# Thread: searching for Curves and Surfaces in the space

1. ## searching for Curves and Surfaces in the space

suppose someone tell you to plot this equation
Pow(x,4) + Pow(y,4) + Pow(z,4) - Pow(x*x + y*y + z*z,2) + 3 * (x*x + y*y + z*z) = 0
and you don't have any clue how to solve it first such as saying:
z = f(x,y) , so how to plot it ?
there is a plan: is to search the points in space one by one in which this equation is approximately true such as:
If k <= 0.1 And k >= -0.1 Then ...
k is the value of the equation.
change it to:
If k <= 0.5 And k >= -0.5 Then
and you get a thicker surface curve with more points.

now if we tried the above equation but replacing Pow to '^' (uncomment line 178 ) then the time is twice than if use Pow. this is not important issue since we can use the speedier version.
try equation in line 175:
k = Sin(x*y)+Sin(y*z)+Sin(z*x)
it is ineresting
in line 217 : TBGL_PointSize 2 : make it 1 or 3 as necessary
change the range in line 162 as the plotting needed
this is an experimental mathematics
i have used the Entity System to position and rotate and look at using Entity system examples by Petr ,2009
also using Oxygen module to speed the calculations
you may wait from 6 to 30 seconds for every graphics since we check every point in the space within the range.

```'Experimental Mathematics                             =
'===============================================================================

Uses "TBGL" , "Math" , "Oxygen"
#Include Once "%APP_INCLUDEPATH%\thinbasic_gl.inc"
#Include Once "%APP_INCLUDEPATH%\thinbasic_glu.inc"

BEGIN CONST
' -- Scene IDs
%sScene  = 1

' -- Entity IDs
%eCamera = 1

%eContour
%eLight
%texOne
%lMyPoints
End Const

Type Point3D
x As Single
y As Single
z As Single
red As Single
green As Single
blue As Single
tu As Single
tv As Single
End Type

Global Nb As DWord = 2000000 '401880 '8120601
Global x, y, z,zz As Single
Global FrameRate As Long
Global Vertex(Nb) As Point3D ' single
Global total As Long
'Global ColorA(Nb)  As TBGL_TRGB      ' Byte

FUNCTION TBMAIN()
LOCAL hWnd As DWORD
Global FrameRate As Double
Global ang, earthX, earthZ, OrbitRadius As Single
Global flag, mask As Long
flag = 1 : mask = 1
OrbitRadius = 2.5

' -- Create and show window
hWnd = TBGL_CreateWindowEx("press Space to toggle the camera position , press 'M' to set a mask , 'R' reset mask to default ", 800, 600, 32, %TBGL_WS_WINDOWED Or %TBGL_WS_CLOSEBOX)
TBGL_ShowWindow

' -- Create scene
TBGL_SceneCreate(%sScene)

' -- Create basic entities
' -- Create camera to look from 0, 8, 20 to 0, 0, 0
TBGL_EntityCreateCamera(%sScene, %eCamera)
TBGL_EntitySetPos(%sScene, %eCamera, 0, 8, 20)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)
' -- Create point light
TBGL_EntityCreateLight(%sScene, %eLight)
TBGL_EntitySetPos(%sScene, %eLight, 10, 20, 50)

' -- Create something to look at
'---Start time
Dim T0  As Double = Timer
CreatePointsList()
Dim T1  As Double = Timer
MsgBox(0, "Total time to create points List "  & Format\$(T1 - T0, "#0.00") & " secs" & " ...   number of points = " & Str\$(total))

TBGL_EntityCreateDLSlot(%sScene, %eContour, 0, %lMyPoints)

TBGL_EntitySetColor(%sScene, %eContour, 255, 255, 255)

