Bullet Collision Detection & Physics Library: gim_linear_math.h File Reference

Bullet Collision Detection & Physics Library

Macros
gim_linear_math.h File Reference
`#include "gim_math.h"`
`#include "gim_geom_types.h"`
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## Macros
#define | VEC_ZERO_2(a)
| Zero out a 2D vector. More...
#define | VEC_ZERO(a)
| Zero out a 3D vector. More...
#define | VEC_ZERO_4(a)
| Zero out a 4D vector. More...
#define | VEC_COPY_2(b, a)
| Vector copy. More...
#define | VEC_COPY(b, a)
| Copy 3D vector. More...
#define | VEC_COPY_4(b, a)
| Copy 4D vector. More...
#define | VEC_SWAP(b, a)
| VECTOR SWAP. More...
#define | VEC_DIFF_2(v21, v2, v1)
| Vector difference. More...
#define | VEC_DIFF(v21, v2, v1)
| Vector difference. More...
#define | VEC_DIFF_4(v21, v2, v1)
| Vector difference. More...
#define | VEC_SUM_2(v21, v2, v1)
| Vector sum. More...
#define | VEC_SUM(v21, v2, v1)
| Vector sum. More...
#define | VEC_SUM_4(v21, v2, v1)
| Vector sum. More...
#define | VEC_SCALE_2(c, a, b)
| scalar times vector More...
#define | VEC_SCALE(c, a, b)
| scalar times vector More...
#define | VEC_SCALE_4(c, a, b)
| scalar times vector More...
#define | VEC_ACCUM_2(c, a, b)
| accumulate scaled vector More...
#define | VEC_ACCUM(c, a, b)
| accumulate scaled vector More...
#define | VEC_ACCUM_4(c, a, b)
| accumulate scaled vector More...
#define | VEC_DOT_2(a, b) ((a)[0]*(b)[0] + (a)[1]*(b)[1])
| Vector dot product. More...
#define | VEC_DOT(a, b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2])
| Vector dot product. More...
#define | VEC_DOT_4(a, b) ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2] + (a)[3]*(b)[3])
| Vector dot product. More...
#define | VEC_IMPACT_SQ(bsq, direction, position)
| vector impact parameter (squared) More...
#define | VEC_IMPACT(bsq, direction, position)
| vector impact parameter More...
#define | VEC_LENGTH_2(a, l)
| Vector length. More...
#define | VEC_LENGTH(a, l)
| Vector length. More...
#define | VEC_LENGTH_4(a, l)
| Vector length. More...
#define | VEC_INV_LENGTH_2(a, l)
| Vector inv length. More...
#define | VEC_INV_LENGTH(a, l)
| Vector inv length. More...
#define | VEC_INV_LENGTH_4(a, l)
| Vector inv length. More...
#define | VEC_DISTANCE(_len, _va, _vb)
| distance between two points More...
#define | VEC_CONJUGATE_LENGTH(a, l)
| Vector length. More...
#define | VEC_NORMALIZE(a)
| Vector length. More...
#define | VEC_RENORMALIZE(a, newlen)
| Set Vector size. More...
#define | VEC_CROSS(c, a, b)
| Vector cross. More...
#define | VEC_PERPENDICULAR(vp, v, n)
#define | VEC_PARALLEL(vp, v, n)
#define | VEC_PROJECT(vp, v, n)
#define | VEC_UNPROJECT(vp, v, n)
#define | VEC_REFLECT(vr, v, n)
#define | VEC_BLEND_AB(vr, sa, a, sb, b)
#define | VEC_BLEND(vr, a, b, s) VEC_BLEND_AB(vr,(1-s),a,s,b)
#define | VEC_SET3(a, b, op, c) a[0]=b[0] op c[0]; a[1]=b[1] op c[1]; a[2]=b[2] op c[2];
#define | VEC_MAYOR_COORD(vec, maxc)
| Finds the bigger cartesian coordinate from a vector. More...
#define | VEC_MINOR_AXES(vec, i0, i1)
| Finds the 2 smallest cartesian coordinates from a vector. More...
#define | VEC_EQUAL(v1, v2) (v1[0]==v2[0]&&v1[1]==v2[1]&&v1[2]==v2[2])
#define | VEC_NEAR_EQUAL(v1, v2) (GIM_NEAR_EQUAL(v1[0],v2[0])&&GIM_NEAR_EQUAL(v1[1],v2[1])&&GIM_NEAR_EQUAL(v1[2],v2[2]))
#define | X_AXIS_CROSS_VEC(dst, src)
| Vector cross. More...
#define | Y_AXIS_CROSS_VEC(dst, src)
#define | Z_AXIS_CROSS_VEC(dst, src)
#define | IDENTIFY_MATRIX_3X3(m)
| initialize matrix More...
#define | IDENTIFY_MATRIX_4X4(m)
#define | ZERO_MATRIX_4X4(m)
#define | ROTX_CS(m, cosine, sine)
#define | ROTY_CS(m, cosine, sine)
#define | ROTZ_CS(m, cosine, sine)
#define | COPY_MATRIX_2X2(b, a)
#define | COPY_MATRIX_2X3(b, a)
#define | COPY_MATRIX_3X3(b, a)
#define | COPY_MATRIX_4X4(b, a)
#define | TRANSPOSE_MATRIX_2X2(b, a)
#define | TRANSPOSE_MATRIX_3X3(b, a)
#define | TRANSPOSE_MATRIX_4X4(b, a)
#define | SCALE_MATRIX_2X2(b, s, a)
#define | SCALE_MATRIX_3X3(b, s, a)
#define | SCALE_MATRIX_4X4(b, s, a)
#define | SCALE_VEC_MATRIX_2X2(b, svec, a)
#define | SCALE_VEC_MATRIX_3X3(b, svec, a)
#define | SCALE_VEC_MATRIX_4X4(b, svec, a)
#define | ACCUM_SCALE_MATRIX_2X2(b, s, a)
#define | ACCUM_SCALE_MATRIX_3X3(b, s, a)
#define | ACCUM_SCALE_MATRIX_4X4(b, s, a)
#define | MATRIX_PRODUCT_2X2(c, a, b)
#define | MATRIX_PRODUCT_3X3(c, a, b)
#define | MATRIX_PRODUCT_4X4(c, a, b)
#define | MAT_DOT_VEC_2X2(p, m, v)
#define | MAT_DOT_VEC_3X3(p, m, v)
#define | MAT_DOT_VEC_4X4(p, m, v)
#define | MAT_DOT_VEC_3X4(p, m, v)
#define | VEC_DOT_MAT_3X3(p, v, m)
#define | MAT_DOT_VEC_2X3(p, m, v)
| The matrix is assumed to be an affine matrix, with last two entries representing a translation. More...
#define | MAT_TRANSFORM_PLANE_4X4(pout, m, plane)
| Transform a plane. More...
#define | INV_TRANSP_MAT_DOT_VEC_2X2(p, m, v)
| inverse transpose of matrix times vector More...
#define | NORM_XFORM_2X2(p, m, v)
| transform normal vector by inverse transpose of matrix and then renormalize the vector More...
#define | OUTER_PRODUCT_2X2(m, v, t)
| outer product of vector times vector transpose More...
#define | OUTER_PRODUCT_3X3(m, v, t)
| outer product of vector times vector transpose More...
#define | OUTER_PRODUCT_4X4(m, v, t)
| outer product of vector times vector transpose More...
#define | ACCUM_OUTER_PRODUCT_2X2(m, v, t)
| outer product of vector times vector transpose More...
#define | ACCUM_OUTER_PRODUCT_3X3(m, v, t)
| outer product of vector times vector transpose More...
#define | ACCUM_OUTER_PRODUCT_4X4(m, v, t)
| outer product of vector times vector transpose More...
#define | DETERMINANT_2X2(d, m)
| determinant of matrix More...
#define | DETERMINANT_3X3(d, m)
| determinant of matrix More...
#define | COFACTOR_4X4_IJ(fac, m, i, j)
| i,j,th cofactor of a 4x4 matrix More...
#define | DETERMINANT_4X4(d, m)
| determinant of matrix More...
#define | COFACTOR_2X2(a, m)
| cofactor of matrix More...
#define | COFACTOR_3X3(a, m)
| cofactor of matrix More...
#define | COFACTOR_4X4(a, m)
| cofactor of matrix More...
#define | ADJOINT_2X2(a, m)
| adjoint of matrix More...
#define | ADJOINT_3X3(a, m)
| adjoint of matrix More...
#define | ADJOINT_4X4(a, m)
| adjoint of matrix More...
#define | SCALE_ADJOINT_2X2(a, s, m)
| compute adjoint of matrix and scale More...
#define | SCALE_ADJOINT_3X3(a, s, m)
| compute adjoint of matrix and scale More...
#define | SCALE_ADJOINT_4X4(a, s, m)
| compute adjoint of matrix and scale More...
#define | INVERT_2X2(b, det, a)
| inverse of matrix More...
#define | INVERT_3X3(b, det, a)
| inverse of matrix More...
#define | INVERT_4X4(b, det, a)
| inverse of matrix More...
#define | MAT_GET_ROW(mat, vec3, rowindex)
| Get the triple(3) row of a transform matrix. More...
#define | MAT_GET_ROW2(mat, vec2, rowindex)
| Get the tuple(2) row of a transform matrix. More...
#define | MAT_GET_ROW4(mat, vec4, rowindex)
| Get the quad (4) row of a transform matrix. More...
#define | MAT_GET_COL(mat, vec3, colindex)
| Get the triple(3) col of a transform matrix. More...
#define | MAT_GET_COL2(mat, vec2, colindex)
| Get the tuple(2) col of a transform matrix. More...
#define | MAT_GET_COL4(mat, vec4, colindex)
| Get the quad (4) col of a transform matrix. More...
#define | MAT_GET_X(mat, vec3)
| Get the triple(3) col of a transform matrix. More...
#define | MAT_GET_Y(mat, vec3)
| Get the triple(3) col of a transform matrix. More...
#define | MAT_GET_Z(mat, vec3)
| Get the triple(3) col of a transform matrix. More...
#define | MAT_SET_X(mat, vec3)
| Get the triple(3) col of a transform matrix. More...
#define | MAT_SET_Y(mat, vec3)
| Get the triple(3) col of a transform matrix. More...
#define | MAT_SET_Z(mat, vec3)
| Get the triple(3) col of a transform matrix. More...
#define | MAT_GET_TRANSLATION(mat, vec3)
| Get the triple(3) col of a transform matrix. More...
#define | MAT_SET_TRANSLATION(mat, vec3)
| Set the triple(3) col of a transform matrix. More...
#define | MAT_DOT_ROW(mat, vec3, rowindex) (vec3[0]*mat[rowindex][0] + vec3[1]*mat[rowindex][1] + vec3[2]*mat[rowindex][2])
| Returns the dot product between a vec3f and the row of a matrix. More...
#define | MAT_DOT_ROW2(mat, vec2, rowindex) (vec2[0]*mat[rowindex][0] + vec2[1]*mat[rowindex][1])
| Returns the dot product between a vec2f and the row of a matrix. More...
#define | MAT_DOT_ROW4(mat, vec4, rowindex) (vec4[0]*mat[rowindex][0] + vec4[1]*mat[rowindex][1] + vec4[2]*mat[rowindex][2] + vec4[3]*mat[rowindex][3])
| Returns the dot product between a vec4f and the row of a matrix. More...
#define | MAT_DOT_COL(mat, vec3, colindex) (vec3[0]*mat[0][colindex] + vec3[1]*mat[1][colindex] + vec3[2]*mat[2][colindex])
| Returns the dot product between a vec3f and the col of a matrix. More...
#define | MAT_DOT_COL2(mat, vec2, colindex) (vec2[0]*mat[0][colindex] + vec2[1]*mat[1][colindex])
| Returns the dot product between a vec2f and the col of a matrix. More...
#define | MAT_DOT_COL4(mat, vec4, colindex) (vec4[0]*mat[0][colindex] + vec4[1]*mat[1][colindex] + vec4[2]*mat[2][colindex] + vec4[3]*mat[3][colindex])
| Returns the dot product between a vec4f and the col of a matrix. More...
#define | INV_MAT_DOT_VEC_3X3(p, m, v)

