DIRECTORY
CoordSys,
Matrix3d,
Rope,
SV3d,
SVError,
SVModelTypes,
SVSceneTypes,
SVTransforms,
SVVector3d;

SVTransformsImpl: PROGRAM
IMPORTS CoordSys, Matrix3d, Rope, SVError, SVVector3d
EXPORTS SVTransforms =
BEGIN

Assembly: TYPE = SVSceneTypes.Assembly;
AssemblyList: TYPE = SVSceneTypes.AssemblyList;
Camera: TYPE = SVModelTypes.Camera;
CoordSystem: TYPE = SVModelTypes.CoordSystem;
CoordSysList: TYPE = SVModelTypes.CoordSysList;
Matrix4by4: TYPE = SV3d.Matrix4by4;
Point3d: TYPE = SV3d.Point3d;
Scene: TYPE = SVSceneTypes.Scene;
Shape: TYPE = SVSceneTypes.Shape;
Vector: TYPE = SV3d.Vector;


IncTransf: PUBLIC PROC [C: CoordSystem, D: CoordSystem, M: Matrix4by4, DFixed: BOOL _ FALSE] = {
P: CoordSystem;

IF C.parent = NIL THEN ERROR; -- cannot translate WORLD for now
IF D = NIL THEN ERROR;
P _ C.parent;
IF MatrixHasScaling[M] THEN {
SVError.Append["SVTransform.IncTransf got illegal matrix.  Ignored."];
SVError.Blink[];
RETURN};

SELECT TRUE FROM
D.parent = NIL => { -- D = WORLD
CWORLD, WORLDP, PWORLD: Matrix4by4;
CWORLD _ CoordSys.FindInTermsOfWorld[C];
PWORLD _ CoordSys.FindInTermsOfWorld[P];
WORLDP _ Matrix3d.Inverse[PWORLD];
C.mat _ Matrix3d.MatMult[Matrix3d.MatMult[WORLDP, M], CWORLD];
};
C = D => { -- local tranformation
C.mat _ Matrix3d.MatMult[C.mat, M];
};
D = P => { -- transformation relative to parent
C.mat _ Matrix3d.MatMult[M, C.mat];
};
ENDCASE => { -- general transformation
CWORLD, DWORLD, CD, WORLDP, PWORLD: Matrix4by4;
CWORLD _ CoordSys.FindInTermsOfWorld[C];
DWORLD _ CoordSys.FindInTermsOfWorld[D]; -- we will preserve this relationship if DFixed
PWORLD _ CoordSys.FindInTermsOfWorld[P];
WORLDP _ Matrix3d.Inverse[PWORLD];
CD _ CoordSys.FindAInTermsOfB[C, D];
C.mat _ Matrix3d.MatMult[Matrix3d.MatMult[Matrix3d.MatMult[WORLDP, DWORLD], M], CD];
IF DFixed THEN {
DPWORLD, DDP: Matrix4by4;
DPWORLD _ CoordSys.FindInTermsOfWorld[D.parent];
DDP _ Matrix3d.WorldToLocal[DPWORLD, DWORLD];
D.mat _ DDP;
};
};
};

IncTransfMatrix: PUBLIC PROC [C: CoordSystem, DWORLD: Matrix4by4, M: Matrix4by4] = {
P: CoordSystem;
CWORLD, CD, WORLDP, PWORLD: Matrix4by4;

IF C.parent = NIL THEN ERROR; -- cannot translate WORLD for now
P _ C.parent;
IF MatrixHasScaling[M] THEN {
SVError.Append["SVTransform.IncTransfMatrix got illegal matrix.  Ignored."];
SVError.Blink[];
RETURN};

CWORLD _ CoordSys.FindInTermsOfWorld[C];
PWORLD _ CoordSys.FindInTermsOfWorld[P];
WORLDP _ Matrix3d.Inverse[PWORLD];
CD _ Matrix3d.WorldToLocal[DWORLD, CWORLD];
C.mat _ Matrix3d.MatMult[Matrix3d.MatMult[Matrix3d.MatMult[WORLDP, DWORLD], M], CD];
};


PlaneOriginRotate: PUBLIC PROC [C: CoordSystem, D: CoordSystem, degrees: REAL, plane: NAT] = {
M, PivotWORLD, CWORLD, DWORLD: Matrix4by4;
origin: Point3d;
xAxis, yAxis, zAxis: Vector;

CWORLD _ CoordSys.FindInTermsOfWorld[C];
DWORLD _ CoordSys.FindInTermsOfWorld[D];
origin _ Matrix3d.OriginOfMatrix[CWORLD];
xAxis _ Matrix3d.XAxisOfMatrix[DWORLD];
yAxis _ Matrix3d.YAxisOfMatrix[DWORLD];
zAxis _ Matrix3d.ZAxisOfMatrix[DWORLD];
PivotWORLD _ Matrix3d.MakeMatFromAxes[xAxis, yAxis, zAxis, origin];

SELECT plane FROM
1 => M _ Matrix3d.MakeRotateXMat[degrees];
2 => M _ Matrix3d.MakeRotateYMat[degrees];
3 => M _ Matrix3d.MakeRotateZMat[degrees];
ENDCASE => ERROR;
IncTransfMatrix[C, PivotWORLD, M];
};

AbsTransf: PUBLIC PROC [C: CoordSystem, D: CoordSystem, N: Matrix4by4, DFixed: BOOL _ FALSE] = {
P: CoordSystem;

IF Rope.Equal[C.name, "SCREEN", TRUE] THEN {C.mat _ N; RETURN};
IF C.parent = NIL THEN ERROR; -- cannot transform WORLD.
IF D = NIL THEN ERROR;
P _ C.parent;
IF MatrixHasScaling[N] THEN {
SVError.Append["SVTransform.AbsTransf got illegal matrix.  Ignored."];
SVError.Blink[];
RETURN};

SELECT TRUE FROM
D.parent = NIL => { -- D = WORLD
WORLDP, PWORLD: Matrix4by4;
PWORLD _ CoordSys.FindInTermsOfWorld[P];
WORLDP _ Matrix3d.Inverse[PWORLD];
C.mat _ Matrix3d.MatMult[WORLDP, N];
};
C = D => { -- local tranformation
C.mat _ Matrix3d.MatMult[C.mat, N];
};
D = P => { -- transformation relative to parent
C.mat _ N;
};
ENDCASE => { -- general transformation
DWORLD, WORLDP, PWORLD: Matrix4by4;
DWORLD _ CoordSys.FindInTermsOfWorld[D];
PWORLD _ CoordSys.FindInTermsOfWorld[P];
WORLDP _ Matrix3d.Inverse[PWORLD];
C.mat _ Matrix3d.MatMult[Matrix3d.MatMult[WORLDP, DWORLD], N];
IF DFixed THEN {
DPWORLD, DDP: Matrix4by4;
DPWORLD _ CoordSys.FindInTermsOfWorld[D.parent];
DDP _ Matrix3d.WorldToLocal[DPWORLD, DWORLD];
D.mat _ DDP;
};
};
};

