class TPainter3dAlgorithms: public TObject, public TAttLine, public TAttFill

 Lego default constructor

 Normal default constructor

  rmin[3], rmax[3] are the limits of the lego object depending on
  the selected coordinate system

 Lego default destructor

 Draw back surfaces of surrounding box

    Input  ANG     - angle between X and Y axis

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

 Clear screen

 Set correspondance between function and color levels

    Input: NL        - number of levels
           FL(NL)    - function levels
           ICL(NL+1) - colors for levels

    Output: IREP     - reply: 0 O.K.
                             -1 error in parameters:
                         illegal number of levels
                         function levels must be in increasing order
                         negative color index

 Define the grid levels drawn in the background of surface and lego plots.
 The grid levels are aligned on the  Z axis' main tick marks.

 Draw face - 1st variant

    Function: Draw face - 1st variant
              (2 colors: 1st for external surface, 2nd for internal)

    References: WCtoNDC

    Input: ICODES(*) - set of codes for the line (not used)
             ICODES(1) - IX
             ICODES(2) - IY
           XYZ(3,*)  - coordinates of nodes
           NP        - number of nodes
           IFACE(NP) - face
           T(NP)     - additional function defined on this face
                       (not used in this routine)

 Draw face - 2nd option

    Function: Draw face - 2nd option
              (fill in correspondance with function levels)

    References: WCtoNDC, FillPolygon

    Input: ICODES(*) - set of codes for the line (not used)
             ICODES(1) - IX
             ICODES(2) - IY
           XYZ(3,*)  - coordinates of nodes
           NP        - number of nodes
           IFACE(NP) - face
           T(NP)     - additional function defined on this face

 Draw face - 3rd option

    Function: Draw face - 3rd option
              (draw face for stacked lego plot)

    References: WCtoNDC

    Input: ICODES(*) - set of codes for the line
             ICODES(1) - IX coordinate of the line cell
             ICODES(2) - IY coordinate of the line cell
             ICODES(3) - lego number
             ICODES(4) - side: 1-face,2-right,3-back,4-left,
                               5-bottom, 6-top
             XYZ(3,*)  - coordinates of nodes
             NP        - number of nodes
             IFACE(NP) - face
             T(*)      - additional function (not used here)

 Draw face - 1st variant for "MOVING SCREEN" algorithm

    Function: Draw face - 1st variant for "MOVING SCREEN" algorithm
              (draw face with level lines)

    References: FindLevelLines, WCtoNDC,
                FindVisibleDraw, ModifyScreen

    Input: ICODES(*) - set of codes for the line (not used)
             ICODES(1) - IX
             ICODES(2) - IY
           XYZ(3,*)  - coordinates of nodes
           NP        - number of nodes
           IFACE(NP) - face
           TT(NP)    - additional function defined on this face
                       (not used in this routine)

 Draw face - 3rd variant for "MOVING SCREEN" algorithm

    Function: Draw face - 1st variant for "MOVING SCREEN" algorithm
              (draw level lines only)

    References: FindLevelLines, WCtoNDC,
                FindVisibleDraw, ModifyScreen

    Input: ICODES(*) - set of codes for the line (not used)
             ICODES(1) - IX
             ICODES(2) - IY
           XYZ(3,*)  - coordinates of nodes
           NP        - number of nodes
           IFACE(NP) - face
           TT(NP)    - additional function defined on this face
                       (not used in this routine)

 Draw face - 2nd variant for "MOVING SCREEN" algorithm

    Function: Draw face - 2nd variant for "MOVING SCREEN" algorithm
              (draw face for stacked lego plot)

    References: FindLevelLines, WCtoNDC,
                FindVisibleDraw, ModifyScreen

    Input: ICODES(*) - set of codes for the line (not used)
             ICODES(1) - IX
             ICODES(2) - IY
             ICODES(3) - line code (N of lego)
           XYZ(3,*)  - coordinates of nodes
           NP        - number of nodes
           IFACE(NP) - face
           TT(NP)    - additional function defined on this face
                       (not used in this routine)

 Draw face - 1st variant for "RASTER SCREEN" algorithm

    Function: Draw face - 1st variant for "RASTER SCREEN" algorithm
              (draw face with level lines)

    References: FindLevelLines, WCtoNDC,
                FindVisibleLine, FillPolygonBorder

