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								 SbMatrix(3IV)

NAME
     SbMatrix (SbMx) - 4x4 matrix class

INHERITS FROM
     SbMatrix

SYNOPSIS
     #include <Inventor_c/SbLinear.h>

     typedef SbMatrix	 SbMx

	  Functions from class SbMatrix:

     void		 SbMxMakeIdent(SbMx *this)
     SbMatrix		 SbMxIdent()
     void		 SbMxSetRot(SbMx *this, const SbRotation *q)
     void		 SbMxSetScale(SbMx *this, float s)
     void		 SbMxScaleVec(SbMx *this, const SbVec3f *s)
     void		 SbMxSetXlate(SbMx *this, const SbVec3f *t)
     void		 SbMxSetXform(SbMx *this, const SbVec3f *translation,
			      const SbRotation *rotation, const SbVec3f
			      *scaleFactor, const SbRotation
			      *scaleOrientation, const SbVec3f *center)
     void		 SbMxGetXform(const SbMx *this, SbVec3f *translation,
			      SbRotation *rotation, SbVec3f *scaleFactor,
			      SbRotation *scaleOrientation, const SbVec3f
			      *center)
     float		 SbMxDet3Mx(const SbMx *this, int r1, int r2, int r3,
			      int c1, int c2, int c3)
     float		 SbMxDet3(const SbMx *this)
     float		 SbMxDet4(const SbMx *this)
     SbBool		 SbMxFactor(const SbMx *this, SbMatrix *r, SbVec3f *s,
			      SbMatrix *u, SbVec3f *t, SbMatrix *proj)
     SbMatrix		 SbMxInverse(const SbMx *this)
     SbBool		 SbMxLUDecomp(SbMx *this, int index[4], float *d)
     void		 SbMxLUBackSub(const SbMx *this, int index[4], float
			      b[4])
     SbMatrix		 SbMxTranspose(const SbMx *this)
     SbMatrix *		 SbMxMultRight(SbMx *this, const SbMatrix *m)
     SbMatrix *		 SbMxMultLeft(SbMx *this, const SbMatrix *m)
     void		 SbMxMultMxVec(const SbMx *this, const SbVec3f *src,
			      SbVec3f *dst)
     void		 SbMxMultVecMx(const SbMx *this, const SbVec3f *src,
			      SbVec3f *dst)
     void		 SbMxMultDirMx(const SbMx *this, const SbVec3f *src,
			      SbVec3f *dst)
     void		 SbMxMultLineMx(const SbMx *this, const SbLine *src,
			      SbLine *dst)
     void		 SbMxPrint(const SbMx *this, FILE *fp)
     SbMatrix *		 SbMxCopy(SbMx *this, const SbMatrix *m)
     SbMatrix *		 SbMxMultBy(SbMx *this, const SbMatrix *m)

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SbMatrix(3IV)

     SbMatrix		 SbMxMult(SbMx *this, const SbMatrix *m1, const
			      SbMatrix *m2)
     int		 SbMxIsEq(SbMx *this, const SbMatrix *m1, const
			      SbMatrix *m2)
     int		 SbMxIsNEq(SbMx *this, const SbMatrix *m1, const
			      SbMatrix *m2)
     SbBool		 SbMxEquals(const SbMx *this, const SbMatrix *m, float
			      tolerance)

DESCRIPTION
     4x4 matrix class/datatype used by many Inventor node and action classes.
     The matrices are stored in row-major order.  Note that this class should
     be declared and/or malloc'd as an standard C struct:

	       /* This is defined in Inventor_c/SbMatrix.h: */
	       struct SbMatrix {
		    float mx[4][4];
	       };
	       typedef SbMatrix SbMx

	       /* Your code should look like this: */
	       SbMx  mx, mx_t;

	       mx = SbMxIdent();
	       mx.mx[0][0] = mx.mx[1][1] = mx.mx[2][2] = 3.0;
	       mx_t = SbMxTranspose( &mx );

FUNCTIONS
     void		 SbMxMakeIdent(SbMx *this)
	  Sets matrix to be identity.

     SbMatrix		 SbMxIdent()
	  Returns an identity matrix.

     void		 SbMxSetRot(SbMx *this, const SbRotation *q)
	  Sets matrix to rotate by given rotation.

     void		 SbMxSetScale(SbMx *this, float s)
	  Sets matrix to scale by given uniform factor.

     void		 SbMxScaleVec(SbMx *this, const SbVec3f *s)
	  Sets matrix to scale by given vector.

     void		 SbMxSetXlate(SbMx *this, const SbVec3f *t)
	  Sets matrix to translate by given vector.

     void		 SbMxSetXform(SbMx *this, const SbVec3f *translation,
			      const SbRotation *rotation, const SbVec3f

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								 SbMatrix(3IV)