TugTransf: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem, N: Matrix4by4] = {
F: Matrix4by4 _ CoordSys.FindAInTermsOfB[C, tugBoat];
AbsTransf[tugBoat, D, N];
AbsTransf[C, tugBoat, F];
};

TugTransfLeaveTug: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem, N: Matrix4by4] = {
F: Matrix4by4;
saveTugMat: Matrix4by4 _ tugBoat.mat;

F _ CoordSys.FindAInTermsOfB[C, tugBoat];
AbsTransf[tugBoat, D, N];
AbsTransf[C, tugBoat, F];
tugBoat.mat _ saveTugMat;
};


Translate: PUBLIC PROC [C: CoordSystem, D: CoordSystem, tx, ty, tz: REAL, DFixed: BOOL _ FALSE] = {
M: Matrix4by4;
M _ Matrix3d.MakeTranslateMat[tx, ty, tz];
IncTransf[C, D, M, DFixed];
};

XRotate: PUBLIC PROC [C: CoordSystem, D: CoordSystem, degrees: REAL, DFixed: BOOL _ FALSE] = {
M: Matrix4by4;
M _ Matrix3d.MakeRotateXMat[degrees];
IncTransf[C, D, M, DFixed];
};

YRotate: PUBLIC PROC [C: CoordSystem, D: CoordSystem, degrees: REAL, DFixed: BOOL _ FALSE] = {
M: Matrix4by4;
M _ Matrix3d.MakeRotateYMat[degrees];
IncTransf[C, D, M, DFixed];
};

ZRotate: PUBLIC PROC [C: CoordSystem, D: CoordSystem, degrees: REAL, DFixed: BOOL _ FALSE] = {
M: Matrix4by4;
M _ Matrix3d.MakeRotateZMat[degrees];
IncTransf[C, D, M, DFixed];
};


AbsTranslateOnly: PUBLIC PROC [C: CoordSystem, D: CoordSystem, vD: Point3d] = {
P: CoordSystem; -- parent of C
vP: Vector;

IF Rope.Equal[C.name, "SCREEN", TRUE] THEN {
C.mat[1][4] _ vD[1];
C.mat[2][4] _ vD[2];
C.mat[3][4] _ vD[3];
RETURN};
IF C.parent = NIL THEN ERROR; -- cannot transform WORLD.
IF D = NIL THEN ERROR;
P _ C.parent;

SELECT TRUE FROM
D.parent = NIL => { -- D = WORLD
WORLDP, PWORLD: Matrix4by4;
PWORLD _ CoordSys.FindInTermsOfWorld[P];
WORLDP _ Matrix3d.Inverse[PWORLD];
vP _ Matrix3d.Update[WORLDP, vD];
C.mat[1][4] _ vP[1];
C.mat[2][4] _ vP[2];
C.mat[3][4] _ vP[3];
};
C = D => { -- local tranformation
C.mat _ Matrix3d.LocalTranslate[C.mat, vD[1], vD[2], vD[3]];
};
D = P => { -- transformation relative to parent
C.mat[1][4] _ vD[1];
C.mat[2][4] _ vD[2];
C.mat[3][4] _ vD[3];
};
ENDCASE => { -- general transformation
DWORLD, WORLDP, PWORLD: Matrix4by4;
DWORLD _ CoordSys.FindInTermsOfWorld[D];
PWORLD _ CoordSys.FindInTermsOfWorld[P];
WORLDP _ Matrix3d.Inverse[PWORLD];
vP _ Matrix3d.Update[WORLDP, Matrix3d.Update[DWORLD, vD]];
C.mat[1][4] _ vP[1];
C.mat[2][4] _ vP[2];
C.mat[3][4] _ vP[3];
};
};

Align: PUBLIC PROC [C: CoordSystem, D: CoordSystem] = {
CD: Matrix4by4;
xAxisChoices, zAxisChoices: ARRAY[1..3] OF NAT;
xAxis, zAxis, newXAxis, newYAxis, newZAxis: Vector;
xNegArray, zNegArray: ARRAY[1..3] OF BOOL;
origin: Point3d;

CD _ CoordSys.FindAInTermsOfB[C, D];

xAxis _ Matrix3d.XAxisOfMatrix[CD];
zAxis _ Matrix3d.ZAxisOfMatrix[CD];
origin _ Matrix3d.OriginOfMatrix[CD];
[xAxisChoices, xNegArray] _ IndicesOfMax[xAxis]; -- Find largest component
[zAxisChoices, zNegArray] _ IndicesOfMax[zAxis];
IF zAxisChoices[1] = xAxisChoices[1] THEN zAxisChoices[1] _ zAxisChoices[2];
newXAxis _ [0,0,0];
newXAxis[xAxisChoices[1]] _ SVVector3d.Magnitude[xAxis];
IF xNegArray[xAxisChoices[1]] THEN
newXAxis[xAxisChoices[1]] _ -newXAxis[xAxisChoices[1]];
newZAxis _ [0,0,0];
newZAxis[zAxisChoices[1]] _ SVVector3d.Magnitude[zAxis];
IF zNegArray[zAxisChoices[1]] THEN
newZAxis[zAxisChoices[1]] _ -newZAxis[zAxisChoices[1]];
newYAxis _ SVVector3d.CrossProduct[newZAxis, newXAxis];
CD _ Matrix3d.MakeMatFromAxes[newXAxis, newYAxis, newZAxis, origin];
 