    Input: ICODES(*) - set of codes for the line (not used)
             ICODES(1) - IX
             ICODES(2) - IY
           XYZ(3,*)  - coordinates of nodes
           NP        - number of nodes
           IFACE(NP) - face
           TT(NP)    - additional function defined on this face
                       (not used in this routine)

 Draw face - 2nd variant for "RASTER SCREEN" algorithm

    Function: Draw face - 2nd variant for "RASTER SCREEN" algorithm
              (draw face for stacked lego plot)

    References: WCtoNDC, FindVisibleLine, FillPolygonBorder

    Input: ICODES(*) - set of codes for the line (not used)
             ICODES(1) - IX
             ICODES(2) - IY
             ICODES(3) - line code (N of lego)
           XYZ(3,*)  - coordinates of nodes
           NP        - number of nodes
           IFACE(NP) - face
           TT(NP)    - additional function defined on this face
                       (not used in this routine)

 Fill polygon with function values at vertexes

    Input: N      - number of vertexes
           P(3,*) - polygon
           F(*)   - function values at nodes

    Errors: - illegal number of vertexes in polygon
            - illegal call of FillPolygon: no levels

 Fill a polygon including border ("RASTER SCREEN")

    Input: NN      - number of polygon nodes
           XY(2,*) - polygon nodes

 Find level lines for face

    Input: NP      - number of nodes
           F(3,NP) - face
           T(NP)   - additional function

    Error: number of points for line not equal 2

 Find part of edge

    Function: Find part of edge where function defined on this edge
              has value from FMIN to FMAX

    Input: P1(3) - 1st point
           P2(3) - 2nd point
           F1    - function value at 1st point
           F2    - function value at 2nd point
           FMIN  - min value of layer
           FMAX  - max value of layer

    Output: KPP - current number of point
            PP(3,*) - coordinates of new face

 Find visible parts of line (draw line)

    Input: R1(3)  - 1-st point of the line
           R2(3)  - 2-nd point of the line

 Find visible part of a line ("RASTER SCREEN")

    Input: P1(2) - 1st point of the line
           P2(2) - 2nd point of the line
           NTMAX - max allowed number of visible segments

    Output: NT     - number of visible segments of the line
            T(2,*) - visible segments

 Draw forward faces of surrounding box & axes

    Function: Draw forward faces of surrounding box & axes

    References: AxisVertex, Gaxis

    Input  ANG     - angle between X and Y axis

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

 Find part of surface with luminosity in the corners

              This routine is used for Gouraud shading

 Initialize "MOVING SCREEN" method

    Input: XMIN - left boundary
           XMAX - right boundary

 Initialize hidden lines removal algorithm (RASTER SCREEN)

    Input: XMIN - Xmin in the normalized coordinate system
           YMIN - Ymin in the normalized coordinate system
           XMAX - Xmax in the normalized coordinate system
           YMAX - Ymax in the normalized coordinate system
           NX   - number of pixels along X
           NY   - number of pixels along Y

 Service function for Legos

 Draw stack of lego-plots in cartesian coordinates

    Input: ANG      - angle between X ang Y
           NX       - number of cells along X
           NY       - number of cells along Y

           FUN(IX,IY,NV,XY,V,T) - external routine
             IX     - X number of the cell
             IY     - Y number of the cell
             NV     - number of values for given cell
             XY(2,4)- coordinates of the cell corners
             V(NV)  - cell values
             T(4,NV)- additional function (for example: temperature)

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this line
               ICODES(1) - IX
               ICODES(2) - IY
               ICODES(3) - IV
               ICODES(4) - side: 1-face,2-right,3-back,4-left,
                                 5-bottom, 6-top
               XYZ(3,*)  - coordinates of nodes
               NP        - number of nodes
               IFACE(NP) - face
                T(4)   - additional function (here Z-coordinate)

           CHOPT - options: 'BF' - from BACK to FRONT
                            'FB' - from FRONT to BACK

 Draw stack of lego-plots in polar coordinates

    Input: IORDR - order of variables (0 - R,PHI; 1 - PHI,R)
           NA    - number of steps along 1st variable
           NB    - number of steps along 2nd variable

           FUN(IA,IB,NV,AB,V,TT) - external routine
             IA      - cell number for 1st variable
             IB      - cell number for 2nd variable
             NV      - number of values for given cell
             AB(2,4) - coordinates of the cell corners
             V(NV)   - cell values
             TT(4,*) - additional function

