<JSP>
{ Taala-JSP CODE FOR JSX CONVERSION 8.1.2020 MEP }
{ Muista täpättää LaTeX labels: }

{ Lineaarialgebra: Orthogonal projection matrix 05}

{ JSX board name: OrthProjMatr_05 }
{ JSX element id: orthprojmatr_05 }

MeasurementAccuracy = 100
#CODE	  = "GSP.class"
#CODEBASE = "..\jsp"
#ARCHIVE  = "jsp4.jar"
#WIDTH    = 800
#HEIGHT   = 570
#ALIGN    = Center
*Frame          =  1
*TextFont       =   "Courier"
*TextBold       =   0
*TextSize       =  14
*LabelFont      =   "Courier"
*LabelBold      =   0
*LabelSize      =  14
*MeasureFont        =   "Courier"
*MeasureSize        =  12
*MeasureBold        =   0
*MeasureInDegrees = 1
*DirectedAngles	  = 1
*BackRed	= 255
*BackGreen	= 255
*BackBlue       = 255


{ Direction vector S (the viewpoint) }
{ IMPORTANT }
$LUppS	FixedPoint(0,530)[hidden];
$LLowS	FixedPoint(0,570)[hidden];
$RLowS	FixedPoint(800,570)[hidden];
$RUppS	FixedPoint(800,530)[hidden];
$ULineS	Line($LUppS,$RUppS)[white];
$RectRS	Polygon($LUppS,$LLowS,$RLowS,$RUppS,$LUppS)[color(245,203,200),layer(50)];

$ROS	FixedPoint(400,550)[black,label('0')];
{,LabelAlign(-4,-15)}
$RefS	Translation($ROS,25,0)[hidden];
$RayS	Ray($RefS,$ROS)[black, hidden];
$RykkS	Point on object($RayS,1)[white, label('1')];
{,LabelAlign(-4,-15)}
$RLS	Line($RykkS,$ROS)[black];

$RptS1	Point on object($RLS,9)[label('S1'), red, layer(10)];
{,label('sSUB{1}'),labelAlign(-4,5),psize(2), highlight}
$RptS2	Point on object($RLS,4)[label('S2'), blue, layer(10)];
{,label('sSUB{2}'),labelAlign(-4,8),psize(2), highlight}
$RptS3	Point on object($RLS,2)[label('S3'), color(0,150,0), layer(10)];
{,label('sSUB{3}'),labelAlign(-4,10),psize(2), highlight}

$S1val	Ratio/Points($ROS,$RykkS,$RptS1,  38,540,'')[red];
$FText_s1 FixedText( 85, 546,'s_1')[red];
{,text('\\( sSUB{1} \\, = \\)')}
$S2val	Ratio/Points($ROS,$RykkS,$RptS2,138,540,'')[blue];
$FText_s2 FixedText( 185, 546,'s_2')[blue];
{,text('\\( sSUB{2} \\, = \\)')}
$S3val	Ratio/Points($ROS,$RykkS,$RptS3,238,540,'')[color(0,150,0)];
$FText_s3 FixedText( 285, 546,'s_3')[color(0,150,0)];
{,text('\\( sSUB{3} \\, = \\)')}

{ The projection matrix PS on S }

$PSxFText    FixedText(170,55,'Px =')[black];
{,text('\\( \\large{P} \\mathbf{x} \\ = \\)' ),LabelAlign(0,0)}
$PS_leftPar FixedText(160,40,'(')[black];
{,text('\\( \\Biggl( \\)' ),LabelAlign(0,0)}
$PSnrmsqr Calculate(0,380,'','A2^ B2^ + C2^ + ')($S1val,$S2val,$S3val)[red,hidden];
$PS11	Calculate(130, 40,'','A2^ D /')($S1val,$S2val,$S3val,$PSnrmsqr)[black];
$PS12	Calculate(195, 40,'','AB* D /')($S1val,$S2val,$S3val,$PSnrmsqr)[black];
$PS13	Calculate(260, 40,'','AC* D /')($S1val,$S2val,$S3val,$PSnrmsqr)[black];
$PS21	Calculate(130, 55,'','0A+')($PS12)[black];
$PS22	Calculate(195, 55,'','B2^ D /')($S1val,$S2val,$S3val,$PSnrmsqr)[black];
$PS23	Calculate(260, 55,'','BC* D /')($S1val,$S2val,$S3val,$PSnrmsqr)[black];
$PS31	Calculate(130, 70,'','0A+')($PS13)[black];
$PS32	Calculate(195, 70,'','0A+')($PS23)[black];
$PS33	Calculate(260, 70,'','C2^ D /')($S1val,$S2val,$S3val,$PSnrmsqr)[black];
$PS_rightPar FixedText(350,40,'(')[black];
{,text('\\( \\Biggr) \\)' ),LabelAlign(0,0)}