' -- Resets status of all keys
TBGL_ResetKeyState()
TBGL_EntitySetTexture(%sScene, %eContour, %texOne )
'TBGL_LoadTexture APP_Path+"SampleScripts\TBGL\GBuffers\Textures\Bricks.bmp", %texOne, %TBGL_TEX_MIPMAP
TBGL_LoadTexture APP_Path+"SampleScripts\UI\Dialogs\Images\frogduck.bmp", %texOne, %TBGL_TEX_MIPMAP

' -- Main loop
While TBGL_IsWindow(hWnd)
FrameRate = TBGL_GetFrameRate
TBGL_SetWindowTitle( hWnd, "FPS = "+Str\$(FrameRate)+"  press Space to toggle the camera position , press 'M' to set a mask , 'R' reset mask to default ")
TBGL_ClearFrame
If TBGL_GetWindowKeyOnce( hWnd, %VK_SPACE) Then
If flag = 1 Then
TBGL_EntitySetPos(%sScene, %eCamera, 0, 25, 0.1)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)

flag * -1
Else
TBGL_EntitySetPos(%sScene, %eCamera, 0, 12, 20)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)
flag * -1
End If
End If

If TBGL_GetWindowKeyOnce( hWnd, %VK_M) Then
If mask = 1 Then
TBGL_EntitySetColorMask(%sScene, %eCamera, %TBGL_RED  )
mask * -1
Else
TBGL_EntitySetColorMask(%sScene, %eCamera, %TBGL_GREEN  )
mask * -1
End If
End If

If TBGL_GetWindowKeyOnce( hWnd, %VK_R) Then
TBGL_EntitySetColorMask(%sScene, %eCamera, %TBGL_DEFAULT)
End If

TBGL_EntitySetRot(%sScene, %eContour, 0, GetTickCount/40, 0)

TBGL_SceneRender(%sScene)

TBGL_DrawFrame

' -- ESCAPE key to exit application
If TBGL_GetWindowKeyState(hWnd, %VK_ESCAPE) Then Exit While

Wend

TBGL_DestroyWindow
END FUNCTION

'==================================
Sub CreatePointsList()

String src = "
' -- Re-declare types

Type Point3D
x As Single
y As Single
z As Single
red As Single
green As Single
blue As Single
tu As Single
tv As Single
End Type

dim oVertex(2000000) At #Vertex As Point3D
dim oTexA(2000000)At #TexA As Point3D

dim N At #total As long
'dim oColorA(2000000) At #ColorA As TBGL_TRGB
Long a, b, c, Nb
Single x, z, k, xMin, yMin, zMin, xMax, yMax, zMax, range, step1

Long NbX
Long NbZ
Long NbY
nbx = 300
nby = 300
nbz = 300

'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 = -4 : yMin = -4: zMin = -4 : xMax = 4: yMax = 4 : zMax = 4
'xMin = -5 : yMin = -5: zMin = -5 : xMax = 5: yMax = 5 : zMax = 5

range = xMax - xMin
step1 = range / NbX
x = xMin: z = zMin : y = yMin
N = 0
For c = 0 To NbY
For b=0 To NbZ

For a=0 To NbX

'k = 320*(((x*x + (9*y*y)/4 +z*z -1)^3) - x*x*z*z*z - (9*y*y*z*z*z)/80)
'k = Sin(x*y)+Sin(y*z)+Sin(z*x)
'k = x^3+y^2+z^2
k = Pow(x,4) + Pow(y,4) + Pow(z,4) - Pow(x*x + y*y + z*z,2) + 3 * (x*x + y*y + z*z)
'k = x^4 + y^4 + z^4 - (x^2 + y^2 + z^2)^2 + 3 * (x^2 + y^2 + z^2)

If k <= 0.1 And k >= -0.1 Then
'If k <= 0.5 And k >= -0.5 Then
N = N+1
oVertex(N).x = x
oVertex(N).y = y
oVertex(N).z = z
oVertex(N).tu = a/NbX
oVertex(N).tv = b/Nbz

End If
x  = x + step1

Next a
x = xMin
z = z + step1

Next b
x = xMin
z = zMin
y = y + step1
Next c
'print str N
terminate
"

' -- Pass the source
'O2_Asmo src
o2_basic src
If Len(o2_error) Then
MsgBox 0, o2_error : Stop
End If
' -- Execute
o2_exec

Long N
TBGL_NewList %lMyPoints
TBGL_PointSize 2
TBGL_UseLighting %FALSE

TBGL_BeginPoly %GL_POINTS
For N=1 To Nb
glTexCoord2f(Vertex(N).tu, Vertex(N).tv)
glVertex3f(Vertex(N).x,Vertex(N).y,Vertex(N).z)
Next

TBGL_EndPoly
TBGL_EndList
TBGL_UseLighting %TRUE
End Sub
```