## Detailed Description

Author
  Francisco Leon Najera Type Independant Vector and matrix operations.

Definition in file gim_linear_math.h.

## Macro Definition Documentation

## ◆ ACCUM_OUTER_PRODUCT_2X2

#define ACCUM_OUTER_PRODUCT_2X2 | ( |  | m,
|  |  | v,
|  |  | t
| ) |  |

Value:
{ \
m[0][0] += v[0] * t[0]; \
m[0][1] += v[0] * t[1]; \
\
m[1][0] += v[1] * t[0]; \
m[1][1] += v[1] * t[1]; \
}\

outer product of vector times vector transpose

The outer product of vector v and vector transpose t yeilds dyadic matrix m.

Definition at line 1117 of file gim_linear_math.h.

## ◆ ACCUM_OUTER_PRODUCT_3X3

#define ACCUM_OUTER_PRODUCT_3X3 | ( |  | m,
|  |  | v,
|  |  | t
| ) |  |

Value:
{ \
m[0][0] += v[0] * t[0]; \
m[0][1] += v[0] * t[1]; \
m[0][2] += v[0] * t[2]; \
\
m[1][0] += v[1] * t[0]; \
m[1][1] += v[1] * t[1]; \
m[1][2] += v[1] * t[2]; \
\
m[2][0] += v[2] * t[0]; \
m[2][1] += v[2] * t[1]; \
m[2][2] += v[2] * t[2]; \
}\

outer product of vector times vector transpose

The outer product of vector v and vector transpose t yeilds dyadic matrix m.

Definition at line 1132 of file gim_linear_math.h.

## ◆ ACCUM_OUTER_PRODUCT_4X4

#define ACCUM_OUTER_PRODUCT_4X4 | ( |  | m,
|  |  | v,
|  |  | t
| ) |  |

Value:
{ \
m[0][0] += v[0] * t[0]; \
m[0][1] += v[0] * t[1]; \
m[0][2] += v[0] * t[2]; \
m[0][3] += v[0] * t[3]; \
\
m[1][0] += v[1] * t[0]; \
m[1][1] += v[1] * t[1]; \
m[1][2] += v[1] * t[2]; \
m[1][3] += v[1] * t[3]; \
\
m[2][0] += v[2] * t[0]; \
m[2][1] += v[2] * t[1]; \
m[2][2] += v[2] * t[2]; \
m[2][3] += v[2] * t[3]; \
\
m[3][0] += v[3] * t[0]; \
m[3][1] += v[3] * t[1]; \
m[3][2] += v[3] * t[2]; \
m[3][3] += v[3] * t[3]; \
}\

outer product of vector times vector transpose

The outer product of vector v and vector transpose t yeilds dyadic matrix m.

Definition at line 1153 of file gim_linear_math.h.

## ◆ ACCUM_SCALE_MATRIX_2X2

#define ACCUM_SCALE_MATRIX_2X2 | ( |  | b,
|  |  | s,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] += (s) * a[0][0]; \
b[0][1] += (s) * a[0][1]; \
\
b[1][0] += (s) * a[1][0]; \
b[1][1] += (s) * a[1][1]; \
}\

multiply matrix by scalar

Definition at line 816 of file gim_linear_math.h.

## ◆ ACCUM_SCALE_MATRIX_3X3

#define ACCUM_SCALE_MATRIX_3X3 | ( |  | b,
|  |  | s,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] += (s) * a[0][0]; \
b[0][1] += (s) * a[0][1]; \
b[0][2] += (s) * a[0][2]; \
\
b[1][0] += (s) * a[1][0]; \
b[1][1] += (s) * a[1][1]; \
b[1][2] += (s) * a[1][2]; \
\
b[2][0] += (s) * a[2][0]; \
b[2][1] += (s) * a[2][1]; \
b[2][2] += (s) * a[2][2]; \
}\

multiply matrix by scalar

Definition at line 827 of file gim_linear_math.h.

## ◆ ACCUM_SCALE_MATRIX_4X4

#define ACCUM_SCALE_MATRIX_4X4 | ( |  | b,
|  |  | s,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] += (s) * a[0][0]; \
b[0][1] += (s) * a[0][1]; \
b[0][2] += (s) * a[0][2]; \
b[0][3] += (s) * a[0][3]; \
\
b[1][0] += (s) * a[1][0]; \
b[1][1] += (s) * a[1][1]; \
b[1][2] += (s) * a[1][2]; \
b[1][3] += (s) * a[1][3]; \
\
b[2][0] += (s) * a[2][0]; \
b[2][1] += (s) * a[2][1]; \
b[2][2] += (s) * a[2][2]; \
b[2][3] += (s) * a[2][3]; \
\
b[3][0] += (s) * a[3][0]; \
b[3][1] += (s) * a[3][1]; \
b[3][2] += (s) * a[3][2]; \
b[3][3] += (s) * a[3][3]; \
}\

multiply matrix by scalar

Definition at line 844 of file gim_linear_math.h.

## ◆ ADJOINT_2X2

#define ADJOINT_2X2 | ( |  | a,
|  |  | m
| ) |  |

Value:
{ \
a[0][0] = (m)[1][1]; \
a[1][0] = - (m)[1][0]; \
a[0][1] = - (m)[0][1]; \
a[1][1] = (m)[0][0]; \
}\

adjoint of matrix

Computes adjoint of matrix m, returning a (Note that adjoint is just the transpose of the cofactor matrix)

Definition at line 1295 of file gim_linear_math.h.

## ◆ ADJOINT_3X3

#define ADJOINT_3X3 | ( |  | a,
|  |  | m
| ) |  |

Value:
{ \
a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1]; \
a[1][0] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]); \
a[2][0] = m[1][0]*m[2][1] - m[1][1]*m[2][0]; \
a[0][1] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]); \
a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0]; \
a[2][1] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]); \
a[0][2] = m[0][1]*m[1][2] - m[0][2]*m[1][1]; \
a[1][2] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]); \
a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0]); \
}\

adjoint of matrix

Computes adjoint of matrix m, returning a (Note that adjoint is just the transpose of the cofactor matrix)

Definition at line 1309 of file gim_linear_math.h.

## ◆ ADJOINT_4X4

#define ADJOINT_4X4 | ( |  | a,
|  |  | m
| ) |  |

Value:
{ \
char _i_,_j_; \
\
for (_i_=0; _i_<4; _i_++) { \
for (_j_=0; _j_<4; _j_++) { \
COFACTOR_4X4_IJ (a[_j_][_i_], m, _i_, _j_); \
} \
} \
}\

adjoint of matrix

Computes adjoint of matrix m, returning a (Note that adjoint is just the transpose of the cofactor matrix)

Definition at line 1328 of file gim_linear_math.h.

## ◆ COFACTOR_2X2

#define COFACTOR_2X2 | ( |  | a,
|  |  | m
| ) |  |

Value:
{ \
a[0][0] = (m)[1][1]; \
a[0][1] = - (m)[1][0]; \
a[1][0] = - (m)[0][1]; \
a[1][1] = (m)[0][0]; \
}\

cofactor of matrix

Computes cofactor of matrix m, returning a

Definition at line 1247 of file gim_linear_math.h.

## ◆ COFACTOR_3X3

#define COFACTOR_3X3 | ( |  | a,
|  |  | m
| ) |  |

Value:
{ \
a[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1]; \
a[0][1] = - (m[1][0]*m[2][2] - m[2][0]*m[1][2]); \
a[0][2] = m[1][0]*m[2][1] - m[1][1]*m[2][0]; \
a[1][0] = - (m[0][1]*m[2][2] - m[0][2]*m[2][1]); \
a[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0]; \
a[1][2] = - (m[0][0]*m[2][1] - m[0][1]*m[2][0]); \
a[2][0] = m[0][1]*m[1][2] - m[0][2]*m[1][1]; \
a[2][1] = - (m[0][0]*m[1][2] - m[0][2]*m[1][0]); \
a[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0]); \
}\

cofactor of matrix

Computes cofactor of matrix m, returning a

Definition at line 1260 of file gim_linear_math.h.

