third_party/lcms/src/cmsmtrx.c

//---------------------------------------------------------------------------------
//
//  Little Color Management System
//  Copyright (c) 1998-2017 Marti Maria Saguer
//
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// a copy of this software and associated documentation files (the "Software"),
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// THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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//---------------------------------------------------------------------------------
//

#include "lcms2_internal.h"


#define DSWAP(x, y)     {cmsFloat64Number tmp = (x); (x)=(y); (y)=tmp;}


// Initiate a vector
void CMSEXPORT _cmsVEC3init(cmsVEC3* r, cmsFloat64Number x, cmsFloat64Number y, cmsFloat64Number z)
{
    r -> n[VX] = x;
    r -> n[VY] = y;
    r -> n[VZ] = z;
}

// Vector subtraction
void CMSEXPORT _cmsVEC3minus(cmsVEC3* r, const cmsVEC3* a, const cmsVEC3* b)
{
  r -> n[VX] = a -> n[VX] - b -> n[VX];
  r -> n[VY] = a -> n[VY] - b -> n[VY];
  r -> n[VZ] = a -> n[VZ] - b -> n[VZ];
}

// Vector cross product
void CMSEXPORT _cmsVEC3cross(cmsVEC3* r, const cmsVEC3* u, const cmsVEC3* v)
{
    r ->n[VX] = u->n[VY] * v->n[VZ] - v->n[VY] * u->n[VZ];
    r ->n[VY] = u->n[VZ] * v->n[VX] - v->n[VZ] * u->n[VX];
    r ->n[VZ] = u->n[VX] * v->n[VY] - v->n[VX] * u->n[VY];
}

// Vector dot product
cmsFloat64Number CMSEXPORT _cmsVEC3dot(const cmsVEC3* u, const cmsVEC3* v)
{
    return u->n[VX] * v->n[VX] + u->n[VY] * v->n[VY] + u->n[VZ] * v->n[VZ];
}

// Euclidean length
cmsFloat64Number CMSEXPORT _cmsVEC3length(const cmsVEC3* a)
{
    return sqrt(a ->n[VX] * a ->n[VX] +
                a ->n[VY] * a ->n[VY] +
                a ->n[VZ] * a ->n[VZ]);
}

// Euclidean distance
cmsFloat64Number CMSEXPORT _cmsVEC3distance(const cmsVEC3* a, const cmsVEC3* b)
{
    cmsFloat64Number d1 = a ->n[VX] - b ->n[VX];
    cmsFloat64Number d2 = a ->n[VY] - b ->n[VY];
    cmsFloat64Number d3 = a ->n[VZ] - b ->n[VZ];

    return sqrt(d1*d1 + d2*d2 + d3*d3);
}



// 3x3 Identity
void CMSEXPORT _cmsMAT3identity(cmsMAT3* a)
{
    _cmsVEC3init(&a-> v[0], 1.0, 0.0, 0.0);
    _cmsVEC3init(&a-> v[1], 0.0, 1.0, 0.0);
    _cmsVEC3init(&a-> v[2], 0.0, 0.0, 1.0);
}

static
cmsBool CloseEnough(cmsFloat64Number a, cmsFloat64Number b)
{
    return fabs(b - a) < (1.0 / 65535.0);
}


cmsBool CMSEXPORT _cmsMAT3isIdentity(const cmsMAT3* a)
{
    cmsMAT3 Identity;
    int i, j;

    _cmsMAT3identity(&Identity);

    for (i=0; i < 3; i++)
        for (j=0; j < 3; j++)
            if (!CloseEnough(a ->v[i].n[j], Identity.v[i].n[j])) return FALSE;

    return TRUE;
}


// Multiply two matrices
void CMSEXPORT _cmsMAT3per(cmsMAT3* r, const cmsMAT3* a, const cmsMAT3* b)
{
#define ROWCOL(i, j) \
    a->v[i].n[0]*b->v[0].n[j] + a->v[i].n[1]*b->v[1].n[j] + a->v[i].n[2]*b->v[2].n[j]

    _cmsVEC3init(&r-> v[0], ROWCOL(0,0), ROWCOL(0,1), ROWCOL(0,2));
    _cmsVEC3init(&r-> v[1], ROWCOL(1,0), ROWCOL(1,1), ROWCOL(1,2));
    _cmsVEC3init(&r-> v[2], ROWCOL(2,0), ROWCOL(2,1), ROWCOL(2,2));

#undef ROWCOL //(i, j)
}



// Inverse of a matrix b = a^(-1)
cmsBool  CMSEXPORT _cmsMAT3inverse(const cmsMAT3* a, cmsMAT3* b)
{
   cmsFloat64Number det, c0, c1, c2;

   c0 =  a -> v[1].n[1]*a -> v[2].n[2] - a -> v[1].n[2]*a -> v[2].n[1];
   c1 = -a -> v[1].n[0]*a -> v[2].n[2] + a -> v[1].n[2]*a -> v[2].n[0];
   c2 =  a -> v[1].n[0]*a -> v[2].n[1] - a -> v[1].n[1]*a -> v[2].n[0];

   det = a -> v[0].n[0]*c0 + a -> v[0].n[1]*c1 + a -> v[0].n[2]*c2;

   if (fabs(det) < MATRIX_DET_TOLERANCE) return FALSE;  // singular matrix; can't invert

   b -> v[0].n[0] = c0/det;
   b -> v[0].n[1] = (a -> v[0].n[2]*a -> v[2].n[1] - a -> v[0].n[1]*a -> v[2].n[2])/det;
   b -> v[0].n[2] = (a -> v[0].n[1]*a -> v[1].n[2] - a -> v[0].n[2]*a -> v[1].n[1])/det;
   b -> v[1].n[0] = c1/det;
   b -> v[1].n[1] = (a -> v[0].n[0]*a -> v[2].n[2] - a -> v[0].n[2]*a -> v[2].n[0])/det;
   b -> v[1].n[2] = (a -> v[0].n[2]*a -> v[1].n[0] - a -> v[0].n[0]*a -> v[1].n[2])/det;
   b -> v[2].n[0] = c2/det;
   b -> v[2].n[1] = (a -> v[0].n[1]*a -> v[2].n[0] - a -> v[0].n[0]*a -> v[2].n[1])/det;
   b -> v[2].n[2] = (a -> v[0].n[0]*a -> v[1].n[1] - a -> v[0].n[1]*a -> v[1].n[0])/det;

   return TRUE;
}


// Solve a system in the form Ax = b
cmsBool  CMSEXPORT _cmsMAT3solve(cmsVEC3* x, cmsMAT3* a, cmsVEC3* b)
{
    cmsMAT3 m, a_1;

    memmove(&m, a, sizeof(cmsMAT3));

    if (!_cmsMAT3inverse(&m, &a_1)) return FALSE;  // Singular matrix

    _cmsMAT3eval(x, &a_1, b);
    return TRUE;
}

// Evaluate a vector across a matrix
void CMSEXPORT _cmsMAT3eval(cmsVEC3* r, const cmsMAT3* a, const cmsVEC3* v)
{
    r->n[VX] = a->v[0].n[VX]*v->n[VX] + a->v[0].n[VY]*v->n[VY] + a->v[0].n[VZ]*v->n[VZ];
    r->n[VY] = a->v[1].n[VX]*v->n[VX] + a->v[1].n[VY]*v->n[VY] + a->v[1].n[VZ]*v->n[VZ];
    r->n[VZ] = a->v[2].n[VX]*v->n[VX] + a->v[2].n[VY]*v->n[VY] + a->v[2].n[VZ]*v->n[VZ];
}