2. Wow

My math is so poor but my eyes remains always so fascinated looking at what math can do.
Thanks so much

3. Sorry if I ask but it would be great to have arrow keys navigate inside the object moving in 3D

4. yes Eros , here is the navigation with the camera with arrows,
up/down: go inside/outside
left/right
A/Z: up/down
there is still the camera rotation with the Mouse+keys
now i think the while/wend is better than For/Next since we can decide how much points we need, will look at later.
in fact i like to Generate the Average 3D Face:
http://www1.cs.columbia.edu/~jebara/...IS/node48.html
there is a matrix , who have any idea will be great.
```'Experimental Mathematics                             =
'===============================================================================

Uses "TBGL" , "Math" , "Oxygen"
#Include Once "%APP_INCLUDEPATH%\thinbasic_gl.inc"
#Include Once "%APP_INCLUDEPATH%\thinbasic_glu.inc"

Begin Const
' -- Scene IDs
%sScene  = 1

' -- Entity IDs
%eCamera = 1

%eContour
%eLight
%texOne
%lMyPoints
End Const

Type Point3D
x As Single
y As Single
z As Single
red As Single
green As Single
blue As Single
tu As Single
tv As Single
End Type

Global Nb As DWord = 2000000 '401880 '8120601
Global x, y, z, xx, yy,zz As Single
Global FrameRate As Long
Global Vertex(Nb) As Point3D ' single
Global total As Long
'Global ColorA(Nb)  As TBGL_TRGB      ' Byte

Function TBMain()
Local hWnd As DWord
Global FrameRate As Double
Global ang, earthX, earthZ, OrbitRadius As Single
Global flag, mask As Long
flag = 1 : mask = 1
OrbitRadius = 2.5

' -- Create and show window
hWnd = TBGL_CreateWindowEx("press Space to toggle the camera position , press 'M' to set a mask , 'R' reset mask to default ", 800, 600, 32, %TBGL_WS_WINDOWED Or %TBGL_WS_CLOSEBOX)
TBGL_ShowWindow

' -- Create scene
TBGL_SceneCreate(%sScene)

' -- Create basic entities
' -- Create camera to look from 0, 8, 20 to 0, 0, 0
TBGL_EntityCreateCamera(%sScene, %eCamera)
TBGL_EntitySetPos(%sScene, %eCamera, 0, 8, 20)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)
' -- Create point light
TBGL_EntityCreateLight(%sScene, %eLight)
TBGL_EntitySetPos(%sScene, %eLight, 10, 20, 50)

' -- Create something to look at
'---Start time
Dim T0  As Double = Timer
CreatePointsList()
Dim T1  As Double = Timer
MsgBox(0, "Total time to create points List "  & Format\$(T1 - T0, "#0.00") & " secs" & " ...   number of points = " & Str\$(total))

TBGL_EntityCreateDLSlot(%sScene, %eContour, 0, %lMyPoints)

TBGL_EntitySetColor(%sScene, %eContour, 255, 255, 255)

' -- Resets status of all keys
TBGL_ResetKeyState()
TBGL_EntitySetTexture(%sScene, %eContour, %texOne )
'TBGL_LoadTexture APP_Path+"SampleScripts\TBGL\GBuffers\Textures\Bricks.bmp", %texOne, %TBGL_TEX_MIPMAP
TBGL_LoadTexture APP_Path+"SampleScripts\UI\Dialogs\Images\frogduck.bmp", %texOne, %TBGL_TEX_MIPMAP

' -- Main loop
While TBGL_IsWindow(hWnd)
FrameRate = TBGL_GetFrameRate
TBGL_SetWindowTitle( hWnd, "FPS = "+Str\$(FrameRate)+"  press Space to toggle the camera position , press 'M' to set a mask , 'R' reset mask to default ")
TBGL_ClearFrame
If TBGL_GetWindowKeyOnce( hWnd, %VK_SPACE) Then
If flag = 1 Then
TBGL_EntitySetPos(%sScene, %eCamera, 0, 25, 0.1)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)

flag * -1
Else
TBGL_EntitySetPos(%sScene, %eCamera, 0, 12, 20)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)
