<JSP>
{ Taala-JSP CODE FOR JSX CONVERSION 19.11.2019 MEP }
{ Muista täpättää LaTeX points: }

{ Lineaarialgebra: Orthogonal projection to a general plane }

{ JSX board name: OrtogProj_32 }
{ JSX element id: ortogproj_32 }

#CODEBASE = "http://cs.uef.fi/matematiikka/java/javasketchpad"
#CODEBASE = "../jsp"
#ARCHIVE  = "jsp4.jar"
#CODE     = "GSP.class"
#WIDTH    = 400
#HEIGHT   = 540
#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   =  0
*MeasureInDegrees   =   0
*DirectedAngles     =   1
*Backblue       = 255
*BackGreen      = 255
*Backred        = 255

$ax_x1	FixedText( 60, 400,'x1')[ plain, font('Helvetica'), bold,     red, justifyCenter];
{,text('\\( xSUB{1} \\)')}
$ax_x2  FixedText(430, 330,'x2')[ plain, font('Helvetica'), bold,    blue, justifyCenter];
{,text('\\( xSUB{2} \\)')}
$ax_x3  FixedText(265, 20,'x3')[ plain, font('Helvetica'), bold,   color(0,150,0), justifyCenter];
{,text('\\( xSUB{3} \\)')}
	
{ The real lines }

$LUpp	FixedPoint(0,475)[hidden];
$LLow	FixedPoint(0,540)[hidden];
$RLow	FixedPoint(400,540)[hidden];
$RUpp	FixedPoint(400,475)[hidden];
$ULine	Line($LUpp,$RUpp)[black, hidden];
$RectR	Polygon($LUpp,$LLow,$RLow,$RUpp,$LUpp)[color(240,200,100)];

$ROu	FixedPoint(200,495)[black,label('0')];
{,LabelAlign(-3,7)}
$Refu	Translation($ROu,25,0)[hidden];
$Rayu	Ray($Refu,$ROu)[black, hidden];
$Rykku	Point on object($Rayu,1)[white, label('1'), hidden];
$R1u	FixedPoint(225,495)[white,label('1')];
{,LabelAlign(-3,7)}
$RLu	Line($Rykku,$ROu)[black, hidden];

$ROv	FixedPoint(200,520)[black,label('0')];
{,LabelAlign(-3,-12)}
$Refv	Translation($ROv,25,0)[hidden];
$Rayv	Ray($Refv,$ROv)[black, hidden];
$Rykkv	Point on object($Rayv,1)[white, label('1'), hidden];
$R1v	FixedPoint(225,520)[white,label('1')];
{,LabelAlign(-3,-12)}
$RLv	Line($Rykkv,$ROv)[black, hidden];

{ Direction vector S (viewpoint) }

$LUppS	FixedPoint(0,520)[hidden];
$LLowS	FixedPoint(0,550)[hidden];
$RLowS	FixedPoint(800,550)[hidden];
$RUppS	FixedPoint(800,520)[hidden];
$ULineS	Line($LUppS,$RUppS)[black, hidden];
$RectRS	Polygon($LUppS,$LLowS,$RLowS,$RUppS,$LUppS)[color(245,203,200),layer(50),hidden];

$ROS	FixedPoint(400,530)[black,label('0'),hidden];
$RefS	Translation($ROS,25,0)[hidden];
$RayS	Ray($RefS,$ROS)[black, hidden];
$RykkS	Point on object($RayS,1)[white, label('1'),hidden];
$RLS	Line($RykkS,$ROS)[black,hidden];

$RptS1	Point on object($RLS,9)[label('S1'), red, layer(10),hidden];
$RptS2	Point on object($RLS,4)[label('S2'), blue, layer(10),hidden];
$RptS3	Point on object($RLS,2)[label('S3'), color(0,150,0), layer(10),hidden];
$S1val	Ratio/Points($ROS,$RykkS,$RptS1,  5,543,'S1 = ')[red,hidden];
$S2val	Ratio/Points($ROS,$RykkS,$RptS2,105,543,'S2 = ')[blue,hidden];
$S3val	Ratio/Points($ROS,$RykkS,$RptS3,205,543,'S3 = ')[color(0,150,0),hidden];

$xykkalfa1	Calculate(0,360,'xykkalfa1 = ','0B- A2^ B2^ + @sqrt / ')($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];

