Texture mappingTexture mapping is a method for mapping a texture on a . Texture here can be high frequency detail, surface texture, or color. The original technique was pioneered by Edwin Catmull in 1974. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object).
Least squaresThe method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.
Linear least squaresLinear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. The three main linear least squares formulations are: Ordinary least squares (OLS) is the most common estimator.
Ordinary least squaresIn statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable.
Non-linear least squaresNon-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences.
Texture filteringIn computer graphics, texture filtering or texture smoothing is the method used to determine the texture color for a texture mapped pixel, using the colors of nearby texels (pixels of the texture). There are two main categories of texture filtering, magnification filtering and minification filtering. Depending on the situation texture filtering is either a type of reconstruction filter where sparse data is interpolated to fill gaps (magnification), or a type of anti-aliasing (AA), where texture samples exist at a higher frequency than required for the sample frequency needed for texture fill (minification).
Displacement mappingDisplacement mapping is an alternative computer graphics technique in contrast to bump, normal, and parallax mapping, using a texture or height map to cause an effect where the actual geometric position of points over the textured surface are displaced, often along the local surface normal, according to the value the texture function evaluates to at each point on the surface. It gives surfaces a great sense of depth and detail, permitting in particular self-occlusion, self-shadowing and silhouettes; on the other hand, it is the most costly of this class of techniques owing to the large amount of additional geometry.
Bump mappingBump mapping is a texture mapping technique in computer graphics for simulating bumps and wrinkles on the surface of an object. This is achieved by perturbing the surface normals of the object and using the perturbed normal during lighting calculations. The result is an apparently bumpy surface rather than a smooth surface although the surface of the underlying object is not changed. Bump mapping was introduced by James Blinn in 1978. Normal mapping is the most common variation of bump mapping used.
Reflection mappingIn computer graphics, environment mapping, or reflection mapping, is an efficient technique for approximating the appearance of a reflective surface by means of a precomputed texture. The texture is used to store the of the distant environment surrounding the rendered object. Several ways of storing the surrounding environment have been employed. The first technique was sphere mapping, in which a single texture contains the image of the surroundings as reflected on a spherical mirror.
Optimization problemIn mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
