|
Marching Cubes
Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels). The applications of this algorithm are mainly concerned with medical visualizations such as CT and MRI scan data images, and special effects or 3-D modelling with what is usually called metaballs or other metasurfaces. The marching cubes algorithm is meant to be used for 3-D; the 2-D version of this algorithm is called the marching squares algorithm. History The algorithm was developed by William E. Lorensen (1946-2019) and Harvey E. Cline as a result of their research for General Electric General Electric Company (GE) was an American Multinational corporation, multinational Conglomerate (company), conglomerate founded in 1892, incorporated in the New York (state), state of New York and headquartere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reconstruction Filter
In a mixed-signal system ( analog and digital), a reconstruction filter, sometimes called an anti-imaging filter, is used to construct a smooth analog signal from a digital input, as in the case of a digital to analog converter ( DAC) or other sampled data output device. Sampled data reconstruction filters The sampling theorem describes why the input of an ADC requires a low-pass analog electronic filter, called the anti-aliasing filter: the sampled ''input'' signal must be bandlimited to prevent aliasing (here meaning waves of higher frequency being ''recorded'' as a lower frequency). For the same reason, the output of a DAC requires a low-pass analog filter, called a reconstruction filter - because the ''output'' signal must be bandlimited, to prevent imaging (meaning Fourier coefficients being reconstructed as spurious high-frequency 'mirrors'). This is an implementation of the Whittaker–Shannon interpolation formula. Ideally, both filters should be brickwall filters, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Computer Graphics
3D computer graphics, sometimes called Computer-generated imagery, CGI, 3D-CGI or three-dimensional Computer-generated imagery, computer graphics, are graphics that use a three-dimensional representation of geometric data (often Cartesian coordinate system#Cartesian coordinates in three dimensions, Cartesian) that is stored in the computer for the purposes of performing calculations and rendering digital images, usually 2D images but sometimes 3D images. The resulting images may be stored for viewing later (possibly as an Computer animation, animation) or displayed in Real-time computer graphics, real time. 3D computer graphics, contrary to what the name suggests, are most often displayed on two-dimensional displays. Unlike 3D film and similar techniques, the result is two-dimensional, without visual depth perception, depth. More often, 3D graphics are being displayed on 3D displays, like in virtual reality systems. 3D graphics stand in contrast to 2D computer graphics which t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics Algorithms
A computer is a machine that can be programmed to automatically carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as ''programs'', which enable computers to perform a wide range of tasks. The term computer system may refer to a nominally complete computer that includes the hardware, operating system, software, and peripheral equipment needed and used for full operation; or to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems, including simple special-purpose devices like microwave ovens and remote controls, and factory devices like industrial robots. Computers are at the core of general-purpose devices such as personal computers and mobile devices such as smartphones. Computers power the Internet, which links billions of computer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Tetrahedra
Marching tetrahedra is an algorithm in the field of computer graphics to render implicit surfaces. It clarifies a minor ambiguity problem of the marching cubes algorithm with some cube configurations. It was originally introduced in 1991. While the original marching cubes algorithm was protected by a software patent, marching tetrahedrons offered an alternative algorithm that did not require a patent license. More than 20 years have passed from the patent filing date (June 5, 1985), and the marching cubes algorithm can now be used freely. Optionally, the minor improvements of marching tetrahedrons may be used to correct the aforementioned ambiguity in some configurations. In ''marching tetrahedra'', each cube is split into six irregular tetrahedron, tetrahedra by cutting the cube in half three times, cutting diagonally through each of the three pairs of opposing faces. In this way, the tetrahedra all share one of the main diagonals of the cube. Instead of the twelve edges of the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image-based Meshing
Image-based meshing is the automated process of creating computer models for computational fluid dynamics (CFD) and finite element analysis (FEA) from 3D image data (such as magnetic resonance imaging (MRI), computed tomography (CT) or microtomography). Although a wide range of mesh generation techniques are currently available, these were usually developed to generate models from computer-aided design (CAD), and therefore have difficulties meshing from 3D imaging data. Mesh generation from 3D imaging data Meshing from 3D imaging data presents a number of challenges but also unique opportunities for presenting a more realistic and accurate geometrical description of the computational domain. There are generally two ways of meshing from 3D imaging data: CAD-based approach The majority of approaches used to date still follow the traditional CAD route by using an intermediary step of surface reconstruction which is then followed by a traditional CAD-based meshing algorithm. CAD-based ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Tetrahedra
Marching tetrahedra is an algorithm in the field of computer graphics to render implicit surfaces. It clarifies a minor ambiguity problem of the marching cubes algorithm with some cube configurations. It was originally introduced in 1991. While the original marching cubes algorithm was protected by a software patent, marching tetrahedrons offered an alternative algorithm that did not require a patent license. More than 20 years have passed from the patent filing date (June 5, 1985), and the marching cubes algorithm can now be used freely. Optionally, the minor improvements of marching tetrahedrons may be used to correct the aforementioned ambiguity in some configurations. In ''marching tetrahedra'', each cube is split into six irregular tetrahedron, tetrahedra by cutting the cube in half three times, cutting diagonally through each of the three pairs of opposing faces. In this way, the tetrahedra all share one of the main diagonals of the cube. Instead of the twelve edges of the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Illumination Model
{{Short description, none This article lists common shading algorithms used in computer graphics. Interpolation techniques These techniques can be combined with any illumination model: * Flat shading * Gouraud shading * Phong shading Illumination models Realistic The illumination models listed here attempt to model the perceived brightness of a surface or a component of the brightness in a way that looks realistic. Some take physical aspects into consideration, like for example the Fresnel equations, microfacets, the rendering equation and subsurface scattering. Diffuse reflection Light that is reflected on a non-metallic and/or a very rough surface gives rise to a diffuse reflection. Models that describe the perceived brightness due to diffuse reflection include: * Lambert * Oren–Nayar (Rough opaque diffuse surfaces) * Minnaert Specular reflection Light that is reflected on a relatively smooth surface gives rise to a specular reflection. This kind of reflection is especia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Interpolation
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points. Linear interpolation between two known points If the two known points are given by the coordinates (x_0,y_0) and the linear interpolant is the straight line between these points. For a value x in the interval the value y along the straight line is given from the equation of slopes \frac = \frac, which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with Solving this equation for y, which is the unknown value at x, gives \begin y &= y_0 + (x-x_0)\frac \\ &= \frac + \frac\\ &= \frac \\ &= \frac, \end which is the formula for linear interpolation in the interval Outside this interval, the formula is identical to linear extrapolation. This formula can also be understood as a weighted average. The weights are inversely related to the dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of f. If the gradient of a function is non-zero at a point p, the direction of the gradient is the direction in which the function increases most quickly from p, and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to minimize a function by gradient descent. In coordinate-free terms, the gradient of a function f(\mathbf) may be defined by: df=\nabla f \cdot d\mathbf where df is the total infinitesimal change in f for a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Decider
In scientific visualization the asymptotic decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some "bad" topology, but can also be considered an algorithm in its own right. Principle The algorithm first divides the scalar field into uniform cubes. It draws topologically correct contours on the sides (interface) of the cubes. These contours can then be connected to polygons and triangulation, triangulated. The triangles of all cubes form the isosurfaces and are thus the output of the algorithm. Sometimes there is more than one way to connect adjacent constructs. This algorithm describes a method for resolving these ambiguous configurations in a consistent manner. Ambiguous cases often occur if diagonally opposing points are found on the same side of the isoline, but on a different side to the other points in the square (for 2D system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