## ◆ COFACTOR_4X4

#define COFACTOR_4X4 | ( |  | a,
|  |  | m
| ) |  |

Value:
{ \
int i,j; \
\
for (i=0; i<4; i++) { \
for (j=0; j<4; j++) { \
COFACTOR_4X4_IJ (a[i][j], m, i, j); \
} \
} \
}\

cofactor of matrix

Computes cofactor of matrix m, returning a

Definition at line 1278 of file gim_linear_math.h.

## ◆ COFACTOR_4X4_IJ

#define COFACTOR_4X4_IJ | ( |  | fac,
|  |  | m,
|  |  | i,
|  |  | j
| ) |  |

Value:
{ \
GUINT __ii[4], __jj[4], __k; \
\
for (__k=0; __k<i; __k++) __ii[__k] = __k; \
for (__k=i; __k<3; __k++) __ii[__k] = __k+1; \
for (__k=0; __k<j; __k++) __jj[__k] = __k; \
for (__k=j; __k<3; __k++) __jj[__k] = __k+1; \
\
(fac) = m[__ii[0]][__jj[0]] * (m[__ii[1]][__jj[1]]*m[__ii[2]][__jj[2]] \
- m[__ii[1]][__jj[2]]*m[__ii[2]][__jj[1]]); \
(fac) -= m[__ii[0]][__jj[1]] * (m[__ii[1]][__jj[0]]*m[__ii[2]][__jj[2]] \
- m[__ii[1]][__jj[2]]*m[__ii[2]][__jj[0]]);\
(fac) += m[__ii[0]][__jj[2]] * (m[__ii[1]][__jj[0]]*m[__ii[2]][__jj[1]] \
- m[__ii[1]][__jj[1]]*m[__ii[2]][__jj[0]]);\
\
__k = i+j; \
if ( __k != (__k/2)*2) { \
(fac) = -(fac); \
} \
}\

i,j,th cofactor of a 4x4 matrix

Definition at line 1202 of file gim_linear_math.h.

## ◆ COPY_MATRIX_2X2

#define COPY_MATRIX_2X2 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = a[0][0]; \
b[0][1] = a[0][1]; \
\
b[1][0] = a[1][0]; \
b[1][1] = a[1][1]; \
\
}\

matrix copy

Definition at line 590 of file gim_linear_math.h.

## ◆ COPY_MATRIX_2X3

#define COPY_MATRIX_2X3 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = a[0][0]; \
b[0][1] = a[0][1]; \
b[0][2] = a[0][2]; \
\
b[1][0] = a[1][0]; \
b[1][1] = a[1][1]; \
b[1][2] = a[1][2]; \
}\

matrix copy

Definition at line 602 of file gim_linear_math.h.

## ◆ COPY_MATRIX_3X3

#define COPY_MATRIX_3X3 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = a[0][0]; \
b[0][1] = a[0][1]; \
b[0][2] = a[0][2]; \
\
b[1][0] = a[1][0]; \
b[1][1] = a[1][1]; \
b[1][2] = a[1][2]; \
\
b[2][0] = a[2][0]; \
b[2][1] = a[2][1]; \
b[2][2] = a[2][2]; \
}\

matrix copy

Definition at line 615 of file gim_linear_math.h.

## ◆ COPY_MATRIX_4X4

#define COPY_MATRIX_4X4 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = a[0][0]; \
b[0][1] = a[0][1]; \
b[0][2] = a[0][2]; \
b[0][3] = a[0][3]; \
\
b[1][0] = a[1][0]; \
b[1][1] = a[1][1]; \
b[1][2] = a[1][2]; \
b[1][3] = a[1][3]; \
\
b[2][0] = a[2][0]; \
b[2][1] = a[2][1]; \
b[2][2] = a[2][2]; \
b[2][3] = a[2][3]; \
\
b[3][0] = a[3][0]; \
b[3][1] = a[3][1]; \
b[3][2] = a[3][2]; \
b[3][3] = a[3][3]; \
}\

matrix copy

Definition at line 632 of file gim_linear_math.h.

## ◆ DETERMINANT_2X2

#define DETERMINANT_2X2 | ( |  | d,
|  |  | m
| ) |  |

Value:
{ \
d = m[0][0] * m[1][1] - m[0][1] * m[1][0]; \
}\

determinant of matrix

Computes determinant of matrix m, returning d

Definition at line 1181 of file gim_linear_math.h.

## ◆ DETERMINANT_3X3

#define DETERMINANT_3X3 | ( |  | d,
|  |  | m
| ) |  |

Value:
{ \
d = m[0][0] * (m[1][1]*m[2][2] - m[1][2] * m[2][1]); \
d -= m[0][1] * (m[1][0]*m[2][2] - m[1][2] * m[2][0]); \
d += m[0][2] * (m[1][0]*m[2][1] - m[1][1] * m[2][0]); \
}\

determinant of matrix

Computes determinant of matrix m, returning d

Definition at line 1191 of file gim_linear_math.h.

## ◆ DETERMINANT_4X4

#define DETERMINANT_4X4 | ( |  | d,
|  |  | m
| ) |  |

Value:
{ \
GREAL cofac; \
COFACTOR_4X4_IJ (cofac, m, 0, 0); \
d = m[0][0] * cofac; \
COFACTOR_4X4_IJ (cofac, m, 0, 1); \
d += m[0][1] * cofac; \
COFACTOR_4X4_IJ (cofac, m, 0, 2); \
d += m[0][2] * cofac; \
COFACTOR_4X4_IJ (cofac, m, 0, 3); \
d += m[0][3] * cofac; \
}\

determinant of matrix

Computes determinant of matrix m, returning d

Definition at line 1229 of file gim_linear_math.h.

## ◆ IDENTIFY_MATRIX_3X3

#define IDENTIFY_MATRIX_3X3 | ( |  | m | ) |

Value:
{ \
m[0][0] = 1.0; \
m[0][1] = 0.0; \
m[0][2] = 0.0; \
\
m[1][0] = 0.0; \
m[1][1] = 1.0; \
m[1][2] = 0.0; \
\
m[2][0] = 0.0; \
m[2][1] = 0.0; \
m[2][2] = 1.0; \
}\

initialize matrix

Definition at line 448 of file gim_linear_math.h.

## ◆ IDENTIFY_MATRIX_4X4

#define IDENTIFY_MATRIX_4X4 | ( |  | m | ) |

Value:
{ \
m[0][0] = 1.0; \
m[0][1] = 0.0; \
m[0][2] = 0.0; \
m[0][3] = 0.0; \
\
m[1][0] = 0.0; \
m[1][1] = 1.0; \
m[1][2] = 0.0; \
m[1][3] = 0.0; \
\
m[2][0] = 0.0; \
m[2][1] = 0.0; \
m[2][2] = 1.0; \
m[2][3] = 0.0; \
\
m[3][0] = 0.0; \
m[3][1] = 0.0; \
m[3][2] = 0.0; \
m[3][3] = 1.0; \
}\

initialize matrix

Definition at line 464 of file gim_linear_math.h.

## ◆ INV_MAT_DOT_VEC_3X3

#define INV_MAT_DOT_VEC_3X3 | ( |  | p,
|  |  | m,
|  |  | v
| ) |  |

Value:
{ \
p[0] = MAT_DOT_COL(m,v,0); \
p[1] = MAT_DOT_COL(m,v,1); \
p[2] = MAT_DOT_COL(m,v,2); \
}\
MAT_DOT_COL
#define MAT_DOT_COL(mat, vec3, colindex)
Returns the dot product between a vec3f and the col of a matrix.
Definition: gim_linear_math.h:1552

Transpose matrix times vector v is a vec3f and m is a mat4f

Definition at line 1564 of file gim_linear_math.h.

## ◆ INV_TRANSP_MAT_DOT_VEC_2X2

#define INV_TRANSP_MAT_DOT_VEC_2X2 | ( |  | p,
|  |  | m,
|  |  | v
| ) |  |

Value:
{ \
GREAL det; \
\
det = m[0][0]*m[1][1] - m[0][1]*m[1][0]; \
p[0] = m[1][1]*v[0] - m[1][0]*v[1]; \
p[1] = - m[0][1]*v[0] + m[0][0]*v[1]; \
\
/* if matrix not singular, and not orthonormal, then renormalize */ \
if ((det!=1.0f) && (det != 0.0f)) { \
det = 1.0f / det; \
p[0] *= det; \
p[1] *= det; \
} \
}\

inverse transpose of matrix times vector

This macro computes inverse transpose of matrix m, and multiplies vector v into it, to yeild vector p

DANGER !!! Do Not use this on normal vectors!!! It will leave normals the wrong length !!! See macro below for use on normals.

Definition at line 1003 of file gim_linear_math.h.

## ◆ INVERT_2X2

#define INVERT_2X2 | ( |  | b,
|  |  | det,
|  |  | a
| ) |  |

Value:
{ \
GREAL _tmp_; \
DETERMINANT_2X2 (det, a); \
_tmp_ = 1.0 / (det); \
SCALE_ADJOINT_2X2 (b, _tmp_, a); \
}\

inverse of matrix

Compute inverse of matrix a, returning determinant m and inverse b

Definition at line 1393 of file gim_linear_math.h.

## ◆ INVERT_3X3

#define INVERT_3X3 | ( |  | b,
|  |  | det,
|  |  | a
| ) |  |

Value:
{ \
GREAL _tmp_; \
DETERMINANT_3X3 (det, a); \
_tmp_ = 1.0 / (det); \
SCALE_ADJOINT_3X3 (b, _tmp_, a); \
}\

inverse of matrix

Compute inverse of matrix a, returning determinant m and inverse b

Definition at line 1407 of file gim_linear_math.h.

## ◆ INVERT_4X4

#define INVERT_4X4 | ( |  | b,
|  |  | det,
|  |  | a
| ) |  |

Value:
{ \
GREAL _tmp_; \
DETERMINANT_4X4 (det, a); \
_tmp_ = 1.0 / (det); \
SCALE_ADJOINT_4X4 (b, _tmp_, a); \
}\

inverse of matrix

Compute inverse of matrix a, returning determinant m and inverse b

Definition at line 1421 of file gim_linear_math.h.

