4D Mandelbrot

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Joel

Betreff: 4D Mandelbrot

 BeitragSo, März 11, 2012 14:50
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Ich habe letztlich einen Code verfasst der die Mandelbrotmenge in Quaternionen berechnet, stat wie normalerweise in den Komplexen Zahlen.
Allerdings ist der Rendervorgang etwas langsam.

Das Mandelbrot wird auf die Koordinaten x,y,z und w gerechnet woraus dann ein 3D schnitt gezeigt wird.
Mit den Tasten Hoch/Runter,Links/Rechts,A/Y Bewegt man sich.
Mit den Tasten S/X kann man sich durch die w-Achse bewegen
BlitzMax: [AUSKLAPPEN] 
SuperStrict

Const GWIDTH:Int = 400, GHEIGHT:Int = 300
Const stp:Byte = 2

Global GWIDTH2:Float = GWIDTH / 2.0, GHEIGHT2:Float = GHEIGHT / 2.0

Graphics GWIDTH, GHEIGHT

Const Res:Int = 100
Global Voxel:Byte[Res, Res, Res, Res]

Global CamX:Float, CamY:Float, CamZ:Float, CamW:Float
Global CamYaw:Float
CamX = Res / 3
CamY = Res / 2
CamZ = 0
CamW = Res / 2

Const CamSpeed:Float = 4

Global Light:Int

Global Res2:Int = Res / 2
Local Res5:Float = Res / 4

Print ""
Print "Calculate Mandelbrot"
For Local x:Int = 0 Until Res
	For Local y:Int = 0 Until Res
		For Local z:Int = 0 Until Res
			For Local w:Int = 0 Until Res
				If Mandelbrot4D(100, (x - Res2) / Res5, (y - Res2) / Res5, (z - Res2) / Res5, (w - Res2) / Res5) Then Voxel[x, y, z, w] = 1
			Next
		Next
	Next
	Print x + "/" + Res
Next

Print "Compute Light"
For Local x:Int = 0 Until Res
	For Local y:Int = 0 Until Res
		For Local z:Int = 0 Until Res
			For Local w:Int = 0 Until Res
				If voxel[x, y, z, w] > 0
					If GetVoxel(x - 1, y, z, w) > 0 Then Light:+1
					If GetVoxel(x - 1, y - 1, z, w) > 0 Then Light:+1
					If GetVoxel(x - 1, y - 1, z - 1, w) > 0 Then Light:+1
					If GetVoxel(x, y - 1, z, w) > 0 Then Light:+1
					If GetVoxel(x, y - 1, z - 1, w) > 0 Then Light:+1
					If GetVoxel(x, y, z - 1, w) > 0 Then Light:+1
					If GetVoxel(x - 1, y, z - 1, w) > 0 Then Light:+1
					voxel[x, y, z, w] = 255 - (25 * Light)
					Light = 0
				EndIf
			Next
		Next
	Next
Next

Print "Finished"

Global millis:Int


While Not KeyHit(KEY_ESCAPE)
	If KeyDown(KEY_A)
		CamX:+Cos(CamYaw + 90) * CamSpeed
		CamZ:+Sin(CamYaw + 90) * CamSpeed
	End If
	If KeyDown(KEY_Y)
		CamX:-Cos(CamYaw + 90) * CamSpeed
		CamZ:-Sin(CamYaw + 90) * CamSpeed
	End If
	CamY:+(KeyDown(KEY_DOWN) - KeyDown(KEY_UP)) * CamSpeed
	CamYaw:+(KeyDown(KEY_LEFT) - KeyDown(KEY_RIGHT)) * CamSpeed * 5
	CamW:+(KeyDown(KEY_S) - KeyDown(KEY_X))
	millis = MilliSecs()
	Render()
	DrawText "Render Time: " + (MilliSecs() - millis) + "ms", 0, 0
	Flip 0
	Cls
Wend

Function Render()
	For Local x:Int = 0 Until GWIDTH Step stp
		For Local y:Int = 0 Until GHEIGHT Step stp
			Local PickX:Float = CamX
			Local PickY:Float = CamY
			Local PickZ:Float = CamZ
			Local PickSX:Float = (x - GWIDTH2) / GWIDTH2
			Local PickSY:Float = (y - GHEIGHT2) / GHEIGHT2
			Local PickSZ:Float = 1
			
			Local Dist:Float = Sqr(PickSX * PickSX + PickSZ * PickSZ)
			
			Local winkel:Float = ATan2(PickSZ, PickSX) + CamYaw
			PickSX = Cos(winkel) * Dist
			PickSZ = Sin(winkel) * Dist
			For Local n:Int = 0 To Res2
				PickX:+PickSX
				PickY:+PickSY
				PickZ:+PickSZ
				If GetVoxel(PickX, PickY, PickZ, CamW) > 0
					SetColor voxel[PickX, PickY, PickZ, CamW], voxel[PickX, PickY, PickZ, CamW], voxel[PickX, PickY, PickZ, CamW]
					DrawRect x, y, stp, stp
					Exit
				End If
			Next
		Next
	Next
End Function

Function GetVoxel:Byte(x:Int, y:Int, z:Int, w:Int = 50)
	If x >= 0 And x < Res And y >= 0 And y < Res And z >= 0 And z < Res
		Return Voxel[x, y, z, w]
	EndIf
	Return 0
End Function

