mtxlib.cpp

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  x = xIn;
  y = yIn;
  z = zIn;
  w = wIn;
}

// Get length of a vector4
float vector4::length() const 
{
  return (float) sqrt(x*x + y*y + z*z + w*w);
}

// Get squared length of a vector4
float vector4::lengthSqr() const 
{
  return (x*x + y*y + z*z + w*w);
}

// Does vector4 equal (0, 0, 0, 0)?
bool vector4::isZero() const 
{
  return ((x == 0.0F) && (y == 0.0F) && (z == 0.0F) && (w == 0.0F));
}

// Normalize a vector4
vector4 &vector4::normalize() 
{
  float m = length();

  if (m > 0.0F) 
    m = 1.0F / m;
  else 
    m = 0.0F;
  x *= m;
  y *= m;
  z *= m;
  w *= m;

  return *this;
}


////////////////////////////////////////////////////////////
// Miscellaneous vector functions
//

// Return Normal of vector2's
vector2 Normalized(const vector2 &a)
{
  vector2 ret(a);
  return ret.normalize();
}
// Return Normal of vector3's
vector3 Normalized(const vector3 &a)
{
  vector3 ret(a);
  return ret.normalize();
}
// Return Normal of vector4's
vector4 Normalized(const vector4 &a)
{
  vector4 ret(a);
  return ret.normalize();
}

// Dot product of two vector2's
float DotProduct(const vector2 &a, const vector2 &b) 
{
  return a.x*b.x + a.y*b.y;
}

// Dot product of two vector3's
float DotProduct(const vector3 &a, const vector3 &b) 
{
  return a.x*b.x + a.y*b.y + a.z*b.z;
}

// Dot product of two vector4's
float DotProduct(const vector4 &a, const vector4 &b) 
{
  return a.x*b.x + a.y*b.y + a.z*b.z + a.w*b.w;
}

// Swap two vector2's
void SwapVec(vector2 &a, vector2 &b) 
{
  vector2 tmp(a);

  a = b;
  b = tmp;
}

// Swap two vector3's
void SwapVec(vector3 &a, vector3 &b) 
{
  vector3 tmp(a);

  a = b;
  b = tmp;
}

// Swap two vector4's
void SwapVec(vector4 &a, vector4 &b) 
{
  vector4 tmp(a);

  a = b;
  b = tmp;
}

// Cross product of two vector3's
vector3 CrossProduct(const vector3 &a, const vector3 &b) 
{
  return vector3(a.y*b.z - a.z*b.y,
                 a.z*b.x - a.x*b.z,
                 a.x*b.y - a.y*b.x);
}

// Are these two vector2's nearly equal?
bool NearlyEquals( const vector2& a, const vector2& b, float r ) 
{
  vector2 diff = a - b; // difference

  return (DotProduct(diff, diff) < r*r); // radius
}

// Are these two vector3's nearly equal?
bool NearlyEquals( const vector3& a, const vector3& b, float r ) 
{
  vector3 diff = a - b; // difference

  return (DotProduct(diff, diff) < r*r); // radius
}

// Are these two vector4's nearly equal?
bool NearlyEquals( const vector4& a, const vector4& b, float r ) 
{
  vector4 diff = a - b; // difference

  return (DotProduct(diff, diff) < r*r); // radius
}


////////////////////////////////////////////////////////////
// matrix33 class
//

// Constructor with initializing value
matrix33::matrix33(float v) 
{
  col[0].set(v, v, v);
  col[1].set(v, v, v);
  col[2].set(v, v, v);
}

// Constructor with initializing matrix33
matrix33::matrix33(const matrix33 &m) 
{
  col[0] = m[0];
  col[1] = m[1];
  col[2] = m[2];
}

// Constructor with initializing vector3's
matrix33::matrix33(const vector3 &v0, const vector3 &v1, const vector3 &v2) 
{
  col[0] = v0;
  col[1] = v1;
  col[2] = v2;
}

// Array indexing
vector3 &matrix33::operator [] (unsigned int i) 
{
  assert (i<3);
        
  return (vector3&)col[i];
}

// Array indexing
const vector3 &matrix33::operator [] (unsigned int i) const 
{
  assert (i<3);

  return (vector3&)col[i];
}

// Assign
matrix33 &matrix33::operator = (const matrix33 &m) 
{
  col[0] = m[0];
  col[1] = m[1];
  col[2] = m[2];

  return *this;
}

// Add a matrix33 to this one
matrix33 &matrix33::operator += (const matrix33 &m) 
{
  col[0] += m[0];
  col[1] += m[1];
  col[2] += m[2];

