Patent Document ID: 8089670
Application ID: 11961425
Patent Status: 1

Claim One:
1. A method of forming a multidimensional upsampled table comprising a plurality of upsampled contents, a plurality of upsampled columns, and a plurality of upsampled rows, the method comprising: (A) reading a multidimensional unsampled table including a plurality of unsampled content values, the multidimensional unsampled table having a plurality of unsampled columns and a plurality of unsampled rows, the multidimensional unsampled table being monotonic in each of the plurality of unsampled columns and being monotonic in each of the plurality of unsampled rows; (B) performing an upsampling algorithm on the plurality of unsampled content values of the multidimensional unsampled table to create the multidimensional upsampled table, wherein: (a) the multidimensional unsampled table includes a plurality of nodes corresponding to the plurality of unsampled content values that correspond to the intersections of unsampled rows and unsampled columns of the multidimensional unsampled table and a plurality of unsampled boundary nodes corresponding to the plurality of unsampled content values at an end-point of each of at least one of the plurality of unsampled rows of the multidimensional unsampled table or at an end-point of each of the at least one of the plurality of unsampled columns of the multidimensional unsampled table; (b) the multidimensional unsampled table includes at least one of: (i) an increasing column direction corresponding to the direction in which the plurality of unsampled content values in the at least one unsampled column increases in value, wherein the at least one unsampled column has a greater column node corresponding to the unsampled boundary having the greater unsampled content value, and a lower column node corresponding to the unsampled boundary node having the lower unsampled content value; and (ii) an increasing unsampled row direction corresponding to the direction in which the plurality of unsampled content values in the at least one unsampled row increases in value, wherein the at least one unsampled row has a greater row node corresponding to the unsampled boundary node having the greater unsampled content value, and a lower row node corresponding to the unsampled boundary node having the lower unsampled content value; (c) based on the properties of the upsampling algorithm, the multidimensional upsampled table has at least one of the following properties: (i) no upsampled content value in a given upsampled column of the multidimensional upsampled table being greater than the greater column node in the corresponding unsampled column of the multidimensional unsampled table; (ii) no upsampled content value in a given upsampled column of the multidimensional upsampled table being less than the lower column node in the corresponding unsampled column of the multidimensional unsampled table; (iii) no upsampled content value in a given upsampled row of the upsampled table being greater than the greater row node in the corresponding unsampled row of the multidimensional unsampled table; and (iv) no upsampled content value in a given upsampled row of the multidimensional upsampled table being less than the lower row node in the corresponding unsampled row of the multidimensional unsampled table; and (C) at least one of storing the multidimensional upsampled table, outputting the upsampled table and displaying the upsampled table; wherein the performing of the upsampling algorithm includes interpolating a plurality of values, each value being based on a pair of sequential unsampled nodes in a primary direction as determined by tetrahedral interpolation, wherein values are interpolated in each of the primary directions as determined by tetrahedral interpolation and the interpolation of each value is based on only the pair of sequential unsampled nodes; the upsampling algorithm is a Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation; each pair of nodes includes an original value of each node before being interpolated; and each of the above steps is performed by a processor.