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Trilinear Map
Trilinear may refer to: * Trilinear filtering, a method in computer graphics for choosing the color of a texture * Trilinear form, a type of mathematical function from a vector space to the underlying field * Trilinear interpolation, an extension of linear interpolation for interpolating functions of three variables on a rectilinear 3D grid * Trilinear map, a type of mathematical function between vector spaces * Trilinear coordinates In geometry, the trilinear coordinates of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates are an example of homogeneous coordinates. The ratio is ... * Trilinear polarity, in geometry {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trilinear Filtering
Trilinear filtering is an extension of the bilinear texture filtering method, which also performs linear interpolation between mipmaps. Bilinear filtering has several weaknesses that make it an unattractive choice in many cases: using it on a full-detail texture when scaling to a very small size causes accuracy problems from missed texels, and compensating for this by using multiple mipmaps throughout the polygon leads to abrupt changes in blurriness, which is most pronounced in polygons that are steeply angled relative to the camera. To solve this problem, trilinear filtering interpolates between the results of bilinear filtering on the two mipmaps nearest to the detail required for the polygon at the pixel. If the pixel would take up 1/100 of the texture in one direction, trilinear filtering would interpolate between the result of filtering the 128×128 mipmap as y1 with x1 as 128, and the result of filtering on the 64×64 mipmap as y2 with x2 as 64, and then interpolate to . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trilinear Form
In abstract algebra and multilinear algebra, a multilinear form on a vector space V over a field K is a map :f\colon V^k \to K that is separately K-linear in each of its k arguments. More generally, one can define multilinear forms on a module over a commutative ring. The rest of this article, however, will only consider multilinear forms on finite-dimensional vector spaces. A multilinear k-form on V over \R is called a (covariant) \boldsymbol-tensor, and the vector space of such forms is usually denoted \mathcal^k(V) or \mathcal^k(V). Tensor product Given a k-tensor f\in\mathcal^k(V) and an \ell-tensor g\in\mathcal^\ell(V), a product f\otimes g\in\mathcal^(V), known as the tensor product, can be defined by the property : (f\otimes g)(v_1,\ldots,v_k,v_,\ldots, v_)=f(v_1,\ldots,v_k)g(v_,\ldots, v_), for all v_1,\ldots,v_\in V. The tensor product of multilinear forms is not commutative; however it is bilinear and associative: : f\otimes(ag_1+bg_2)=a(f\otimes g_1)+b(f\otimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trilinear Interpolation
Trilinear interpolation is a method of multivariate interpolation on a Three dimensional space, 3-dimensional regular grid. It approximates the value of a function at an intermediate point (x, y, z) within the local axial rectangular prism (geometry), prism linearly, using function data on the lattice points. Trilinear interpolation is frequently used in numerical analysis, data analysis, and computer graphics. Related methods Trilinear interpolation is the extension of linear interpolation, which operates in spaces with dimension D = 1, and bilinear interpolation, which operates with dimension D = 2, to dimension D = 3. These interpolation schemes all use polynomials of order 1, giving an accuracy of order 2, and it requires 2^D = 8 adjacent pre-defined values surrounding the interpolation point. There are several ways to arrive at trilinear interpolation, which is equivalent to 3-dimensional tensor B-spline interpolation of order 1, and the trilinear interpolation operator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trilinear Map
Trilinear may refer to: * Trilinear filtering, a method in computer graphics for choosing the color of a texture * Trilinear form, a type of mathematical function from a vector space to the underlying field * Trilinear interpolation, an extension of linear interpolation for interpolating functions of three variables on a rectilinear 3D grid * Trilinear map, a type of mathematical function between vector spaces * Trilinear coordinates In geometry, the trilinear coordinates of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates are an example of homogeneous coordinates. The ratio is ... * Trilinear polarity, in geometry {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trilinear Coordinates
In geometry, the trilinear coordinates of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates are an example of homogeneous coordinates. The ratio is the ratio of the perpendicular distances from the point to the sides (extended if necessary) opposite vertices and respectively; the ratio is the ratio of the perpendicular distances from the point to the sidelines opposite vertices and respectively; and likewise for and vertices and . In the diagram at right, the trilinear coordinates of the indicated interior point are the actual distances (, , ), or equivalently in ratio form, for any positive constant . If a point is on a sideline of the reference triangle, its corresponding trilinear coordinate is 0. If an exterior point is on the opposite side of a sideline from the interior of the triangle, its trilinear coordinate associated with that sideline is negative. It is impossible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
