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nullschritt

Coordinate Calculations (Volume, Distance, and more!) [in 3d]

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Hello, I originally started writing these functions in autoit, because of how easy it was to debug my code (the algorithms are actually implemented in php, though the same functionality could be used without conversion by using aucgi).
 
My original intended purpose for these functions was to allow my web server to calculate if a player was between two points(inside a "region") in a game(minecraft).
 
Currently my functions can do the following:

  • Calculate the absolute distance between two points
  • Calculate the volume between two points(to the nearest whole number)
  • Calculate all points between two points, including their volume(to the nearest whole numbers)
  • Check is a point is between two points(to the nearest whole number)
  • ​(Maybe more I haven't though of?)

I then expanded on the code to add some additional functionality. This code could be used with little modification to create a voxel style game engine. (It could actually even be further modified to support decimal values, though this would significantly slow it's performance exponentially per decimal place, though this shouldn't be necessary, except in rare cases such precision collision detection[ex: detect if a bullet hit a player or npc])
 
I encourage everyone to submit your modifications/optimizations to my code so everyone can use them. I know my code isn't perfect, and it's functions could be expanded on with the right knowledge(things like collision detection, world generation, etc).
 
If you use any of my code in your project, please link to this page! And while not required, I would like it if you please linked me to your project, I love to see my code in use!
 
So finally here's the code(including examples of all functions being used):

voxel.au3

Edited by nullschritt

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Known Bugs:
  • Second set of coordinates cannot = 0,0,0
  • -> (Fixed by conditionally swapping values)
  • Quick count does not accuratley return the volume.
Edited by nullschritt