  return *this;
}

// Subtract a matrix33 from this one
matrix33 &matrix33::operator -= (const matrix33 &m) 
{
  col[0] -= m[0];
  col[1] -= m[1];
  col[2] -= m[2];

  return *this;
}

// Multiply the matrix33 by another matrix33
matrix33 &matrix33::operator *= (const matrix33 &m) 
{
  matrix33 t;
  
  for (unsigned int r = 0; r < 3; r++) 
  {
    for (unsigned int c = 0; c < 3; c++) 
    {
      float f = 0;
          
      f += col[0][r] * m[c][0];
      f += col[1][r] * m[c][1];
      f += col[2][r] * m[c][2];
          
      t[c][r] = f;
    }
  }
  
  *this = t;
  
  return *this;
}

// Multiply the matrix33 by a float
matrix33 &matrix33::operator *= (float f) 
{
  col[0] *= f;
  col[1] *= f;
  col[2] *= f;

  return *this;
}

// Are these two matrix33's equal?
bool operator == (const matrix33 &a, const matrix33 &b) 
{
  return ((a[0] == b[0]) && (a[1] == b[1]) && (a[2] == b[2]));
}

// Are these two matrix33's not equal?
bool operator != (const matrix33 &a, const matrix33 &b) 
{
  return ((a[0] != b[0]) || (a[1] != b[1]) || (a[2] != b[2]));
}

// Add two matrix33's
matrix33 operator + (const matrix33 &a, const matrix33 &b) 
{
  matrix33 ret(a);

  ret += b;

  return ret;
}

// Subtract one matrix33 from another
matrix33 operator - (const matrix33 &a, const matrix33 &b) 
{
  matrix33 ret(a);

  ret -= b;

  return ret;
}

// Multiply matrix33 by another matrix33
matrix33 operator * (const matrix33 &a, const matrix33 &b) 
{
  matrix33 ret(a);

  ret *= b;

  return ret;
}

// Multiply a vector3 by this matrix33
vector3 operator * (const matrix33 &m, const vector3 &v) 
{
  vector3 ret;

  ret.x = v.x * m[0][0] + v.y * m[1][0] + v.z * m[2][0];
  ret.y = v.x * m[0][1] + v.y * m[1][1] + v.z * m[2][1];
  ret.z = v.x * m[0][2] + v.y * m[1][2] + v.z * m[2][2];

  return ret;
}

// Multiply a vector3 by this matrix33
vector3 operator * (const vector3 &v, const matrix33 &m) 
{
  vector3 ret;

  ret.x = DotProduct(m[0], v);
  ret.y = DotProduct(m[1], v);
  ret.z = DotProduct(m[2], v);

  return ret;

}

// Multiply matrix33 by a float
matrix33 operator * (float f, const matrix33 &m) 
{
  matrix33 ret(m);

  ret *= f;

  return ret;
}

// Multiply matrix33 by a float
matrix33 operator * (const matrix33 &m, float f) 
{
  matrix33 ret(m);

  ret *= f;

  return ret;
}

// Set matrix33 to the identity matrix
matrix33 &matrix33::identity() 
{
  for (unsigned int c = 0; c < 3; c++) 
  {
    for (unsigned int r = 0; r < 3; r++) 
    {
      if (c == r) 
        col[c][r] = 1.0F;
      else 
        col[c][r] = 0.0F;
    } 
  }
  
  return *this;
}

// Transpose the matrix33
matrix33 &matrix33::transpose() 
{
  float t;
  
  for (unsigned int c = 0; c < 3; c++) 
  {
    for (unsigned int r = c + 1; r < 3; r++) 
    {
      t = col[c][r];
      col[c][r] = col[r][c];
      col[r][c] = t;
    } 
  }
  
  return *this;
}

// Invert the matrix33
matrix33 &matrix33::invert() 
{
  matrix33 a(*this);
  matrix33 b(IdentityMatrix33());

  unsigned int c, r;
  unsigned int cc;
  unsigned int rowMax; // Points to max abs value row in this column
  unsigned int row;
  float tmp;

  // Go through columns
  for (c=0; c<3; c++) 
  {
    // Find the row with max value in this column
    rowMax = c;
    for (r=c+1; r<3; r++) 
    {
      if (fabs(a[c][r]) > fabs(a[c][rowMax])) 
      {
        rowMax = r;
      }
    }
      
    // If the max value here is 0, we can't invert.  Return identity.
    if (a[rowMax][c] == 0.0F) 
      return (identity());
      