flag * -1
End If
End If

If TBGL_GetWindowKeyOnce( hWnd, %VK_M) Then
If mask = 1 Then
TBGL_EntitySetColorMask(%sScene, %eCamera, %TBGL_RED  )
mask * -1
Else
TBGL_EntitySetColorMask(%sScene, %eCamera, %TBGL_GREEN  )
mask * -1
End If
End If

If TBGL_GetWindowKeyOnce( hWnd, %VK_R) Then
TBGL_EntitySetColorMask(%sScene, %eCamera, %TBGL_DEFAULT)
End If

If TBGL_GetWindowKeyState( hWnd, %VK_UP ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
zz-0.1
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)
ElseIf TBGL_GetWindowKeyState( hWnd, %VK_DOWN ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
zz+0.1
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)

ElseIf TBGL_GetWindowKeyState( hWnd, %VK_Z ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
yy+0.1
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)
ElseIf TBGL_GetWindowKeyState( hWnd, %VK_A ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
yy-0.1
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)

ElseIf TBGL_GetWindowKeyState( hWnd, %VK_RIGHT ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
xx-0.1
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)
ElseIf TBGL_GetWindowKeyState( hWnd, %VK_LEFT ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
xx+0.1
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)

End If

TBGL_EntitySetRot(%sScene, %eContour, 0, GetTickCount/40, 0)

TBGL_SceneRender(%sScene)

TBGL_DrawFrame

' -- ESCAPE key to exit application
If TBGL_GetWindowKeyState(hWnd, %VK_ESCAPE) Then Exit While

Wend

TBGL_DestroyWindow
End Function

'==================================
Sub CreatePointsList()

String src = "
' -- Re-declare types

Type Point3D
x As Single
y As Single
z As Single
red As Single
green As Single
blue As Single
tu As Single
tv As Single
End Type

dim oVertex(2000000) At #Vertex As Point3D

dim N At #total As long
'dim oColorA(2000000) At #ColorA As TBGL_TRGB
Long a, b, c, Nb
Single x, z, k, xMin, yMin, zMin, xMax, yMax, zMax, range, step1

Long NbX
Long NbZ
Long NbY
nbx = 300
nby = 300
nbz = 300

'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 = -4 : yMin = -4: zMin = -4 : xMax = 4: yMax = 4 : zMax = 4
'xMin = -5 : yMin = -5: zMin = -5 : xMax = 5: yMax = 5 : zMax = 5

range = xMax - xMin
step1 = range / NbX
x = xMin: z = zMin : y = yMin
N = 0
For c = 0 To NbY
For b=0 To NbZ

For a=0 To NbX

'k = 320*(((x*x + (9*y*y)/4 +z*z -1)^3) - x*x*z*z*z - (9*y*y*z*z*z)/80)
k = Sin(x*y)+Sin(y*z)+Sin(z*x)
'k = x^3+y^2+z^2
'k = Pow(x,4) + Pow(y,4) + Pow(z,4) - Pow(x*x + y*y + z*z,2) + 3 * (x*x + y*y + z*z)
'k = x^4 + y^4 + z^4 - (x^2 + y^2 + z^2)^2 + 3 * (x^2 + y^2 + z^2)

If k <= 0.1 And k >= -0.1 Then
'If k <= 0.5 And k >= -0.5 Then
N = N+1
oVertex(N).x = x
oVertex(N).y = y
oVertex(N).z = z
oVertex(N).tu = a/NbX
oVertex(N).tv = b/Nbz

End If
x  = x + step1

Next a
x = xMin
z = z + step1

Next b
x = xMin
z = zMin
y = y + step1
Next c
'print str N
terminate
"

' -- Pass the source
'O2_Asmo src
o2_basic src
If Len(o2_error) Then
MsgBox 0, o2_error : Stop
End If
' -- Execute
o2_exec

Long N
TBGL_NewList %lMyPoints
TBGL_PointSize 2
TBGL_UseLighting %FALSE

TBGL_BeginPoly %GL_POINTS
For N=1 To Nb
glTexCoord2f(Vertex(N).tu, Vertex(N).tv)
glVertex3f(Vertex(N).x,Vertex(N).y,Vertex(N).z)
Next

TBGL_EndPoly
TBGL_EndList
TBGL_UseLighting %TRUE
End Sub
```