## ◆ MAT_DOT_COL

#define MAT_DOT_COL | ( |  | mat,
|  |  | vec3,
|  |  | colindex
| ) |  | (vec3[0]*mat[0][colindex] + vec3[1]*mat[1][colindex] + vec3[2]*mat[2][colindex])

Returns the dot product between a vec3f and the col of a matrix.

Definition at line 1552 of file gim_linear_math.h.

## ◆ MAT_DOT_COL2

#define MAT_DOT_COL2 | ( |  | mat,
|  |  | vec2,
|  |  | colindex
| ) |  | (vec2[0]*mat[0][colindex] + vec2[1]*mat[1][colindex])

Returns the dot product between a vec2f and the col of a matrix.

Definition at line 1555 of file gim_linear_math.h.

## ◆ MAT_DOT_COL4

#define MAT_DOT_COL4 | ( |  | mat,
|  |  | vec4,
|  |  | colindex
| ) |  | (vec4[0]*mat[0][colindex] + vec4[1]*mat[1][colindex] + vec4[2]*mat[2][colindex] + vec4[3]*mat[3][colindex])

Returns the dot product between a vec4f and the col of a matrix.

Definition at line 1558 of file gim_linear_math.h.

## ◆ MAT_DOT_ROW

#define MAT_DOT_ROW | ( |  | mat,
|  |  | vec3,
|  |  | rowindex
| ) |  | (vec3[0]*mat[rowindex][0] + vec3[1]*mat[rowindex][1] + vec3[2]*mat[rowindex][2])

Returns the dot product between a vec3f and the row of a matrix.

Definition at line 1542 of file gim_linear_math.h.

## ◆ MAT_DOT_ROW2

#define MAT_DOT_ROW2 | ( |  | mat,
|  |  | vec2,
|  |  | rowindex
| ) |  | (vec2[0]*mat[rowindex][0] + vec2[1]*mat[rowindex][1])

Returns the dot product between a vec2f and the row of a matrix.

Definition at line 1545 of file gim_linear_math.h.

## ◆ MAT_DOT_ROW4

#define MAT_DOT_ROW4 | ( |  | mat,
|  |  | vec4,
|  |  | rowindex
| ) |  | (vec4[0]*mat[rowindex][0] + vec4[1]*mat[rowindex][1] + vec4[2]*mat[rowindex][2] + vec4[3]*mat[rowindex][3])

Returns the dot product between a vec4f and the row of a matrix.

Definition at line 1548 of file gim_linear_math.h.

## ◆ MAT_DOT_VEC_2X2

#define MAT_DOT_VEC_2X2 | ( |  | p,
|  |  | m,
|  |  | v
| ) |  |

Value:
{ \
p[0] = m[0][0]*v[0] + m[0][1]*v[1]; \
p[1] = m[1][0]*v[0] + m[1][1]*v[1]; \
}\

matrix times vector

Definition at line 924 of file gim_linear_math.h.

## ◆ MAT_DOT_VEC_2X3

#define MAT_DOT_VEC_2X3 | ( |  | p,
|  |  | m,
|  |  | v
| ) |  |

Value:
{ \
p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]; \
p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]; \
}\

The matrix is assumed to be an affine matrix, with last two entries representing a translation.

affine matrix times vector

Definition at line 977 of file gim_linear_math.h.

## ◆ MAT_DOT_VEC_3X3

#define MAT_DOT_VEC_3X3 | ( |  | p,
|  |  | m,
|  |  | v
| ) |  |

Value:
{ \
p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2]; \
p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2]; \
p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2]; \
}\

matrix times vector

Definition at line 932 of file gim_linear_math.h.

## ◆ MAT_DOT_VEC_3X4

#define MAT_DOT_VEC_3X4 | ( |  | p,
|  |  | m,
|  |  | v
| ) |  |

Value:
{ \
p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]; \
p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]; \
p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]; \
}\

matrix times vector v is a vec3f and m is a mat4f
Last column is added as the position

Definition at line 956 of file gim_linear_math.h.

## ◆ MAT_DOT_VEC_4X4

#define MAT_DOT_VEC_4X4 | ( |  | p,
|  |  | m,
|  |  | v
| ) |  |

Value:
{ \
p[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2] + m[0][3]*v[3]; \
p[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2] + m[1][3]*v[3]; \
p[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2] + m[2][3]*v[3]; \
p[3] = m[3][0]*v[0] + m[3][1]*v[1] + m[3][2]*v[2] + m[3][3]*v[3]; \
}\

matrix times vector v is a vec4f

Definition at line 943 of file gim_linear_math.h.

## ◆ MAT_GET_COL

#define MAT_GET_COL | ( |  | mat,
|  |  | vec3,
|  |  | colindex
| ) |  |

Value:
{\
vec3[0] = mat[0][colindex];\
vec3[1] = mat[1][colindex];\
vec3[2] = mat[2][colindex]; \
}\

Get the triple(3) col of a transform matrix.

Definition at line 1455 of file gim_linear_math.h.

## ◆ MAT_GET_COL2

#define MAT_GET_COL2 | ( |  | mat,
|  |  | vec2,
|  |  | colindex
| ) |  |

Value:
{\
vec2[0] = mat[0][colindex];\
vec2[1] = mat[1][colindex];\
}\

Get the tuple(2) col of a transform matrix.

Definition at line 1463 of file gim_linear_math.h.

## ◆ MAT_GET_COL4

#define MAT_GET_COL4 | ( |  | mat,
|  |  | vec4,
|  |  | colindex
| ) |  |

Value:
{\
vec4[0] = mat[0][colindex];\
vec4[1] = mat[1][colindex];\
vec4[2] = mat[2][colindex];\
vec4[3] = mat[3][colindex];\
}\

Get the quad (4) col of a transform matrix.

Definition at line 1471 of file gim_linear_math.h.

## ◆ MAT_GET_ROW

#define MAT_GET_ROW | ( |  | mat,
|  |  | vec3,
|  |  | rowindex
| ) |  |

Value:
{\
vec3[0] = mat[rowindex][0];\
vec3[1] = mat[rowindex][1];\
vec3[2] = mat[rowindex][2]; \
}\

Get the triple(3) row of a transform matrix.

Definition at line 1430 of file gim_linear_math.h.

## ◆ MAT_GET_ROW2

#define MAT_GET_ROW2 | ( |  | mat,
|  |  | vec2,
|  |  | rowindex
| ) |  |

Value:
{\
vec2[0] = mat[rowindex][0];\
vec2[1] = mat[rowindex][1];\
}\

Get the tuple(2) row of a transform matrix.

Definition at line 1438 of file gim_linear_math.h.

## ◆ MAT_GET_ROW4

#define MAT_GET_ROW4 | ( |  | mat,
|  |  | vec4,
|  |  | rowindex
| ) |  |

Value:
{\
vec4[0] = mat[rowindex][0];\
vec4[1] = mat[rowindex][1];\
vec4[2] = mat[rowindex][2];\
vec4[3] = mat[rowindex][3];\
}\

Get the quad (4) row of a transform matrix.

Definition at line 1446 of file gim_linear_math.h.

## ◆ MAT_GET_TRANSLATION

#define MAT_GET_TRANSLATION | ( |  | mat,
|  |  | vec3
| ) |  |

Value:
{\
vec3[0] = mat[0][3];\
vec3[1] = mat[1][3];\
vec3[2] = mat[2][3]; \
}\

Get the triple(3) col of a transform matrix.

Definition at line 1524 of file gim_linear_math.h.

## ◆ MAT_GET_X

#define MAT_GET_X | ( |  | mat,
|  |  | vec3
| ) |  |

Value:
{\
MAT_GET_COL(mat,vec3,0);\
}\

Get the triple(3) col of a transform matrix.

Definition at line 1480 of file gim_linear_math.h.

## ◆ MAT_GET_Y

#define MAT_GET_Y | ( |  | mat,
|  |  | vec3
| ) |  |

Value:
{\
MAT_GET_COL(mat,vec3,1);\
}\

Get the triple(3) col of a transform matrix.

Definition at line 1486 of file gim_linear_math.h.

## ◆ MAT_GET_Z

#define MAT_GET_Z | ( |  | mat,
|  |  | vec3
| ) |  |

Value:
{\
MAT_GET_COL(mat,vec3,2);\
}\

Get the triple(3) col of a transform matrix.

Definition at line 1492 of file gim_linear_math.h.

## ◆ MAT_SET_TRANSLATION

#define MAT_SET_TRANSLATION | ( |  | mat,
|  |  | vec3
| ) |  |

Value:
{\
mat[0][3] = vec3[0];\
mat[1][3] = vec3[1];\
mat[2][3] = vec3[2]; \
}\

Set the triple(3) col of a transform matrix.

Definition at line 1532 of file gim_linear_math.h.

## ◆ MAT_SET_X

#define MAT_SET_X | ( |  | mat,
|  |  | vec3
| ) |  |

Value:
{\
mat[0][0] = vec3[0];\
mat[1][0] = vec3[1];\
mat[2][0] = vec3[2];\
}\

Get the triple(3) col of a transform matrix.

Definition at line 1499 of file gim_linear_math.h.

## ◆ MAT_SET_Y

#define MAT_SET_Y | ( |  | mat,
|  |  | vec3
| ) |  |

Value:
{\
mat[0][1] = vec3[0];\
mat[1][1] = vec3[1];\
mat[2][1] = vec3[2];\
}\

Get the triple(3) col of a transform matrix.

Definition at line 1507 of file gim_linear_math.h.

## ◆ MAT_SET_Z

#define MAT_SET_Z | ( |  | mat,
|  |  | vec3
| ) |  |

Value:
{\
mat[0][2] = vec3[0];\
mat[1][2] = vec3[1];\
mat[2][2] = vec3[2];\
}\

Get the triple(3) col of a transform matrix.

Definition at line 1515 of file gim_linear_math.h.

## ◆ MAT_TRANSFORM_PLANE_4X4

#define MAT_TRANSFORM_PLANE_4X4 | ( |  | pout,
|  |  | m,
|  |  | plane
| ) |  |

Value:
{ \
pout[0] = m[0][0]*plane[0] + m[0][1]*plane[1] + m[0][2]*plane[2];\
pout[1] = m[1][0]*plane[0] + m[1][1]*plane[1] + m[1][2]*plane[2];\
pout[2] = m[2][0]*plane[0] + m[2][1]*plane[1] + m[2][2]*plane[2];\
pout[3] = m[0][3]*pout[0] + m[1][3]*pout[1] + m[2][3]*pout[2] + plane[3];\
}\

Transform a plane.

