NAME¶

m_alloc2, m_free2, v_alloc2, v_free2, m_alloc3, m_free3, v_alloc3, v_free3, m_cpy2, m_unity2, v_cpy2, v_fill2, v_unity2, v_zero2, m_cpy3, m_unity3, v_cpy3, v_fill3, v_unity3, v_zero3, m_det2, v_len2, vtmv_mul2, vv_inprod2, m_inv2, m_tra2, mm_add2, mm_mul2, mm_sub2, mtmm_mul2, sm_mul2, mv_mul2, sv_mul2, v_homo2, v_norm2, vv_add2, vv_sub2, vvt_mul2, m_det3, v_len3, vtmv_mul3, vv_inprod3, m_inv3, m_tra3, mm_add3, mm_mul3, mm_sub3, mtmm_mul3, sm_mul3, mv_mul3, sv_mul3, v_homo3, v_norm3, vv_add3, vv_cross3, vv_sub3, vvt_mul3, miraxis2, mirorig2, mirplane2, rot2, scaorig2, scaplane2, scaxis2, transl2, miraxis3, mirorig3, mirplane3, prjorthaxis, prjpersaxis, rot3, scaorig3, scaplane3, scaxis3, transl3 - 3d graphics and associated matrix and vector routines

SYNOPSIS¶

#include <graphmat.h>

/* Data initialisation */

hmat2_t 	*m_alloc2(m_result)


hmat2_t 	*m_result;
void		m_free2(matrix)


hmat2_t	*matrix;
hvec2_t 	*v_alloc2(v_result)


hvec2_t 	*v_result;
void		v_free2(vector)


hmat2_t	*vector;
hmat3_t 	*m_alloc3(m_result)


hmat3_t 	*m_result;
void		m_free3(matrix)


hmat3_t	*matrix;
hvec3_t 	*v_alloc3(v_result)


hvec3_t 	*v_result;
void		v_free3(vector)


hmat3_t	*vector;
hmat2_t 	*m_cpy2(m_source, m_result)


hmat2_t 	*m_source, *m_result;
hmat2_t 	*m_unity2( m_result)


hmat2_t 	*m_result;
hvec2_t 	*v_cpy2(v_source, v_result)


hvec2_t 	*v_source, *v_result;
hvec2_t 	*v_fill2(x, y, w, v_result)


double 	x, y, w;


hvec2_t	*v_result;
hvec2_t 	*v_unity2(axis, v_result)


b_axis 	axis;


hvec2_t 	*v_result;
hvec2_t 	*v_zero2(v_result)


hvec2_t 	*v_result;
hmat3_t 	*m_cpy3(m_source, m_result)


hmat3_t 	*m_source, *m_result;
hmat3_t 	*m_unity3(m_result)


hmat3_t 	*m_result;
hvec3_t 	*v_cpy3(v_source, v_result)


hvec3_t 	*v_source, *v_result;
hvec3_t 	*v_fill3(x, y, z, w, v_result)


double 	x, y, z, w;


hvec3_t	*v_result;
hvec3_t 	*v_unity3(axis, v_result)


b_axis 	axis;


hvec3_t 	*v_result;
hvec3_t 	*v_zero3(vector)


hvec3_t 	*vector;

/* Basic Linear Algebra */

double 	m_det2(matrix)


hmat2_t 	*matrix;
double 	v_len2(vector)


hvec2_t 	*vector;
double 	vtmv_mul2(vector, matrix)


hvec2_t 	*vector;


hmat2_t 	*matrix;
double 	vv_inprod2(vectorA, vectorB)


hvec2_t 	*vectorA, *vectorB;
hmat2_t 	*m_inv2(matrix, m_result)


hmat2_t 	*matrix, *m_result;
hmat2_t 	*m_tra2(matrix, m_result)


hmat2_t 	*matrix, *m_result;
hmat2_t 	*mm_add2(matrixA, matrixB, m_result)


hmat2_t 	*matrixA, *matrixB, *m_result;
hmat2_t 	*mm_mul2(matrixA, matrixB, m_result)


hmat2_t 	*matrixA, *matrixB, *m_result;
hmat2_t 	*mm_sub2(matrixA, matrixB, m_result)


hmat2_t 	*matrixA, *matrixB, *m_result;
hmat2_t 	*mtmm_mul2(matrixA, matrixB, m_result)


hmat2_t 	*matrixA, *matrixB, *m_result;
hmat2_t 	*sm_mul2(scalar, matrix, m_result)


double 	scalar;


hmat2_t 	*matrix, *m_result;
hmat2_t	*vvt_mul2(vectorA, vectorB, m_result)


hvec2_t	*vectorA, *vectorB;