AbsTransf[C, D, CD];
}; -- end of Align

IndicesOfMax: PRIVATE PROC [v: Vector] RETURNS [indices: ARRAY[1..3] OF NAT, negArray: ARRAY[1..3] OF BOOL] = {
temp: REAL;
tempIndex: NAT;
IF v[1] < 0 THEN {negArray[1] _ TRUE; v[1] _ -v[1]}
ELSE negArray[1] _ FALSE;
IF v[2] < 0 THEN {negArray[2] _ TRUE; v[2] _ -v[2]}
ELSE negArray[2] _ FALSE;
IF v[3] < 0 THEN {negArray[3] _ TRUE; v[3] _ -v[3]}
ELSE negArray[3] _ FALSE;
indices _ [1,2,3];
IF v[1] < v[2] THEN {
temp _ v[1]; v[1] _ v[2]; v[2] _ temp;
tempIndex _ indices[1]; indices[1] _ indices[2]; indices[2] _ tempIndex};
IF v[2] < v[3] THEN {
temp _ v[2]; v[2] _ v[3]; v[3] _ temp;
tempIndex _ indices[2]; indices[2] _ indices[3]; indices[3] _ tempIndex};
IF v[1] < v[2] THEN {
temp _ v[1]; v[1] _ v[2]; v[2] _ temp;
tempIndex _ indices[1]; indices[1] _ indices[2]; indices[2] _ tempIndex};
};

Abut: PUBLIC PROC [C: CoordSystem, D: CoordSystem] = {
AbsTranslateOnly[C, D, [0,0,0]];
};

AbutX: PUBLIC PROC [C: CoordSystem, D: CoordSystem] = {
vD: Vector;

vD _ CoordSys.FindTranslationOfAinTermsOfB[C, D];
AbsTranslateOnly[C, D, [0, vD[2], vD[3]]];
};

AbutY: PUBLIC PROC [C: CoordSystem, D: CoordSystem] = {
vD: Vector;

vD _ CoordSys.FindTranslationOfAinTermsOfB[C, D];
AbsTranslateOnly[C, D, [vD[1], 0, vD[3]]];
};

AbutZ: PUBLIC PROC [C: CoordSystem, D: CoordSystem] = {
vD: Vector;

vD _ CoordSys.FindTranslationOfAinTermsOfB[C, D];
AbsTranslateOnly[C, D, [vD[1], vD[2], 0]];
};

NormalizeRot: PUBLIC PROC [C: CoordSystem, D: CoordSystem] = {
oldMat, newMat: Matrix4by4;
oldMat _ CoordSys.FindAInTermsOfB[a: C, b: D];
newMat _ Matrix3d.NormalizeNoRotation[oldMat];
AbsTransf[C, D, newMat];
};

Normalize: PUBLIC PROC [C: CoordSystem, D: CoordSystem] = {
AbsTransf[C, D, Matrix3d.Identity[]];
};
NormalizeRotTug: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem] = {
F: Matrix4by4 _ CoordSys.FindAInTermsOfB[C, tugBoat];
NormalizeRot[tugBoat, D];
AbsTransf[C, tugBoat, F, TRUE];
};
NormalizeTug: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem] = {
F: Matrix4by4 _ CoordSys.FindAInTermsOfB[C, tugBoat];
Normalize[tugBoat, D];
AbsTransf[C, tugBoat, F, TRUE];
};
AlignTug: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem] = {
F: Matrix4by4 _ CoordSys.FindAInTermsOfB[C, tugBoat];
Align[tugBoat, D];
AbsTransf[C, tugBoat, F, TRUE];
};
AbutTug: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem] = {
F: Matrix4by4 _ CoordSys.FindAInTermsOfB[C, tugBoat];
Abut[tugBoat, D];
AbsTransf[C, tugBoat, F, TRUE];
};
AbutXTug: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem] = {
F: Matrix4by4 _ CoordSys.FindAInTermsOfB[C, tugBoat];
AbutX[tugBoat, D];
AbsTransf[C, tugBoat, F, TRUE];
};
AbutYTug: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem] = {
F: Matrix4by4 _ CoordSys.FindAInTermsOfB[C, tugBoat];
AbutY[tugBoat, D];
AbsTransf[C, tugBoat, F, TRUE];
};
AbutZTug: PUBLIC PROC [C: CoordSystem, tugBoat: CoordSystem, D: CoordSystem] = {
F: Matrix4by4 _ CoordSys.FindAInTermsOfB[C, tugBoat];
AbutZ[tugBoat, D];
AbsTransf[C, tugBoat, F, TRUE];
};

DirtyAssembly: PUBLIC PROC [a: Assembly] = {
WITH a.shape SELECT FROM
shape: Shape => {
a.coordSys.dirty _ TRUE;
};
alist: AssemblyList => {
a.coordSys.dirty _ TRUE;
DirtyAssemblyList[alist];
};
ENDCASE => ERROR;
}; -- end of DirtyAssembly

 DirtyAssemblyList: PRIVATE PROC [alist: AssemblyList] = {
FOR list: LIST OF Assembly _ alist.list, list.rest UNTIL list = NIL DO
DirtyAssembly[list.first];
ENDLOOP;
};

TidyUpCoordSysTree: PUBLIC PROC [root: CoordSystem] = {
parent: CoordSystem _ root.parent;
IF root.scalarsOnly THEN {
IF root.children # NIL THEN ERROR; -- scalars-only coordinate systems must be leaves.
root.scalars _ Matrix3d.TidyUpVector[root.scalars];
}
ELSE {
root.mat _ Matrix3d.TidyUpMatrix[root.mat];
IF root.children # NIL THEN { -- Process the children as well
FOR list: CoordSysList _ root.children, list.rest UNTIL list = NIL DO
TidyUpCoordSysTree[list.first];
ENDLOOP;
};
};
}; -- end of TidyUpCoordSysTree

TellAboutCameraAndWorld: PUBLIC PROC [root: CoordSystem, camera: Camera, scene: Scene] = {
camera.coordSys.wrtWorld _ CoordSys.FindInTermsOfWorld[camera.coordSys];
TellAboutCameraAndWorldAux[root, camera, scene];
};

TellAboutCameraAndWorldAux: PRIVATE PROC [root: CoordSystem, camera: Camera, scene: Scene] = {
parent: CoordSystem _ root.parent;
IF root.scalarsOnly THEN {
IF root.children # NIL THEN ERROR; -- scalars only coordinate systems must be leaves.
root.wrtCamera _ Matrix3d.LocalScale[CoordSys.FindInTermsOfCamera[parent, camera.coordSys], root.scalars[1], root.scalars[2], root.scalars[3]];
root.wrtWorld _ Matrix3d.LocalScale[CoordSys.FindInTermsOfWorld[parent], root.scalars[1], root.scalars[2], root.scalars[3]];
root.cameraWRTlocal _ Matrix3d.Inverse[root.wrtCamera];
root.worldWRTlocal _ Matrix3d.Inverse[root.wrtWorld];
}
ELSE {
root.wrtCamera _ CoordSys.FindInTermsOfCamera[root, camera.coordSys];
root.wrtWorld _ CoordSys.FindInTermsOfWorld[root];
root.cameraWRTlocal _ Matrix3d.Inverse[root.wrtCamera];
root.worldWRTlocal _ Matrix3d.Inverse[root.wrtWorld];
IF root.children # NIL THEN { -- Process the children as well
FOR list: CoordSysList _ root.children, list.rest UNTIL list = NIL DO
TellAboutCameraAndWorldAux[list.first, camera, scene];
ENDLOOP;
};
};
}; -- end of TellAboutCameraAndWorldAux

