Method and apparatus for generating m-degree forms in a n-dimension space

Abstract

A method and apparatus is disclosed for generating a m-degree form in a n-dimension space. A framework is used to generate the form. The framework comprises a defined number of sections, lines and control points depending on the complexity of the form to generate. An iterative solving process is then used in order to provide the algebraic coefficients of the m-degree form using at least data related to the control points.

1 . A method for generating an m-degree form using algebraic coefficients of an equation defining the m-degree form in an n-dimension space using a plurality of points defining the form, the method comprising: 
 providing a framework, comprising more than one geometric surface, each of the more than one geometric surface comprising at least one line, each of the at least one line comprising at least one point of the plurality of points;    providing a solving equation using the equation defining the m-degree form, the solving equation depending on at least three points;    for each of the plurality of points, generating a corresponding equation by applying the. solving equation to each of the plurality of points and two points located on one of the more than one geometric surface, the two selected points defining the line of the framework where each of the plurality of points is;    resolving the generated corresponding equations in an iterative manner to provide the algebraic coefficients of the m-degree form; the iterative manner consisting in handling the generated equation using each of the plurality of points in a certain order, the certain order consisting in selecting the generated corresponding equation corresponding to a point located on the line having the highest number of points on it and the line located in the at least one geometric surface of the framework where there is the highest number of lines on it; and    generating the m-degree form using the provided algebraic coefficients of the m-degree form.    
   
   
       2 . The method as claimed in  claim 1 , wherein a point may be a polar point or a non-polar point, the solving equation being generated using the equation defining the m-degree form and a polarity relation, the solving equation depending on four points, two of the four points being a polar and its related non-polar point, the two other points of the four points defining the line of the framework where the polar point and its related non-polar point are.  
   
   
       3 . The method as claimed in  claim 1 , wherein the more than one geometric surface is a plane.  
   
   
       4 . The method as claimed in  claim 1 , wherein the n-dimension space is a projective space.  
   
   
       5 . The method as claimed in  claim 1 , wherein the geometric space is an (n+1)-dimension euclidian space.  
   
   
       6 . The method as claimed in  claim 1 , further comprising the step of storing the algebraic coefficients of the m-degree form with an identifier.  
   
   
       7 . The method as claimed in  claim 4 , wherein the projective space is a 4-dimension space.  
   
   
       8 . The method as claimed in  claim 1 , wherein the generating of the m-degree form using the provided algebraic coefficients of the m-degree form is performed using a raytracing technique.  
   
   
       9 . An apparatus for generating a m-degree form using algebraic coefficients of an equation defining the m-degree form in an n-dimension space using a plurality of points defining the form, the apparatus comprising: 
 an object memory, comprising more than one geometric surface, each of the more than one geometric surface comprising at least one line, each of the at least one line comprising at least one point of the plurality of points;    a control point to algebraic coefficient converter unit receiving each of the plurality of points and a solving equation defined using the equation defining the m-degree form and depending on at least three points, the control point to algebraic converter unit generating a corresponding equation by applying the solving equation to each of the plurality of points and two points located on one of the more than one geometric surface, the two selected points defining the line of the framework where each of the plurality of points is and resolving the generated corresponding equations in an iterative manner to provide the algebraic coefficients of the m-degree form; the iterative manner consisting in handling the generated equation using each of the plurality of points in a certain order, the certain order consisting in selecting the generated corresponding equation corresponding to a point located on the line having the highest number of points on it and the line located in the at least one geometric surface of the framework where there is the highest number of lines on it; and    an outputting unit, receiving the provided algebraic coefficients of the m-degree form and generating the m-degree form.    
   
   
       10 . The apparatus as claimed in  claim 9 , wherein the outputting unit comprises a raytracer unit, the raytracer unit further receiving a point of view signal.  
   
   
       11 . A method for monitoring a deformation of an m-degree form using algebraic coefficients of an equation defining the m-degree form in an n-dimension space using a plurality of points defining the form, the method comprising: 
 providing a framework in accordance with a modification of a form planned, the framework comprising more than one geometric surface, each of the more than one geometric surface comprising at least one line, each of the at least one line comprising at least one point of the plurality of points;    modifying at least one part of the provided framework in accordance with the modification of the form planned;    providing a solving equation using the equation defining the m-degree form, the solving equation depending on at least three points;    for each of the plurality of points, generating a corresponding equation by applying the solving equation to each of the plurality of points and two points located on one of the more than one geometric surface, the two selected points defining the line of the framework where each of the plurality of points is;    resolving the generated corresponding equations in an iterative manner to provide the algebraic coefficients of the m-degree modified form; the iterative manner consisting in handling the generated equation using each of the plurality of points in a certain order, the certain order consisting in selecting the generated corresponding equation corresponding to a point located on the line having the highest number of points on it and the line located in the at least one geometric surface of the framework where there is the highest number of lines on it; and    outputting the algebraic coefficients of the modified form.    
   
   
       12 . The method as claimed in  claim 11 , further comprising the step of generating the modified m-degree form using the outputted algebraic coefficients of the modified m-degree form.