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
               ICODES(1) - IA
               ICODES(2) - IB
               ICODES(3) - IV
               ICODES(4) - side: 1-internal,2-right,3-external,4-left
                                 5-bottom, 6-top
             XYZ(3,*)  - coordinates of nodes
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

            CHOPT       - options: 'BF' - from BACK to FRONT
                                   'FB' - from FRONT to BACK

 Draw stack of lego-plots in cylindrical coordinates

    Input: IORDR - order of variables (0 - Z,PHI; 1 - PHI,Z)
           NA    - number of steps along 1st variable
           NPHI  - number of steps along 2nd variable

           FUN(IA,IB,NV,AB,V,TT) - external routine
             IA      - cell number for 1st variable
             IB      - cell number for 2nd variable
             NV      - number of values for given cell
             AB(2,4) - coordinates of the cell corners
             V(NV)   - cell values
             TT(4,*) - additional function

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
               ICODES(1) - IA
               ICODES(2) - IB
               ICODES(3) - IV
               ICODES(4) - side: 1,2,3,4 - ordinary sides
                                 5-bottom,6-top
             XYZ(3,*)  - coordinates of nodes
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

           CHOPT       - options: 'BF' - from BACK to FRONT
                                  'FB' - from FRONT to BACK

 Draw stack of lego-plots spheric coordinates

    Input: IPSDR - pseudo-rapidity flag
           IORDR - order of variables (0 - THETA,PHI; 1 - PHI,THETA)
           NA    - number of steps along 1st variable
           NB    - number of steps along 2nd variable

           FUN(IA,IB,NV,AB,V,TT) - external routine
             IA      - cell number for 1st variable
             IB      - cell number for 2nd variable
             NV      - number of values for given cell
             AB(2,4) - coordinates of the cell corners
             V(NV)   - cell values
             TT(4,*) - additional function

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
               ICODES(1) - IA
               ICODES(2) - IB
               ICODES(3) - IV
               ICODES(4) - side: 1,2,3,4 - ordinary sides
                                 5-bottom,6-top
             XYZ(3,*)  - coordinates of nodes
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

           CHOPT       - options: 'BF' - from BACK to FRONT
                                  'FB' - from FRONT to BACK

 Set light source

    Input: NL   - source number: -1 off all light sources
                                  0 set diffused light
           YL   - intensity of the light source
           XSCR |
           YSCR  > direction of the light (in respect of the screen)
           ZSCR |

    Output: IREP   - reply : 0 - O.K.
                            -1 - error in light sources definition:
                                 negative intensity
                                 source number greater than max
                                 light source is placed at origin

 Find surface luminosity at given point
                                         --
    Lightness model formula: Y = YD*QA + > YLi*(QD*cosNi+QS*cosRi)
                                         --

            B1     = VN(3)*VL(2) - VN(2)*VL(3)
            B2     = VN(1)*VL(3) - VN(3)*VL(1)
            B3     = VN(2)*VL(1) - VN(1)*VL(2)
            B4     = VN(1)*VL(1) + VN(2)*VL(2) + VN(3)*VL(3)
            VR(1)  = VN(3)*B2 - VN(2)*B3 + VN(1)*B4
            VR(2)  =-VN(3)*B1 + VN(1)*B3 + VN(2)*B4
            VR(3)  = VN(2)*B1 - VN(1)*B2 + VN(3)*B4
            S      = SQRT(VR(1)*VR(1)+VR(2)*VR(2)+VR(3)*VR(3))
            VR(1)  = VR(1)/S
            VR(2)  = VR(2)/S
            VR(3)  = VR(3)/S
            COSR   = VR(1)*0. + VR(2)*0. + VR(3)*1.

    References: WCtoNDC

    Input: ANORM(3) - surface normal at given point

    Output: FLUM - luminosity

 Modify SCREEN

    Input: R1(3) - 1-st point of the line
           R2(3) - 2-nd point of the line

 Store pointer to current algorithm to draw faces

 Store pointer to current lego function

 Store pointer to current surface function

 Static function
 Store pointer to current implicit function

 static function
 Set the implicit function clipping box "off".

 static function
 Set the implicit function clipping box "on" and define the clipping box.
 xclip, yclip and zclip is a point within the function range. All the
 function value having x<=xclip and y<=yclip and z>=zclip are clipped.

