Method of plotting surfaces in a 3D volume

Claim 1

A method of plotting surfaces in a volume which represents values of a parameter sampled along three mutually orthogonal X, Y, Z axes and showing extrema organized along said surfaces, said values of the parameter being so distributed in said volume to form a set of Z axis columns over nodes of a grid defined in a plane parallel to the X, Y, axes, said method comprising the steps of: (a) generating a Peano-Hilbert curve adapted to pass through all the nodes of said grid such that said curve crosses each of said nodes only once; (b) establishing a one-to-one relationship R between a Peano order associated with the Peano-Hilbert curve and the coordinates of the nodes of the grid associated with each of said Z axis columns, said Peano order corresponding to an order of encountering the nodes when the Peano-Hilbert curve is followed starting from one of its ends; (c) classifying the Z axis columns using said relationship R so as to transform said volume containing the columns into a two dimensional picture wherein said columns are juxtaposed according to the Peano order of their corresponding nodes; (d) applying an automatic plotting program to said two dimensional picture enabling extrema correlating one column to the next to be connected in segments; (e) performing an inverse relationship R -1 on each of said segments to reposition each of the extrema located on each selected segment in its actual position in said volume and to transform said selected segment into a contour line which connects these extrema in said volume and limits an elementary surface element; and (f) grouping and displaying the elementary surface elements obtained by the transformation.

Claim 2

A method of plotting surfaces in a volume which represents values of a parameter sampled along three mutually orthogonal X, Y, Z axes and showing extrema organized along said surfaces, said values of the parameter being so distributed in said volume to form a set of Z axis columns over nodes of a grid defined in a plane parallel to the X, Y, axes, said method comprising the steps of: (a) generating a Peano-Hilbert curve adapted to pass through all the nodes of said grid such that said curve crosses each of said nodes only once; (b) establishing a one-to-one relationship R between a Peano order associated with the Peano-Hilbert curve and the coordinates of the nodes of the grid associated with each of said Z axis columns, said Peano order corresponding to an order of encountering the nodes when the Peano-Hilbert curve is followed starting from one of its ends; (c) classifying the Z axis columns using said relationship R so as to transform said volume containing the columns into a two dimensional picture wherein said columns are juxtaposed according to the Peano order of their corresponding nodes; (d) applying an automatic plotting program to said two dimensional picture enabling extrema correlating one column to the next to be connected in segments; (e) performing an inverse relationship R -1 on each of said segments to reposition each of the extrema located on each selected segment in its actual position in said volume and to transform said selected segment into a contour line which connects these extrema in said volume and limits an elementary surface element; and (f) grouping and displaying the elementary surface elements obtained by the transformation.