5. this demo using a thinbasic without calling Oxygen, it display the progress in the taskbar, the speed depends on several factors
my neighbor said: you want my son to be lazy and not solving the equations by himself but by crawling like a rabbit sniffing if the equation correct here and there or not !! and he suspect that this is not a correct program and producing a fake shapes , but i show him an equation in a trusted site , the mathematica site, here: https://www.wolfram.com/mathematica/...ojections.html
the first graphics show this equation:
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
it produce the same graphics as this program, just uncomment line 159 (note we have moved the +1 from right to left -1)
interestingly thinbasic math '^' is speedier than Pow by two seconds (uncomment line 158 )
don't forget to comment the unused equations

```Uses "TBGL" , "Math"
#Include Once "%APP_INCLUDEPATH%\thinbasic_gl.inc"
#Include Once "%APP_INCLUDEPATH%\thinbasic_glu.inc"

BEGIN CONST
' -- Scene IDs
%sScene  = 1

' -- Entity IDs
%eCamera = 1

%eContour

%quat
%lMyPoints
%texOne
END CONST

Global x, y, z, xx, yy,zz As Single
Global FrameRate, total As Long

FUNCTION TBMAIN()
Global hWnd As DWord
Global FrameRate As Double
Global flag As Long
flag = 1

' -- Create and show window
hWnd = TBGL_CreateWindowEx("press Space to toggle the camera position , press 'M' to set a mask , 'R' reset mask to default ", 800, 600, 32, %TBGL_WS_WINDOWED Or %TBGL_WS_CLOSEBOX)
TBGL_ShowWindow

' -- Create scene
TBGL_SceneCreate(%sScene)

' -- Create basic entities
' -- Create camera to look from 0, 5, 15 to 0, 0, 0
TBGL_EntityCreateCamera(%sScene, %eCamera)
TBGL_EntitySetPos(%sScene, %eCamera, 0, 5, 15)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)

Dim T0  As Double = Timer
' -- Create something to look at
CreatePointsList()
Dim T1  As Double = Timer
MsgBox(0, "Total time to create points List "  & Format\$(T1 - T0, "#0.00") & " secs" & " ...   number of points = " & Str\$(total))

TBGL_EntityCreateDLSlot(%sScene, %eContour, 0, %lMyPoints)

TBGL_EntitySetColor(%sScene, %eContour, 255, 255, 255)
TBGL_EntitySetPos(%sScene, %eContour, 0, 0, 0)

' -- Resets status of all keys
TBGL_ResetKeyState()
TBGL_EntitySetTexture(%sScene, %eContour, %texOne )
TBGL_LoadTexture APP_Path+"SampleScripts\TBGL\GBuffers\Textures\Bricks.bmp", %texOne, %TBGL_TEX_MIPMAP
'TBGL_LoadTexture APP_Path+"SampleScripts\UI\Dialogs\Images\frogduck.bmp", %texOne, %TBGL_TEX_MIPMAP
'TBGL_LoadTexture APP_SourcePath+"Marble-Wood.bmp", %texOne, %TBGL_TEX_MIPMAP

'TBGL_PolygonLook %GL_LINE
' -- Main loop
While TBGL_IsWindow(hWnd)
FrameRate = TBGL_GetFrameRate
TBGL_SetWindowTitle( hWnd, "FPS = "+Str\$(FrameRate)+"   use arrow keys and A/Z to navigate the scene")
TBGL_ClearFrame
If TBGL_GetWindowKeyOnce( hWnd, %VK_SPACE) Then
If flag = 1 Then
TBGL_EntitySetPos(%sScene, %eCamera, 0, 25, 0.1)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)
flag * -1
Else
TBGL_EntitySetPos(%sScene, %eCamera, 0, 5, 15)
TBGL_EntitySetTargetPos(%sScene, %eCamera, 0, 0, 0)
flag * -1
End If
End If

If TBGL_GetWindowKeyState( hWnd, %VK_UP ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
zz-0.2
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)
ElseIf TBGL_GetWindowKeyState( hWnd, %VK_DOWN ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
zz+0.2
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)

ElseIf TBGL_GetWindowKeyState( hWnd, %VK_Z ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
yy+0.2
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)
ElseIf TBGL_GetWindowKeyState( hWnd, %VK_A ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
yy-0.2
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)

ElseIf TBGL_GetWindowKeyState( hWnd, %VK_RIGHT ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
xx-0.2
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)
ElseIf TBGL_GetWindowKeyState( hWnd, %VK_LEFT ) Then
TBGL_EntityGetPos( %sScene, %eCamera, xx, yy, zz)
xx+0.2
TBGL_EntitySetPos(%sScene, %eCamera, xx, yy, zz)

End If

TBGL_EntitySetRot(%sScene, %eContour, 90, GetTickCount/40, 0)
TBGL_SceneRender(%sScene)

TBGL_DrawFrame

' -- ESCAPE key to exit application
If TBGL_GetWindowKeyState(hWnd, %VK_ESCAPE) Then Exit While

Wend

TBGL_DestroyWindow
END FUNCTION

' -- Render procedure

'==================================
Sub CreatePointsList()
Dim zz As Single
String plotted
Long a, b, c, Nb
Single x, z, k, xMin, yMin, zMin, xMax, yMax, zMax, range, step1

Long NbX=150
Long NbZ=150
Long NbY=150

'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

range = xMax - xMin
step1 = range / NbX
x = xMin: z = zMin : y = yMin

TBGL_NewList %lMyPoints
TBGL_PointSize 2
TBGL_UseLighting %FALSE

TBGL_BeginPoly %GL_POINTS
For c = 0 To NbY
For b=0 To NbZ

For a=0 To NbX

'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 = Pow(x,4) + Pow(y,4) + Pow(z,4) - Pow(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 = Pow(x,6) - 5* Pow(x,4)* y* z + 3* Pow(x,4)* Pow(y,2) + 10* Pow(x,2)* Pow(y,3)* z + 3* Pow(x,2)* Pow(y,4) - Pow(y,5)* z + Pow(y,6) + Pow(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

'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
total+1
glTexCoord2f(a/NbX, b/Nbz)
'glColor3f(0,1,0)
glVertex3f(x,y,z)

End If
x + step1

Next a

x = xMin
z + step1

Next b
plotted = Str\$(Int((c/nby)*100) )+" % "+" ..... please wait "
TBGL_SetWindowTitle( hWnd, plotted)
x = xMin
z = zMin
y + step1
Next c
TBGL_EndPoly
TBGL_EndList

End Sub
```