			      *scaleFactor, const SbRotation
			      *scaleOrientation, const SbVec3f *center)
	  Composes the matrix based on a translation, rotation, scale,
	  orientation for scale, and center. The center is the center point
	  for scaling and rotation. The scaleOrientation chooses the primary
	  axes for the scale.

     void		 SbMxGetXform(const SbMx *this, SbVec3f *translation,
			      SbRotation *rotation, SbVec3f *scaleFactor,
			      SbRotation *scaleOrientation, const SbVec3f
			      *center)
	  Decomposes the matrix into a translation, rotation, scale, and scale
	  orientation. Any projection information is discarded. The
	  decomposition depends upon choice of center point for rotation and
	  scaling, which is optional as the last parameter. Note that if the
	  center is 0, decompose() is the same as factor() where t is
	  translation, u is rotation, s is scaleFactor, and r is
	  ScaleOrientation.

     float		 SbMxDet3Mx(const SbMx *this, int r1, int r2, int r3,
			      int c1, int c2, int c3)
	  Returns determinant of 3x3 submatrix composed of given row and
	  column indices (0-3 for each).

     float		 SbMxDet3(const SbMx *this)
	  Returns determinant of upper-left 3x3 submatrix.

     float		 SbMxDet4(const SbMx *this)
	  Returns determinant of entire matrix.

     SbBool		 SbMxFactor(const SbMx *this, SbMatrix *r, SbVec3f *s,
			      SbMatrix *u, SbVec3f *t, SbMatrix *proj)
	  Factors a matrix m into 5 pieces: m = r s r^ u t, where r^ means
	  transpose of r, and r and u are rotations, s is a scale, and t is a
	  translation. Any projection information is returned in proj. NOTE:
	  the projection matrix is always set to identity.

     SbMatrix		 SbMxInverse(const SbMx *this)
	  Returns inverse of matrix. Results are undefined for singular
	  matrices. Uses LU decomposition.

     SbBool		 SbMxLUDecomp(SbMx *this, int index[4], float *d)
	  Perform in-place LU decomposition of matrix. index is index of rows
	  in matrix. d is the parity of row swaps. Returns FALSE if singular.

     void		 SbMxLUBackSub(const SbMx *this, int index[4], float
			      b[4])
	  Perform back-substitution on LU-decomposed matrix. Index is
	  permutation of rows from original matrix.

     SbMatrix		 SbMxTranspose(const SbMx *this)
	  Returns transpose of matrix.

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SbMatrix(3IV)

     SbMatrix *		 SbMxMultRight(SbMx *this, const SbMatrix *m)
     SbMatrix *		 SbMxMultLeft(SbMx *this, const SbMatrix *m)
	  Multiplies matrix by given matrix on right or left.

     void		 SbMxMultMxVec(const SbMx *this, const SbVec3f *src,
			      SbVec3f *dst)
	  Multiplies matrix by given column vector, giving vector result.

     void		 SbMxMultVecMx(const SbMx *this, const SbVec3f *src,
			      SbVec3f *dst)
	  Multiplies given row vector by matrix, giving vector result.

     void		 SbMxMultDirMx(const SbMx *this, const SbVec3f *src,
			      SbVec3f *dst)
	  Multiplies given row vector by matrix, giving vector result. src is
	  assumed to be a direction vector, so translation part of matrix is
	  ignored. Note: if you wish to transform surface points and normals
	  by a matrix, call  SbMxMultVecMatrix() for the points and call
	  SbMxMultDirMatrix() on the inverse transpose of the matrix for the
	  normals.

     void		 SbMxMultLineMx(const SbMx *this, const SbLine *src,
			      SbLine *dst)
	  Multiplies the given line's origin by the matrix, and the line's
	  direction by the rotation portion of the matrix.

     void		 SbMxPrint(const SbMx *this, FILE *fp)
	  Prints a formatted version of the matrix to the given file pointer.

     SbMatrix *		 SbMxCopy(SbMx *this, const SbMatrix *m)
	  Set the matrix from another SbMatrix.

     SbMatrix *		 SbMxMultBy(SbMx *this, const SbMatrix *m)
	  Performs right multiplication with another matrix.

     SbMatrix		 SbMxMult(SbMx *this, const SbMatrix *m1, const
			      SbMatrix *m2)
	  Binary multiplication of matrices.

     int		 SbMxIsEq(SbMx *this, const SbMatrix *m1, const
			      SbMatrix *m2)
     int		 SbMxIsNEq(SbMx *this, const SbMatrix *m1, const
			      SbMatrix *m2)
	  Equality comparison operators.

     SbBool		 SbMxEquals(const SbMx *this, const SbMatrix *m, float
			      tolerance)
	  Equality comparison within given tolerance, for each component.

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								 SbMatrix(3IV)

FILE FORMAT/DEFAULTS
     Matrix {
     }

SEE ALSO
     SbVec3f, SbRotation

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