Hunting for curves and surfaces in the space

**primo** · 21-09-2019, 14:30

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

**Petr Schreiber** · 22-09-2019, 20:46

I wonder why there is not any comment yet - this is excellent use of latest thinBASIC.

TBGL for gfx, freeBasic for number crunching, thinBASIC orchestrating it all together.

Thank you, primo, excellent example!

Petr

**primo** · 23-09-2019, 08:33

Thank you Petr, Eros and you have done nice work in connecting thinbasic with freebasic easily. and even the TB debugger can pinpoint the error in the freebasic block and catch its debugger output. such as write tot + 1 and the debugger will report >error 10: Expected '=' in 'tot + 1' while it accept that in TB code block since its legal.
thinbasic is more wise, say she is like a philosopher, while freebasic have big muscles. the people who like the mechanical machines will like the TB-FB Hybrid entity, they have the same spirit and novelty.

I wonder why there is not any comment yet

as a general subject this is a universal phenomena, due to the global unprecedented dangers threatening the world in everything. also the people are busy with their smart phones and their interest in programming is too much diminished. . and in the 3D area it is normal in most programming Languages especially Basic Languages.

**ErosOlmi** · 23-09-2019, 21:43

Originally Posted by Petr Schreiber

I wonder why there is not any comment yet - this is excellent use of latest thinBASIC.

My fault. I'm a little bit absent from forum. So busy at work that I only have time to check if there are technical problems in forum and nothing more.
Sorry.

Yes, a perfect example of thinBasic/FreeBasic compiled power/primo intelligence mix and wow: a great example working so fine.
Is so fascinating to see math at work, thanks a lot primo.
Following image is: k = x^3 * y^2 * z^2

Capture.PNG

Next step in thinBasic/Freebasic connection is to try to share thinBasic types into FreeBasic compiled code in order to avoid the need to double define them.