Definition at line 984 of file gim_linear_math.h.

## ◆ MATRIX_PRODUCT_2X2

#define MATRIX_PRODUCT_2X2 | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]; \
c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]; \
\
c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]; \
c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]; \
\
}\

matrix product
c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];

Definition at line 869 of file gim_linear_math.h.

## ◆ MATRIX_PRODUCT_3X3

#define MATRIX_PRODUCT_3X3 | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]; \
c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]; \
c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]; \
\
c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]; \
c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]; \
c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]; \
\
c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]; \
c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]; \
c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]; \
}\

matrix product
c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];

Definition at line 881 of file gim_linear_math.h.

## ◆ MATRIX_PRODUCT_4X4

#define MATRIX_PRODUCT_4X4 | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
c[0][0] = a[0][0]*b[0][0]+a[0][1]*b[1][0]+a[0][2]*b[2][0]+a[0][3]*b[3][0];\
c[0][1] = a[0][0]*b[0][1]+a[0][1]*b[1][1]+a[0][2]*b[2][1]+a[0][3]*b[3][1];\
c[0][2] = a[0][0]*b[0][2]+a[0][1]*b[1][2]+a[0][2]*b[2][2]+a[0][3]*b[3][2];\
c[0][3] = a[0][0]*b[0][3]+a[0][1]*b[1][3]+a[0][2]*b[2][3]+a[0][3]*b[3][3];\
\
c[1][0] = a[1][0]*b[0][0]+a[1][1]*b[1][0]+a[1][2]*b[2][0]+a[1][3]*b[3][0];\
c[1][1] = a[1][0]*b[0][1]+a[1][1]*b[1][1]+a[1][2]*b[2][1]+a[1][3]*b[3][1];\
c[1][2] = a[1][0]*b[0][2]+a[1][1]*b[1][2]+a[1][2]*b[2][2]+a[1][3]*b[3][2];\
c[1][3] = a[1][0]*b[0][3]+a[1][1]*b[1][3]+a[1][2]*b[2][3]+a[1][3]*b[3][3];\
\
c[2][0] = a[2][0]*b[0][0]+a[2][1]*b[1][0]+a[2][2]*b[2][0]+a[2][3]*b[3][0];\
c[2][1] = a[2][0]*b[0][1]+a[2][1]*b[1][1]+a[2][2]*b[2][1]+a[2][3]*b[3][1];\
c[2][2] = a[2][0]*b[0][2]+a[2][1]*b[1][2]+a[2][2]*b[2][2]+a[2][3]*b[3][2];\
c[2][3] = a[2][0]*b[0][3]+a[2][1]*b[1][3]+a[2][2]*b[2][3]+a[2][3]*b[3][3];\
\
c[3][0] = a[3][0]*b[0][0]+a[3][1]*b[1][0]+a[3][2]*b[2][0]+a[3][3]*b[3][0];\
c[3][1] = a[3][0]*b[0][1]+a[3][1]*b[1][1]+a[3][2]*b[2][1]+a[3][3]*b[3][1];\
c[3][2] = a[3][0]*b[0][2]+a[3][1]*b[1][2]+a[3][2]*b[2][2]+a[3][3]*b[3][2];\
c[3][3] = a[3][0]*b[0][3]+a[3][1]*b[1][3]+a[3][2]*b[2][3]+a[3][3]*b[3][3];\
}\

matrix product
c[x][y] = a[x][0]*b[0][y]+a[x][1]*b[1][y]+a[x][2]*b[2][y]+a[x][3]*b[3][y];

Definition at line 899 of file gim_linear_math.h.

## ◆ NORM_XFORM_2X2

#define NORM_XFORM_2X2 | ( |  | p,
|  |  | m,
|  |  | v
| ) |  |

Value:
{ \
GREAL len; \
\
/* do nothing if off-diagonals are zero and diagonals are \
* equal */ \
if ((m[0][1] != 0.0) || (m[1][0] != 0.0) || (m[0][0] != m[1][1])) { \
p[0] = m[1][1]*v[0] - m[1][0]*v[1]; \
p[1] = - m[0][1]*v[0] + m[0][0]*v[1]; \
\
len = p[0]*p[0] + p[1]*p[1]; \
GIM_INV_SQRT(len,len); \
p[0] *= len; \
p[1] *= len; \
} else { \
VEC_COPY_2 (p, v); \
} \
}\

transform normal vector by inverse transpose of matrix and then renormalize the vector

This macro computes inverse transpose of matrix m, and multiplies vector v into it, to yeild vector p Vector p is then normalized.

Definition at line 1027 of file gim_linear_math.h.

## ◆ OUTER_PRODUCT_2X2

#define OUTER_PRODUCT_2X2 | ( |  | m,
|  |  | v,
|  |  | t
| ) |  |

Value:
{ \
m[0][0] = v[0] * t[0]; \
m[0][1] = v[0] * t[1]; \
\
m[1][0] = v[1] * t[0]; \
m[1][1] = v[1] * t[1]; \
}\

outer product of vector times vector transpose

The outer product of vector v and vector transpose t yeilds dyadic matrix m.

Definition at line 1052 of file gim_linear_math.h.

## ◆ OUTER_PRODUCT_3X3

#define OUTER_PRODUCT_3X3 | ( |  | m,
|  |  | v,
|  |  | t
| ) |  |

Value:
{ \
m[0][0] = v[0] * t[0]; \
m[0][1] = v[0] * t[1]; \
m[0][2] = v[0] * t[2]; \
\
m[1][0] = v[1] * t[0]; \
m[1][1] = v[1] * t[1]; \
m[1][2] = v[1] * t[2]; \
\
m[2][0] = v[2] * t[0]; \
m[2][1] = v[2] * t[1]; \
m[2][2] = v[2] * t[2]; \
}\

outer product of vector times vector transpose

The outer product of vector v and vector transpose t yeilds dyadic matrix m.

Definition at line 1067 of file gim_linear_math.h.

## ◆ OUTER_PRODUCT_4X4

#define OUTER_PRODUCT_4X4 | ( |  | m,
|  |  | v,
|  |  | t
| ) |  |

Value:
{ \
m[0][0] = v[0] * t[0]; \
m[0][1] = v[0] * t[1]; \
m[0][2] = v[0] * t[2]; \
m[0][3] = v[0] * t[3]; \
\
m[1][0] = v[1] * t[0]; \
m[1][1] = v[1] * t[1]; \
m[1][2] = v[1] * t[2]; \
m[1][3] = v[1] * t[3]; \
\
m[2][0] = v[2] * t[0]; \
m[2][1] = v[2] * t[1]; \
m[2][2] = v[2] * t[2]; \
m[2][3] = v[2] * t[3]; \
\
m[3][0] = v[3] * t[0]; \
m[3][1] = v[3] * t[1]; \
m[3][2] = v[3] * t[2]; \
m[3][3] = v[3] * t[3]; \
}\

outer product of vector times vector transpose

The outer product of vector v and vector transpose t yeilds dyadic matrix m.

Definition at line 1088 of file gim_linear_math.h.

## ◆ ROTX_CS

#define ROTX_CS | ( |  | m,
|  |  | cosine,
|  |  | sine
| ) |  |

Value:
{ \
/* rotation about the x-axis */ \
\
m[0][0] = 1.0; \
m[0][1] = 0.0; \
m[0][2] = 0.0; \
m[0][3] = 0.0; \
\
m[1][0] = 0.0; \
m[1][1] = (cosine); \
m[1][2] = (sine); \
m[1][3] = 0.0; \
\
m[2][0] = 0.0; \
m[2][1] = -(sine); \
m[2][2] = (cosine); \
m[2][3] = 0.0; \
\
m[3][0] = 0.0; \
m[3][1] = 0.0; \
m[3][2] = 0.0; \
m[3][3] = 1.0; \
}\

matrix rotation X

Definition at line 512 of file gim_linear_math.h.

## ◆ ROTY_CS

#define ROTY_CS | ( |  | m,
|  |  | cosine,
|  |  | sine
| ) |  |

Value:
{ \
/* rotation about the y-axis */ \
\
m[0][0] = (cosine); \
m[0][1] = 0.0; \
m[0][2] = -(sine); \
m[0][3] = 0.0; \
\
m[1][0] = 0.0; \
m[1][1] = 1.0; \
m[1][2] = 0.0; \
m[1][3] = 0.0; \
\
m[2][0] = (sine); \
m[2][1] = 0.0; \
m[2][2] = (cosine); \
m[2][3] = 0.0; \
\
m[3][0] = 0.0; \
m[3][1] = 0.0; \
m[3][2] = 0.0; \
m[3][3] = 1.0; \
}\

matrix rotation Y

Definition at line 538 of file gim_linear_math.h.

## ◆ ROTZ_CS

#define ROTZ_CS | ( |  | m,
|  |  | cosine,
|  |  | sine
| ) |  |

Value:
{ \
/* rotation about the z-axis */ \
\
m[0][0] = (cosine); \
m[0][1] = (sine); \
m[0][2] = 0.0; \
m[0][3] = 0.0; \
\
m[1][0] = -(sine); \
m[1][1] = (cosine); \
m[1][2] = 0.0; \
m[1][3] = 0.0; \
\
m[2][0] = 0.0; \
m[2][1] = 0.0; \
m[2][2] = 1.0; \
m[2][3] = 0.0; \
\
m[3][0] = 0.0; \
m[3][1] = 0.0; \
m[3][2] = 0.0; \
m[3][3] = 1.0; \
}\

matrix rotation Z

Definition at line 564 of file gim_linear_math.h.

## ◆ SCALE_ADJOINT_2X2

#define SCALE_ADJOINT_2X2 | ( |  | a,
|  |  | s,
|  |  | m
| ) |  |

Value:
{ \
a[0][0] = (s) * m[1][1]; \
a[1][0] = - (s) * m[1][0]; \
a[0][1] = - (s) * m[0][1]; \
a[1][1] = (s) * m[0][0]; \
}\

compute adjoint of matrix and scale

Computes adjoint of matrix m, scales it by s, returning a

Definition at line 1344 of file gim_linear_math.h.