{ Units on the x1x2x3 coordinates based on S }

$xykkalfa1	Calculate(0,360,'xykkalfa1 = ','0B- A2^ B2^ + @sqrt / ')($S1val,$S2val,$S3val)[red,hidden];
$xykkalfa2	Calculate(0,380,'xykkalfa2 = ','0AC*- A2^ B2^ + @sqrt / A2^ B2^ + C2^ + @sqrt / ')($S1val,$S2val,$S3val)[red,hidden];
$yykkalfa1	Calculate(0,400,'yykkalfa1 = ','A A2^ B2^ + @sqrt / ')($S1val,$S2val,$S3val)[blue,hidden];
$yykkalfa2	Calculate(0,420,'yykkalfa2 = ','0BC*- A2^ B2^ + @sqrt / A2^ B2^ + C2^ + @sqrt / ')($S1val,$S2val,$S3val)[blue,hidden];
$zykkalfa1	Calculate(0,440,'zykkalfa1 = ','0A*')($S1val,$S2val,$S3val)[color(0,150,0),hidden];
$zykkalfa2	Calculate(0,460,'zykkalfa2 = ','A2^ B2^ + A2^ B2^ + @sqrt / A2^ B2^ + C2^ + @sqrt / ')($S1val,$S2val,$S3val)[color(0,150,0),hidden];

$SBRLS	ShowButton(410,500,'Change direction')($ROS,$RykkS,$RLS,$RptS1,$RptS2,$RptS3,$S1val,$S2val,$S3val,$RectRS,$FText_s1,$FText_s2,$FText_s3)[black,bold];
$HBRLS	HideButton(510,500,'Fix')(             $ROS,$RykkS,$RLS,$RptS1,$RptS2,$RptS3,$S1val,$S2val,$S3val,$RectRS,$FText_s1,$FText_s2,$FText_s3)[black];

{ The virtual 3-space system: axes}

$Origo	FixedPoint(200,320)[black, label('0')];
$unitp  UnitPoint($Origo,50)[white, hidden];
$coord  Origin&Unit($Origo,$unitp)[black,hidden];

$xykk	PlotXY($xykkalfa2,$coord,$xykkalfa1)[white, label('1'),layer(10)];
{,LabelAlign(-3,-12)}
$yykk	PlotXY($yykkalfa2,$coord,$yykkalfa1)[white, label('1'),layer(10)];
{,LabelAlign(-3,-8)}
$zykk	PlotXY($zykkalfa2,$coord,$zykkalfa1)[white, label('1'),layer(10)];
{,LabelAlign(-15,-5)}

$xykkyykk   VectorTranslation($xykk,$Origo,$yykk)[white,hidden];
$SpacePolyUnitsquare Polygon($Origo,$xykk,$xykkyykk,$yykk,$Origo)[color(220,200,175)];

$xRay	Ray($xykk,$Origo)[ hidden];
$xRL	Line($xykk,$Origo)[ red, hidden];
$yRay	Ray($yykk,$Origo)[ hidden];
$yRL	Line($yykk,$Origo)[ blue,hidden];
$zRay	Ray($zykk,$Origo)[ hidden];
$zRL	Line($zykk,$Origo)[color(0,150,0),hidden];

$xM		Point on object($xRL,-9)[red,hidden];
$xP		Point on object($xRL, 9)[red,hidden];
$xRLvis		Segment($xM,$xP)[red];
{,arrowL}
$xP2		Point on object($xRL, 8)[red,hidden];
$SxPxP2         Segment($xP2,$xP)[red];
{,label('x SUB{1}'),labelAlign(5,5)}

