[SOLVED] Line, coordinates

[algiuxas]

Hello everybody

I don't know how to explain this, but there are RED and BLUE dots, they make up a line, and I want to find out where is GREEN dot, in what side, and it would output TRUE or FALSE.
(there's coordinates/positions in picture)

Sorry for my bad English.

Edited July 7, 2016 by algiuxas
Updated picture

[JLogan3o13]

@algiuxas your screenshot is not viewable. Please try uploading it again.

[algiuxas]

10 minutes ago, JLogan3o13 said:

@algiuxas your screenshot is not viewable. Please try uploading it again.

Uploaded, you should see this picture now.

[UEZ]

What if blue and red are swapped? Where is true  / false then?

[algiuxas]

Just now, UEZ said:

What if blue and red are swapped? Where is true  / false then?

Then true / false will swap too.

[SadBunny]

ConsoleWrite(isTrue(4,1 , 10,10 , 3,9) & @CRLF)

Func isTrue($red_x, $red_y, $blue_x, $blue_y, $green_x, $green_y)
    Return (($blue_x - $red_x) * ($green_y - $red_y) - ($blue_y - $red_y) * ($green_x - $red_x) > 0)
EndFunc   ;==>isTrue

Note that this will also return "false" if the point is ON the line (you didn't specify that so I don't know whether that matters).

I'm not sure what you want to happen if the line goes from bottom left to top right or maybe the red/blue points are reversed, i.e. if the line is directed (i.e. the order of the red/blue determines the orientation of true/false), but this solution should work in reverse if the red/blue are reversed. Try it out with a few test values to make sure that this is what you wanted, if not, clarify with a few more examples.

This is really more of a math question I guess?

Edited July 7, 2016 by SadBunny
Added example line to code

[UEZ]

Try this:

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#include <GDIPlus.au3>
_GDIPlus_Startup()
$fRedX = 4
$fRedY = 1
$fBlueX = 10
$fBlueY = 10

$fGreenX = 3
$fGreenY = 9

Global $bResult = Check($fRedX, $fRedY, $fBlueX, $fBlueY, $fGreenX, $fGreenY)
MsgBox(0, "Test", $bResult)

_GDIPlus_Shutdown()

Func Check($fRX, $fRY, $fBX, $fBY, $fGX, $fGY, $iHeight = 5000)
    Local $hPath = _GDIPlus_PathCreate(), $bResult, $m, $b
    $m = ($fRX - $fBY) / ($fRY - $fBY) ;y = mx+b
    $b = $fRY - $m * $fRedX
    Local $aPoints[7][2] = [[6]]
    $aPoints[1][0] = 0
    $aPoints[1][1] = 0
    $aPoints[2][0] = -$b / $m   ;x at position $y = 0
    $aPoints[2][1] = 0
    $aPoints[3][0] = $fRX
    $aPoints[3][1] = $fRY
    $aPoints[4][0] = $fBX
    $aPoints[4][1] = $fBX
    $aPoints[5][0] = ($iHeight - $b) / $m
    $aPoints[5][1] = $iHeight
    $aPoints[6][0] = 0
    $aPoints[6][1] = $iHeight
    _GDIPlus_PathAddPolygon($hPath, $aPoints)
    $bResult = _GDIPlus_PathIsVisiblePoint($hPath, $fGX, $fGY)
    _GDIPlus_PathDispose($hPath)
    Switch $fRedY < $fBlueY
        Case True
            Return $bResult
        Case False
            Return $bResult * -1
    EndSwitch
EndFunc

 

Not tested!

Edited July 7, 2016 by UEZ

[algiuxas]

5 minutes ago, UEZ said:

Try this:

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#include <GDIPlus.au3>
_GDIPlus_Startup()
$fRedX = 4
$fRedY = 1
$fBlueX = 10
$fBlueY = 10

$fGreenX = 3
$fGreenY = 9

Global $bResult = Check($fRedX, $fRedY, $fBlueX, $fBlueY, $fGreenX, $fGreenY)
MsgBox(0, "Test", $bResult)

_GDIPlus_Shutdown()