hmat2_t	*m_result;
hvec2_t 	*mv_mul2(matrix, vector, v_result)


hmat2 	*matrix;


hvec2_t 	*vector, *v_result;
hvec2_t 	*sv_mul2(scalar, vector, v_result)


double 	scalar;


hvec2_t 	*vector, *v_result;
hvec2_t 	*v_homo2(vector, v_result)


hvec2_t 	*vector, *v_result;
hvec2_t 	*v_norm2(vector, v_result)


hvec2_t 	*vector, *v_result;
hvec2_t 	*vv_add2(vectorA, vectorB, v_result)


hvec2_t 	*vectorA, *vectorB, *v_result;
hvec2_t 	*vv_sub2(vectorA, vectorB, v_result)


hvec2_t 	*vectorA, *vectorB, *v_result;
double 	m_det3(matrix)


hmat3_t 	*matrix;
double 	v_len3(vector)


hvec3_t 	*vector;
double 	vtmv_mul3(vector, matrix)


hvec3_t 	*vector;


hmat3_t 	*matrix;
double 	vv_inprod3(vectorA, vectorB)


hvec3_t 	*vectorA, *vectorB;
hmat3_t 	*m_inv3(matrix, m_result)


hmat3_t 	*matrix, *m_result;
hmat3_t 	*m_tra3(matrix, m_result)


hmat3_t 	*matrix, *m_result;
hmat3_t 	*mm_add3(matrixA, matrixB, m_result)


hmat3_t 	*matrixA, *matrixB, *m_result;
hmat3_t 	*mm_mul3(matrixA, matrixB, m_result)


hmat3_t 	*matrixA, *matrixB, *m_result;
hmat3_t 	*mm_sub3(matrixA, matrixB, m_result)


hmat3_t 	*matrixA, *matrixB, *m_result;
hmat3_t 	*mtmm_mul3(matrixA, matrixB, m_result)


hmat3_t 	*matrixA, *matrixB, *m_result;
hmat3_t 	*sm_mul3(scalar, matrix, m_result)


double 	scalar;


hmat3_t 	*matrix, *m_result;
hmat3_t	*vvt_mul3(vectorA, vectorB, m_result)


hvec3_t	*vectorA, *vectorB;


hmat3_t	*m_result;
hvec3_t 	*mv_mul3(matrix, vector, v_result)


hmat3_t 	*matrix;


*hvec3_t 	*vector, *v_result;
hvec3_t 	*sv_mul3(scalar, vec, v_result)


double 	scalar;


hvec3_t 	*vector, *v_result;
hvec3_t 	*v_homo3(vector, v_result)


hvec3_t 	*vector, *v_result;
hvec3_t 	*v_norm3(vector, v_result)


hvec3_t 	*vector, *v_result;
hvec3_t 	*vv_add3(vectorA, vectorB, v_result)


hvec3_t 	*vectorA, *vectorB, *v_result;
hvec3_t 	*vv_cross3(vectorA, vectorB, v_result)


hvec3_t 	*vectorA, *vectorB, *v_result;
hvec3_t 	*vv_sub3(vectorA, vectorB, v_result)


hvec3_t 	*vectorA, *vectorB, *v_result;

/* Elementary transformations */

hmat2_t	*miraxis2(axis, m_result)


b_axis	axis;


hmat2_t	*m_result;
hmat2_t	*mirorig2(m_result)


hmat2_t	*m_result;
hmat2_t	*rot2( rotation, m_result)


double 	rotation;


hmat2_t	*m_result;
hmat2_t	*scaorig2(scale, m_result)


double 	scale;


hmat2_t	*m_result;
hmat2_t	*scaxis2(scale, axis, m_result)


double 	scale;


b_axis	axis;


hmat2_t	*m_result;
hmat2_t	*transl2(translation, m_result)


hvec2_t	*translation;


hmat2_t	*m_result;
hmat3_t	*miraxis3(axis, m_result)


b_axis	axis;


hmat3_t	*m_result;
hmat3_t	*mirorig3(m_result)


hmat3_t	*m_result;
hmat3_t	*mirplane3(plane, m_result)


b_axis	plane;


hmat3_t	*m_result;
hmat3_t	*prjorthaxis(axis, m_result)


b_axis	axis;


hmat3_t	*m_result;
hmat3_t	*prjpersaxis(axis, m_result)


b_axis	axis;


hmat3_t	*m_result;
hmat3_t	*rot3( rotation, axis, m_result)


double 	rotation;


b_axis	axis;


hmat3_t	*m_result;
hmat3_t	*scaorig3(scale, m_result)


double 	scale;


hmat3_t	*m_result;
hmat3_t	*scaplane(scale, plane, m_result)


double 	scale;


b_axis	plane;


hmat3_t	*m_result;
hmat3_t	*scaxis3(scale, axis, m_result)


double 	scale;


b_axis	axis;


hmat3_t	*m_result;
hmat3_t	*transl3(translation, m_result)


hvec3_t 	*translation;


hmat3_t	*m_result;

DESCRIPTION¶

Matrix and vector routines associated with 3d graphics in homogeneous coordinates, such as basic linear algebra and elementary transformations.