{ The virtual space with movable unit points }
$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)];
$yykk	PlotXY($yykkalfa2,$coord,$yykkalfa1)[white, label('1'),layer(10)];
$zykk	PlotXY($zykkalfa2,$coord,$zykkalfa1)[white, label('1'),layer(10)];

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

{ restricting the real lines }

$RLuLeftEndUp  FixedPoint(0,495)[hidden];
$RLvLeftEndLow FixedPoint(0,520)[hidden];
$RLuRightEndUp FixedPoint(400,495)[hidden];
$RLvRightEndLow FixedPoint(400,520)[hidden];

$RLuvis 	Segment($RLuLeftEndUp,$RLuRightEndUp)[black];
{,arrowL}
$RLvvis 	Segment($RLvLeftEndLow,$RLvRightEndLow)[black];
{,arrowL}
$xM		Point on object($xRL,-4)[red,hidden];
$xP		Point on object($xRL, 5)[red,hidden];

$xRLvis		Segment($xM,$xP)[red];

$yM		Point on object($yRL,-3.5)[blue,hidden];
$yP		Point on object($yRL, 3.5)[blue,hidden];

$yRLvis		Segment($yM,$yP)[blue];

$zM		Point on object($zRL,-3)[color(0,150,0),hidden];
$zP		Point on object($zRL, 5)[color(0,150,0),hidden];

$zRLvis		Segment($zM,$zP)[color(0,150,0)];

$FTV	 	FixedText(70,  22,'V')[black,bold];
{,text('\\( V \\)')}
$V_leftPar       FixedText(50,40,'(')[black];
{,text('\\( \\Biggl( \\)' ),LabelAlign(0,0)}
$V_rightPar       FixedText(260,40,'(')[black];
{,text('\\( \\Biggr) = (\\mathbf{v}\\ \\ \\mathbf{w}) \\)' ),LabelAlign(0,0)}

{ Points and values U and V }

$Rptu1	Point on object($RLu,3)[label('v1'), red, layer(10)];
{,label('vSUB{1}'),LabelAlign(-7,5),highlight}
$Rptu2	Point on object($RLu,1)[label('v2'), blue, layer(10)];
{,label('vSUB{2}'),LabelAlign(-7,8),highlight}
$Rptu3	Point on object($RLu,0)[label('v3'), color(0,150,0), layer(10)];
{,label('vSUB{3}'),LabelAlign(-7,10),highlight}
$Rptv1	Point on object($RLv,-1)[label('w1'), red, layer(10)];
{,label('wSUB{1}'),LabelAlign(-7,5),highlight}
$Rptv2	Point on object($RLv,2)[label('w2'), blue, layer(10)];
{,label('wSUB{2}'),LabelAlign(-7,8),highlight}
$Rptv3	Point on object($RLv,0)[label('w3'), color(0,150,0), layer(10)];
{,label('wSUB{3}'),LabelAlign(-7,10),highlight}

$u1val	Ratio/Points($ROu,$Rykku,$Rptu1,15,40,'')[red];
$u2val	Ratio/Points($ROu,$Rykku,$Rptu2,15,55,'')[blue];
$u3val	Ratio/Points($ROu,$Rykku,$Rptu3,15,70,'')[color(0,150,0)];
$v1val	Ratio/Points($ROv,$Rykkv,$Rptv1,65,40,'')[red];
$v2val	Ratio/Points($ROv,$Rykkv,$Rptv2,65,55,'')[blue];
$v3val	Ratio/Points($ROv,$Rykkv,$Rptv3,65,70,'')[color(0,150,0)];

$SBRLuv	ShowButton(  0,450,'Change v,w')($ROu,$R1u,$RLuvis,$Rptu1,$Rptu2,$Rptu3,$ROv,$R1v,$RLvvis,$Rptv1,$Rptv2,$Rptv3,$RectR)[black,bold];
{,text('Change \\( \\mathbf{v}, \\mathbf{w} \\)')}
$HBRLuv	HideButton(100,450,'Fix')(         $ROu,$R1u,$RLuvis,$Rptu1,$Rptu2,$Rptu3,$ROv,$R1v,$RLvvis,$Rptv1,$Rptv2,$Rptv3,$RectR)[black];