 TellAboutCameraAndWorldInList: PRIVATE PROC [clist: CoordSysList, camera: Camera, scene: Scene] = {
FOR list: CoordSysList _ clist, list.rest UNTIL list = NIL DO
TellAboutCameraAndWorld[list.first, camera, scene];
ENDLOOP;
};

TellAboutParent: PUBLIC PROC [cs: CoordSystem] = {
cs.wrtWorld _ Matrix3d.MatMult[cs.parent.wrtWorld, cs.mat];
cs.wrtCamera _ Matrix3d.MatMult[cs.parent.wrtCamera, cs.mat];
cs.worldWRTlocal _ Matrix3d.Inverse[cs.wrtWorld];
cs.cameraWRTlocal _ Matrix3d.Inverse[cs.wrtCamera];
};



ScalePrimitive: PUBLIC PROC [a: Assembly, sx, sy, sz: REAL] = {
shape: Shape;
scalarCS: CoordSystem;
IF NOT ISTYPE[a.shape, Shape] THEN ERROR;
shape _ NARROW[a.shape];
scalarCS _ shape.coordSys;
scalarCS.scalars[1] _ scalarCS.scalars[1]*sx;
scalarCS.scalars[2] _ scalarCS.scalars[2]*sy;
scalarCS.scalars[3] _ scalarCS.scalars[3]*sz;
};

ScalePrimitives: PUBLIC PROC [a: Assembly, sx, sy, sz: REAL] = {
WITH a.shape SELECT FROM
shape: Shape => ScalePrimitive[a, sx, sy, sz];
alist: AssemblyList => {
FOR list: LIST OF Assembly _ alist.list, list.rest UNTIL list = NIL DO
ScalePrimitives[list.first, sx, sy, sz];
ENDLOOP;
};
ENDCASE; -- IF a.shape = NIL or something else, do nothing.
};

ScaleEven: PUBLIC PROC [a: Assembly, cs: CoordSystem, scalar: REAL] = {
displacements: Vector;
WITH a.shape SELECT FROM
shape: Shape => {
ScalePrimitive[a, scalar, scalar, scalar];
displacements _ CoordSys.FindTranslationOfAinTermsOfB[a.coordSys, cs];
displacements _ SVVector3d.Scale[displacements, scalar];
AbsTranslateOnly[a.coordSys, cs, displacements];
};
alist: AssemblyList => {
FOR list: LIST OF Assembly _ alist.list, list.rest UNTIL list = NIL DO
ScaleEven[list.first, a.coordSys, scalar];
ENDLOOP;
displacements _ CoordSys.FindTranslationOfAinTermsOfB[a.coordSys, cs];
displacements _ SVVector3d.Scale[displacements, scalar];
AbsTranslateOnly[a.coordSys, cs, displacements];
};
ENDCASE; -- IF a.shape = NIL or something else, do nothing.
};

AssemblyHasNoChildren: PUBLIC ERROR = CODE;
ScaleEvenChildren: PUBLIC PROC [a: Assembly, cs: CoordSystem, scalar: REAL] ~ {
WITH a.shape SELECT FROM
shape: Shape => ERROR AssemblyHasNoChildren;
alist: AssemblyList => {
FOR list: LIST OF Assembly _ alist.list, list.rest UNTIL list = NIL DO
ScaleEven[list.first, list.first.coordSys, scalar];
ENDLOOP;
};
ENDCASE => ERROR AssemblyHasNoChildren; -- IF a.shape = NIL or something else, report a problem.
};

ScaleDistancesChildren: PUBLIC PROC [a: Assembly, cs: CoordSystem, sx, sy, sz: REAL] = {
displacements: Vector;
WITH a.shape SELECT FROM
shape: Shape => ERROR AssemblyHasNoChildren;
alist: AssemblyList => {
FOR list: LIST OF Assembly _ alist.list, list.rest UNTIL list = NIL DO
displacements _ CoordSys.FindTranslationOfAinTermsOfB[list.first.coordSys, cs];
displacements[1] _ displacements[1]*sx;
displacements[2] _ displacements[2]*sy;
displacements[3] _ displacements[3]*sz;
AbsTranslateOnly[list.first.coordSys, cs, displacements];
ENDLOOP;
};
ENDCASE => ERROR AssemblyHasNoChildren; -- IF a.shape = NIL or something else, report a problem.
};

ScaleAndShear: PUBLIC PROC [a: Assembly, cs: CoordSystem, sx, sy, sz: REAL] = {
};
ScaleNoShear: PUBLIC PROC [a: Assembly, cs: CoordSystem, sx, sy, sz: REAL] = {
};
Scale: PUBLIC PROC [a: Assembly, cs: CoordSystem, sx, sy, sz: REAL] = {
IF ISTYPE[a.shape, Shape] AND cs = a.coordSys THEN ScalePrimitive[a, sx, sy, sz]
ELSE ScaleEven[a, cs, sx];
};

MatrixHasScaling: PRIVATE PROC [mat: Matrix4by4] RETURNS [BOOL] = {
sx, sy, sz: REAL;
almostZero: REAL _ 1.0e-4;
[sx, sy, sz] _ Matrix3d.ScaleFromMatrix[mat];
IF ABS[sx - 1.0] > almostZero OR ABS[sy-1.0] > almostZero OR ABS[sz - 1.0] > almostZero
THEN RETURN[TRUE]
ELSE RETURN [FALSE];
};