This library is setup with a multi-level approach.
Level1 : the data level.
Level 2: the data initialisation level.
Level 3: basic linear algebra level.
Level 4: elementary transformation level.

Level 1, the data structures, is realised as follows :
typedef union
{
double a[3];
struct
{
double x, y, w;
} s;
} hvec2_t;

typedef union
{
double a[4];
struct
{
double x, y, z, w;
} s;
} hvec3_t;

typedef struct
{
double m[3][3];
} hmat2_t;

typedef struct
{
double m[4][4];
} hmat3_t;

To access the data elements of a vector or a matrix can be accessed with the macros:

#define v_x( vec ) ((vec).s.x)
#define v_y( vec ) ((vec).s.y)
#define v_z( vec ) ((vec).s.z)
#define v_w( vec ) ((vec).s.w)
#define v_elem( vec, i ) ((vec).a[(i)])
#define m_elem( mat, i, j ) ((mat).m[(i)][(j)])

typedef enum
{
X_AXIS, Y_AXIS, Z_AXIS
} b_axis;

The functions are as follows sorted:
first on the level in which they belong, then on their return value and then on their name.

NAMES¶

The function names begin with an abbreviation of the type of operand, and in which order the operations will be carried out on that operand. Then the order of and which operation will be carried out, followed by the type of coordinates. (i.e vtmv_mul3(vector, matrix) : first take the transpose of vector, multiply the transpose with matrix, this result is multiplied by the incoming vector, all coordinates are homogeneous 3d coordinates.)

USAGE¶

All the "functions" may have been implemented as macro's, so you can't take the address of a function. It is however guaranteed that arguments of each function/macro will be evaluated only once, except for the result argument, which can be evaluated multiple times.

All operations can be used in place, but overlapping data gives unspecified results.

If the parameter v_result or m_result of a function or the parameter of an initialisation function equals NULL, space for the parameter will be dynamically allocated using malloc(), otherwise the parameter is assumed to hold a pointer to a memory area which can be used. A pointer to the used area (which may have been new allocated) is always returned.
If an error occurred like memory could not be allocated, an attempt to divide by zero occurs, or an attempt to invert a singular matrix a general error-routine will be called, which has two parameters : gm_errno and gm_func.
gm_errno is the error type which is one of the following constants : DIV0, NOMEM or MATSING. gm_func is a pointer to a string which contains the name of the function where the error occurred.

A pointer to the error routine is defined as follows :
void (* gm_error)(gm_errno, gm_func);
gm_error_t gm_errno;
char *gm_func;

With gm_error_t is defined as :
typedef enum
{
DIV0, NOMEM, MATSING
} gm_error_t;

The default error handler will abort after printing a diagnostic. You can redirect gm_error to your own error handler. It is not advisable to return from the error handler as error recovery is not expected to take place.

Matrices are of type hmat3_t or hmat2_t for 2d or 3d coordinates, respectively.
Vectors are of type hvec3_t or hvec2_t.

The elements of a vector can be accessed in two manners, the first one is by name of an element of a structure, the second is like an array.

A plane is described by the normal to that plane, with the assumption made that the origin is an element of the plane.

rotation is assumed to be a radial.

If a function is deallocating memory, it will check if the incoming pointer is a NULL pointer.

/* Level2 : Data initialisation */

m_alloc2(), v_alloc2(), m_alloc3(), v_alloc3() allocate memory for a data item of type hmat2_t, hvec2_t, hmat3_t and hvec3_t respectively.
m_free2(), v_free2(), m_free3(), v_free3() reclaim the storage allocated previously.
m_cpy2(), m_cpy3() copies m_matrix into m_result.
m_unity2(), m_unity3() returns the unity matrix. (2d respectively 3d homogeneous coordinates)
v_cpy2(), v_cpy3() copies v_source into v_result. (2d respectively 3d homogeneous coordinates)
v_fill2(), v_fill3() fills v_result according the given values.
v_unity2(), v_unity3() returns the unity vector with w = 1.0, the incoming basic axis axis = 1.0, and the other element(s) are 0.0; (2d respectively 3d homogeneous coordinates)
v_zero2(), v_zero3() return a vector with w = 1.0 and the other elements 0.0;
m_cpy2(), m_cpy3() copies m_source into m_result. (2d respectively 3d homogeneous coordinates)

