Colour coding a range of values of f( x, y)

NB This program calls dlls, so is LB only, although you can use RB if you are prepared to load the bmp as a binary file and look up each pixel...

To demonstrate ways of colour coding smoothly a function of x and y, I calculate it (scaled to range f( x, y) >=0 and <=72 in this case), then draw it with different colour ranges. Some uniquely represent each height by one colour; others here cycle four times, so any one colour could represent any one of four heights. You gain in dramatic effect, but lose on interpretation! The red dot shows which colour gradient it is currently using.

The surface involved is simply equal to the radius, so represents a conical depression.

The colour scales were created with graduated fills in the GIMP (any paint software would do) and saved as a 24 bit bmp, which LB can load and interrogate pixel by pixel to get the rgb values. This is much more flexible than any method relying on calculating r g and b from f( x, y).

Which do YOU think best represents the surface? Five are uni-valued. The others are multi-valued. The program automatically saves them as BMPs.

    nomainwin

    UpperLeftX    = 200
    UpperLeftY    = 100
    WindowWidth   = 450
    WindowHeight  = 200

    graphicbox #w.g0,  10, 10, 256, 140
    graphicbox #w.g1, 320, 30, 100, 100
    graphicbox #w.g2, 280, 10,  20, 140

    dim ColLookUp$( 256, 12), v( 12)

    open "3D surface" for graphics_nsb as #w

    #w.g1, "down ; fill black"

    #w, "trapclose [quit]"

    handleg0 =hwnd( #w.g0)
    calldll #user32, "GetDC", uhandleg0 as long, hDC as ulong

    loadbmp "Scale", "QuadSpectrum.bmp"             '   NB must be a 24 bit bmp...
    #w.g0, "down ; drawbmp Scale 0 0"
    #w.g0, "flush"

    for l =1 to 11                                  '   since my bmp has 11 graduated colour stripes
            read yy                                 '   which is how far down next colour stripe is centred
            v( l) =yy
            for v =0 to 255
                 calldll #gdi32, "GetPixel",_
                    hDC as ulong,_
                    v   as long,_
                    yy  as long,_
                    pixcol as long

                bl = int(  pixcol /( 256*256))
                gr = int( (pixcol               -bl *256*256) / 256)
                re = int(  pixcol               -bl *256*256 - gr *256)

                ColLookUp$( v, l) =str$( re) +" " +str$( gr) +" " +str$( bl)
            next v
            scan
    next l

    unloadbmp "Scale"

    callDll #user32, "ReleaseDC",_
        handleg0 as ulong,_                          '   handle of graphic box
        hDC as ulong,_                               '   dc from GetDC
        result as ushort                            '   returns non-zero if successful

    c =-1

[start]
    timer 0
    c =( c +1) mod 11                               '   choose in turn each of 11 colour sequences. ( c =0 to 10)
    ch =c +1                                        '       ch =1 to 11
    #w.g2 "goto 10 "; v( ch); " ; down ; color red ; backcolor red ; circlefilled 5 ; up"
    for x =0 to 99
        scan
        for y =0 to 99
            r =( ( x -50)^2 +( y -50)^2)^0.5        '   r is radius from centre, between 0 and about 71
            r =int( r)

            #w.g1 "color "; ColLookUp$( int( r /72 *255), ch)

            #w.g1 "set ";  x; " "; y
        next y
    next x

    sv$ ="Bump"; str$( ch)
    #w.g1 "flush ; getbmp "; sv$; " 0 0 99 99"
    bmpsave sv$, sv$+".bmp"
    unloadbmp sv$

    #w.g2 "goto 10 "; v( ch); " ; down ; color white ; backcolor white ; circlefilled 4 ; up"
    timer 2000, [start]
    wait

data 5, 18, 33, 44, 53, 62, 80, 93, 105, 118, 129

[quit]
    confirm "Really exit?"; answer$
    if answer$ ="no" then goto [start]
    close #w
    end

If you want to run this program, you need a 24 bit image of one or more colour ranges, 256n pixels wide and up to about 130 deep. You also need to know how far down each colour strip is- this is then used in the data statement.
You could also copy the following GIF and resave it as a BMP. ( I put it here as a GIF since all browsers can show these- only MicroSofty loads BMPs.