END.
���Ž��File: SVTransformsImpl.mesa
Last edited by Bier on January 4, 1985 6:07:07 pm PST
Copyright c 1984 by Xerox Corporation.  All rights reserved.
Contents: Procedures for Scaling, Translating, and Rotating assemblies with respect to an arbitrary coordinate system
Incrementally transform C with respect to D by M.  If D is a descendent of C, this could result in D moving as well.  If this is not desired, set DFixed to TRUE and IncTransf makes sure that D doesn't move.
Make sure that D hasn't moved.
Rotates C about an axis parallel to the plane axis of D, passing thru the origin of C.
Absolutely transform C with respect to D by M.  If D is a descendent of C, this could result in D moving as well.  If this is not desired, set DFixed to TRUE and AbsTransf makes sure that D doesn't move.
Now make sure that D hasn't moved.
Like TugTransf, but returns the Tugboat to its original position.
A set of routines which call IncTransf

Simple rotate C's coordsys wrt D by degrees about the x axis
Simple rotate C's coordsys wrt D by degrees about the y axis
Simple rotate C's coordsys wrt D by degrees about the z axis
Here is an example of the way these operations used to be performed.  This is fairly fast because it uses Matrix3d.RotateAboutXAxis instead of Matrix3d.MatMult, but the IncTransf, AbsTransf, TugTransf pathway is much cleaner.
XRotateAwrtB: PUBLIC PROC [a: CoordSystem, b: CoordSystem, degrees: REAL] = {
aWorld, bWorld, aInTermsOfb, newAWorld, withRespectToWorld, aInTermsOfWRT: Matrix4by4;
parent: CoordSystem;
IF b = NIL THEN ERROR
ELSE bWorld _ CoordSys.FindInTermsOfWorld[b];
aWorld _ CoordSys.FindInTermsOfWorld[a];
aInTermsOfb _ IF a = b THEN Matrix3d.Identity[] ELSE Matrix3d.WorldToLocal[bWorld,aWorld];
aInTermsOfb _ Matrix3d.RotateAboutXAxis[aInTermsOfb, degrees]; -- must be a global translate.
newAWorld _ Matrix3d.MatMult[bWorld, aInTermsOfb];
IF a.parent = NIL THEN ERROR; -- cannot translate WORLD for now
parent _ a.parent;
withRespectToWorld _ CoordSys.FindInTermsOfWorld[parent];
aInTermsOfWRT _ Matrix3d.WorldToLocal[withRespectToWorld, newAWorld];
a.mat _ aInTermsOfWRT;
};

ScaleAwrtB: PRIVATE PROC [a: CoordSystem, b: CoordSystem, sx, sy, sz: REAL] = {
Because scaling is only allowed at primitive assemblies, we define the arbitrary scaling of an assembly with respect to a coordinate system as follows:  If the assembly is a primitive, change its scalar vector 
aWorld, bWorld, aInTermsOfb, newAWorld, withRespectToWorld, aInTermsOfWRT: Matrix4by4;
parent: CoordSystem;
IF b = NIL THEN ERROR
ELSE bWorld _ CoordSys.FindInTermsOfWorld[b];
aWorld _ CoordSys.FindInTermsOfWorld[a];
aInTermsOfb _ IF a = b THEN Matrix3d.Identity[] ELSE Matrix3d.WorldToLocal[bWorld,aWorld];
aInTermsOfb _ Matrix3d.Scale[aInTermsOfb, sx, sy, sz]; -- must be a global translate.
newAWorld _ Matrix3d.MatMult[bWorld, aInTermsOfb];
IF a.parent = NIL THEN ERROR; -- cannot translate WORLD for now
parent _ a.parent;
withRespectToWorld _ CoordSys.FindInTermsOfWorld[parent];
aInTermsOfWRT _ Matrix3d.WorldToLocal[withRespectToWorld, newAWorld];
a.mat _ aInTermsOfWRT;
};

A set of routines which call AbsTransf

Places C so that the rotation from C to D remains as it is, but the translation becomes vD.
Find CD.  Compute the magnitude of its axes.  Make CD have axes of the same magnitude, aligned with respect to the nearest axes of D.
 This direction is now taken.  z axis must find another.
zAxis gets second choice if xAxis has its first choice
Bubble sort
Leaving the rotation of C as it is, put C's origin coincident with the origin of D.
Leave the rotation of C as it is.  Put C's origin in the x = 0 plane of D.
Leave the rotation of C as it is.  Put C's origin in the y = 0 plane of D.
Leave the rotation of C as it is.  Put C's origin in the z = 0 plane of D.
Leave translation between C and D as is.  The axes of C become parallel to the axes of D.
C becomes identical to D.

A set of routines which specialize TugTransf

Routines for updating cached matrices:

TellAboutCameraAndWorld1: PUBLIC PROC [a: Assembly, camera: Camera, scene: Scene] = {
Flatten the tree to get the leaf assemblies then update their cached values. 
camera.coordSys.wrtWorld _ CoordSys.FindInTermsOfWorld[camera.coordSys];
FOR list: LIST OF Assembly _ DisplayList3d.ListOfPrimAssemblies[a, scene], list.rest
UNTIL list = NIL DO
list.first.coordSys.wrtCamera _  Matrix3d.LocalScale[CoordSys.FindInTermsOfCamera[list.first.coordSys, camera.coordSys],  list.first.scalars[1], list.first.scalars[2], list.first.scalars[3]];
list.first.coordSys.wrtWorld _  Matrix3d.LocalScale[CoordSys.FindInTermsOfWorld[list.first.coordSys], list.first.scalars[1], list.first.scalars[2], list.first.scalars[3]];
list.first.coordSys.cameraWRTlocal _ Matrix3d.Inverse[list.first.coordSys.wrtCamera];
list.first.coordSys.worldWRTlocal _ Matrix3d.Inverse[list.first.coordSys.wrtWorld];
ENDLOOP;
}; -- end of TellAboutCameraAndWorld1

This assembly has moved.  Mark its coordinate system and those of its children as dirty.
If a component is almost a multiple of .5, make it exactly so.
Tree walk through the tree and concatenate all matrices (will later concatenate matrices as it goes).  This computes values for intermediate matrices as well as primitive matrices.  Can be started using any assembly as root.
Our matrices result from scaling our parent's matrices.
Updates the wrtWorld, and wrtCamera fields of cs by premultiplying cs.mat by cs.parent.wrtWorld and cs.parent.wrtCamera respectively
Scaling operations (IncTransf derivatives but more complicated).
There are five ways to scale a cluster assembly
1) (ScalePrimitives)  Scale each primitive in place, evenly or differentially.
2) (ScaleEven)  If sx = sy = sz.  Scale primitives in place and then translate all intermediate assemblies so the cluster assembly scales evenly as a unit
3) (ScaleNoShear)  IF sx # sy or sy # sz.  Scale the primitives evenly so that their dimension in the direction of scaling increases or decreases to the same quantity it would have reached by method 3.  This preserves shape of primitives.   Global shape is not preserved (but almost).
4) (ScaleEvenChildren) Perform a ScaleEven on each of the children of the cluster assembly but leave their relative translations fixed.  This is equivalent to performing a ScaleEven (child, child's cs, scalar) on each child individually.
5) (ScaleDistancesChildren) Doesn't change the size or shape of any of the children of assembly.  Simply translates all of the children as they would be translated by a Scale even of assembly.
Just a bit tricky.
If a is a Primitive and cs is any coordinate frame, just scale and translate it from the center of cs by scalar times its current translation.
If a is a cluster, and cs is any coordinate frame, evenly scale each component of a about a's center, then translate a as a unit, the appropriate distance from the center of cs.
now translate a's coordSys so that its displacement from the origin of cs is scaled by scalar
Recursively scale subassemblies with respect to their own coordinate systems
Now translate a's coordSys so that its displacement from the origin of cs is scaled by scalar
For each child of a, find its current displacement from the center of cs.  Scale this displacement by [sx, sy, sz].
not yet implemented.

not yet implemented.

�Ê×��˜�Iheadš
œ™Jš
œ5™5Jšœ
Ïm
œ1™<Jš
œu™uJ˜�š
Ïk	˜	Jš
œ	˜	Jš
œ	˜	J˜J˜J˜Jš
œ
˜
Jš
œ
˜
Jš
œ
˜
Jš
œ˜—J˜�Jšœž˜Jšžœ.˜5Jšžœ˜Jš
ž˜˜�Jšœ
žœ˜'Jšœžœ˜/Jšœžœ˜#Jšœ
žœ˜-Jšœžœ˜/Jšœžœ˜#Jšœ	žœ˜Jšœžœ˜!Jš
œ!˜!Jšœžœ˜J˜�J˜�—šÏn	œžœ
žœž
œž
œž
œžœžœ˜`Jšœž
œž
œž
œž
œž
œž
œ8žœž
œ™Î
Iprocšž
œ˜L˜�Lšžœ
ž
œ
žœ
žœ
žœÏc!˜?Lš
žœ
ž
œžœ
žœ
žœ
˜Lšž
œž
œ˜
šžœž
œžœ˜Jš
œF˜FJš
œ˜Jšžœ˜—L˜�Lšžœ
žœ
ž˜šž
œ
žœ ˜ Lš	ž
Ðkuœž¡
Ïuž
¢œ
˜#Lšž
¢œž
œ˜(Lšž
¢œž
œ˜(LšÐks¡
œž
¢œ˜"Lš
ž
œ)ž¡
œž
œž
¢œ˜>L˜—šž
œž
œ ˜!Lšž
œž
œž
œ˜#L˜—šž
œž
œ $˜/Lšž
œž
œž
œ˜#L˜—šžœ ˜&Lšž
¢œž
¢œž
¡
¢ž¡
¢ž
¢œ
˜/Lšž
¢œž
œ˜(Lšž
¡œž
œ %œ
 	˜XLšž
¢œž
œ˜(Lš£¡
œž
¢œ˜"Lšž
¢
œ"˜$Lš
ž
œ:£¡
œž
¢œž
œž
¡
œ˜Tšžœžœ˜L™Lšž¡œž
¡œ
˜Lšž¡œž
œ	˜0Lš	ž
¡œž¡œž
¡œ˜-Lšž
œž
¡œ
˜L˜—L˜—Lš
œ˜L˜�—š
Ÿœžœ
žœž
œž
¡œž
œ˜TLšž
œ˜Lšž
¢œž
¡
œ
¢
ž¡
œ
¢
ž
¢œ
˜'L˜�Lšžœ
ž
œ
žœ
žœ
žœ !˜?Lšž
œž
œ˜
šžœž
œžœ˜Jš
œL˜LJš
œ˜Jšžœ˜—L˜�Lšž
¢œž
œ˜(Lšž
¢œž
œ˜(Lš£¡
œž
¢œ˜"Lš	ž
¢
œž
¢œž
¢œ˜+Lš
ž
œ:£¡
œž
¢œž
œž
¡
œ˜TLš
œ˜L˜�J˜�—šŸœžœ
žœž
œž
œžœ	žœ˜^J™VJš	ž
œ¢ž
¡¢ž
¡œ
˜*Jš
œ˜Jš
œ˜J˜�Jšž
¡œž
œ˜(Jšž
¡œž
œ˜(Jšœ!ž
¡œ˜)Jšœž
¡œ˜'Jšœž
¡œ˜'Jšœž
¡œ˜'Jšœ¢œ9˜CJ˜�Jšžœž˜Jšœž
œ$˜*Jšœž
œ$˜*Jšœž
œ$˜*Jšžœžœ
˜Lšœž
œ¢œž
œ˜"Jš
œ˜J˜�—šŸ	œžœ
žœž
œž
œž
œžœžœ˜`Jšœž
œž
œž
œž
œž
œž
œ8žœž
œ™Ë
Lšž
œ˜L˜�Lšžœž
œžœžœž
œž
œžœ˜?Lšžœ
ž
œ
žœ
žœ
žœ ˜8Lš
žœ
ž
œžœ
žœ
žœ
˜Lšž
œž
œ˜
šžœž
œžœ˜Jš
œF˜FJš
œ˜Jšžœ˜—L˜�Lšžœ
žœ
ž˜šž
œ
žœ ˜ Lšž¡
¢ž
¡œ
˜Lšž
¡œž
œ˜(Lš£¡
œž
¡œ˜"Lšž
œž¡
œž
œ˜$L˜—šž
œž
œ ˜!Lšž
œž
œž
œ˜#L˜—šž
œž
œ $˜/Lšž
œž
œ
˜
L˜—šžœ ˜&Lš	ž
¡¢ž¡
¢ž
¡œ
˜#Lšž
¡œž
œ˜(Lšž
¡œž
œ˜(Lš£¡
œž
¡œ˜"Lš
ž
œ)£¡
œž
¡œž
œ˜>šžœžœ˜L™"Lšž¡œž
¡œ
˜Lšž¡œž
œ	˜0Lš	ž
¡œž¡œž
¡œ˜-Lšž
œž
¡œ
˜L˜—L˜—Lš
œ˜L˜�—šŸ	œžœ
žœž
œ%ž
œž
œ˜`Jšž
œ(ž
œ˜5Jšœž
œž
œ˜Jšœ
ž
œž
œ˜J˜J˜�—š
Ðbnœžœž
œ%ž
œž
œ˜hJ™AJšž
œ
˜Jš
œ%˜%J˜�Jšž
œž
œ˜)Jšœž
œž
œ˜Jšœ
ž
œž
œ˜Jš
œ˜J˜J˜�J˜�—JšœŸ	™&J™�šŸ	œžœ
žœž
œž
œžœ
žœžœ˜cLšž
œ
˜Lšž
œ)˜*Lšœ
ž
œž
œžœ˜Lš
œ˜L˜�—šŸœžœ
žœž
œž
œžœ
žœžœ˜^Jš
œ<™<Jšž
œ
˜Lšž
œ$˜%Lš	œ
ž
œž
œž
œ
ž
œ˜Jš
œ˜J˜�—šŸœžœ
žœž
œž
œžœ
žœžœ˜^Jš
œ<™<Jšž
œ
˜Lšž
œ$˜%Lš	œ
ž
œž
œž
œ
ž
œ˜Jš
œ˜J˜�—šŸœžœ
žœž
œž
œžœ
žœžœ˜^Jš
œ<™<Jšž
œ
˜Lšž
œ$˜%Lš	œ
ž
œž
œž
œ
ž
œ˜Jš
œ˜J˜�—J˜�Lš
χ
™á
šŸœžœ
žœ+žœ™MLš
œV™VLš
œ™Lšžœžœ
žœ
ž™Lšžœ)™-Lš
œ(™(Lšœžœžœžœ&™ZLšœ? ™]Lš
œ2™2Lš	žœžœ
žœ
žœ !™?Lš
œ™Lš
œ9™9Lš
œE™ELš
œ™Lš
œ™L™�—šŸ
œžœ
žœ.žœ™OLš
œÒ
™Ò
Lš
œV™VLš
œ™Lšžœžœ
žœ
ž™Lšžœ)™-Lš
œ(™(Lšœžœžœžœ&™ZLšœ7 ™ULš
œ2™2Lš	žœžœ
žœ
žœ !™?Lš
œ™Lš
œ9™9Lš
œE™ELš
œ™Lš
œ™—J™�JšœŸ	™&J™�šŸœžœ
žœ#¢
œ˜OLšœY¢
œ
™[Lšž
œ˜Lšœ
¢
œ	˜L˜�šžœž
œžœžœ˜,Lšž
Ϣ
œ˜Lšž
Ϣ
œ˜Lšž
Ϣ
œ˜Lšžœ˜—Lšžœ
ž
œ
žœ
žœ
žœ ˜8Lš
žœ
ž
œžœ
žœ
žœ
˜Lšž
œž
œ˜
L˜�Lšžœ
žœ
ž˜šž
œ
žœ ˜ Lšž¡
¢ž
¡œ
˜Lšž
¡œž
œ˜(Lš£¡
œž
¡œ˜"Lšœ
¢
œž¡
Ϣ
œ˜!Lšž
Ϣ
œ˜Lšž
Ϣ
œ˜Lšž
Ϣ
œ˜L˜—šž
œž
œ ˜!Lšž
œž
Ϣ
Ϣ
œ
¢
Ϣ
œ
¢
œ˜<L˜—šž
œž
œ $˜/Lšž
Ϣ
œ˜Lšž
Ϣ
œ˜Lšž
Ϣ
œ˜L˜—šžœ ˜&Lš	ž
¡¢ž¡
¢ž
¡œ
˜#Lšž
¡œž
œ˜(Lšž
¡œž
œ˜(Lš£¡
œž
¡œ˜"Lšœ
¢
œž¡
œž
¡œ¢
œ˜:Lšž
Ϣ
œ˜Lšž
Ϣ
œ˜Lšž
Ϣ
œ˜L˜—Lš
œ˜L˜�—š
Ÿœžœ
žœž
œž
œ˜7Lšœ¢
œ-¢
œP™…
Lšž
¡
œ
˜Lšœžœžœ
žœ
˜/Lš
œ3˜3Lšœžœžœ
žœ
˜*Lš
œ˜L˜�Lšž
¡
œž
œž
œ˜$L˜�Lšœž
¡
œ˜#Lšœž
¡
œ˜#Lšœ!ž
¡
œ˜%Lšœ1 ˜JLš
œ8™8Lš
œ0˜0Lšžœ#žœ#˜LLš
œ6™6Lš
œ˜Lš
œ8˜8šžœž˜"Lš
œ7˜7—Lš
œ˜Lš
œ8˜8šžœž˜"Lš
œ7˜7—Lš
œ7˜7Lšž
¡
œB˜DLš
œ
˜
Lšœ
ž
œž
œž
¡
œ˜Lš
œ˜L˜�—šŸœžœ
žœ
žœžœžœ
žœžœžœ
žœ˜oLš
œ™Lšœžœ
˜Lšœžœ
˜Lšžœ
žœžœ˜3Lšžœžœ
˜Lšžœ
žœžœ˜3Lšžœžœ
˜Lšžœ
žœžœ˜3Lšžœžœ
˜Lš
œ˜šžœ
žœ˜Lš
œ&˜&Lš
œI˜I—šžœ
žœ˜Lš
œ&˜&Lš
œI˜I—šžœ
žœ˜Lš
œ&˜&Lš
œI˜I—Lš
œ˜L˜�—šŸœ
žœ
žœ%˜6L™SL˜ Lš
œ˜L˜�—šŸœžœ
žœ%˜7L™JLšœ
¢
œ	˜L˜�Lšœ
¢
œ)ž
œž
œ˜1Lš
œž
œž
œ¡
œ
¢
œ¡
œ
¢
œ˜*Lš
œ˜L˜�—šŸœžœ
žœ%˜7L™JLšœ
¢
œ	˜L˜�Lšœ
¢
œ)ž
œž
œ˜1Lš
œž
œž
Ϣ
œ¡
œ¡
œ
¢
œ˜*Lš
œ˜L˜�—šŸœžœ
žœ%˜7L™JLšœ
¢
œ	˜L˜�Lšœ
¢
œ)ž
œž
œ˜1Lš
œž
œž
Ϣ
œ¡
œ
¢
œ¡
œ˜*Lš
œ˜L˜�—šŸœžœž
œž
œ˜>L™YJš
œ˜Jš
œ.˜.Jš
œ.˜.Jš
œ˜J˜L˜�—šŸ	œžœž
œž
œ˜;L™Lš
œ%˜%L˜—J™�Jšœ#Ÿ	™,J™�š
Ÿœžœ
žœž
œ%ž
œ˜WJšž
œ(ž
œ˜5JšÏbœ
ž
œ˜Jšœ
ž
œžœ˜Jš
œ˜—š
Ÿœžœ
žœž
œ%ž
œ˜TJšž
œ(ž
œ˜5Jš¥	œ
ž
œ˜Jšœ
ž
œžœ˜Jš
œ˜—šŸœžœ
žœ;˜PJš
œ5˜5Jš¥œ
˜Jšœžœ˜Jš
œ˜—šŸœžœ
žœ;˜OJš
œ5˜5Jš¥œ
˜Jšœžœ˜Jš
œ˜—š
Ÿœžœ
žœž
œ%ž
œ˜PJšž
œ(ž
œ˜5Jš¥œ
ž
œ˜Jšœ
ž
œžœ˜Jš
œ˜—š
Ÿœžœ
žœž
œ%ž
œ˜PJšž
œ(ž
œ˜5Jš¥œ
ž
œ˜Jšœ
ž
œžœ˜Jš
œ˜—š
Ÿœžœ
žœž
œ%ž
œ˜PJšž
œ(ž
œ˜5Jš¥œ
ž
œ˜Jšœ
ž
œžœ˜Jš
œ˜J˜�—Jšœ¥œ
™&J™�šŸœžœ
žœ0™UJ™MJš
œH™HJšžœžœ
žœC™Tšžœžœ
ž™Jš
œ¿
™¿
Jš
œ«
™«
Jš
œU™UJš
œS™S—Jšžœ
™Jšœ "™%J™�—šŸ
œžœ
žœ˜,J™Xšžœ	žœ
ž˜š
œ˜Jšœžœ
˜Jš
œ˜—š
œ˜Jšœžœ
˜Jš
œ˜Jš
œ˜—Jšžœžœ
˜—Jšœ ˜J˜�—šœ
Ÿœžœ
žœ˜:šžœžœ
žœ"žœžœ
ž˜FJš
œ˜—Jšžœ
˜Jš
œ˜—J˜�šŸœžœ
žœ˜7J™>Jš
œ"˜"šžœžœ˜Jš	žœžœ
žœ
žœ 2˜UJš
œ3˜3J˜
—šžœ˜Jš
œ+˜+šžœžœ
žœ ˜=šžœ/žœžœ
ž˜EJš¥œ
˜—Jšžœ
˜Jš
œ˜—Jš
œ˜—Jšœ ˜J˜�—šŸœžœ
žœ6˜ZJš
ψ
™à
Jš
œH˜HJš
œ0˜0J˜J˜�—šŸœžœ
žœ6˜^Jš
œ"˜"šžœžœ˜š	žœžœ
žœ
žœ 2˜UJ™7—Jš
œ
˜
Jš
œ|˜|Jš
œ7˜7Jš
œ5˜5J˜
—šžœ˜Jš
œE˜EJš
œ2˜2Jš
œ7˜7Jš
œ5˜5šžœžœ
žœ ˜=šžœ/žœžœ
ž˜EJš¥œ˜6—Jšžœ
˜Jš
œ˜—Jš
œ˜—Jšœ $˜'J˜�—šœ
Ÿœžœ
žœ8˜dšžœ'žœžœ
ž˜=Jš
œ3˜3—Jšžœ
˜Jš
œ˜J˜�—šŸœžœ
žœ˜2Lš
œ„
™„
Lš
œ;˜;Lš
œ=˜=Lš
œ1˜1Lš
œ3˜3Lš
œ˜—J˜�Jš¥œ9™@˜�Jš
œ/™/Jš
œN™NJš
œš
™š
Jš
œœ™œJš
ϒ
™í
J™À
—J˜�šŸœžœ
žœžœ˜?Jš
œ
˜
J˜Jš
žœ
žœ
žœžœ
žœ
˜)Jš
œ˜Jš
œ˜Jš
œ-˜-Jš
œ-˜-Jš
œ-˜-Jš
œ˜J˜�—šŸœžœ
žœžœ˜@šžœ	žœ
ž˜Jš
œ.˜.š
œ˜šžœžœ
žœ"žœžœ
ž˜FJš
œ(˜(—Jšžœ
˜Jš
œ˜—Jšžœ
 3˜;—Jš
œ˜J˜�—šŸ	œžœ
žœ(žœ˜GJ™J™Ž
J™±
Jš
œ˜šžœ	žœ
ž˜š
œ˜Jš
œ*˜*Jš
œ]™]Jš
œF˜FJš
œ8˜8Jš
œ0˜0Jš
œ˜—š
œ˜šžœžœ
žœ"žœžœ
ž˜Fš
œ*˜*Jš
œL™L——Jšžœ
˜Jš
œ]™]Jš
œF˜FJš
œ8˜8Jš
œ0˜0Jš
œ˜—Jšžœ 2˜;—Jš
œ˜J˜�—Jšœžœ
žœžœ
˜+šŸœžœ(žœ˜Ošžœ	žœ
ž˜Jš
œ,˜,š
œ˜šžœžœ
žœ"žœžœ
ž˜FJš
œ3˜3—Jšžœ
˜Jš
œ˜—Jšžœ 9˜`—Jš
œ˜—šŸœžœ,žœ˜XJš
œs™sJš
œ˜šžœ	žœ
ž˜Jšœžœ˜,š
œ˜šžœžœ
žœ"žœžœ
ž˜FJš
œO˜OJš
œ'˜'Jš
œ'˜'Jš
œ'˜'Jš
œ9˜9—Jšžœ
˜Jš
œ˜—Jšžœžœ 9˜`—Jš
œ˜—šŸ
œžœ,žœ˜OJš
œ˜Jš
œ™—šŸœžœ,žœ˜NJš
œ˜Jš
œ™—šŸœžœ
žœ,žœ˜GJšžœ
žœžœžœ˜PJšžœ˜Jš
œ˜—J˜�š
Ÿœžœ
žœžœžœ˜CJšœžœ
˜Jšœžœ
˜Jš
œ-˜-Jšžœ
žœžœ
žœžœ
žœ˜WJšžœ
žœ
žœ
˜Jšžœ
žœžœ˜Jš
œ˜—J˜�Jšžœ
˜—�…—����AÂ��z'��