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n-Simplex Interpolation

Hemingway, Peter

HPL-2002-320

Keyword(s): interpolation; colour; frame buffer algorithms; halftoning & dithering; level of detail algorithms; rendering; printing; texture mapping

Abstract: Interpolation has wide application, and in the field of computer graphics is used for colour maps, sampling pixel images and generating points on surfaces. The performance of an interpolation algorithm is important for computer graphics because the computation is typically carried out repetitively over the typically large number of data points in an image with the modest resources of an appliance like a digital camera. The paper describes a new and practical method of interpolation that selects fewer points to interpolate between. Using fewer points for the interpolation is computationally more efficient because it reduces the number of table accesses and because there are fewer terms and operators in the interpolation equation. It is particularly good when interpolating between values that are close together (i.e. large tables) and can be just as accurate as methods that use more points. The interpolation method is based on n-simplexes so that it can be applied to problems in any dimension.

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