Func Check($fRX, $fRY, $fBX, $fBY, $fGX, $fGY, $iHeight = 5000)
    Local $hPath = _GDIPlus_PathCreate(), $bResult, $m, $b
    $m = ($fRX - $fBY) / ($fRY - $fBY) ;y = mx+b
    $b = $fRY - $m * $fRedX
    Local $aPoints[7][2] = [[6]]
    $aPoints[1][0] = 0
    $aPoints[1][1] = 0
    $aPoints[2][0] = -$b / $m   ;x at position $y = 0
    $aPoints[2][1] = 0
    $aPoints[3][0] = $fRX
    $aPoints[3][1] = $fRY
    $aPoints[4][0] = $fBX
    $aPoints[4][1] = $fBX
    $aPoints[5][0] = ($iHeight - $b) / $m
    $aPoints[5][1] = $iHeight
    $aPoints[6][0] = 0
    $aPoints[6][1] = $iHeight
    _GDIPlus_PathAddPolygon($hPath, $aPoints)
    $bResult = _GDIPlus_PathIsVisiblePoint($hPath, $fGX, $fGY)
    _GDIPlus_PathDispose($hPath)
    Switch $fRedY < $fBlueY
        Case True
            Return $bResult
        Case False
            Return False
    EndSwitch
EndFunc

 

Not tested!

Thank you very much! It would be really great if you would made it a bit faster... It took about 12 ms for me, if I would need to run this function for 50 times script would be a bit slow... I'm making 3D graphics, so I need to make it work fast enough

[SadBunny]

UEZ' code works with the given numbers, but:

1. It risks division by zero (if $fRY - $fBY equals zero)
2. Return $bResult * -1 is incorrect, as multiplying a boolean with *-1 returns -0 (for true) or -1 (for false). You probably meant Return Not $bResult

Have you tried my version? It is much shorter, much faster and probably works better too

 

[algiuxas]

5 minutes ago, SadBunny said:

UEZ' code works with the given numbers, but:

1. It risks division by zero (if $fRY - $fBY equals zero)
2. Return $bResult * -1 is incorrect, as multiplying a boolean with *-1 returns -0 (for true) or -1 (for false). You probably meant Return Not $bResult

Have you tried my version? It is much shorter, much faster and probably works better too

 

Sorry, I didn't checked it, but now I checked, it works perfectly! Thank you very much!

You are awesome!

Edited July 7, 2016 by algiuxas

[SadBunny]

10 minutes ago, algiuxas said:

You are awesome!

 

[UEZ]

1 hour ago, SadBunny said:

UEZ' code works with the given numbers, but:

1. It risks division by zero (if $fRY - $fBY equals zero)
2. Return $bResult * -1 is incorrect, as multiplying a boolean with *-1 returns -0 (for true) or -1 (for false). You probably meant Return Not $bResult

Have you tried my version? It is much shorter, much faster and probably works better too

 

Yes you are right, Return $bResult * -1 is bullshit. I was in a hurry because of the football match. Of course it must be Return Not $bResult to invert the result.

Btw, there are many ways to solve a problem. Further if your result is = 0 then the green dot is on the line. What is the status then?

 

Your version is of course the fastest and best solution. 

Edited July 7, 2016 by UEZ

[SadBunny]

1 minute ago, UEZ said:

I was in a hurry because of the football match.

Judging from the beautiful moustache on your profile picture I guess I will have to say congratulations

[UEZ]

1 minute ago, SadBunny said:

Judging from the beautiful moustache on your profile picture I guess I will have to say congratulations

[SadBunny]

3 minutes ago, UEZ said:

Ah, in that case mein herzliches Beileid  Being Dutch myself I don't care either way  It's just that Dalí's moustache seemed French rather than German.

Edited July 7, 2016 by SadBunny

[UEZ]

1 minute ago, SadBunny said:

Ah, in that case mein herzliches Beileid  Being Dutch myself I don't care either way  It's just that Dalí's moustache seemed French rather than German.

More Spanish.

[SadBunny]

Just now, UEZ said:

More Spanish.