## ◆ SCALE_ADJOINT_3X3

#define SCALE_ADJOINT_3X3 | ( |  | a,
|  |  | s,
|  |  | m
| ) |  |

Value:
{ \
a[0][0] = (s) * (m[1][1] * m[2][2] - m[1][2] * m[2][1]); \
a[1][0] = (s) * (m[1][2] * m[2][0] - m[1][0] * m[2][2]); \
a[2][0] = (s) * (m[1][0] * m[2][1] - m[1][1] * m[2][0]); \
\
a[0][1] = (s) * (m[0][2] * m[2][1] - m[0][1] * m[2][2]); \
a[1][1] = (s) * (m[0][0] * m[2][2] - m[0][2] * m[2][0]); \
a[2][1] = (s) * (m[0][1] * m[2][0] - m[0][0] * m[2][1]); \
\
a[0][2] = (s) * (m[0][1] * m[1][2] - m[0][2] * m[1][1]); \
a[1][2] = (s) * (m[0][2] * m[1][0] - m[0][0] * m[1][2]); \
a[2][2] = (s) * (m[0][0] * m[1][1] - m[0][1] * m[1][0]); \
}\

compute adjoint of matrix and scale

Computes adjoint of matrix m, scales it by s, returning a

Definition at line 1357 of file gim_linear_math.h.

## ◆ SCALE_ADJOINT_4X4

#define SCALE_ADJOINT_4X4 | ( |  | a,
|  |  | s,
|  |  | m
| ) |  |

Value:
{ \
char _i_,_j_; \
for (_i_=0; _i_<4; _i_++) { \
for (_j_=0; _j_<4; _j_++) { \
COFACTOR_4X4_IJ (a[_j_][_i_], m, _i_, _j_); \
a[_j_][_i_] *= s; \
} \
} \
}\

compute adjoint of matrix and scale

Computes adjoint of matrix m, scales it by s, returning a

Definition at line 1377 of file gim_linear_math.h.

## ◆ SCALE_MATRIX_2X2

#define SCALE_MATRIX_2X2 | ( |  | b,
|  |  | s,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = (s) * a[0][0]; \
b[0][1] = (s) * a[0][1]; \
\
b[1][0] = (s) * a[1][0]; \
b[1][1] = (s) * a[1][1]; \
}\

multiply matrix by scalar

Definition at line 710 of file gim_linear_math.h.

## ◆ SCALE_MATRIX_3X3

#define SCALE_MATRIX_3X3 | ( |  | b,
|  |  | s,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = (s) * a[0][0]; \
b[0][1] = (s) * a[0][1]; \
b[0][2] = (s) * a[0][2]; \
\
b[1][0] = (s) * a[1][0]; \
b[1][1] = (s) * a[1][1]; \
b[1][2] = (s) * a[1][2]; \
\
b[2][0] = (s) * a[2][0]; \
b[2][1] = (s) * a[2][1]; \
b[2][2] = (s) * a[2][2]; \
}\

multiply matrix by scalar

Definition at line 721 of file gim_linear_math.h.

## ◆ SCALE_MATRIX_4X4

#define SCALE_MATRIX_4X4 | ( |  | b,
|  |  | s,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = (s) * a[0][0]; \
b[0][1] = (s) * a[0][1]; \
b[0][2] = (s) * a[0][2]; \
b[0][3] = (s) * a[0][3]; \
\
b[1][0] = (s) * a[1][0]; \
b[1][1] = (s) * a[1][1]; \
b[1][2] = (s) * a[1][2]; \
b[1][3] = (s) * a[1][3]; \
\
b[2][0] = (s) * a[2][0]; \
b[2][1] = (s) * a[2][1]; \
b[2][2] = (s) * a[2][2]; \
b[2][3] = (s) * a[2][3]; \
\
b[3][0] = s * a[3][0]; \
b[3][1] = s * a[3][1]; \
b[3][2] = s * a[3][2]; \
b[3][3] = s * a[3][3]; \
}\

multiply matrix by scalar

Definition at line 738 of file gim_linear_math.h.

## ◆ SCALE_VEC_MATRIX_2X2

#define SCALE_VEC_MATRIX_2X2 | ( |  | b,
|  |  | svec,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = svec[0] * a[0][0]; \
b[1][0] = svec[0] * a[1][0]; \
\
b[0][1] = svec[1] * a[0][1]; \
b[1][1] = svec[1] * a[1][1]; \
}\

multiply matrix by scalar

Definition at line 763 of file gim_linear_math.h.

## ◆ SCALE_VEC_MATRIX_3X3

#define SCALE_VEC_MATRIX_3X3 | ( |  | b,
|  |  | svec,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = svec[0] * a[0][0]; \
b[1][0] = svec[0] * a[1][0]; \
b[2][0] = svec[0] * a[2][0]; \
\
b[0][1] = svec[1] * a[0][1]; \
b[1][1] = svec[1] * a[1][1]; \
b[2][1] = svec[1] * a[2][1]; \
\
b[0][2] = svec[2] * a[0][2]; \
b[1][2] = svec[2] * a[1][2]; \
b[2][2] = svec[2] * a[2][2]; \
}\

multiply matrix by scalar. Each columns is scaled by each scalar vector component

Definition at line 774 of file gim_linear_math.h.

## ◆ SCALE_VEC_MATRIX_4X4

#define SCALE_VEC_MATRIX_4X4 | ( |  | b,
|  |  | svec,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = svec[0] * a[0][0]; \
b[1][0] = svec[0] * a[1][0]; \
b[2][0] = svec[0] * a[2][0]; \
b[3][0] = svec[0] * a[3][0]; \
\
b[0][1] = svec[1] * a[0][1]; \
b[1][1] = svec[1] * a[1][1]; \
b[2][1] = svec[1] * a[2][1]; \
b[3][1] = svec[1] * a[3][1]; \
\
b[0][2] = svec[2] * a[0][2]; \
b[1][2] = svec[2] * a[1][2]; \
b[2][2] = svec[2] * a[2][2]; \
b[3][2] = svec[2] * a[3][2]; \
\
b[0][3] = svec[3] * a[0][3]; \
b[1][3] = svec[3] * a[1][3]; \
b[2][3] = svec[3] * a[2][3]; \
b[3][3] = svec[3] * a[3][3]; \
}\

multiply matrix by scalar

Definition at line 791 of file gim_linear_math.h.

## ◆ TRANSPOSE_MATRIX_2X2

#define TRANSPOSE_MATRIX_2X2 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = a[0][0]; \
b[0][1] = a[1][0]; \
\
b[1][0] = a[0][1]; \
b[1][1] = a[1][1]; \
}\

matrix transpose

Definition at line 657 of file gim_linear_math.h.

## ◆ TRANSPOSE_MATRIX_3X3

#define TRANSPOSE_MATRIX_3X3 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = a[0][0]; \
b[0][1] = a[1][0]; \
b[0][2] = a[2][0]; \
\
b[1][0] = a[0][1]; \
b[1][1] = a[1][1]; \
b[1][2] = a[2][1]; \
\
b[2][0] = a[0][2]; \
b[2][1] = a[1][2]; \
b[2][2] = a[2][2]; \
}\

matrix transpose

Definition at line 668 of file gim_linear_math.h.

## ◆ TRANSPOSE_MATRIX_4X4

#define TRANSPOSE_MATRIX_4X4 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
b[0][0] = a[0][0]; \
b[0][1] = a[1][0]; \
b[0][2] = a[2][0]; \
b[0][3] = a[3][0]; \
\
b[1][0] = a[0][1]; \
b[1][1] = a[1][1]; \
b[1][2] = a[2][1]; \
b[1][3] = a[3][1]; \
\
b[2][0] = a[0][2]; \
b[2][1] = a[1][2]; \
b[2][2] = a[2][2]; \
b[2][3] = a[3][2]; \
\
b[3][0] = a[0][3]; \
b[3][1] = a[1][3]; \
b[3][2] = a[2][3]; \
b[3][3] = a[3][3]; \
}\

matrix transpose

Definition at line 685 of file gim_linear_math.h.

## ◆ VEC_ACCUM

#define VEC_ACCUM | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
(c)[0] += (a)*(b)[0]; \
(c)[1] += (a)*(b)[1]; \
(c)[2] += (a)*(b)[2]; \
}\

accumulate scaled vector

Definition at line 189 of file gim_linear_math.h.

## ◆ VEC_ACCUM_2

#define VEC_ACCUM_2 | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
(c)[0] += (a)*(b)[0]; \
(c)[1] += (a)*(b)[1]; \
}\

accumulate scaled vector

Definition at line 181 of file gim_linear_math.h.

## ◆ VEC_ACCUM_4

#define VEC_ACCUM_4 | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
(c)[0] += (a)*(b)[0]; \
(c)[1] += (a)*(b)[1]; \
(c)[2] += (a)*(b)[2]; \
(c)[3] += (a)*(b)[3]; \
}\

accumulate scaled vector

Definition at line 198 of file gim_linear_math.h.

## ◆ VEC_BLEND

#define VEC_BLEND | ( |  | vr,
|  |  | a,
|  |  | b,
|  |  | s
| ) |  | VEC_BLEND_AB(vr,(1-s),a,s,b)

Vector blending Takes two vectors a, b, blends them together with s <=1

Definition at line 393 of file gim_linear_math.h.

## ◆ VEC_BLEND_AB

#define VEC_BLEND_AB | ( |  | vr,
|  |  | sa,
|  |  | a,
|  |  | sb,
|  |  | b
| ) |  |

Value:
{ \
vr[0] = (sa) * (a)[0] + (sb) * (b)[0]; \
vr[1] = (sa) * (a)[1] + (sb) * (b)[1]; \
vr[2] = (sa) * (a)[2] + (sb) * (b)[2]; \
}\

Vector blending Takes two vectors a, b, blends them together with two scalars

Definition at line 384 of file gim_linear_math.h.

