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  2. Tricubic interpolation - Wikipedia

    en.wikipedia.org/wiki/Tricubic_interpolation

    In other contexts, we can obtain the 64 coefficients by considering a 3×3×3 grid of small cubes surrounding the cube inside which we evaluate the function, and fitting the function at the 64 points on the corners of this grid.

  3. Arnold's cat map - Wikipedia

    en.wikipedia.org/wiki/Arnold's_cat_map

    In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name. [1] It is a simple and pedagogical example for hyperbolic toral automorphisms .

  4. Z-order curve - Wikipedia

    en.wikipedia.org/wiki/Z-order_curve

    The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.

  5. Trilinear interpolation - Wikipedia

    en.wikipedia.org/wiki/Trilinear_interpolation

    The above operations can be visualized as follows: First we find the eight corners of a cube that surround our point of interest. These corners have the values c 000 {\displaystyle c_{000}} , c 100 {\displaystyle c_{100}} , c 010 {\displaystyle c_{010}} , c 110 {\displaystyle c_{110}} , c 001 {\displaystyle c_{001}} , c 101 {\displaystyle c ...

  6. List of named matrices - Wikipedia

    en.wikipedia.org/wiki/List_of_named_matrices

    A matrix with all entries equal to one. a ij = 1. Pascal matrix: A matrix containing the entries of Pascal's triangle. Pauli matrices: A set of three 2 × 2 complex Hermitian and unitary matrices. When combined with the I 2 identity matrix, they form an orthogonal basis for the 2 × 2 complex Hermitian matrices. Redheffer matrix

  7. Cube mapping - Wikipedia

    en.wikipedia.org/wiki/Cube_mapping

    The lower left image shows a scene with a viewpoint marked with a black dot. The upper image shows the net of the cube mapping as seen from that viewpoint, and the lower right image shows the cube superimposed on the original scene. In computer graphics, cube mapping is a method of environment mapping that uses the six faces of a cube as the ...

  8. Spline interpolation - Wikipedia

    en.wikipedia.org/wiki/Spline_interpolation

    Originally, spline was a term for elastic rulers that were bent to pass through a number of predefined points, or knots. These were used to make technical drawings for shipbuilding and construction by hand, as illustrated in the figure. We wish to model similar kinds of curves using a set of mathematical equations.

  9. Bilinear map - Wikipedia

    en.wikipedia.org/wiki/Bilinear_map

    In general, the bilinear map is not continuous (no matter what topologies the spaces of linear maps are given). We do, however, have the following results: Give all three spaces of linear maps one of the following topologies: give all three the topology of bounded convergence; give all three the topology of compact convergence;