$yM		Point on object($yRL,-4)[blue,hidden];
$yP		Point on object($yRL, 4)[blue,hidden];
$yRLvis		Segment($yM,$yP)[blue];
{,arrowL}
$yP2		Point on object($yRL, 3.5)[red,hidden];
$SyPyP2         Segment($yP2,$yP)[blue];
{,label('x SUB{2}'),labelAlign(5,5)}

$zM		Point on object($zRL,-3)[color(0,150,0),hidden];
$zP		Point on object($zRL, 4)[color(0,150,0),hidden];
$zRLvis		Segment($zM,$zP)[color(0,150,0)];
{,arrowL}
$zP2		Point on object($zRL, 3.5)[red,hidden];
$SzPzP2         Segment($zP2,$zP)[color(0,150,0)];
{,label('x SUB{3}'),labelAlign(5,5)}

{ Unit space vectors }
$SOrigo_xykk   Segment($Origo,$xykk)[red,thick];
{,arrowL}
$SOrigo_yykk   Segment($Origo,$yykk)[blue,thick];
{,arrowL}
$SOrigo_zykk   Segment($Origo,$zykk)[color(0,150,0),thick];
{,arrowL}


{ Segments connecting the unit points }

$Seg12	Segment($xykk,$yykk)[black];
{,dash(1)}
$Seg23	Segment($yykk,$zykk)[black];
{,dash(1)}
$Seg31	Segment($zykk,$xykk)[black];
{,dash(1)}

{ Vector x }

$Rptx1	 Point on object($xRL,2)[red,label('x1')];
{,label('xSUB{1}'),LabelAlign(-3,5),psize(2),highlight}
$Rptx2	 Point on object($yRL,2)[blue,label('x2')];
{,label('xSUB{2}'),LabelAlign(-3,5),psize(2),highlight}
$Rptx3	 Point on object($zRL,2)[color(0,150,0),label('x3')];
{,label('xSUB{3}'),LabelAlign(-3,5),psize(2),highlight}
$x1x2	VectorTranslation($Rptx1,$Origo,$Rptx2)[magenta, label('(x1,x2)')];
{,label('( xSUB{1},, xSUB{2} )'),LabelAlign(7,5)}
$Sx1x2x	Segment($Rptx1,$x1x2)[blue];
{,dash(2)}
$Sx1x2y	Segment($Rptx2,$x1x2)[red];
{,dash(2)}
$SOx1x2	Segment($Origo,$x1x2)[magenta];
{,dash(2)}

$X	VectorTranslation($x1x2,$Origo,$Rptx3)[black, label('X')];
{,label('\\mathbf{x}'),LabelAlign(0,5)}
$SOX	Segment($Origo,$X)[black,thick];
{,arrowL}
$SXx1x2	Segment($x1x2,$X)[color(0,150,0)];
{,dash(2)}
$SXx3	Segment($Rptx3,$X)[magenta];
{,dash(2)}

$FText_x	    FixedText(400,  25,'x')[black,bold];
{,text('\\( \\mathbf{x} \\)')}
$x_leftPar  FixedText(365,40,'(')[black];
{,text('\\( \\Biggl( \\)' ),LabelAlign(0,0)}
$x_rightPar       FixedText(450,40,'(')[black];
{,text('\\( \\Biggr) \\quad = \\)' ),LabelAlign(0,0)}

$x1	 	Ratio/Points($Origo,$xykk,$Rptx1,330,40,'')[black];
$x2	 	Ratio/Points($Origo,$yykk,$Rptx2,330,55,'')[black];
$x3	 	Ratio/Points($Origo,$zykk,$Rptx3,330,70,'')[black];

