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/**
* libdmtx - Data Matrix Encoding/Decoding Library
* Copyright 2008, 2009 Mike Laughton. All rights reserved.
* Copyright 2012-2016 Vadim A. Misbakh-Soloviov. All rights reserved.
*
* See LICENSE file in the main project directory for full
* terms of use and distribution.
*
* Contact:
* Vadim A. Misbakh-Soloviov <dmtx@mva.name>
* Mike Laughton <mike@dragonflylogic.com>
*
* \file dmtxmatrix3.c
* \brief 2D Matrix (3x3) math
*/
/**
* \brief Copy matrix contents
* \param m0 Copy target
* \param m1 Copy source
* \return void
*/
extern void
dmtxMatrix3Copy(DmtxMatrix3 m0, DmtxMatrix3 m1)
{
memcpy(m0, m1, sizeof(DmtxMatrix3));
}
/**
* \brief Generate identity transformation matrix
* \param m Generated matrix
* \return void
*
* | 1 0 0 |
* m = | 0 1 0 |
* | 0 0 1 |
*
* Transform "m"
* (doesn't change anything)
* |\
* (0,1) x----o +--+ \ (0,1) x----o
* | | | \ | |
* | | | / | |
* +----* +--+ / +----*
* (0,0) (1,0) |/ (0,0) (1,0)
*
*/
extern void
dmtxMatrix3Identity(DmtxMatrix3 m)
{
static DmtxMatrix3 tmp = { {1, 0, 0},
{0, 1, 0},
{0, 0, 1} };
dmtxMatrix3Copy(m, tmp);
}
/**
* \brief Generate translate transformation matrix
* \param m Generated matrix
* \param tx
* \param ty
* \return void
*
* | 1 0 0 |
* m = | 0 1 0 |
* | tx ty 1 |
*
* Transform "m"
* _____ (tx,1+ty) x----o (1+tx,1+ty)
* \ | | |
* (0,1) x----o / | (0,1) +-|--+ |
* | | / /\| | +----* (1+tx,ty)
* | | \ / | |
* +----* ` +----+
* (0,0) (1,0) (0,0) (1,0)
*
*/
void dmtxMatrix3Translate(DmtxMatrix3 m, double tx, double ty)
{
dmtxMatrix3Identity(m);
m[2][0] = tx;
m[2][1] = ty;
}
/**
* \brief Generate rotate transformation
* \param m Generated matrix
* \param angle
* \return void
*
* | cos(a) sin(a) 0 |
* m = | -sin(a) cos(a) 0 |
* | 0 0 1 |
* o
* Transform "m" / `
* ___ / `
* (0,1) x----o |/ \ x * (cos(a),sin(a))
* | | '-- | ` /
* | | ___/ ` / a
* +----* `+ - - - - - -
* (0,0) (1,0) (0,0)
*
*/
extern void
dmtxMatrix3Rotate(DmtxMatrix3 m, double angle)
{
double sinAngle, cosAngle;
sinAngle = sin(angle);
cosAngle = cos(angle);
dmtxMatrix3Identity(m);
m[0][0] = cosAngle;
m[0][1] = sinAngle;
m[1][0] = -sinAngle;
m[1][1] = cosAngle;
}
/**
* \brief Generate scale transformation matrix
* \param m Generated matrix
* \param sx
* \param sy
* \return void
*
* | sx 0 0 |
* m = | 0 sy 0 |
* | 0 0 1 |
*
* Transform "m"
* _____ (0,sy) x-------o (sx,sy)
* \ | | |
* (0,1) x----o / | (0,1) +----+ |
* | | / /\| | | |
* | | \ / | | |
* +----* ` +----+--*
* (0,0) (1,0) (0,0) (sx,0)
*
*/
extern void
dmtxMatrix3Scale(DmtxMatrix3 m, double sx, double sy)
{
dmtxMatrix3Identity(m);
m[0][0] = sx;
m[1][1] = sy;
}
/**
* \brief Generate shear transformation matrix
* \param m Generated matrix
* \param shx
* \param shy
* \return void
*
* | 0 shy 0 |
* m = | shx 0 0 |
* | 0 0 1 |
*/
extern void
dmtxMatrix3Shear(DmtxMatrix3 m, double shx, double shy)
{
dmtxMatrix3Identity(m);
m[1][0] = shx;
m[0][1] = shy;
}
/**
* \brief Generate top line skew transformation
* \param m
* \param b0
* \param b1
* \param sz
* \return void
*
* | b1/b0 0 (b1-b0)/(sz*b0) |
* m = | 0 sz/b0 0 |
* | 0 0 1 |
*
* (sz,b1) o
* /| Transform "m"
* / |
* / | +--+
* / | | |
* (0,b0) x | | |