 Store dark color for stack number n

 Store color for stack number n

 Decode side visibilities and order along R for sector

    Input: VAL - encoded value

    Output: IV1 ... IV6  - visibility of the sides
            IR           - increment along R

 Encode side visibilities and order along R for sector

    Input: IOPT - options: 1 - from BACK to FRONT 'BF'
                           2 - from FRONT to BACK 'FB'
           PHI1 - 1st phi of sector
           PHI2 - 2nd phi of sector

    Output: VAL - encoded value

 Set Spectrum

    Input: NL   - number of levels
           FMIN - MIN function value
           FMAX - MAX function value
           IC   - initial color index (for 1st level)
           IDC  - color index increment

    Output: IREP - reply: 0 O.K.
                         -1 error in parameters
                            F_max less than F_min
                            illegal number of levels
                            initial color index is negative
                            color index increment must be positive

 Draw surface in cartesian coordinate system

    Input: ANG      - angle between X ang Y
           NX       - number of steps along X
           NY       - number of steps along Y

           FUN(IX,IY,F,T) - external routine
             IX     - X number of the cell
             IY     - Y number of the cell
             F(3,4) - face which corresponds to the cell
             T(4)   - additional function (for example: temperature)

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
               ICODES(1) - IX
               ICODES(2) - IY
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

           CHOPT - options: 'BF' - from BACK to FRONT
                            'FB' - from FRONT to BACK

 Service function for Surfaces

 Draw surface in polar coordinates

    Input: IORDR - order of variables (0 - R,PHI, 1 - PHI,R)
           NA    - number of steps along 1st variable
           NB    - number of steps along 2nd variable

           FUN(IA,IB,F,T) - external routine
             IA     - cell number for 1st variable
             IB     - cell number for 2nd variable
             F(3,4) - face which corresponds to the cell
               F(1,*) - A
               F(2,*) - B
               F(3,*) - Z
             T(4)   - additional function (for example: temperature)

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
               ICODES(1) - IA
               ICODES(2) - IB
             XYZ(3,*)  - coordinates of nodes
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

           CHOPT       - options: 'BF' - from BACK to FRONT
                                  'FB' - from FRONT to BACK

 Draw surface in cylindrical coordinates

    Input: IORDR - order of variables (0 - Z,PHI, 1 - PHI,Z)
           NA    - number of steps along 1st variable
           NB    - number of steps along 2nd variable

           FUN(IA,IB,F,T) - external routine
             IA     - cell number for 1st variable
             IB     - cell number for 2nd variable
             F(3,4) - face which corresponds to the cell
               F(1,*) - A
               F(2,*) - B
               F(3,*) - R
             T(4)   - additional function (for example: temperature)

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
               ICODES(1) - IA
               ICODES(2) - IB
             XYZ(3,*)  - coordinates of nodes
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

           CHOPT       - options: 'BF' - from BACK to FRONT
                                  'FB' - from FRONT to BACK

 Draw surface in spheric coordinates

    Input: IPSDR - pseudo-rapidity flag
           IORDR - order of variables (0 - THETA,PHI; 1 - PHI,THETA)
           NA    - number of steps along 1st variable
           NB    - number of steps along 2nd variable

           FUN(IA,IB,F,T) - external routine
             IA     - cell number for 1st variable
             IB     - cell number for 2nd variable
             F(3,4) - face which corresponds to the cell
               F(1,*) - A
               F(2,*) - B
               F(3,*) - R
             T(4)   - additional function (for example: temperature)

           DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
             ICODES(*) - set of codes for this face
               ICODES(1) - IA
               ICODES(2) - IB
             XYZ(3,*)  - coordinates of nodes
             NP        - number of nodes in face
             IFACE(NP) - face
             T(NP)     - additional function

           CHOPT       - options: 'BF' - from BACK to FRONT
                                  'FB' - from FRONT to BACK

 Set surface property coefficients

    Input: QQA  - diffusion coefficient for diffused light  [0.,1.]
           QQD  - diffusion coefficient for direct light    [0.,1.]
           QQS  - diffusion coefficient for reflected light [0.,1.]
           NNCS - power coefficient for reflected light     (.GE.1)

                                         --
    Lightness model formula: Y = YD*QA + > YLi*(QD*cosNi+QS*cosRi)
                                         --

    Output: IREP   - reply : 0 - O.K.
                            -1 - error in cooefficients

 Draw implicit function FUN(X,Y,Z) = 0 in cartesian coordinates using
 hidden surface removal algorithm "Painter".