{ Vector X' }

$FText_xpr		FixedText(510,  20,'X''')[black,bold];
{,text('\\( \\mathbf{x}'' \\)')}
$xpr_leftPar  FixedText(470,40,'(')[black];
{,text('\\( \\Biggl( \\)' ),LabelAlign(0,0)}
$x1prval	Calculate(433, 40,'','AD* BE* + CF* +')($PS11,$PS12,$PS13,$x1,$x2,$x3)[black];
$x2prval	Calculate(433, 55,'','AD* BE* + CF* +')($PS21,$PS22,$PS23,$x1,$x2,$x3)[black];
$x3prval	Calculate(433, 70,'','AD* BE* + CF* +')($PS31,$PS32,$PS33,$x1,$x2,$x3)[black];
$xpr_rightPar       FixedText(530,40,'(')[black];
{,text('\\( \\Biggr) \\)' ),LabelAlign(0,0)}

$x1pr	Dilation/MarkedRatio($xykk,$Origo,$x1prval)[red,label('x1'''),hidden];
{,label(' x SUB{1}'' '),LabelAlign(7,-10)}
$x2pr	Dilation/MarkedRatio($yykk,$Origo,$x2prval)[blue,label('x2'''),hidden];
{,label(' x SUB{2}'' '),LabelAlign(7,-10)}
$x3pr	Dilation/MarkedRatio($zykk,$Origo,$x3prval)[red,label('x3'''),hidden];
{,label(' x SUB{3}'' '),LabelAlign(7,-10)}


$x1prx2pr	VectorTranslation($x1pr,$Origo,$x2pr)[magenta, label('(x1'',x2'')'),hidden];
{,label('( xSUB{1}'', xSUB{2}'' )'),LabelAlign(7,-10)}
$Sx1prx2prx	Segment($x1pr,$x1prx2pr)[blue,hidden];
{,dash(3)}
$Sx1prx2pry	Segment($x2pr,$x1prx2pr)[red,hidden];
{,dash(3)}
$SOx1prx2pr	Segment($Origo,$x1prx2pr)[magenta,hidden];
{,dash(3)}
$Xpr		VectorTranslation($x1prx2pr,$Origo,$x3pr)[black, label('X''')];
{,label('\\mathbf{x}'''),LabelAlign(-3,-12)}

$SOXpr		Segment($Origo,$Xpr)[color(0,230,40),thick,layer(30)];
{,arrowL}
$SXx1prx2pr	Segment($x1prx2pr,$Xpr)[color(0,150,0),hidden];
{,dash(3)}
$SXprx3pr	Segment($x3pr,$Xpr)[magenta,hidden];
{,dash(3)}
$SXXpr Segment($Xpr,$X)[color(153,76,0),thick];
{,arrowL}
$PolXXpr	Polygon($Origo,$X,$Xpr)[color(9,247,255),layer(20)];


$SBXSegm	ShowButton(5, 90,'X segments')($X,$SOX,$Rptx1,$Rptx2,$Rptx3,$x1x2,$Sx1x2x,$Sx1x2y,$SXx3,$SXx1x2,$SOx1x2)[black,bold];
{,text('\\( \\mathbf{x} \\) segments' ),LabelAlign(0,0)}
$HBXSegm	HideButton(90,90,'Hide')($Rptx1,$Rptx2,$Rptx3,$x1x2,$Sx1x2x,$Sx1x2y,$SXx3,$SXx1x2,$SOx1x2)[black];

$SBXprSegm	ShowButton(5, 110,'X'' segments')($x1pr,$x2pr,$x3pr,$x1prx2pr,$Sx1prx2prx,$Sx1prx2pry,$SOx1prx2pr,$SXx1prx2pr,$SXprx3pr)[black,bold];
{,text('\\( \\mathbf{x}'' \\) segments' ),LabelAlign(0,0)}
$HBXprSegm	HideButton(90,110,'Hide')(       $x1pr,$x2pr,$x3pr,$x1prx2pr,$Sx1prx2prx,$Sx1prx2pry,$SOx1prx2pr,$SXx1prx2pr,$SXprx3pr)[black];

$SBX	        ShowButton(5, 130,'Vector X')($X,$SOX)[black,bold];
{,text('Vector \\( \\mathbf{x} \\)'),LabelAlign(0,0)}
$HBX	HideButton(90,130,'Hide')($X,$SOX,$SXXpr,$PolXXpr,$Rptx1,$Rptx2,$Rptx3,$x1x2,$Sx1x2x,$Sx1x2y,$SXx3,$SXx1x2,$SOx1x2)[black];

