Apparatus for evaluating a mathematical function

Abstract

An apparatus for evaluating a mathematical function at an input value is provided. The apparatus includes a device for selecting a mathematical function, a device for inputting a value at which to evaluate the function, a device for identifying an interval containing the input value, the interval being described by at least one polynomial function, a device for retrieving at least one control point representing the polynomial function from at least one look up table, a device for deriving the polynomial function from the control points, a device for evaluating the function for the input value and a device for providing data representing the evaluated function at an output.

1 . A method for evaluating a mathematical function at an input value comprising the steps of;
 selecting a mathematical function;   inputting a value at which to evaluate the function;   identifying an interval containing the input value, the interval being described by at least one polynomial function;   retrieving at least one control point representing the polynomial function from at least one look up table,   deriving the polynomial function from the control points, evaluating the function for the input value, and   providing data representing the evaluated function at an output.   
     
     
         2 . A method for evaluating a mathematical function at an input value according to  claim 1  comprising the further step of interpolating the polynomial function, wherein the step of evaluating the function for an input value is performed using the interpolation. 
     
     
         3 . A method for evaluating a mathematical function at an input value according to  claim 1  wherein the control points are B-spline control points. 
     
     
         4 . A method for evaluating a mathematical function at an input value according to  claim 2  wherein the control points are B-spline control points. 
     
     
         5 . A method for evaluating a mathematical function at an input value according to  claim 3  comprising the further steps of deriving B-Spline representation from the B-spline control points and mapping the B-spline representation to a Bezier representation in order to allow the use of the de Casteljau evaluation method. 
     
     
         6 . A method for evaluating a mathematical function at an input value according to  claim 4  comprising the further steps of deriving B-Spline representation from the B-spline control points and mapping the B-spline representation to a Bezier representation in order to allow the use of the de Casteljau evaluation method. 
     
     
         7 . A method for evaluating a mathematical function at an input value according to  claim 1  comprising the further step of removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         8 . A method for evaluating a mathematical function at an input value according to  claim 2  comprising the further step of removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         9 . A method for evaluating a mathematical function at an input value according to  claim 3  comprising the further step of removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         10 . A method for evaluating a mathematical function at an input value according to  claim 4  comprising the further step of removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         11 . A method for evaluating a mathematical function at an input value according to  claim 5  comprising the further step of removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         12 . A method for evaluating a mathematical function at an input value according to  claim 6  comprising the further step of removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         13 . A method for evaluating a mathematical function at an input value according to  claim 1  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         14 . A method for evaluating a mathematical function at an input value according to  claim 2  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         15 . A method for evaluating a mathematical function at an input value according to  claim 3  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         16 . A method for evaluating a mathematical function at an input value according to  claim 4  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         17 . A method for evaluating a mathematical function at an input value according to  claim 5  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         18 . A method for evaluating a mathematical function at an input value according to  claim 6  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         19 . A method for evaluating a mathematical function at an input value according to  claim 7  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         20 . A method for evaluating a mathematical function at an input value according to  claim 8  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         21 . A method for evaluating a mathematical function at an input value according to  claim 9  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         22 . A method for evaluating a mathematical function at an input value according to  claim 10  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         23 . A method for evaluating a mathematical function at an input value according to  claim 11  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         24 . A method for evaluating a mathematical function at an input value according to  claim 12  wherein the positions in the lookup tables from which control points are retrieved are defined by lookup index values, comprising the further steps of manipulating the lookup index values such that, when one control point is retrieved from each of a plurality of lookup tables, the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         25 . An apparatus for evaluating a mathematical function at an input value comprising;
 means for selecting a mathematical function;   means for inputting a value at which to evaluate the function;   means for identifying an interval containing the input value, the interval being described by at least one polynomial function;   means for retrieving at least one control point representing the polynomial function from at least one look up table,   means for deriving the polynomial function from the control points,   means for interpolating the polynomial function;   means for evaluating the function for the input value using the interpolation, and   means for providing data representing the evaluated function at an output.   
     
     
         26 . An apparatus for evaluating a mathematical function at an input value according to  claim 25  comprising means for interpolating the polynomial function wherein the means for evaluating the function for the input value uses the interpolation. 
     
     
         27 . An apparatus for evaluating a mathematical function at an input value according to  claim 25  wherein the control points are B-spline control points. 
     
     
         28 . An apparatus for evaluating a mathematical function at an input value according to  claim 26  wherein the control points are B-spline control points. 
     
     
         29 . An apparatus for evaluating a mathematical function at an input value according to  claim 27  comprising means for deriving B-Spline representation from the B-spline control points and means for mapping the B-spline representation to a Bezier representation in order to allow the use of the de Casteljau evaluation method. 
     
     
         30 . An apparatus for evaluating a mathematical function at an input value according to  claim 28  comprising means for deriving B-Spline representation from the B-spline control points and means for mapping the B-spline representation to a Bezier representation in order to allow the use of the de Casteljau evaluation method. 
     
     
         31 . An apparatus for evaluating a mathematical function at an input value according to  claim 25  comprising means for removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         32 . An apparatus for evaluating a mathematical function at an input value according to  claim 26  comprising means for removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         33 . An apparatus for evaluating a mathematical function at an input value according to  claim 27  comprising means for removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         34 . An apparatus for evaluating a mathematical function at an input value according to  claim 28  comprising means for removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         35 . An apparatus for evaluating a mathematical function at an input value according to  claim 29  comprising means for removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         36 . An apparatus for evaluating a mathematical function at an input value according to  claim 30  comprising means for removing a linear term from the function before evaluating the function and re-applying the linear function after the evaluation. 
     
     
         37 . An apparatus for evaluating a mathematical function at an input value according to  claim 25  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         38 . An apparatus for evaluating a mathematical function at an input value according to  claim 26  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         39 . An apparatus for evaluating a mathematical function at an input value according to  claim 27  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         40 . An apparatus for evaluating a mathematical function at an input value according to  claim 28  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         41 . An apparatus for evaluating a mathematical function at an input value according to  claim 29  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         42 . An apparatus for evaluating a mathematical function at an input value according to  claim 30  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         43 . An apparatus for evaluating a mathematical function at an input value according to  claim 31  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         44 . An apparatus for evaluating a mathematical function at an input value according to  claim 32  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         45 . An apparatus for evaluating a mathematical function at an input value according to  claim 33  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         46 . An apparatus for evaluating a mathematical function at an input value according to  claim 34  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         47 . An apparatus for evaluating a mathematical function at an input value according to  claim 35  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order. 
     
     
         48 . An apparatus for evaluating a mathematical function at an input value according to  claim 36  wherein the positions in the lookup tables from which the control points are read are defined by lookup index values, comprising means for manipulating the lookup index values such that when one control point is retrieved from each of a plurality of lookup tables the control points retrieved are sufficient to evaluate the function at the position specified by the index value, and means for rotating the retrieved control points so as to present the control points to an evaluation unit in the required order.