     Input: FUN      - external routine FUN(X,Y,Z)
            RMIN(3)  - min scope coordinates
            RMAX(3)  - max scope coordinates
            NX       - number of steps along X
            NY       - number of steps along Y
            NZ       - number of steps along Z

            DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
              ICODES(*) - set of codes for this face
                ICODES(1) - 1
                ICODES(2) - 1
                ICODES(3) - 1
              NP        - number of nodes in face
              IFACE(NP) - face
              T(NP)     - additional function (lightness)

            CHOPT - options: 'BF' - from BACK to FRONT
                             'FB' - from FRONT to BACK

 Topological decider for "Marching Cubes" algorithm Find set of triangles
 aproximating the isosurface F(x,y,z)=Fiso inside the cube
 (improved version)

 Input: FISO   - function value for isosurface
        P(3,8) - cube vertexes
        F(8)   - function values at the vertexes
        G(3,8) - function gradients at the vertexes

 Output: NNOD       - number of nodes     (maximum 13)
         NTRIA      - number of triangles (maximum 12)
         XYZ(3,*)   - nodes
         GRAD(3,*)  - node normales       (not normalized)
         ITRIA(3,*) - triangles

 Consideration of trivial cases: 1,2,5,8,9,11,14

 Input: K1,...,K6 - edges intersected with isosurface

 Output: the same as for IHMCUB

 Consider case No 3

 Input: see common HCMCUB

 Output: the same as for IHMCUB

 Consider case No 4

 Input: see common HCMCUB

 Output: the same as for IHMCUB

 Consider case No 6

 Input: see common HCMCUB

 Output: the same as for IHMCUB

 Consider case No 7

 Input: see common HCMCUB

 Output: the same as for IHMCUB

 Consider case No 10

 Input: see common HCMCUB

 Output: the same as for IHMCUB

 Consider case No 12

 Input: see common HCMCUB

 Output: the same as for IHMCUB

 Consider case No 13

 Input: see common HCMCUB

 Output: the same as for IHMCUB

 Set triangles (if parameter IALL=1, all edges will be visible)

 Input: NTRIA   - number of triangles
        IT(3,*) - triangles

 Output: ITRIA(3,*) - triangles

 Find middle point of a polygon

 Input: NNOD      - number of nodes in the polygon
        XYZ(3,*)  - node coordinates
        GRAD(3,*) - node normales
        IT(3,*)   - division of the polygons into triangles

 Output: PXYZ(3)  - middle point coordinates
         PGRAD(3) - middle point normale

 Check for surface penetration ("bottle neck")

 Input: A00,A10,A11,A01 - vertex values for 1st face
        B00,B10,B11,B01 - vertex values for opposite face

 Output: IREP - 1,2 - there is surface penetration
                0   - there is not surface penetration

 Find nodes and normales

 Input: NNOD  - number of nodes
        IE(*) - edges which have section node

 Output: XYZ(3,*)  - nodes
         GRAD(3,*) - node normales (not normalized)

 Z-depth algorithm for set of triangles

 Input: XYZ(3,*)   - nodes
        NFACE      - number of triangular faces
        IFACE(3,*) - faces (triangles)

 Arrays: DFACE(6,*) - array for min-max scopes
         ABCD(4,*)  - array for face plane equations

 Output: IORDER(*) - face order

 Test edge against face (triangle)

 Input: DEL      - precision
        XYZ(3,*) - nodes
        I1       - 1-st node of edge
        I2       - 2-nd node of edge
        IFACE(3) - triangular face
        ABCD(4)  - face plane

 Output: IREP:-1 - edge under face
               0 - no decision
              +1 - edge before face

 Draw set of isosurfaces for a scalar function defined on a grid.

     Input: NS          - number of isosurfaces
            S(*)        - isosurface values
            NX          - number of slices along X
            NY          - number of slices along Y
            NZ          - number of slices along Z
            X(*)        - slices along X
            Y(*)        - slices along Y
            Z(*)        - slices along Z
            F(NX,NY,NZ) - function values <- Not used, current histo used instead

            DRFACE(ICODES,XYZ,NP,IFACE,T) - routine for face drawing
              ICODES(1) - isosurface number
              ICODES(2) - isosurface number
              ICODES(3) - isosurface number
              NP        - number of nodes in face
              IFACE(NP) - face
              T(NP)     - additional function (lightness)

            CHOPT - options: 'BF' - from BACK to FRONT
                             'FB' - from FRONT to BACK

 Draw the faces for the Gouraud Shaded Iso surfaces