$SBXpr	ShowButton(5, 150,'Vector X''')($Xpr,$SOXpr)[black,bold];
{,text('Vector \\( \\mathbf{x}'' \\)' ),LabelAlign(0,0)}
$HBXpr	HideButton(90,150,'Hide')($Xpr,$SOXpr,       $x1pr,$x2pr,$x3pr,$x1prx2pr,$Sx1prx2prx,$Sx1prx2pry,$SOx1prx2pr,$SXx1prx2pr,$SXprx3pr)[black];

$SBXXpr	        ShowButton(5, 170,'Segment Xx''')($X,$Xpr,$SXXpr)[black,bold];
{,text('Segment \\( \\mathbf{x} \\mathbf{x}'' \\)'),LabelAlign(0,0)}
$HBXXpr	HideButton(90,170,'Hide')($SXXpr)[black];

{ The x1x2-Plane }

$x1x2Origo	FixedPoint(570,300)[black, label('0')];
{,LabelAlign(-12,-12)}
$x1ykk	      FixedPoint(620,300)[white, label('1')];
{,LabelAlign(-4,7)}
$x2ykk	      FixedPoint(570,250)[white, label('1')];
{,LabelAlign(5,-2)}

{ Unit plane vectors }
$Sx1x2Origo_x1ykk   Segment($x1x2Origo,$x1ykk)[red,thick];
{,arrowL}
$Sx1x2Origo_x2ykk   Segment($x1x2Origo,$x2ykk)[blue,thick];
{,arrowL}

$x1ykkx2ykk   VectorTranslation($x1ykk,$x1x2Origo,$x2ykk)[white,label('(x1,x2)'),hidden];
$PolyUnitsquare	Polygon($x1x2Origo,$x1ykk,$x1ykkx2ykk,$x2ykk,$x1x2Origo)[color(220,200,175)];


$x1AxisLeft  FixedPoint(420,300) [white,hidden];
$x1AxisRight FixedPoint(720,300) [white,hidden];
$x1Axis      Segment($x1AxisLeft,$x1AxisRight)[red];
{,arrowL}
$FTextx1 FixedText(770, 290,'x1')[red];
{,text('\\( x SUB{1} \\)')}

$x2AxisLow  FixedPoint(570,450) [white,hidden];
$x2AxisHigh FixedPoint(570,150) [white,hidden];
$x2Axis      Segment($x2AxisLow,$x2AxisHigh)[blue];
{,arrowL}
$FTextx2 FixedText(640, 160,'x2')[blue];
{,text('\\( x SUB{2} \\)')}

$x1Plane	Dilation/MarkedRatio($x1ykk,$x1x2Origo,$x1)[red,label('x1')];
{,label(' x SUB{1}'),LabelAlign(-4,-14)}
$x2Plane	Dilation/MarkedRatio($x2ykk,$x1x2Origo,$x2)[blue,label('x2')];
{,label(' x SUB{2}'),LabelAlign(-20,-5)}

$x1x2Plane	VectorTranslation($x1Plane,$x1x2Origo,$x2Plane)[white, label('xp =(x1,x2)')];
{,label('{\\mathbf{x}} SUB{p} = ( xSUB{1},, xSUB{2} )'),LabelAlign(7,5)}
$Sx1x1x2Plane	Segment($x1Plane,$x1x2Plane)[blue];
{,dash(2)}
$Sx2x1x2Plane	Segment($x2Plane,$x1x2Plane)[red];
{,dash(2)}
$XProjPlane Segment($x1x2Origo,$x1x2Plane)[black,thick];
{,arrowL}

$x1prPlane	Dilation/MarkedRatio($x1ykk,$x1x2Origo,$x1prval)[red,label('x1''')];
{,label(' x SUB{1}'' '),LabelAlign(-5,-14)}
$x2prPlane	Dilation/MarkedRatio($x2ykk,$x1x2Origo,$x2prval)[blue,label('x2''')];
{,label(' x SUB{2}'' '),LabelAlign(-25,-5)}

