing parts of standard lighting equations with spherical functions that have been projected into frequency space using the spherical harmonics as a basis. To take a simple example, a cube map used for environment mapping might be reduced to just nine SH coefficients if preserving high-frequency detail is not a concern. More intriguing techniques use SH to encode multiple functions—usually the global lighting environment and a per-vertex radiance transfer function. The generalized lighting equation involves, among other things, integrating the product of the incoming radiance and the BRDF over a sphere—something that is far too expensive for real-time rendering. But if the two functions are projected into SH coefficients, the integral of their product over the sphere i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real-time Rendering
Real-time computer graphics or real-time rendering is the sub-field of computer graphics focused on producing and analyzing images in real time. The term can refer to anything from rendering an application's graphical user interface ( GUI) to real-time image analysis, but is most often used in reference to interactive 3D computer graphics, typically using a graphics processing unit (GPU). One example of this concept is a video game that rapidly renders changing 3D environments to produce an illusion of motion. Computers have been capable of generating 2D images such as simple lines, images and polygons in real time since their invention. However, quickly rendering detailed 3D objects is a daunting task for traditional Von Neumann architecture-based systems. An early workaround to this problem was the use of sprites, 2D images that could imitate 3D graphics. Different techniques for rendering now exist, such as ray-tracing and rasterization. Using these techniques and adv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. The table of spherical harmonics contains a list of common spherical harmonics. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, every function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency, as seen in the rows of functions in the illustration on the right. Further, spherical harmonics are basis functions for irreducible representations of SO(3), the group of rotations in three dimensions, and thus play a cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube Map
A cube or regular hexahedron is a three-dimensional solid object in geometry, which is bounded by six congruent square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped, with pairs of parallel opposite faces, and more specifically a rhombohedron, with congruent edges, and a rectangular cuboid, with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron. The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family of polytopes also including the two-dimensional square and four-dimensional tesseract. A cube with unit side length is the canonical unit of volume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bidirectional Reflectance Distribution Function
The bidirectional reflectance distribution function (BRDF), symbol f_(\omega_,\, \omega_), is a function of four real variables that defines how light from a source is reflected off an Opacity (optics), opaque surface. It is employed in the optics of real-world light, in computer graphics algorithms, and in computer vision algorithms. The function takes an incoming light direction, \omega_, and outgoing direction, \omega_ (taken in a coordinate system where the Normal (geometry), surface normal \mathbf n lies along the ''z''-axis), and returns the ratio of reflected radiance exiting along \omega_ to the irradiance incident on the surface from direction \omega_. Each direction \omega is itself Spherical coordinate system, parameterized by azimuth angle \phi and zenith angle \theta, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr−1, with steradians (sr) being a unit of solid angle. Definition The BRDF was first defined by Fred Nicodemus around 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. Not to be confused with scalar multiplication. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two Euclidean vector, vectors is widely used. It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see ''Inner product space'' for more). It should not be confused with the cross product. Algebraically, the dot product is the sum of the Product (mathematics), products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precomputed Radiance Transfer
Precomputed Radiance Transfer (PRT) is a computer graphics technique used to render a scene in real time with complex light interactions being precomputed to save time. Radiosity methods can be used to determine the diffuse lighting of the scene, however PRT offers a method to dynamically change the lighting environment. In essence, PRT computes the illumination of a point as a linear combination of incident irradiance. An efficient method must be used to encode this data, such as spherical harmonics. When spherical harmonics are used to approximate the light transport function, only low-frequency effects can be handled with a reasonable number of parameters. Ren Ng et al. extended this work to handle higher frequency shadows by replacing spherical harmonics with non-linear wavelets. Teemu Mäki-Patola gives a clear introduction to the topic based on the work of Peter-Pike Sloan et al. At SIGGRAPH SIGGRAPH (Special Interest Group on Computer Graphics and Interactive T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radiosity (3D Computer Graphics)
In 3D computer graphics, radiosity is an application of the finite element method to solving the rendering equation for scenes with surfaces that reflect light diffusely. Unlike rendering methods that use Monte Carlo algorithms (such as path tracing), which handle all types of light paths, typical radiosity only account for paths (represented by the code "LD*E") which leave a light source and are reflected diffusely some number of times (possibly zero) before hitting the eye. Radiosity is a global illumination algorithm in the sense that the illumination arriving on a surface comes not just directly from the light sources, but also from other surfaces reflecting light. Radiosity is viewpoint independent, which increases the calculations involved, but makes them useful for all viewpoints. Radiosity methods were first developed in about 1950 in the engineering field of heat transfer. They were later refined specifically for the problem of rendering computer graphics in 1984198 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