* | | +-+ +-+
* (0,sz) +----+ \ / (0,sz) x----o
* | | \ / | |
* | | \/ | |
* +----+ +----+
* (0,0) (sz,0) (0,0) (sz,0)
*
*/
extern void
dmtxMatrix3LineSkewTop(DmtxMatrix3 m, double b0, double b1, double sz)
{
assert(b0 >= DmtxAlmostZero);
dmtxMatrix3Identity(m);
m[0][0] = b1/b0;
m[1][1] = sz/b0;
m[0][2] = (b1 - b0)/(sz*b0);
}
/**
* \brief Generate top line skew transformation (inverse)
* \param m
* \param b0
* \param b1
* \param sz
* \return void
*/
extern void
dmtxMatrix3LineSkewTopInv(DmtxMatrix3 m, double b0, double b1, double sz)
{
assert(b1 >= DmtxAlmostZero);
dmtxMatrix3Identity(m);
m[0][0] = b0/b1;
m[1][1] = b0/sz;
m[0][2] = (b0 - b1)/(sz*b1);
}
/**
* \brief Generate side line skew transformation
* \param m
* \param b0
* \param b1
* \param sz
* \return void
*/
extern void
dmtxMatrix3LineSkewSide(DmtxMatrix3 m, double b0, double b1, double sz)
{
assert(b0 >= DmtxAlmostZero);
dmtxMatrix3Identity(m);
m[0][0] = sz/b0;
m[1][1] = b1/b0;
m[1][2] = (b1 - b0)/(sz*b0);
}
/**
* \brief Generate side line skew transformation (inverse)
* \param m
* \param b0
* \param b1
* \param sz
* \return void
*/
extern void
dmtxMatrix3LineSkewSideInv(DmtxMatrix3 m, double b0, double b1, double sz)
{
assert(b1 >= DmtxAlmostZero);
dmtxMatrix3Identity(m);
m[0][0] = b0/sz;
m[1][1] = b0/b1;
m[1][2] = (b0 - b1)/(sz*b1);
}
/**
* \brief Multiply two matrices to create a third
* \param mOut
* \param m0
* \param m1
* \return void
*/
extern void
dmtxMatrix3Multiply(DmtxMatrix3 mOut, DmtxMatrix3 m0, DmtxMatrix3 m1)
{
int i, j, k;
double val;
for(i = 0; i < 3; i++) {
for(j = 0; j < 3; j++) {
val = 0.0;
for(k = 0; k < 3; k++) {
val += m0[i][k] * m1[k][j];
}
mOut[i][j] = val;
}
}
}
/**
* \brief Multiply two matrices in place
* \param m0
* \param m1
* \return void
*/
extern void
dmtxMatrix3MultiplyBy(DmtxMatrix3 m0, DmtxMatrix3 m1)
{
DmtxMatrix3 mTmp;
dmtxMatrix3Copy(mTmp, m0);
dmtxMatrix3Multiply(m0, mTmp, m1);
}
/**
* \brief Multiply vector and matrix
* \param vOut Vector (output)
* \param vIn Vector (input)
* \param m Matrix to be multiplied
* \return DmtxPass | DmtxFail
*/
extern int
dmtxMatrix3VMultiply(DmtxVector2 *vOut, DmtxVector2 *vIn, DmtxMatrix3 m)
{
double w;
w = vIn->X*m[0][2] + vIn->Y*m[1][2] + m[2][2];
if(fabs(w) <= DmtxAlmostZero) {
vOut->X = FLT_MAX;
vOut->Y = FLT_MAX;
return DmtxFail;
}
vOut->X = (vIn->X*m[0][0] + vIn->Y*m[1][0] + m[2][0])/w;
vOut->Y = (vIn->X*m[0][1] + vIn->Y*m[1][1] + m[2][1])/w;
return DmtxPass;
}
/**
* \brief Multiply vector and matrix in place
* \param v Vector (input and output)
* \param m Matrix to be multiplied
* \return DmtxPass | DmtxFail
*/
extern int
dmtxMatrix3VMultiplyBy(DmtxVector2 *v, DmtxMatrix3 m)
{
int success;
DmtxVector2 vOut;
success = dmtxMatrix3VMultiply(&vOut, v, m);
*v = vOut;
return success;
}
/**
* \brief Print matrix contents to STDOUT
* \param m
* \return void
*/
extern void
dmtxMatrix3Print(DmtxMatrix3 m)
{
fprintf(stdout, "%8.8f\t%8.8f\t%8.8f\n", m[0][0], m[0][1], m[0][2]);
fprintf(stdout, "%8.8f\t%8.8f\t%8.8f\n", m[1][0], m[1][1], m[1][2]);
fprintf(stdout, "%8.8f\t%8.8f\t%8.8f\n", m[2][0], m[2][1], m[2][2]);
fprintf(stdout, "\n");
}
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