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  2. Trilinear interpolation - Wikipedia

    en.wikipedia.org/wiki/Trilinear_interpolation

    Trilinear interpolation is the extension of linear interpolation, which operates in spaces with dimension =, and bilinear interpolation, which operates with dimension =, to dimension =. These interpolation schemes all use polynomials of order 1, giving an accuracy of order 2, and it requires 2 D = 8 {\displaystyle 2^{D}=8} adjacent pre-defined ...

  3. Tricubic interpolation - Wikipedia

    en.wikipedia.org/wiki/Tricubic_interpolation

    In the mathematical subfield numerical analysis, tricubic interpolation is a method for obtaining values at arbitrary points in 3D space of a function defined on a regular grid. The approach involves approximating the function locally by an expression of the form f ( x , y , z ) = ∑ i = 0 3 ∑ j = 0 3 ∑ k = 0 3 a i j k x i y j z k ...

  4. Linear interpolation - Wikipedia

    en.wikipedia.org/wiki/Linear_interpolation

    A description of linear interpolation can be found in the ancient Chinese mathematical text called The Nine Chapters on the Mathematical Art (九章算術), [1] dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. The basic operation of linear interpolation between two values is commonly used in computer graphics.

  5. Slerp - Wikipedia

    en.wikipedia.org/wiki/Slerp

    In computer graphics, slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake [1] in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1.

  6. Marching squares - Wikipedia

    en.wikipedia.org/wiki/Marching_squares

    For example, a triangular mesh may represent a 2D data surface embedded in 3D space, where spatial positions of the vertices and interpolated points along a contour will all have 3 coordinates. Note that the case of squares is ambiguous again, because a quadrilateral embedded in 3-dimensional space is not necessarily planar, so there is a ...

  7. Interpolation space - Wikipedia

    en.wikipedia.org/wiki/Interpolation_space

    The theory of interpolation of vector spaces began by an observation of Józef Marcinkiewicz, later generalized and now known as the Riesz-Thorin theorem.In simple terms, if a linear function is continuous on a certain space L p and also on a certain space L q, then it is also continuous on the space L r, for any intermediate r between p and q.

  8. Trilinear - Wikipedia

    en.wikipedia.org/wiki/Trilinear

    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; Trilinear polarity, in ...

  9. Bilinear interpolation - Wikipedia

    en.wikipedia.org/wiki/Bilinear_interpolation

    In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid , though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals .