DIRECTORYSV2d,SVVector2d;SVMatrix2d: CEDAR DEFINITIONS =BEGINMatrix3by3: TYPE = SV2d.Matrix3by3;Point2d: TYPE = SV2d.Point2d;Vector2d: TYPE = SVVector2d.Vector2d;Identity: PROC [] RETURNS [identityMat: Matrix3by3];Update: PROC [mat: Matrix3by3, point: Point2d] RETURNS [newPoint: Point2d];UpdateVector: PROC [mat: Matrix3by3, vec: Vector2d] RETURNS [newVec: Vector2d];Scale: PROC [mat: Matrix3by3, sx, sy: REAL] RETURNS [transMat: Matrix3by3];Translate: PROC [mat: Matrix3by3, dx, dy: REAL] RETURNS [transMat: Matrix3by3];RotateCCW: PROC [mat: Matrix3by3, degrees: REAL] RETURNS [transMat: Matrix3by3];LocalScale: PROC [mat: Matrix3by3, sx, sy: REAL] RETURNS [transMat: Matrix3by3];LocalTranslate: PROC [mat: Matrix3by3, dx, dy: REAL] RETURNS [transMat: Matrix3by3];LocalRotateCCW: PROC [mat: Matrix3by3, degrees: REAL] RETURNS [transMat: Matrix3by3];MatMult: PROC [left, right: Matrix3by3] RETURNS [transMat: Matrix3by3];MakeScaleMat: PROC [sx, sy: REAL] RETURNS [scale: Matrix3by3];MakeTranslateMat: PROC [dx, dy: REAL] RETURNS [trans: Matrix3by3];MakeRotateCCWMat: PROC [degrees: REAL] RETURNS [rot: Matrix3by3];MakeMatFromXAxis: PROC [xAxis: Vector2d, origin: Point2d] RETURNS [mat: Matrix3by3];MakeMatFromYAxis: PROC [yAxis: Vector2d, origin: Point2d] RETURNS [mat: Matrix3by3];MakeMatFromAxes: PROC [xAxis, yAxis: Vector2d, origin: Point2d] RETURNS [mat: Matrix3by3];ScaleFromMatrix: PROC [mat: Matrix3by3] RETURNS [sx, sy: REAL];OriginOfMatrix: PROC [mat: Matrix3by3] RETURNS [origin: Point2d];XAxisOfMatrix: PROC [mat: Matrix3by3] RETURNS [xAxis: Vector2d];YAxisOfMatrix: PROC [mat: Matrix3by3] RETURNS [yAxis: Vector2d];RotationOfMatrix: PROC [mat: Matrix3by3] RETURNS [degrees: REAL];Cofactor: PROC [mat: Matrix3by3, row, col: NAT] RETURNS [cof: REAL];Determinant: PROC [mat: Matrix3by3] RETURNS [det: REAL];Transpose: PROC [mat: Matrix3by3] RETURNS [MatT: Matrix3by3];Inverse: PROC [mat: Matrix3by3] RETURNS [inverse: Matrix3by3];DegenerateInverse: SIGNAL;WorldToLocal: PROC [AinWorld,BinWorld: Matrix3by3] RETURNS [BinTermsOfA: Matrix3by3];END.   D  File: SVMatrix2d.mesaLast edited by Bier on June 1, 1984 4:38:07 pm PDTAuthor: Eric Bier on January 28, 1987 12:34:52 pm PSTContents: My own package for manipulating Homogenous 3 x 3 matrices.  Parallels SVMatrix3d in many placesvectors can be rotated and scaled, but not translatedThe next three procedures perform an efficient matrix multiplication as though mat were being multiplied to its left (a transform in reference coordinates) by a matrix which translates or rotates respectively (See Paul).The next three procedures perform an efficient matrix multiplication as though mat were being multiplied on its right (a transform in local coordinates) by a matrix which translates or rotates respectively (See Paul).MatMult is almost a general 3 by 3 matrix operation.  However, it assumes that the last row of each matrix is [0 0 1].not yet implementednot yet implementeduses the axes directly.  Doesn't even check to see if they are orthogonalfinds out how much this matrix will scale an object it is applied toinverts any matrix of the given form (even with scaling) Ê  ˜ Iheadšœ™Jšœ2™2Jšœ5™5Jšœi™iJ˜ šÏk	˜	Jšœ˜Jšœ˜—J˜ Jšœœ˜Jš˜˜ Jšœœœ˜#Jšœ	œ˜Jšœ
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