6. Great

This is my preferred.

7. This is so hypnotic, can't stop viewing it

Just one tip - instead of:
```If k <= 0.2 And k >= -0.2 Then
```
you can do simply:
```If between(k, -0.2, 0.2) Then
```
It is not just a syntactic sugar, it can give you a boost in performance as well!

Petr

8. Between !!!!!! certainly it is a syntactic sugar, and speedier than the infinitely complex syntax :
If k <= 0.2 And k >= -0.2 Then.
albiet this function appears very natural, alas no basic language have implemented it before .
also it is including -0.2 and 0.2 in the checking like what is wanted
but what if we want it to express this If k < 0.2 And k > -0.2 Then, i have checked "Inside" it seems to behave like "between"
```Uses "Console"
Long i
For i=1 To 20
'If Between(i, 7, 14) Then
If Inside(i, 7, 14) Then
'If MinMax(i, 7, 14) Then
'If Outside(i, 7, 14) Then
Print i
PrintL
End If
Next
WaitKey()
```
its output is:
7
8
9
10
11
12
13
14

and what comes to my mind is that it should exclude 7, 14.
Thanks Petr for the continuous support

9. Between and Inside do the same check but result has a different meaning.

Inside is just a check that the expression is inside the limits (limits included).
http://www.thinbasic.com/public/prod...tml?inside.htm

Between does the same check but returns a number between 1 and 100 depending if numeric expression is closer to lower or upper bound.
It was asked and developed with the idea of "distance" and not just true/false
http://www.thinbasic.com/public/prod...ml?between.htm

Some would say RTFM but, as you know, here we do not use that acronym

10. The idea of distance for the between function is great, it reminds me with the idea of distance in Mandelbrot set plotting, will think about that.
this makes me understand the 'between' function and distance idea more:
```Uses "Console"
Single i, x
i = 7
x = Between(i, 7, 14)
PrintL x

i = 10.5
x = Between(i, 7, 14)
PrintL x

i = 14
x = Between(i, 7, 14)
PrintL x

WaitKey()
```
the output is:
1
50
100

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