Function Mandelbrot4D:Byte(Iterationen:Int, x:Float, y:Float, z:Float, w:Float, a:Float=0, b:Float=0, c:Float=0, d:Float=0)
	Local a1:Float, b1:Float, c1:Float, d1:Float
	Local itr:Int = 0
	Repeat
		If itr = Iterationen Then Return 1
		
		a1 = a * a - b * b - c * c - d * d + x
		b1 = 2 * a * b + y
		c1 = 2 * a * c + z
		d1 = 2 * a * d + w
		
		a = a1
		b = b1
		c = c1
		d = d1
		
		itr:+1
		
	Until a * a + b * b + c * c + d * d >= 4
	Return 0
End Function


Da man mit einem 4D-Array keine sehr grosse Auflösung hinbekommt, hier noch eine Version in der die w-Achse nicht berechnet wird BlitzMax: [AUSKLAPPEN] 
SuperStrict

Const GWIDTH:Int = 400, GHEIGHT:Int = 300
Const stp:Byte = 2

Global GWIDTH2:Float = GWIDTH / 2, GHEIGHT2:Float = GHEIGHT / 2

Graphics GWIDTH, GHEIGHT

Const Res:Int = 300
Global Voxel:Byte[Res, Res, Res]

Global CamX:Float, CamY:Float, CamZ:Float, CamW:Float
Global CamYaw:Float
CamX = Res / 3
CamY = Res / 2
CamZ = 0
CamW = Res / 2

Const CamSpeed:Float = 4

Global Light:Int

Global Res2:Int = Res / 2
Local Res5:Float = Res / 4

DrawText "Calculate Mandelbrot", 0, 0
Flip 0
For Local x:Int = 0 Until Res
	For Local y:Int = 0 Until Res
		For Local z:Int = 0 Until Res
			If Mandelbrot4D(100, (x - Res2) / Res5, (y - Res2) / Res5, (z - Res2) / Res5, 0) Then Voxel[x, y, z] = 1
		Next
	Next
	Print x + "/" + Res
Next

DrawText "Compute Light", 0, 15
Flip 0
For Local x:Int = 0 Until Res
	For Local y:Int = 0 Until Res
		For Local z:Int = 0 Until Res
			If voxel[x, y, z] > 0
				If GetVoxel(x - 1, y, z) > 0 Then Light:+1
				If GetVoxel(x - 1, y - 1, z) > 0 Then Light:+1
				If GetVoxel(x - 1, y - 1, z - 1) > 0 Then Light:+1
				If GetVoxel(x, y - 1, z) > 0 Then Light:+1
				If GetVoxel(x, y - 1, z - 1) > 0 Then Light:+1
				If GetVoxel(x, y, z - 1) > 0 Then Light:+1
				If GetVoxel(x - 1, y, z - 1) > 0 Then Light:+1
				voxel[x, y, z] = 255 - (25 * Light)
				Light = 0
			EndIf
		Next
	Next
	Print x + "/" + Res
Next

Print "Finished"

Global millis:Int


While Not KeyHit(KEY_ESCAPE)
	If KeyDown(KEY_A)
		CamX:+Cos(CamYaw + 90) * CamSpeed
		CamZ:+Sin(CamYaw + 90) * CamSpeed
	End If
	If KeyDown(KEY_Y)
		CamX:-Cos(CamYaw + 90) * CamSpeed
		CamZ:-Sin(CamYaw + 90) * CamSpeed
	End If
	CamY:+(KeyDown(KEY_DOWN) - KeyDown(KEY_UP)) * CamSpeed
	CamYaw:+(KeyDown(KEY_LEFT) - KeyDown(KEY_RIGHT)) * CamSpeed * 2
	CamW:+(KeyDown(KEY_S) - KeyDown(KEY_X))
	millis = MilliSecs()
	Render()
	DrawText "Render Time: " + (MilliSecs() - millis) + "ms", 0, 0
	Flip 0
	Cls
Wend

Function Render()
	For Local x:Int = 0 Until GWIDTH Step stp
		For Local y:Int = 0 Until GHEIGHT Step stp
			Local PickX:Float = CamX
			Local PickY:Float = CamY
			Local PickZ:Float = CamZ
			Local PickSX:Float = (x - GWIDTH2) / GWIDTH2
			Local PickSY:Float = (y - GHEIGHT2) / GHEIGHT2
			Local PickSZ:Float = 1
			
			Local Dist:Float = Sqr(PickSX * PickSX + PickSZ * PickSZ)
			
			Local winkel:Float = ATan2(PickSZ, PickSX) + CamYaw
			PickSX = Cos(winkel) * Dist
			PickSZ = Sin(winkel) * Dist
			For Local n:Int = 0 To Res2
				PickX:+PickSX
				PickY:+PickSY
				PickZ:+PickSZ
				If GetVoxel(PickX, PickY, PickZ) > 0
					SetColor voxel[PickX, PickY, PickZ], voxel[PickX, PickY, PickZ], voxel[PickX, PickY, PickZ]
					DrawRect x, y, stp, stp
					Exit
				End If
			Next
		Next
	Next
End Function

Function GetVoxel:Byte(x:Int, y:Int, z:Int)
	If x >= 0 And x < Res And y >= 0 And y < Res And z >= 0 And z < Res
		Return Voxel[x, y, z]
	EndIf
	Return 0
End Function

Function Mandelbrot4D:Byte(Iterationen:Int, x:Float, y:Float, z:Float, w:Float, a:Float=0, b:Float=0, c:Float=0, d:Float=0)
	Local a1:Float, b1:Float, c1:Float, d1:Float
	Local itr:Int = 0
	Repeat
		If itr = Iterationen Then Return 1
		
		a1 = a * a - b * b - c * c - d * d + x
		b1 = 2 * a * b + y
		c1 = 2 * a * c + z
		d1 = 2 * a * d + w
		
		a = a1
		b = b1
		c = c1
		d = d1
		
		itr:+1
		
	Until a * a + b * b + c * c + d * d >= 4
	Return 0
End Function

Viel Spass!

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