 Guess so  But I had to choose between French and German for obvious reasons and I had nothing else to go on  

[algiuxas]

expandcollapse popup

Global $ver = "by algiuxas"
Global $GUITitle = "3D render " & $ver


Global $GUI_Loading = GUICreate($GUITitle, 616, 37, -1, 100, -2147483648)
GUISetBkColor(0x000000)
Global $GUI_Loading_Ctrl_Label = GUICtrlCreateLabel("Loading...", 8, 8, 600, 23, 1)
GUICtrlSetFont(-1, 12, 800, 0, "Consolas")
GUICtrlSetColor(-1, 0xFFFFFF)
GUISetState(@SW_SHOW)
Func _GUI_CL($Text)
    GUICtrlSetData($GUI_Loading_Ctrl_Label, $Text)
EndFunc   ;==>_GUI_CL

#Region # Data
_GUI_CL("Loading data...")
Global $SizeX = 480
Global $SizeY = 320
Global $CtrX = $SizeX / 2
Global $CtrY = $SizeY / 2
Global $DPI = 84

Global $GM_BgColor = 0x33AAFF
Global $GM_FPS_MAX = 0
#EndRegion # Data
#Region # P-Data
Global $GM_EXT = False
#EndRegion # P-Data
#Region # GUI
_GUI_CL("Loading GUI...")
#include <GUIConstantsEx.au3>
Global $GUI = GUICreate($GUITitle, $SizeX, $SizeY)
GUISetBkColor(0x000000)

Opt("GUIOnEventMode", 1)
OnAutoItExitRegister("GM_Exit")
GUISetOnEvent($GUI_EVENT_CLOSE, "GM_Exit", $GUI)
#EndRegion # GUI
#Region # GDIPlus
_GUI_CL("Loading GDI+ functions...")
#include <GDIPlus.au3>
_GDIPlus_Startup()
Global $Graphics = _GDIPlus_GraphicsCreateFromHWND($GUI)
Global $Bitmap = _GDIPlus_BitmapCreateFromGraphics($SizeX, $SizeY, $Graphics)
Global $GfxCtxt = _GDIPlus_ImageGetGraphicsContext($Bitmap)
#EndRegion # GDIPlus
#Region # Images
_GUI_CL("Loading images...")
#EndRegion # Images
#Region # Keyboard Data
_GUI_CL("Loading input data...")
#include <Misc.au3>


#EndRegion # Keyboard Data
#Region # Calculation
#include <Math.au3>
Const $PI = 3.14159256358979
ConsoleWrite("PI=" & $PI & @CRLF)
Const $PI180 = $PI / 180
ConsoleWrite("PI180=" & $PI180 & @CRLF)
Const $DRAD = Round($PI180, 7)
ConsoleWrite("DRAD=" & $DRAD & @CRLF)

#EndRegion # Calculation
#Region # Colors
Global $Brush_T77_000000 = _GDIPlus_BrushCreateSolid(0x77000000)
Global $Brush_T77_FFFFFF = _GDIPlus_BrushCreateSolid(0x77FFFFFF)
Global $Pen_TFF_000000 = _GDIPlus_PenCreate(0xFF000000)
Global $Pen_TFF_FFFFFF = _GDIPlus_PenCreate(0xFFFFFFFF)

#EndRegion # Colors
#Region # Etc. Data
_GUI_CL("Loading other things...")
Global $GM_CFPS = 0
Global $GM_CFPS_F = 0
Global $GM_CFPS_TI = TimerInit()
Global $GMS = 0
Global $GM_SH = TimerInit()
Global $GM_Cursor[5]
Global $GM_Active = 0
#EndRegion # Etc. Data
#Region # Render Data
Global $FOV = FOV(90)

#EndRegion # Game Data
#cs
    $GM_Cursor[0-3] = [X,Y,1,2]
    $GM_Active = ACTIVE I/O
    $GMS = 1/FPS
#ce

$x = 0
$y = 0
$z = 0

GUIDelete($GUI_Loading)
GUISetState(@SW_SHOW)

While 1
    GM_Loop()
    #Region# Testing area
    Local $posarrn[4][3] = [[0, 5, 4], [-2, 7, 4], [0, 7, 4], [0, 7, 6]]
    Local $rotarr[3] = [$GM_Cursor[1]/150-$CtrX, -$GM_Cursor[0]/150-$CtrY, $z]
    Local $posarr = _3DrotArrMulti($rotarr, $posarrn,4)
    _3D_Pyra_3base($posarr)
    #EndRegion # Testing area
    _GDIPlus_GraphicsDrawString($GfxCtxt, "FPS: " & $GM_CFPS, 10, 10)
    _GDIPlus_GraphicsDrawString($GfxCtxt, "3DG " & $ver, 10, $SizeY - 30)
WEnd

Func _3D_Vector($pa, $lbrush = 0x77000000)
    ;[3][3] = [[x,y,z],[x,y,z],[x,y,z]]
    ;Triangle