    // Swap row "rowMax" with row "c"
    for (cc=0; cc<3; cc++) 
    {
      tmp = a[cc][c];
      a[cc][c] = a[cc][rowMax];
      a[cc][rowMax] = tmp;
      tmp = b[cc][c];
      b[cc][c] = b[cc][rowMax];
      b[cc][rowMax] = tmp;
    }
      
    // Now everything we do is on row "c".
    // Set the max cell to 1 by dividing the entire row by that value
    tmp = a[c][c];
    for (cc=0; cc<3; cc++) 
    {
      a[cc][c] /= tmp;
      b[cc][c] /= tmp;
    }
      
    // Now do the other rows, so that this column only has a 1 and 0's
    for (row = 0; row < 3; row++) 
    {
      if (row != c) 
      {
        tmp = a[c][row];
        for (cc=0; cc<3; cc++) 
        {
          a[cc][row] -= a[cc][c] * tmp;
          b[cc][row] -= b[cc][c] * tmp;
        }
      }
    }
      
  }
  
  *this = b;
  
  return *this;
}

// Return a matrix33 set to the identity matrix
matrix33 IdentityMatrix33() 
{
  matrix33 ret;

  return ret.identity();
}

// Return the transpose of the matrix33
matrix33 TransposeMatrix33(const matrix33 &m) 
{
  matrix33 ret(m);

  return ret.transpose();
}

// Return the inverted matrix33
matrix33 InvertMatrix33(const matrix33 &m) 
{
  matrix33 ret(m);

  return ret.invert();
}

// Return a 2D rotation matrix33
matrix33 RotateRadMatrix33(float rad) 
{
  matrix33 ret;
  float sinA, cosA;

  sinA = (float)sin(rad);
  cosA = (float)cos(rad);

  ret[0][0] = cosA; ret[1][0] = -sinA; ret[2][0] = 0.0F;
  ret[0][1] = sinA; ret[1][1] =  cosA; ret[2][1] = 0.0F;
  ret[0][2] = 0.0F; ret[1][2] =  0.0F; ret[2][2] = 1.0F;

  return ret;
}

// Return a 2D translation matrix33
matrix33 TranslateMatrix33(float x, float y) 
{
  matrix33 ret;

  ret.identity();
  ret[2][0] = x;
  ret[2][1] = y;

  return ret;
}

// Return a 2D/3D scale matrix33
matrix33 ScaleMatrix33(float x, float y, float z) 
{
  matrix33 ret;

  ret.identity();
  ret[0][0] = x;
  ret[1][1] = y;
  ret[2][2] = z;

  return ret;
}


////////////////////////////////////////////////////////////
// matrix44 class
//

// Constructor with initializing value
matrix44::matrix44(float v) 
{
  col[0].set(v, v, v, v);
  col[1].set(v, v, v, v);
  col[2].set(v, v, v, v);
  col[3].set(v, v, v, v);
}

// Constructor with initializing matrix44
matrix44::matrix44(const matrix44 &m) 
{
  col[0] = m[0];
  col[1] = m[1];
  col[2] = m[2];
  col[3] = m[3];
}

// Constructor with initializing matrix33
matrix44::matrix44(const matrix33 &m) 
{
  col[0] = m[0];
  col[1] = m[1];
  col[2] = m[2];
  col[3] = vector4(0.0, 0.0, 0.0, 1.0);
}

// Constructor with initializing vector4's
matrix44::matrix44(const vector4 &v0, const vector4 &v1, 
                   const vector4 &v2, const vector4 &v3) 
{
  col[0] = v0;
  col[1] = v1;
  col[2] = v2;
  col[3] = v3;
}

// Array indexing
vector4 &matrix44::operator [] (unsigned int i) 
{
  assert (i<4);

  return (vector4&) col[i];
}

// Array indexing
const vector4 &matrix44::operator [] (unsigned int i) const 
{
  assert (i<4);
  
  return (vector4&) col[i];
}

// Assign
matrix44 &matrix44::operator = (const matrix44 &m) 
{
  col[0] = m[0];
  col[1] = m[1];
  col[2] = m[2];
  col[3] = m[3];

  return *this;
}

// Assign a matrix33 to the matrix44
matrix44 &matrix44::operator = (const matrix33 &m) 
{
  col[0] = m[0];
  col[1] = m[1];
  col[2] = m[2];
  col[3] = vector4(0.0, 0.0, 0.0, 1.0);

  return *this;
}

// Add a matrix44 to this one
matrix44 &matrix44::operator += (const matrix44 &m) 
{
  col[0] += m[0];
  col[1] += m[1];
  col[2] += m[2];
  col[3] += m[3];

  return *this;
}

// Subtract a matrix44 from this one
matrix44 &matrix44::operator -= (const matrix44 &m) 
{