{ the space vectors }
$u1	Dilation/3PtRatio($xykk,$Origo,$ROu,$Rykku,$Rptu1)[red,  label('V11'),hidden];
{,label('vSUB{1}'),LabelAlign(-7,6)}
$u2	Dilation/3PtRatio($yykk,$Origo,$ROu,$Rykku,$Rptu2)[blue, label('V21'),hidden];
{,label('vSUB{2}'),LabelAlign(-7,6)}
$u3	Dilation/3PtRatio($zykk,$Origo,$ROu,$Rykku,$Rptu3)[color(0,150,0), label('V31'),hidden];
{,label('vSUB{3}'),LabelAlign(-7,6)}

$u1u2	VectorTranslation($u1,$Origo,$u2)[magenta, label('(V11,V21)'),hidden];
{,label('(vSUB{1},,vSUB{2} )'),LabelAlign(-7,6)}

$Su1u2x	Segment($u1,$u1u2)[blue,hidden];
$Su1u2y	Segment($u2,$u1u2)[red,hidden];
$SOu1u2	Segment($Origo,$u1u2)[magenta,hidden];

$U	VectorTranslation($u1u2,$Origo,$u3)[color(255,168,17), label('V1')];
{,label('\\mathbf{v}'),LabelAlign(-7,5)}

$SUu1u2	Segment($u1u2,$U)[color(0,150,0),hidden];
$SOU	Segment($Origo,$U)[color(255,168,17),thick];
{,arrowL}
$SUu3	Segment($u3,$U)[magenta,hidden];

$v1	Dilation/3PtRatio($xykk,$Origo,$ROv,$Rykkv,$Rptv1)[red,  label('V12'),hidden];
{,label('wSUB{1}'),LabelAlign(-7,6)}
$v2	Dilation/3PtRatio($yykk,$Origo,$ROv,$Rykkv,$Rptv2)[blue, label('V22'),hidden];
{,label('wSUB{2}'),LabelAlign(-7,6)}
$v3	Dilation/3PtRatio($zykk,$Origo,$ROv,$Rykkv,$Rptv3)[color(0,150,0), label('V32'),hidden];
{,label('wSUB{3}'),LabelAlign(-7,6)}

$v1v2	VectorTranslation($v1,$Origo,$v2)[magenta, label('(V12,V22)'),hidden];
{,label('(wSUB{1},,wSUB{2} )'),LabelAlign(-7,6)}

$Sv1v2x	Segment($v1,$v1v2)[blue,hidden];
$Sv1v2y	Segment($v2,$v1v2)[red,hidden];
$SOv1v2	Segment($Origo,$v1v2)[magenta,hidden];

$V	VectorTranslation($v1v2,$Origo,$v3)[color(255,168,17), label('V2')];
{,label('\\mathbf{w}'),LabelAlign(-7,5)}
$SVv1v2	Segment($v1v2,$V)[color(0,150,0),hidden];
$SOV	Segment($Origo,$V)[color(255,168,17),thick];
{,arrowL}
$SVv3	Segment($v3,$V)[magenta,hidden];

$UplusV	VectorTranslation($U,$Origo,$V)[hidden];
$PlPol	Polygon($Origo,$U,$UplusV,$V)[yellow,layer(20)];
$UminusV	VectorTranslation($U,$V,$Origo)[hidden];
$UminusV	VectorTranslation($U,$V,$Origo)[hidden];
$VminusU	VectorTranslation($V,$U,$Origo)[hidden];
$minusUplusV	VectorTranslation($VminusU,$UplusV,$UminusV)[hidden];
$PUV		Polygon($UplusV,$VminusU,$minusUplusV,$UminusV)[color(236,245,175)];

$a11	Calculate(550, 150,'','AA* BB* + CC* +')($u1val,$u2val,$u3val)[black,hidden];
$a12	Calculate(610, 150,'','AD* BE* + CF* +')($u1val,$u2val,$u3val,$v1val,$v2val,$v3val)[black,hidden];
$a21	Calculate(550, 170,'','A0+')($a12)[black,hidden];
$a22	Calculate(610, 170,'','AA* BB* + CC* +')($v1val,$v2val,$v3val)[black,hidden];


$det	Calculate(  0, 200,'det = ','AD* BC* -')($a11,$a12,$a21,$a22)[black,hidden];

