## anim3D/src/Matrix4.i3

Copyright (C) 1994, Digital Equipment Corporation
Digital Internal Use Only

Last modified on Tue Aug 22 11:53:41 PDT 1995 by najork
Created on Wed Mar 16 21:47:10 PST 1994 by najork

INTERFACE Matrix4;

IMPORT Point3;

TYPE T   = ARRAY [0 .. 3] OF Row;
Row = ARRAY [0 .. 3] OF REAL;

CONST Id = T {Row {1.0, 0.0, 0.0, 0.0},
Row {0.0, 1.0, 0.0, 0.0},
Row {0.0, 0.0, 1.0, 0.0},
Row {0.0, 0.0, 0.0, 1.0}};

PROCEDURE Multiply (READONLY M, N : T) : T;

PROCEDURE Identity () : T;
PROCEDURE Translate (READONLY M : T; x, y, z : REAL) : T;
PROCEDURE Scale (READONLY M : T; x, y, z : REAL) : T;
PROCEDURE RotateX (READONLY M : T; theta : REAL) : T;
PROCEDURE RotateY (READONLY M : T; theta : REAL) : T;
PROCEDURE RotateZ (READONLY M : T; theta : REAL) : T;
PROCEDURE TransformPoint3 (READONLY M : T; READONLY p : Point3.T) : Point3.T;

PROCEDURE TransformUnitCube (p, a, b, c : Point3.T) : T;

This function is useful to map prototypes of geometric objects (circles, spheres, disks, cylinders, etc) onto actual instances. TransformUnitCube(p,a,b,c) returns a matrix M, such that \begin{verbatim} TransformPoint3(M,Point3.T{0.0,0.0,0.0}) = p TransformPoint3(M,Point3.T{1.0,0.0,0.0}) = a TransformPoint3(M,Point3.T{0.0,1.0,0.0}) = b TransformPoint3(M,Point3.T{0.0,0.0,1.0}) = c \end{verbatim}

The above 4 equations over points define a system of linear equations, which can be solved statically (i.e.\ no gaussian elimination is needed at run time). So, calls to TransformUnitCube are very cheap.

PROCEDURE UnitSphereMaxSquishFactor (READONLY M : T) : REAL;

EXCEPTION Error;

PROCEDURE Decomp (M : T; VAR tx, ty, tz, s : REAL) : T RAISES {Error};

Decompose(M,tx,ty,tz,s,angX,angY,angZ) takes a matrix M, which must have been constructed by using only translations, rotations, and uniform(!) scalings, and returns values tx, ty, tz, s, and R such that M = T(tx,ty,tz) S(s) R holds. If the initial matrix M was indeed valid, then R is an orthogonal matrix. If M was not valid, then Error is raised.

PROCEDURE Transpose (READONLY M : T) : T;

Transpose(M) takes a matrix M and returns its transpose. Note that for an orthonormal matrix, its transpose is also its inverse.

PROCEDURE Invert (A : T) : T RAISES {Error};

Invert(M) takes a matrix M and returns its inverse. If M is singular, the exception Error is raised.

PROCEDURE Equal (READONLY A, B : T) : BOOLEAN;

PROCEDURE Orthonormal (READONLY M : T) : BOOLEAN;

Orthonormal(M) is true if the columns of M form an orthonormal basis.

PROCEDURE OrthoProjMatrix (height, aspect, near, far: REAL): T;

This procedure returns what PEX calls a view mapping matrix, and what OpenGL calls a projection transformation matrix. The projection is orthographic.

PROCEDURE PerspProjMatrix (fovy, distance, aspect, near, far: REAL): T;

Returns a projection matrix for a perspective projection.

PROCEDURE LookatViewMatrix (from, to, up: Point3.T): T;

Returns a viewing transformation matrix. We place three (pretty reasonable) restrictions on the arguments: (1) from differs from to (2) up is non-zero (3) (from - to) and up are not collinear

LookatViewMatrix is similar to Digital PEXlib's PEXLookatViewMatrix function and to OpenGL's gluLookAt function.


END Matrix4.