$x1x2prPlane	VectorTranslation($x1prPlane,$x1x2Origo,$x2prPlane)[white, label('Xp'' = (x1'',x2'')')];
{,label('{\\mathbf{x}} SUB{p}'' =( xSUB{1}'' , xSUB{2}'' )'),LabelAlign(7,8)}
$Sx1prx1prx2prPlane	Segment($x1prPlane,$x1x2prPlane)[blue];
{,dash(1)}
$Sx2prx1prx2prPlane	Segment($x2prPlane,$x1x2prPlane)[red];
{,dash(1)}
$XprProjPlane Segment($x1x2Origo,$x1x2prPlane)[color(0,230,40),thick];
{,arrowL}

$SXXprPlane Segment($x1x2prPlane,$x1x2Plane)[color(153,76,0),thick];
{,arrowL}
$PolXXprPlane	Polygon($x1x2Origo,$x1x2Plane,$x1x2prPlane)[color(9,247,255),layer(20)];

$SBPlaneXSegm	ShowButton(410, 90,'Projection Xp')($XProjPlane,$x1Plane,$x2Plane,$x1x2Plane,$Sx1x1x2Plane,$Sx2x1x2Plane)[black,bold];
{,text('Projection \\( {\\mathbf{x}} SUB{p} \\)' ),LabelAlign(0,0)}
$HBPlaneXSegm	HideButton(505,90,'Hide')($SXXprPlane,$PolXXprPlane,$XProjPlane,$x1Plane,$x2Plane,$x1x2Plane,$Sx1x1x2Plane,$Sx2x1x2Plane)[black];

$SBPlaneXprSegm	ShowButton(410, 115,'Projection Xp''')($x1prPlane,$x2prPlane,$x1x2prPlane,$Sx1prx1prx2prPlane,$Sx2prx1prx2prPlane,$XprProjPlane)[black,bold];
{,text('Projection \\( {\\mathbf{x}} SUB{p}'' \\)' ),LabelAlign(0,0)}
$HBPlaneXprSegm	HideButton(505,115,'Hide')($SXXprPlane,$PolXXprPlane,$x1prPlane,$x2prPlane,$x1x2prPlane,$Sx1prx1prx2prPlane,$Sx2prx1prx2prPlane,$XprProjPlane)[black];

$SBPlaneXXpr	        ShowButton(410, 140,'Segment XpXp''')($XProjPlane,$XprProjPlane,$x1x2prPlane,$x1x2prPlane,$x1x2Plane,$SXXprPlane,$PolXXprPlane)[black,bold];
{,text('Segment \\( {\\mathbf{x}} SUB{p} {\\mathbf{x}} SUB{p}'' \\)'),LabelAlign(0,0)}
$HBPlaneXXpr	HideButton(505,140,'Hide')($SXXprPlane,$PolXXprPlane)[black];

{ The orthogonal component line }

$OCO	FixedPoint(770,350)[black,label('X''')];
{,label('\\mathbf{x}'''),LabelAlign(5,0)}
$OCykk	FixedPoint(770,300)[white,label('1')];
{,LabelAlign(5,0)}
$OCline	Line($OCO,$OCykk)[blue,hidden];
$OCUp	FixedPoint(770,25)[hidden];
$OClinevis Segment($OCO,$OCUp)[white];
{,arrowL}
$DistXXpr Calculate(665, 100,'','AD-2^ BE-2^ + CF-2^ + @sqrt')($x1,$x2,$x3,$x1prval,$x2prval,$x3prval)[black,hidden];
$OCOXXpr Dilation/MarkedRatio($OCykk,$OCO,$DistXXpr)[color(153,76,0),label('X')];
{,label('\\mathbf{x}'),LabelAlign(5,0)}
$SOCOXXpr Segment($OCO,$OCOXXpr)[color(153,76,0),thick];
{,arrowL}

{ Dividing vertical segments }

$UpperPt 	FixedPoint(400,100)[hidden];
$LowerPt 	FixedPoint(400,530)[hidden];
$VLine 		Segment($UpperPt,$LowerPt)[color(235,235,240),thick];
$UpperPt2 	FixedPoint(750, 0)[hidden];
$LowerPt2 	FixedPoint(750,530)[hidden];
$VLine2 	Segment($UpperPt2,$LowerPt2)[color(235,235,240),thick];
</JSP>