$Ia11	Calculate(185, 100,'','AB/')($a22,$det)[black,hidden];
$Ia12	Calculate(250, 100,'','0A- B/')($a21,$det)[black,hidden];
$Ia21	Calculate(185, 120,'','0A+')($Ia12)[black,hidden];
$Ia22	Calculate(250, 120,'','AB/')($a11,$det)[black,hidden];

$c11	Calculate(350, 40,'','AC* BD* +')($Ia11,$Ia12,$u1val,$v1val)[black,hidden];
$c12	Calculate(350, 40,'','AC* BD* +')($Ia11,$Ia12,$u2val,$v2val)[black,hidden];
$c13	Calculate(350, 40,'','AC* BD* +')($Ia11,$Ia12,$u3val,$v3val)[black,hidden];
$c21	Calculate(350, 40,'','AC* BD* +')($Ia21,$Ia22,$u1val,$v1val)[black,hidden];
$c22	Calculate(350, 40,'','AC* BD* +')($Ia21,$Ia22,$u2val,$v2val)[black,hidden];
$c23	Calculate(350, 40,'','AC* BD* +')($Ia21,$Ia22,$u3val,$v3val)[black,hidden];

$p11	Calculate(500, 40,'','AC* BD* +')($u1val,$v1val,$c11,$c21)[black,hidden];
$p12	Calculate(500, 40,'','AC* BD* +')($u1val,$v1val,$c12,$c22)[black,hidden];
$p13	Calculate(500, 40,'','AC* BD* +')($u1val,$v1val,$c13,$c23)[black,hidden];
$p21	Calculate(500, 40,'','AC* BD* +')($u2val,$v2val,$c11,$c21)[black,hidden];
$p22	Calculate(500, 40,'','AC* BD* +')($u2val,$v2val,$c12,$c22)[black,hidden];
$p23	Calculate(500, 40,'','AC* BD* +')($u2val,$v2val,$c13,$c23)[black,hidden];
$p31	Calculate(500, 40,'','AC* BD* +')($u3val,$v3val,$c11,$c21)[black,hidden];
$p32	Calculate(500, 40,'','AC* BD* +')($u3val,$v3val,$c12,$c22)[black,hidden];
$p33	Calculate(500, 40,'','AC* BD* +')($u3val,$v3val,$c13,$c23)[black,hidden];

$Rptx1	 Point on object($xRL,4)[red,label('u1')];
{,highlight,label('uSUB{1}')}
$Rptx2	 Point on object($yRL,3.5)[blue,label('u2')];
{,highlight,label('uSUB{2}')}
$Rptx3	 Point on object($zRL,3)[color(0,150,0),label('u3')];
{,highlight,label('uSUB{3}')}

$x1x2	VectorTranslation($Rptx1,$Origo,$Rptx2)[magenta, label('(u1,u2)')];
{,label('(uSUB{1},, uSUB{2} )')}
$Sx1x2x	Segment($Rptx1,$x1x2)[blue];
$Sx1x2y	Segment($Rptx2,$x1x2)[red];
$SOx1x2	Segment($Origo,$x1x2)[magenta];


$FTx	 	FixedText(400,  22,'u')[black,bold];
{,text('\\( \\mathbf{u} \\)')}

$X_leftPar       FixedText(365,40,'(')[black];
{,text('\\( \\Biggl( \\)' ),LabelAlign(0,0)}
$X_rightPar       FixedText(415,40,'(')[black];
{,text('\\( \\Biggr) \\)' ),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];


$FTxpr		FixedText(365,  420,'X''')[black,bold];
{,text('\\( \\mathbf{u}SUB{V} \\)'),labelAlign(60,10)}

$Xpr_leftPar       FixedText(365,440,'(')[black];
{,text('\\( \\Biggl( \\)' ),LabelAlign(0,0)}
$Xpr_rightPar       FixedText(415,440,'(')[black];
{,text('\\( \\Biggr) \\)' ),LabelAlign(0,0)}

$x1prval	Calculate(333, 440,'','AD* BE* + CF* +')($p11,$p12,$p13,$x1,$x2,$x3)[black];
$x2prval	Calculate(333, 455,'','AD* BE* + CF* +')($p21,$p22,$p23,$x1,$x2,$x3)[black];
$x3prval	Calculate(333, 470,'','AD* BE* + CF* +')($p31,$p32,$p33,$x1,$x2,$x3)[black];

