Hunting for curves and surfaces in the space

[primo]

version 1 is posted here long time ago https://www.thinbasic.com/community/...s-in-the-space
the description in short: suppose a professor ask you to draw a complex curve like this Sin(x*y)+Sin(y*z)+Sin(z*x) = 0
but we don't have the analytic mental capabilities like Euclid or Archimedes to try finding the functions as z = f(x,y), instead of that we can select a cube of space of size as an example 1x1x1 and we divide it into 150x150x150 cells. we will check every cell if it is fulfilling certain criterion , if the formula needs to be zero we accept -0.1 to 0.1 or even -1 to 1 ie some fuzziness. we then plot a color on that cell. it is like a cat sniffing for food or traces of food.
the previous version is slow since it is using gList now we use GBuffer which is speedier ( i believe it is using glDrawArray as told by Petr somewhere) also we use FreeBasic as a calculation machine
what determine the shape for some formula is:
1- the range of plotting from xMin to xMax ...etc
2- the criterion in :
If k <= 1 And k >= -1 Then
Or If k <= 0.2 And k >= -0.2 Then ... etc

attached the GBuffer version. and also for comparison the glList version
surface2.PNG

needs thinbasic version 1.11.1.0

Uses "TBGL"
'Uses "math"

Type Point3D
  x As Single
  y As Single
  z As Single
End Type

Type Colr
  r As Byte
  g As Byte
  b As Byte
End Type

Function TBMain()

  Local hWnd      As DWord
  Local FrameRate As Double
  Local i         as long
  
  ' -- Create and show window
  hWnd = TBGL_CreateWindowEx("Plotting 3D Data in an array using GBuffers- Calculate with freebasic..Esc to quit", 600, 600, 32, %TBGL_WS_WINDOWED Or %TBGL_WS_CLOSEBOX) 
  TBGL_ShowWindow
  
  TBGL_BackColor 255,255,255 
  'TBGL_SetDrawDistance 250
 
  ' -- Create 3D points buffer
  DWord gbPoints = TBGL_GBufferCreate(%TBGL_POINTS, %TBGL_3D)
    
  Global Nb As DWord = 150
  ' -- Define data for it
  dim VertexA(Nb^3) As Point3D ' single
  dim ColorA(Nb^3) As Colr      ' Byte
  
  'dim VertexA(Nb) As TBGL_TVECTOR3F
  'dim ColorA(Nb)  As TBGL_TRGB
  
  'call freeBasic to fill the arrays with data
  FB_Array_Of_Point3D(VertexA(1), ColorA(1))
  
  ' -- Create buffer dynamically linked to the arrays above
  TBGL_GBufferDefineFromArray(gbPoints, %TBGL_DYNAMIC, CountOf(VertexA), VertexA(1), ColorA(1))
  
  ' -- Resets status of all keys 
  TBGL_ResetKeyState()
  TBGL_PointSize 2
  
  ' -- Main loop
  While TBGL_IsWindow(hWnd)
  'init 
    FrameRate = TBGL_GetFrameRate
    
    TBGL_ClearFrame
      TBGL_Camera(0, 5, 10, 0, 0, 0)
       
      ' -- Turn triangle
      TBGL_Rotate GetTickCount/50, 0, 1, 0
      'TBGL_Scale 0.6, 0.6, 0.6
                                     
      ' -- Render it                              
      TBGL_GBufferRender(gbPoints)   
        
    TBGL_DrawFrame
 
    ' -- ESCAPE key to exit application
    If TBGL_GetWindowKeyState(hWnd, %VK_ESCAPE) Then Exit While
 
  Wend        
  ' -- Destroying the buffer is not necessary,
  ' -- the garbage collector will take care of it
 
  ' -- Destroy window
  TBGL_DestroyWindow
  
End Function

#compiled "===Passing array of UDT==="
  Type Point3D
    x As Single
    y As Single
    z As Single
  End Type

  Type Colr
   r As Byte
   g As Byte
   b As Byte
  End Type

  function FB_Array_Of_Point3D Cdecl (byref pPoint3D as Point3D, byref pColr as Colr) As long Export
    ' passing a Double ByRef means passing a pointer to the memory location where the first Double is allocated
    '----------------------------------------------------------------------------
      
      Dim pArray  As Point3D Ptr
      Dim pArrayColor  As Colr Ptr

      dim N    as Long
     '"We are now inside FreeBasic function"
    '---Get pointer to the first element of the array
      pArray = @pPoint3D
      pArrayColor = @pColr
    dim as single x, y, z, k, t, Pi, xMin, yMin, zMin, xMax, yMax, zMax, range, step1
    dim as byte rd, gr, bl
    dim as long a, b, c  
    Pi = 3.141592
   xMin = -2 : yMin = -2: zMin = -2 : xMax = 2: yMax = 2 : zMax = 2
   'xMin = -3 : yMin = -3: zMin = -3 : xMax = 3: yMax = 3 : zMax = 3
   'xMin = -5 : yMin = -5: zMin = -5 : xMax = 5: yMax = 5 : zMax = 5
    'xMin = -1.5 : yMin = -1.5: zMin = -1.5 : xMax = 1.5: yMax = 1.5 : zMax = 1.5
    'xMin = -1.0 : yMin = -1.0: zMin = -1.0 : xMax = 1.0: yMax = 1.0 : zMax = 1.0
    range = xMax - xMin
    step1 = range /150
    x = xMin: z = zMin : y = yMin
   
    For c = 0 To 150
     rd = rnd*255: gr = rnd*255: bl = rnd*255
     For b=0 To 150
     
      For a=0 To 150
       
      'k = 320*(((x*x + (9*y*y)/4 +z*z -1)^3) - x*x*z*z*z - (9*y*y*z*z*z)/80) 'Heart
      k = x^4 + y^4 + z^4 - (x*x + y*y + z*z)^2 + 3 * (x*x + y*y + z*z)
      'k = Sin(x*y)+Sin(y*z)+Sin(z*x)
       'k =  x^2 + y^2 - z^2 -1
      'k = -y +0.7/Log(x^2+z^2)+.6  'dome
      'k = x^6 - 5* x^4* y* z + 3* x^4* y^2 + 10* x^2* y^3* z + 3* x^2* y^4 - y^5* z + y^6 + z^6 - 1
      'k = x^6 - 5* x^4* y* z + 3* x^4* y^2 + 10* x^2* y^3* z + 3* x^2* y^4 - y^5* z + y^6 + z^6 - 1
      'k = 4* z^4 + 9*(x^2 + y^2 - 4*z^2)-1 'Eight Solid
      'k =  x^2 + y^2 +z^2 'sphere
       
      'If k <= 0.05 And k >= -0.05 Then
      'If k <= 0.01 And k >= -0.01 Then
      'If k <= 0.1 And k >= -0.1 Then
      'If k <= 0.2 And k >= -0.2 Then
      If k <= 1 And k >= -1 Then
       N = N + 1
        
        *(pArray + N).x = x 
        *(pArray + N).y = y 
        *(pArray + N).z = z
        
        *(pArrayColor + N).r = rd
        *(pArrayColor + N).g = gr
        *(pArrayColor + N).b = bl
               
      End If
      x = x + step1
       
    Next a
        
    x = xMin
    z = z + step1
     
  Next b
  
  x = xMin
  z = zMin
  y = y + step1
Next c

  return 0
      
  end Function

#endcompiled