## ◆ VEC_CONJUGATE_LENGTH

#define VEC_CONJUGATE_LENGTH | ( |  | a,
|  |  | l
| ) |  |

Value:
{\
GREAL _pp = 1.0 - a[0]*a[0] - a[1]*a[1] - a[2]*a[2];\
GIM_SQRT(_pp,l);\
}\

Vector length.

Definition at line 287 of file gim_linear_math.h.

## ◆ VEC_COPY

#define VEC_COPY | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
(b)[0] = (a)[0]; \
(b)[1] = (a)[1]; \
(b)[2] = (a)[2]; \
}\

Copy 3D vector.

Definition at line 74 of file gim_linear_math.h.

## ◆ VEC_COPY_2

#define VEC_COPY_2 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
(b)[0] = (a)[0]; \
(b)[1] = (a)[1]; \
}\

Vector copy.

Definition at line 66 of file gim_linear_math.h.

## ◆ VEC_COPY_4

#define VEC_COPY_4 | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
(b)[0] = (a)[0]; \
(b)[1] = (a)[1]; \
(b)[2] = (a)[2]; \
(b)[3] = (a)[3]; \
}\

Copy 4D vector.

Definition at line 83 of file gim_linear_math.h.

## ◆ VEC_CROSS

#define VEC_CROSS | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
c[0] = (a)[1] * (b)[2] - (a)[2] * (b)[1]; \
c[1] = (a)[2] * (b)[0] - (a)[0] * (b)[2]; \
c[2] = (a)[0] * (b)[1] - (a)[1] * (b)[0]; \
}\

Vector cross.

Definition at line 320 of file gim_linear_math.h.

## ◆ VEC_DIFF

#define VEC_DIFF | ( |  | v21,
|  |  | v2,
|  |  | v1
| ) |  |

Value:
{ \
(v21)[0] = (v2)[0] - (v1)[0]; \
(v21)[1] = (v2)[1] - (v1)[1]; \
(v21)[2] = (v2)[2] - (v1)[2]; \
}\

Vector difference.

Definition at line 108 of file gim_linear_math.h.

## ◆ VEC_DIFF_2

#define VEC_DIFF_2 | ( |  | v21,
|  |  | v2,
|  |  | v1
| ) |  |

Value:
{ \
(v21)[0] = (v2)[0] - (v1)[0]; \
(v21)[1] = (v2)[1] - (v1)[1]; \
}\

Vector difference.

Definition at line 100 of file gim_linear_math.h.

## ◆ VEC_DIFF_4

#define VEC_DIFF_4 | ( |  | v21,
|  |  | v2,
|  |  | v1
| ) |  |

Value:
{ \
(v21)[0] = (v2)[0] - (v1)[0]; \
(v21)[1] = (v2)[1] - (v1)[1]; \
(v21)[2] = (v2)[2] - (v1)[2]; \
(v21)[3] = (v2)[3] - (v1)[3]; \
}\

Vector difference.

Definition at line 117 of file gim_linear_math.h.

## ◆ VEC_DISTANCE

#define VEC_DISTANCE | ( |  | _len,
|  |  | _va,
|  |  | _vb
| ) |  |

Value:
{\
vec3f _tmp_; \
VEC_DIFF(_tmp_, _vb, _va); \
VEC_LENGTH(_tmp_,_len); \
}\

distance between two points

Definition at line 279 of file gim_linear_math.h.

## ◆ VEC_DOT

#define VEC_DOT | ( |  | a,
|  |  | b
| ) |  | ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2])

Vector dot product.

Definition at line 212 of file gim_linear_math.h.

## ◆ VEC_DOT_2

#define VEC_DOT_2 | ( |  | a,
|  |  | b
| ) |  | ((a)[0]*(b)[0] + (a)[1]*(b)[1])

Vector dot product.

Definition at line 208 of file gim_linear_math.h.

## ◆ VEC_DOT_4

#define VEC_DOT_4 | ( |  | a,
|  |  | b
| ) |  | ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2] + (a)[3]*(b)[3])

Vector dot product.

Definition at line 215 of file gim_linear_math.h.

## ◆ VEC_DOT_MAT_3X3

#define VEC_DOT_MAT_3X3 | ( |  | p,
|  |  | v,
|  |  | m
| ) |  |

Value:
{ \
p[0] = v[0]*m[0][0] + v[1]*m[1][0] + v[2]*m[2][0]; \
p[1] = v[0]*m[0][1] + v[1]*m[1][1] + v[2]*m[2][1]; \
p[2] = v[0]*m[0][2] + v[1]*m[1][2] + v[2]*m[2][2]; \
}\

vector transpose times matrix
p[j] = v[0]*m[0][j] + v[1]*m[1][j] + v[2]*m[2][j];

Definition at line 966 of file gim_linear_math.h.

## ◆ VEC_EQUAL

#define VEC_EQUAL | ( |  | v1,
|  |  | v2
| ) |  | (v1[0]==v2[0]&&v1[1]==v2[1]&&v1[2]==v2[2])

Definition at line 415 of file gim_linear_math.h.

## ◆ VEC_IMPACT

#define VEC_IMPACT | ( |  | bsq,
|  |  | direction,
|  |  | position
| ) |  |

Value:
{\
VEC_IMPACT_SQ(bsq,direction,position); \
GIM_SQRT(bsq,bsq); \
}\

vector impact parameter

Definition at line 225 of file gim_linear_math.h.

## ◆ VEC_IMPACT_SQ

#define VEC_IMPACT_SQ | ( |  | bsq,
|  |  | direction,
|  |  | position
| ) |  |

Value:
{\
GREAL _llel_ = VEC_DOT(direction, position);\
bsq = VEC_DOT(position, position) - _llel_*_llel_;\
}\
VEC_DOT
#define VEC_DOT(a, b)
Vector dot product.
Definition: gim_linear_math.h:212

vector impact parameter (squared)

Definition at line 218 of file gim_linear_math.h.

## ◆ VEC_INV_LENGTH

#define VEC_INV_LENGTH | ( |  | a,
|  |  | l
| ) |  |

Value:
{\
GREAL _pp = VEC_DOT(a,a);\
GIM_INV_SQRT(_pp,l);\
}\
VEC_DOT
#define VEC_DOT(a, b)
Vector dot product.
Definition: gim_linear_math.h:212

Vector inv length.

Definition at line 262 of file gim_linear_math.h.

## ◆ VEC_INV_LENGTH_2

#define VEC_INV_LENGTH_2 | ( |  | a,
|  |  | l
| ) |  |

Value:
{\
GREAL _pp = VEC_DOT_2(a,a);\
GIM_INV_SQRT(_pp,l);\
}\
VEC_DOT_2
#define VEC_DOT_2(a, b)
Vector dot product.
Definition: gim_linear_math.h:208

Vector inv length.

Definition at line 254 of file gim_linear_math.h.

## ◆ VEC_INV_LENGTH_4

#define VEC_INV_LENGTH_4 | ( |  | a,
|  |  | l
| ) |  |

Value:
{\
GREAL _pp = VEC_DOT_4(a,a);\
GIM_INV_SQRT(_pp,l);\
}\
VEC_DOT_4
#define VEC_DOT_4(a, b)
Vector dot product.
Definition: gim_linear_math.h:215

Vector inv length.

Definition at line 270 of file gim_linear_math.h.

## ◆ VEC_LENGTH

#define VEC_LENGTH | ( |  | a,
|  |  | l
| ) |  |

Value:
{\
GREAL _pp = VEC_DOT(a,a);\
GIM_SQRT(_pp,l);\
}\
VEC_DOT
#define VEC_DOT(a, b)
Vector dot product.
Definition: gim_linear_math.h:212

Vector length.

Definition at line 239 of file gim_linear_math.h.

## ◆ VEC_LENGTH_2

#define VEC_LENGTH_2 | ( |  | a,
|  |  | l
| ) |  |

Value:
{\
GREAL _pp = VEC_DOT_2(a,a);\
GIM_SQRT(_pp,l);\
}\
VEC_DOT_2
#define VEC_DOT_2(a, b)
Vector dot product.
Definition: gim_linear_math.h:208

Vector length.

Definition at line 231 of file gim_linear_math.h.

## ◆ VEC_LENGTH_4

#define VEC_LENGTH_4 | ( |  | a,
|  |  | l
| ) |  |

Value:
{\
GREAL _pp = VEC_DOT_4(a,a);\
GIM_SQRT(_pp,l);\
}\
VEC_DOT_4
#define VEC_DOT_4(a, b)
Vector dot product.
Definition: gim_linear_math.h:215

Vector length.

Definition at line 247 of file gim_linear_math.h.

## ◆ VEC_MAYOR_COORD

#define VEC_MAYOR_COORD | ( |  | vec,
|  |  | maxc
| ) |  |

Value:
{\
GREAL A[] = {fabs(vec[0]),fabs(vec[1]),fabs(vec[2])};\
maxc = A[0]>A[1]?(A[0]>A[2]?0:2):(A[1]>A[2]?1:2);\
}\

Finds the bigger cartesian coordinate from a vector.

Definition at line 398 of file gim_linear_math.h.

## ◆ VEC_MINOR_AXES

#define VEC_MINOR_AXES | ( |  | vec,
|  |  | i0,
|  |  | i1
| ) |  |

Value:
{\
VEC_MAYOR_COORD(vec,i0);\
i0 = (i0+1)%3;\
i1 = (i0+1)%3;\
}\

Finds the 2 smallest cartesian coordinates from a vector.

Definition at line 405 of file gim_linear_math.h.

## ◆ VEC_NEAR_EQUAL

#define VEC_NEAR_EQUAL | ( |  | v1,
|  |  | v2
| ) |  | (GIM_NEAR_EQUAL(v1[0],v2[0])&&GIM_NEAR_EQUAL(v1[1],v2[1])&&GIM_NEAR_EQUAL(v1[2],v2[2]))

Definition at line 417 of file gim_linear_math.h.

## ◆ VEC_NORMALIZE

#define VEC_NORMALIZE | ( |  | a | ) |

Value:
{ \
GREAL len;\
VEC_INV_LENGTH(a,len); \
if(len<G_REAL_INFINITY)\
{\
a[0] *= len; \
a[1] *= len; \
a[2] *= len; \
} \
}\
G_REAL_INFINITY
#define G_REAL_INFINITY
Definition: gim_math.h:58

Vector length.