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      GDI+
      ;coded by UEZ build 2017-01-17 #pragma compile(Icon, "c:\Program Files (x86)\AutoIt3\Icons\au3.ico") #AutoIt3Wrapper_Run_Au3Stripper=y #Au3Stripper_Parameters=/so /pe /rm #AutoIt3Wrapper_Run_After=del /f /q "%scriptdir%\%scriptfile%_stripped.au3" #include <GDIPlus.au3> #include <GuiConstantsEx.au3> #include <WindowsConstants.au3> _GDIPlus_Startup() Global $__f1, $__f2, $__f3, $__fY0, $__fZ0, $__fX1, $__fY1 Global $hGUI, $iFPS = 0, $iShowFPS = 0, $bExit Global Const $iW = @DesktopWidth * 0.75, $iH = @DesktopHeight * 0.75, $iWh = $iW / 2, $iHh = $iH / 2, $sTitle = "GDI+ 3D Sinus Wave v1.0 coded by UEZ" Global Const $fPi = ACos(-1), $fRad = $fPi / 180, $fDeg = 180 / $fPi, $fPi2 = ACos(-1) * 2 AutoItSetOption("GUIOnEventMode", 1) GDIPlus_3DSinusWave() AutoItSetOption("GUIOnEventMode", 0) _GDIPlus_Shutdown() Func GDIPlus_3DSinusWave() $bExit = False $hGUI = GUICreate($sTitle, $iW, $iH) ;, 0, 0, $WS_POPUP) GUISetState(@SW_SHOW, $hGUI) ;~ GUISetCursor(16, 1) ;create canvas elements Local Const $hDC = _WinAPI_GetDC($hGUI) Local Const $hHBitmap = _WinAPI_CreateCompatibleBitmap($hDC, $iW, $iH) Local Const $hDC_backbuffer = _WinAPI_CreateCompatibleDC($hDC) Local Const $DC_obj = _WinAPI_SelectObject($hDC_backbuffer, $hHBitmap) Local Const $hCanvas = _GDIPlus_GraphicsCreateFromHDC($hDC_backbuffer) _GDIPlus_GraphicsSetSmoothingMode($hCanvas, $GDIP_SMOOTHINGMODE_HIGHQUALITY) _GDIPlus_GraphicsSetPixelOffsetMode($hCanvas, $GDIP_PIXELOFFSETMODE_HIGHQUALITY) Local Const $hBrush_Clr = _GDIPlus_BrushCreateSolid(0xFFFFFFFF), _ $hBrush_FPS = _GDIPlus_BrushCreateSolid(0xF0808080), _ $hFormat_FPS = _GDIPlus_StringFormatCreate(), _ $hFamily_FPS = _GDIPlus_FontFamilyCreate("Arial"), _ $hFont_FPS = _GDIPlus_FontCreate($hFamily_FPS, 8), _ $tLayout_FPS = _GDIPlus_RectFCreate(0, 0, 60, 16), _ $hPath = _GDIPlus_PathCreate(), _ $hPen = _GDIPlus_PenCreate(0xCF101010, 1.25) _GDIPlus_PenSetLineJoin($hPen, 2) ;~ _GDIPlus_PenSetDashCap($hPen, $GDIP_DASHCAPROUND) ;~ _GDIPlus_PenSetLineCap($hPen, 0x12, 0x12, 2) $iFPS = 0 Local $fEuler = 2.7182818284 Local $fSpace = 6, $iPoints = 16, $fSpace2 = $fSpace / 2, $iPoints2 = $iPoints / 2 Local $fRotX = Random(-360, 360), $fRotY = Random(-360, 360), $fRotZ = Random(-360, 360), $fZoom = 5.0, $fPower = 20.0 Local $fRx = Random(-1.5, 1,5), $fRy = Random(-1.5, 1,5), $fRz = Random(-1.5, 1,5) Local $c = 0, $t = 0, $aCoords[$iPoints ^ 2][3] Local $i, $j, $x, $y, $z, $x1, $y1, $z1, $x2, $y2, $z2, $x3, $y3, $z3, $fDistance, $r, $g, $b GUISetOnEvent($GUI_EVENT_CLOSE, "_Exit_About") AdlibRegister("CalcFPS", 1000) Do ;~ DllCall($__g_hGDIPDll, "int", "GdipFillRectangle", "handle", $hCanvas, "handle", $hBrush_Clr, "float", 0, "float", 0, _ ;~ "float", $iW, "float", $iH) ;erase canvas background _WinAPI_BitBlt($hDC_backbuffer, 0, 0, $iW, $iH, $hDC_backbuffer, 0, 0, $WHITENESS) $c = 0 For $i = 0 To $iPoints - 1 For $j = 0 To $iPoints - 1 $aCoords[$c][0] = ($fSpace * $i + $fSpace2 - $fSpace * $iPoints2) $aCoords[$c][1] = ($fSpace * $j + $fSpace2 - $fSpace * $iPoints2) $fDistance = Dist(0, 0, $aCoords[$c][0], $aCoords[$c][1]) $aCoords[$c][2] = $fEuler ^ (-$fDistance / 50) * Sin(($fDistance / 10) - $t) * $fPower $c += 1 $t += 0.00075 Next Next For $i = 0 To $iPoints - 2 For $j = 0 To $iPoints - 2 _3Dto2D($aCoords[$j + $iPoints * $i][0], $aCoords[$j + $iPoints * $i][1], $aCoords[$j + $iPoints * $i][2], $fRotX, $fRotY, $fRotZ, $x1, $y1, $z1) _3Dto2D($aCoords[$j + $iPoints * ($i + 1)][0], $aCoords[$j + $iPoints * ($i + 1)][1], $aCoords[$j + $iPoints * ($i + 1)][2], $fRotX, $fRotY, $fRotZ, $x2, $y2, $z2) DllCall($__g_hGDIPDll, "int", "GdipDrawLine", "handle", $hCanvas, "handle", $hPen, _ "float", $iWh + $x1 * $fZoom, "float", $iHh + $y1 * $fZoom, "float", $iWh + $x2 * $fZoom, "float", $iHh + $y2 * $fZoom) _3Dto2D($aCoords[($j + 1) + $iPoints * $i][0], $aCoords[($j + 1) + $iPoints * $i][1], $aCoords[($j + 1) + $iPoints * $i][2], $fRotX, $fRotY, $fRotZ, $x2, $y2, $z2) DllCall($__g_hGDIPDll, "int", "GdipDrawLine", "handle", $hCanvas, "handle", $hPen, _ "float", $iWh + $x1 * $fZoom, "float", $iHh + $y1 * $fZoom, "float", $iWh + $x2 * $fZoom, "float", $iHh + $y2 * $fZoom) Next Next For $i = 0 To $iPoints - 2 _3Dto2D($aCoords[$j + $iPoints * $i][0], $aCoords[$j + $iPoints * $i][1], $aCoords[$j + $iPoints * $i][2], $fRotX, $fRotY, $fRotZ, $x1, $y1, $z1) _3Dto2D($aCoords[$j + $iPoints * ($i + 1)][0], $aCoords[$j + $iPoints * ($i + 1)][1], $aCoords[$j + $iPoints * ($i + 1)][2], $fRotX, $fRotY, $fRotZ, $x2, $y2, $z2) DllCall($__g_hGDIPDll, "int", "GdipDrawLine", "handle", $hCanvas, "handle", $hPen, _ "float", $iWh + $x1 * $fZoom, "float", $iHh + $y1 * $fZoom, "float", $iWh + $x2 * $fZoom, "float", $iHh + $y2 * $fZoom) Next For $j = 0 To $iPoints - 2 _3Dto2D($aCoords[$j + $iPoints * $i][0], $aCoords[$j + $iPoints * $i][1], $aCoords[$j + $iPoints * $i][2], $fRotX, $fRotY, $fRotZ, $x1, $y1, $z1) _3Dto2D($aCoords[($j + 1) + $iPoints * $i][0], $aCoords[($j + 1) + $iPoints * $i][1], $aCoords[($j + 1) + $iPoints * $i][2], $fRotX, $fRotY, $fRotZ, $x2, $y2, $z2) DllCall($__g_hGDIPDll, "int", "GdipDrawLine", "handle", $hCanvas, "handle", $hPen, _ "float", $iWh + $x1 * $fZoom, "float", $iHh + $y1 * $fZoom, "float", $iWh + $x2 * $fZoom, "float", $iHh + $y2 * $fZoom) Next $fRotX += $fRx $fRotY += $fRy $fRotZ += $fRz _GDIPlus_GraphicsDrawStringEx($hCanvas, "FPS: " & $iShowFPS, $hFont_FPS, $tLayout_FPS, $hFormat_FPS, $hBrush_FPS) ;draw background message text _WinAPI_BitBlt($hDC, 0, 0, $iW, $iH, $hDC_backbuffer, 0, 0, $SRCCOPY) ;blit drawn bitmap to GUI $iFPS += 1 If $bExit Then ExitLoop Until Not Sleep(10) AdlibUnRegister("CalcFPS") ;release resources _GDIPlus_PenDispose($hPen) _GDIPlus_PathDispose($hPath) _GDIPlus_FontDispose($hFont_FPS) _GDIPlus_FontFamilyDispose($hFamily_FPS) _GDIPlus_StringFormatDispose($hFormat_FPS) _GDIPlus_BrushDispose($hBrush_Clr) _GDIPlus_BrushDispose($hBrush_FPS) _GDIPlus_GraphicsDispose($hCanvas) _WinAPI_SelectObject($hDC_backbuffer, $DC_obj) _WinAPI_DeleteDC($hDC_backbuffer) _WinAPI_DeleteObject($hHBitmap) _WinAPI_ReleaseDC($hGUI, $hDC) GUIDelete($hGUI) EndFunc ;==>GDIPlus_3DSinusWave Func Dist($x1, $y1, $x2, $y2) Return Sqrt(($x1 - $x2) * ($x1 - $x2) + ($y1 - $y2) * ($y1 - $y2)) EndFunc ;==>Dist Func _3Dto2D($fX, $fY, $fZ, $fRotX, $fRotY, $fRotZ, ByRef $__fXPos, ByRef $__fYPos, ByRef $__fZPos) ;apply the x-axis rotation to transform coordinates ($fX, $fY, $fZ) into coordinates ($fX0, $fY0, $fZ0) $__f1 = $fRotX * $fRad $__f2 = Cos($__f1) $__f3 = Sin($__f1) $__fY0 = $fY * $__f2 + $fZ * $__f3 $__fZ0 = $fZ * $__f2 - $fY * $__f3 ;apply the y-axis rotation to ($fX0, $__fY0, $fZ0) to obtain ($__fX1, $__fY1, $fZ1) $__f1 = $fRotY * $fRad $__f2 = Cos($__f1) $__f3 = Sin($__f1) $__fX1 = $fX * $__f2 - $__fZ0 * $__f3 $__fY1 = $__fY0 ;~ $__fZ1 = $__fZ0 * $__f2 + $fX * $__f2 ;finally, apply the z-axis rotation to obtain the point ($fXPos, $fYPos) $__f1 = $fRotZ * $fRad $__f2 = Cos($__f1) $__f3 = Sin($__f1) $__fXPos = $__fX1 * $__f2 + $__fY1 * $__f3 $__fYPos = $__fY1 * $__f2 - $__fX1 * $__f3 $__fZPos = $__fZ0 EndFunc ;==>_3Dto2D Func _Exit_About() $bExit = True EndFunc ;==>_Exit_About Func CalcFPS() ;display FPS $iShowFPS = $iFPS $iFPS = 0 EndFunc ;==>CalcFPS  
      In the attached 7-Zip file you can find the compiled and also a FreeBasic version. -> DL: 3D Sinus Wave.7z
       
      Have fun. 
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