    Local $aPnt
    Local $aPoints[4][2]
    $aPoints[0][0] = 3
    $aPnt = _3Dpos($pa[0][0], $pa[0][1], $pa[0][2])
    $aPoints[1][0] = $aPnt[0]
    $aPoints[1][1] = $aPnt[1]
    $aPnt = _3Dpos($pa[1][0], $pa[1][1], $pa[1][2])
    $aPoints[2][0] = $aPnt[0]
    $aPoints[2][1] = $aPnt[1]
    $aPnt = _3Dpos($pa[2][0], $pa[2][1], $pa[2][2])
    $aPoints[3][0] = $aPnt[0]
    $aPoints[3][1] = $aPnt[1]
    If lineAbw($aPoints[2][0],$aPoints[2][1],$aPoints[1][0],$aPoints[1][1],$aPoints[3][0],$aPoints[3][1]) Then
        Local $hBrush = _GDIPlus_BrushCreateSolid($lbrush)
        _GDIPlus_GraphicsFillPolygon($GfxCtxt,$aPoints, $hBrush)
        _GDIPlus_BrushDispose($hBrush)
    EndIf
EndFunc   ;==>_Draw_Vector
Func _3D_Pyra_3base($pr, $lBrush1 = 0xFFFF0000, $lBrush2 = 0xFFFFFFFF, $lBrush3 = 0xFF00FF00, $lBrush4 = 0xFF0000FF)
    ;[4][3] = [[x,y,z],[x,y,z],[x,y,z],[x,y,z]]
    ;       0
    ;     /\\
    ;    /  \ \
    ;   /    \  \
    ;  /______\--3
    ;  1      2
    _3D_Vector(_ArrayWR3($pr,0,1,2),$lBrush1)
    _3D_Vector(_ArrayWR3($pr,0,2,3),$lBrush2)
    _3D_Vector(_ArrayWR3($pr,0,3,1),$lBrush3)
    _3D_Vector(_ArrayWR3($pr,3,2,1),$lBrush4)

