#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;
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
{
} hvec2_t;
typedef union
{
} hvec3_t;
typedef struct
{
} hmat2_t;
typedef struct
{
} 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
{
} 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.
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.)
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
{
} 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)
Calculating the determinant of a matrix and the length of a vector is unspecified in the sense of homogeneous coordinates