$x1pr	Dilation/MarkedRatio($xykk,$Origo,$x1prval)[red,label('x1'''),hidden];
$x2pr	Dilation/MarkedRatio($yykk,$Origo,$x2prval)[blue,label('x2'''),hidden];
$x3pr	Dilation/MarkedRatio($zykk,$Origo,$x3prval)[red,label('x3'''),hidden];

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

$x1prx2pr	VectorTranslation($x1pr,$Origo,$x2pr)[magenta, label('(x1'',x2'')'),hidden];
$Sx1prx2prx	Segment($x1pr,$x1prx2pr)[blue,hidden];
$Sx1prx2pry	Segment($x2pr,$x1prx2pr)[red,hidden];
$SOx1prx2pr	Segment($Origo,$x1prx2pr)[magenta,hidden];

$Xpr		VectorTranslation($x1prx2pr,$Origo,$x3pr)[color(0,230,40), label('X''')];
{,label(' \\mathbf{u}SUB{V}'),labelAlign(-8,-15)}
$SXx1prx2pr	Segment($x1prx2pr,$Xpr)[color(0,150,0),hidden];
$SOXpr		Segment($Origo,$Xpr)[color(0,230,40),thick,layer(30)];
{,arrowL}
$SXprx3pr	Segment($x3pr,$Xpr)[magenta,hidden];

$SXXpr 		Segment($X,$Xpr)[blue,thick];
$PolXXpr	Polygon($Origo,$X,$Xpr)[color(9,247,255),layer(40)];

$Ratio	Calculate(665, 100,'','A 0 * 0.15 +')($c11)[black,hidden];
$PtXprX	Dilation/MarkedRatio($X,$Xpr,$Ratio)[blue,hidden];
$PtXprO	Dilation/MarkedRatio($Origo,$Xpr,$Ratio)[blue,hidden];
$PtTr	VectorTranslation($PtXprX,$Xpr,$PtXprO)[blue,hidden];
$OrthPolygon Polygon($Xpr,$PtXprX,$PtTr,$PtXprO)[blue,layer(50)];

$SBV1Segm	ShowButton(0, 150,'V1 segments')($u1,$u2,$u3,$u1u2,$Su1u2x,$Su1u2y,$SOu1u2,$SUu1u2,$SUu3)[black,bold];
{,text('\\( \\mathbf{v}\\) segments')}
$HBV1Segm	HideButton(90,150,'Hide')($u1,$u2,$u3,$u1u2,$Su1u2x,$Su1u2y,$SOu1u2,$SUu1u2,$SUu3)[black];

$SBV2Segm	ShowButton(0, 170,'V2 segments')($v1,$v2,$v3,$v1v2,$Sv1v2x,$Sv1v2y,$SOv1v2,$SVv1v2,$SVv3)[black,bold];
{,text('\\( \\mathbf{w}\\) segments')}
$HBV2Segm	HideButton(90,170,'Hide')($v1,$v2,$v3,$v1v2,$Sv1v2x,$Sv1v2y,$SOv1v2,$SVv1v2,$SVv3)[black];

$SBXSegm	ShowButton(0, 190,'X segments')($Rptx1,$Rptx2,$Rptx3,$x1x2,$Sx1x2x,$Sx1x2y,$SXx3,$SOx1x2,$SXx1x2)[black,bold];
{,text('\\( \\mathbf{u}\\) segments')}
$HBXSegm	HideButton(90,190,'Hide')($Rptx1,$Rptx2,$Rptx3,$x1x2,$Sx1x2x,$Sx1x2y,$SXx3,$SOx1x2,$SXx1x2)[black];

$SBXprSegm	ShowButton(0, 210,'X'' segments')($x1pr,$x2pr,$x3pr,$x1prx2pr,$Sx1prx2prx,$Sx1prx2pry,$SOx1prx2pr,$SXx1prx2pr,$SXprx3pr)[black,bold];
{,text('\\( \\mathbf{u}_V\\) segments')}
$HBXprSegm	HideButton(90,210,'Hide')(       $x1pr,$x2pr,$x3pr,$x1prx2pr,$Sx1prx2prx,$Sx1prx2pry,$SOx1prx2pr,$SXx1prx2pr,$SXprx3pr)[black];
</JSP>