EndFunc   ;==>_3D_Pyra_3base
Func _ArrayWR1($pa,$i)
    Local $paa[3]
    $paa[0] = $pa[$i][0]
    $paa[1] = $pa[$i][1]
    $paa[2] = $pa[$i][2]
    Return $paa
EndFunc
Func _ArrayWR3($pa,$i1,$i2,$i3)
    Local $paa[3][3]
    $paa[0][0] = $pa[$i1][0]
    $paa[0][1] = $pa[$i1][1]
    $paa[0][2] = $pa[$i1][2]
    $paa[1][0] = $pa[$i2][0]
    $paa[1][1] = $pa[$i2][1]
    $paa[1][2] = $pa[$i2][2]
    $paa[2][0] = $pa[$i3][0]
    $paa[2][1] = $pa[$i3][1]
    $paa[2][2] = $pa[$i3][2]
    Return $paa
EndFunc
Func _3DrotArrMulti($pr, $pp, $a=4)
    ;[3],[~][3] = ROTATION, POSITION
    Local $ats[$a][3]
    For $i = 0 to $a-1
    $b = _3Drot($pr[0], $pr[1], $pr[2], $pp[$i][0], $pp[$i][1], $pp[$i][2])
    $ats[$i][0] = $b[0]
    $ats[$i][1] = $b[1]
    $ats[$i][2] = $b[2]
    Next
    Return $ats
EndFunc   ;==>
Func _3DrotArr($pr, $pp)
    ;ROTATION, POSITION
    Return _3Drot($pr[0], $pr[1], $pr[2], $pp[0], $pp[1], $pp[2])
EndFunc   ;==>_3DrotArr
Func _3Drot($x, $y, $z, $xp = 0, $yp = 0, $zp = 0)
    ;ROTATION, POSITION
    $XA = _
            Cos($y) * Cos($z) * $xp + _
            (Cos($z) * Sin($x) * Sin($y) - Cos($x) * Sin($z)) * $yp + _
            (Cos($x) * Cos($z) * Sin($y) + Sin($x) * Sin($z)) * $zp
    $YA = _
            (Cos($y) * Sin($z)) * $xp + _
            (Cos($x) * Cos($z) + Sin($x) * Sin($y) * Sin($z)) * $yp + _
            (-Cos($z) * Sin($x) + Cos($x) * Sin($y) * Sin($z)) * $zp
    $ZA = _
            (-Sin($y)) * $xp + _
            (Cos($y) * Sin($x)) * $yp + _
            (Cos($x) * Cos($y)) * $zp
    Local $pos[3] = [$XA, $YA, $ZA]
    Return $pos
EndFunc   ;==>_3Drot
Func _3DposArr($pos)
    Return _3Dpos($pos[0], $pos[1], $pos[2])
EndFunc   ;==>_3DposArr
Func _3Dpos($x, $y, $z)
    ;REMOVE DISTANCE FROM CENTER!
    $fvz = Round(($z + 15) / $FOV, 10)
    Local $pos[2] = [$x * $CtrX / 2 / $fvz + $CtrX, $y * $CtrY / 2 / $fvz + $CtrY]
    Return $pos
EndFunc   ;==>_3Dpos
Func lineAbw($rx, $ry, $bx, $by, $gx, $gy)
    Return (($bx - $rx) * ($gy - $ry) - ($by - $ry) * ($gx - $rx) > 0)
EndFunc   ;==>isTrue
Func FOV($FOVdegr = 90)
    $FOVdegr /= 2
    Return Round(ATan($DRAD * $FOVdegr) * 2, 7)
EndFunc   ;==>FOV
Func GM_Loop()
    $GMS = Floor(TimerDiff($GM_SH)) / 1000
    $GM_Cursor = GUIGetCursorInfo()
    If $GM_Cursor = 0 Then
        $GM_Active = 0
    Else
        $GM_Active = 1
    EndIf
    If $GM_FPS_MAX Then
        Do
            $GMS = Floor(TimerDiff($GM_SH)) / 1000
        Until $GMS > 1 / $GM_FPS_MAX
    EndIf
    $GM_SH = TimerInit()
    If TimerDiff($GM_CFPS_TI) > 1000 Then GM_FPS_RC()
    $GM_CFPS_F += 1
    _GDIPlus_GraphicsDrawImage($Graphics, $Bitmap, 0, 0)
    _GDIPlus_GraphicsClear($GfxCtxt, 0xFF000000 + $GM_BgColor)
EndFunc   ;==>GM_Loop
Func GM_SaveData()
    GM_CW("Saving data...")
    ;TODO: Save data
    GM_CWK("Saving data DONE!")
EndFunc   ;==>GM_SaveData
Func GM_FPS_RC()
    $GM_CFPS = Floor($GM_CFPS_F * 1000 / Floor(TimerDiff($GM_CFPS_TI)))
    $GM_CFPS_TI = TimerInit()
    $GM_CFPS_F = 0
EndFunc   ;==>GM_FPS_RC
Func GM_Exit()
    If $GM_EXT = True Then Exit
    $GM_EXT = True
    GUIDelete()
    GM_SaveData()
    ;TODO: Execute game closing functions
    _GDIPlus_Shutdown()
    Exit
EndFunc   ;==>GM_Exit
Func GM_CW($CW)
    ConsoleWrite("!> " & $CW & @CRLF)
EndFunc   ;==>GM_CW
Func GM_CWK($CW)
    ConsoleWrite("+> " & $CW & @CRLF)
EndFunc   ;==>GM_CWK


Func getAngle($x1,$y1,$x2,$y2)
    Return ATAN2($x2-$x1,$y2-$y1)
EndFunc
Func ATAN2(Const $NY, Const $NX)
    Const $NPI = 3.14159265358979
    Local $NRESULT
    If IsNumber($NY) = 0 Then
        SetError(1)
        Return 0
    ElseIf IsNumber($NX) = 0 Then
        SetError(1)
        Return 0
    EndIf
    If $NX = 0 Then
        If $NY > 0 Then
            $NRESULT = $NPI / 2
        ElseIf $NY < 0 Then
            $NRESULT = 3 * $NPI / 2
        Else
            SetError(2)
            Return 0
        EndIf
    ElseIf $NX < 0 Then
        $NRESULT = ATan($NY / $NX) + $NPI
    Else
        $NRESULT = ATan($NY / $NX)
    EndIf
    While $NRESULT < 0
        $NRESULT += 2 * $NPI
    WEnd
    Return $NRESULT
EndFunc

I know that this is a huge mess... I will fix everything later, and make it better.
Try this script, and move mouse.

[SadBunny]

Nice demo, works fine!  

[algiuxas]

Just now, SadBunny said:

Nice demo, works fine!  

Thanks