Examples of "trivariate"
approximation into a multidimensional spaces. A modified version of the algorithm designed for trivariate interpolation was developed by Robert J. Renka and is available in Netlib as algorithm 661 in the toms library.
Lai received a B.Sc. from Hangzhou University and a Ph.D. in mathematics from the Texas A&M University in 1989. His dissertation was entitled "On Construction of Bivariate and Trivariate Vertex Splines on Arbitrary Mixed Grid Partitions" and supervised by Charles K. Chui.
A polynomial in one indeterminate is called a "univariate polynomial", a polynomial in more than one indeterminate is called a multivariate polynomial. A polynomial with two indeterminates is called a bivariate polynomial. These notions refer more to the kind of polynomials one is generally working with than to individual polynomials; for instance when working with univariate polynomials one does not exclude constant polynomials (which may result, for instance, from the subtraction of non-constant polynomials), although strictly speaking constant polynomials do not contain any indeterminates at all. It is possible to further classify multivariate polynomials as "bivariate", "trivariate", and so on, according to the maximum number of indeterminates allowed. Again, so that the set of objects under consideration be closed under subtraction, a study of trivariate polynomials usually allows bivariate polynomials, and so on. It is common, also, to say simply "polynomials in , and ", listing the indeterminates allowed.
Friis published three series of thematic maps covering Norway north of the Ofotfjord. First edition in 1861, second in 1888/1890. Each household was coded by a trivariate symbology denoting (1) ethnic group (2) household member's fluency in the Norwegian, Sami and Kven language and (3) whether the family lived in a goahti. These maps, in addition to the censuses of 1865, 1875, 1891 and 1900 provide a valuable resource of knowledge of the ethnicity and language in the circumpolar region decades before the enforcement of Norwegian as the single official language in schools.
Limberger and Oliveira suggested a deterministic technique for plane detection in unorganized point clouds whose cost is formula_9 in the number of samples, achieving real-time performance for relatively large datasets (up to formula_10 points on a 3.4 GHz CPU). It is based on a fast Hough-transform voting strategy for planar regions, inspired by the Kernel-based Hough transform (KHT). This 3D Kernel-based Hough transform (3DKHT) uses a fast and robust algorithm to segment clusters of approximately co-planar samples, and casts votes for individual clusters (instead of for individual samples) on a (formula_11) spherical accumulator using a trivariate Gaussian kernel. The approach is several orders of magnitude faster than existing (non-deterministic) techniques for plane detection in point clouds, such as RHT and RANSAC, and scales better with the size of the datasets. It can be used with any application that requires fast detection of planar features on large datasets.