Definition at line 295 of file gim_linear_math.h.

## ◆ VEC_PARALLEL

#define VEC_PARALLEL | ( |  | vp,
|  |  | v,
|  |  | n
| ) |  |

Value:
{ \
GREAL dot = VEC_DOT(v, n); \
vp[0] = (dot) * (n)[0]; \
vp[1] = (dot) * (n)[1]; \
vp[2] = (dot) * (n)[2]; \
}\
VEC_DOT
#define VEC_DOT(a, b)
Vector dot product.
Definition: gim_linear_math.h:212
dot
btScalar dot(const btQuaternion &q1, const btQuaternion &q2)
Calculate the dot product between two quaternions.
Definition: btQuaternion.h:878

Vector parallel – assumes that n is of unit length

Definition at line 340 of file gim_linear_math.h.

## ◆ VEC_PERPENDICULAR

#define VEC_PERPENDICULAR | ( |  | vp,
|  |  | v,
|  |  | n
| ) |  |

Value:
{ \
GREAL dot = VEC_DOT(v, n); \
vp[0] = (v)[0] - dot*(n)[0]; \
vp[1] = (v)[1] - dot*(n)[1]; \
vp[2] = (v)[2] - dot*(n)[2]; \
}\
VEC_DOT
#define VEC_DOT(a, b)
Vector dot product.
Definition: gim_linear_math.h:212
dot
btScalar dot(const btQuaternion &q1, const btQuaternion &q2)
Calculate the dot product between two quaternions.
Definition: btQuaternion.h:878

Vector perp – assumes that n is of unit length accepts vector v, subtracts out any component parallel to n

Definition at line 330 of file gim_linear_math.h.

## ◆ VEC_PROJECT

#define VEC_PROJECT | ( |  | vp,
|  |  | v,
|  |  | n
| ) |  |

Value:
{ \
GREAL scalar = VEC_DOT(v, n); \
scalar/= VEC_DOT(n, n); \
vp[0] = (scalar) * (n)[0]; \
vp[1] = (scalar) * (n)[1]; \
vp[2] = (scalar) * (n)[2]; \
}\
VEC_DOT
#define VEC_DOT(a, b)
Vector dot product.
Definition: gim_linear_math.h:212

Same as Vector parallel – n can have any length accepts vector v, subtracts out any component perpendicular to n

Definition at line 350 of file gim_linear_math.h.

## ◆ VEC_REFLECT

#define VEC_REFLECT | ( |  | vr,
|  |  | v,
|  |  | n
| ) |  |

Value:
{ \
GREAL dot = VEC_DOT(v, n); \
vr[0] = (v)[0] - 2.0 * (dot) * (n)[0]; \
vr[1] = (v)[1] - 2.0 * (dot) * (n)[1]; \
vr[2] = (v)[2] - 2.0 * (dot) * (n)[2]; \
}\
VEC_DOT
#define VEC_DOT(a, b)
Vector dot product.
Definition: gim_linear_math.h:212
dot
btScalar dot(const btQuaternion &q1, const btQuaternion &q2)
Calculate the dot product between two quaternions.
Definition: btQuaternion.h:878

Vector reflection – assumes n is of unit length Takes vector v, reflects it against reflector n, and returns vr

Definition at line 373 of file gim_linear_math.h.

## ◆ VEC_RENORMALIZE

#define VEC_RENORMALIZE | ( |  | a,
|  |  | newlen
| ) |  |

Value:
{ \
GREAL len;\
VEC_INV_LENGTH(a,len); \
if(len<G_REAL_INFINITY)\
{\
len *= newlen;\
a[0] *= len; \
a[1] *= len; \
a[2] *= len; \
} \
}\
G_REAL_INFINITY
#define G_REAL_INFINITY
Definition: gim_math.h:58

Set Vector size.

Definition at line 307 of file gim_linear_math.h.

## ◆ VEC_SCALE

#define VEC_SCALE | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
(c)[0] = (a)*(b)[0]; \
(c)[1] = (a)*(b)[1]; \
(c)[2] = (a)*(b)[2]; \
}\

scalar times vector

Definition at line 162 of file gim_linear_math.h.

## ◆ VEC_SCALE_2

#define VEC_SCALE_2 | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
(c)[0] = (a)*(b)[0]; \
(c)[1] = (a)*(b)[1]; \
}\

scalar times vector

Definition at line 154 of file gim_linear_math.h.

## ◆ VEC_SCALE_4

#define VEC_SCALE_4 | ( |  | c,
|  |  | a,
|  |  | b
| ) |  |

Value:
{ \
(c)[0] = (a)*(b)[0]; \
(c)[1] = (a)*(b)[1]; \
(c)[2] = (a)*(b)[2]; \
(c)[3] = (a)*(b)[3]; \
}\

scalar times vector

Definition at line 171 of file gim_linear_math.h.

## ◆ VEC_SET3

#define VEC_SET3 | ( |  | a,
|  |  | b,
|  |  | op,
|  |  | c
| ) |  | a[0]=b[0] op c[0]; a[1]=b[1] op c[1]; a[2]=b[2] op c[2];

Definition at line 395 of file gim_linear_math.h.

## ◆ VEC_SUM

#define VEC_SUM | ( |  | v21,
|  |  | v2,
|  |  | v1
| ) |  |

Value:
{ \
(v21)[0] = (v2)[0] + (v1)[0]; \
(v21)[1] = (v2)[1] + (v1)[1]; \
(v21)[2] = (v2)[2] + (v1)[2]; \
}\

Vector sum.

Definition at line 135 of file gim_linear_math.h.

## ◆ VEC_SUM_2

#define VEC_SUM_2 | ( |  | v21,
|  |  | v2,
|  |  | v1
| ) |  |

Value:
{ \
(v21)[0] = (v2)[0] + (v1)[0]; \
(v21)[1] = (v2)[1] + (v1)[1]; \
}\

Vector sum.

Definition at line 127 of file gim_linear_math.h.

## ◆ VEC_SUM_4

#define VEC_SUM_4 | ( |  | v21,
|  |  | v2,
|  |  | v1
| ) |  |

Value:
{ \
(v21)[0] = (v2)[0] + (v1)[0]; \
(v21)[1] = (v2)[1] + (v1)[1]; \
(v21)[2] = (v2)[2] + (v1)[2]; \
(v21)[3] = (v2)[3] + (v1)[3]; \
}\

Vector sum.

Definition at line 144 of file gim_linear_math.h.

## ◆ VEC_SWAP

#define VEC_SWAP | ( |  | b,
|  |  | a
| ) |  |

Value:
{ \
GIM_SWAP_NUMBERS((b)[0],(a)[0]);\
GIM_SWAP_NUMBERS((b)[1],(a)[1]);\
GIM_SWAP_NUMBERS((b)[2],(a)[2]);\
}\

VECTOR SWAP.

Definition at line 92 of file gim_linear_math.h.

## ◆ VEC_UNPROJECT

#define VEC_UNPROJECT | ( |  | vp,
|  |  | v,
|  |  | n
| ) |  |

Value:
{ \
GREAL scalar = VEC_DOT(v, n); \
scalar = VEC_DOT(n, n)/scalar; \
vp[0] = (scalar) * (n)[0]; \
vp[1] = (scalar) * (n)[1]; \
vp[2] = (scalar) * (n)[2]; \
}\
VEC_DOT
#define VEC_DOT(a, b)
Vector dot product.
Definition: gim_linear_math.h:212

accepts vector v

Definition at line 361 of file gim_linear_math.h.

## ◆ VEC_ZERO

#define VEC_ZERO | ( |  | a | ) |

Value:
{ \
(a)[0] = (a)[1] = (a)[2] = 0.0f; \
}\

Zero out a 3D vector.

Definition at line 52 of file gim_linear_math.h.

## ◆ VEC_ZERO_2

#define VEC_ZERO_2 | ( |  | a | ) |

Value:
{ \
(a)[0] = (a)[1] = 0.0f; \
}\

Zero out a 2D vector.

Definition at line 45 of file gim_linear_math.h.

## ◆ VEC_ZERO_4

#define VEC_ZERO_4 | ( |  | a | ) |

Value:
{ \
(a)[0] = (a)[1] = (a)[2] = (a)[3] = 0.0f; \
}\

Zero out a 4D vector.

Definition at line 59 of file gim_linear_math.h.

## ◆ X_AXIS_CROSS_VEC

#define X_AXIS_CROSS_VEC | ( |  | dst,
|  |  | src
| ) |  |

Value:
{ \
dst[0] = 0.0f; \
dst[1] = -src[2]; \
dst[2] = src[1]; \
}\

Vector cross.

Definition at line 421 of file gim_linear_math.h.

## ◆ Y_AXIS_CROSS_VEC

#define Y_AXIS_CROSS_VEC | ( |  | dst,
|  |  | src
| ) |  |

Value:
{ \
dst[0] = src[2]; \
dst[1] = 0.0f; \
dst[2] = -src[0]; \
}\

Definition at line 428 of file gim_linear_math.h.

## ◆ Z_AXIS_CROSS_VEC

#define Z_AXIS_CROSS_VEC | ( |  | dst,
|  |  | src
| ) |  |

Value:
{ \
dst[0] = -src[1]; \
dst[1] = src[0]; \
dst[2] = 0.0f; \
}\

Definition at line 435 of file gim_linear_math.h.

## ◆ ZERO_MATRIX_4X4

#define ZERO_MATRIX_4X4 | ( |  | m | ) |

Value:
{ \
m[0][0] = 0.0; \
m[0][1] = 0.0; \
m[0][2] = 0.0; \
m[0][3] = 0.0; \
\
m[1][0] = 0.0; \
m[1][1] = 0.0; \
m[1][2] = 0.0; \
m[1][3] = 0.0; \
\
m[2][0] = 0.0; \
m[2][1] = 0.0; \
m[2][2] = 0.0; \
m[2][3] = 0.0; \
\
m[3][0] = 0.0; \
m[3][1] = 0.0; \
m[3][2] = 0.0; \
m[3][3] = 0.0; \
}\

initialize matrix

Definition at line 488 of file gim_linear_math.h.