/* level3 : Basic Linear Algebra */

m_det2(), m_det3() calculates the determinant of the incoming matrix. The determinant is calculated in cartesian rather than homogeneous coordinates.
v_len2(), v_len3() calculates the length of the cathesian part of the homogeneous vector.
vtmv_mul2(), vtmv_mul3() calculate the result of the transpose of the incoming vector multiplied by the incoming matrix multiplied by the incoming vector (2d respectively 3d homogeneous coordinates)
vv_inprod2(), vv_inprod3() calculates the geometrical innerproduct (vector . vector) of vectorA and vectorB.
m_inv2(), m_inv3() calculates the inverse of matrix. It is an error if the matrix in singular.
m_tra2(), m_tra3() calculates the transpose matrix. (2d respectively 3d homogeneous coordinates)
mm_add2(), mm_sub2(), mm_add3(), mm_sub3() calculates the result of matrixA + respectively - matrixB. This operation is unspecified in the sense of homogeneous coordinates; the matrices are taken in their normal, mathematial sense.
mm_mul2(), mm_mul3() calculates the result of matrixA*matrixB (2d respectively 3d homogeneous coordinates)
mtmm_mul2(), mtmm_mul3() calculates the result of the transpose of the incoming matrixA multiplied by matrixB multiplied by matrixA (2d respectively 3d homogeneous coordinates)
sm_mul2(), sm_mul3() calculates the result of scalar*matrix (2d respectively 3d homogeneous coordinates)
mv_mul2(), mv_mul3() calculates the result of matrix*vector (2d respectively 3d homogeneous coordinates)
sv_mul2(), sv_mul3() calculates the result of scalar*vector. (2d respectively 3d homogeneous coordinates)
v_homo2(), v_homo3() homogenize vector so that the w component becomes 1.0 but the length of the vector in homogeneous coordinates stays the same. (2d respectively 3d homogeneous coordinates)
v_norm2(), v_norm3() normalises the incoming vector so the length of the cartesian vector becomes 1.0. The homogeneous length stays the same. (2d respectively 3d homogeneous coordinates)
vv_add2(), vv_sub2(), vv_add3(), vv_sub3() calculates the result of vectorA + respectively - vectorB. These operations are done in the mathematical sense. Be careful with homogeneous coordinates, as not every possible input makes sense.
vvt_mul2(), vvt_mul3() calculates the result of vectorA multiplied by the transpose of vectorB (2d respectively 3d homogeneous coordinates)
vv_cross3() calculates the geometrical crossproduct ( vectorA x vectorB) of two vectors (3d homogeneous coordinates)

/* level4 : Elementary transformations */

miraxis2(), miraxis3() calculates the mirror matrix with respect to axis. (2d respectively 3d homogeneous coordinates)
mirorg2(), mirorg3() calculates the mirror matrix relative to the origin. (2d respectively 3d homogeneous coordinates)
mirplane3() calculates the mirror matrix relative to a plane. (3d homogeneous coordinates)
rot2() calculates the rotation matrix over rotation relative to the origin. (2d homogeneous coordinates)
rot3() calculates the rotation matrix over rotation along axis. (3d homogeneous coordinates)
scaorg2(), scaorg3() calculates the matrix of scaling with scale relative to the origin. (2d respectively 3d homogeneous coordinates)
scaplane3() calculates the matrix of scaling with scale relative to a plane of which plane is the normal. (3d homogeneous coordinates)
scaxis2(), scaxis3() calculates the matrix of scaling with scale relative to the line given by axis. (2d respectively 3d homogeneous coordinates)
transl2(), transl3() calculates the translation matrix over translation. (2d respectively 3d homogeneous coordinates)
prjorthaxis() calculates the orthographic projection matrix along axis. (3d homogeneous coordinates)
prjpersaxis() calculates the perspective projection with along axis The focus is in the origin. The projection plane is on distance 1.0 before the camera. (3d homogeneous coordinates)

CAVEATS¶

Vector addition and subtraction and matrix addition and subtraction are not defined for homogeneous coordinates. One can add and subtract a point vector and a free vector, but you have to normalise the point vector first. The result of the subtraction of two point vectors is a free vector.

Calculating the determinant of a matrix and the length of a vector is unspecified in the sense of homogeneous coordinates

RETURN VALUES¶

There are six types of return values: void, double, *hvec3_t, *hvec2_t, *hmat3_t and *hmat2_t.

SEE ALSO¶

graphadd(3), graphmat++(3), fmatpinv(3TV), malloc(3V), Graphics and matrix routines.

NOTE¶

Library file is /usr/local/lib/libgraphmat.a

AUTHOR¶

Hans Gringhuis.
Klamer Schutte