mtxlib.cpp

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/* Copyright (C) Dante Treglia II and Mark A. DeLoura, 2000. 
 * All rights reserved worldwide.
 *
 * This software is provided "as is" without express or implied
 * warranties. You may freely copy and compile this source into
 * applications you distribute provided that the copyright text
 * below is included in the resulting source code, for example:
 * "Portions Copyright (C) Dante Treglia II and Mark A. DeLoura, 2000"
 */
//==========================================================
// C++ Matrix Library
// Version: 2.3 <FINAL>
// Date: March 19, 2000
// Authors: Dante Treglia II and Mark A. DeLoura
// Thanks to: Miguel Gomez, Stan Melax, Pete Isensee, 
//             Gabor Nagy, Scott Bilas, James Boer
//==========================================================

#include <cmath>
#include <cstdio>
#include <cassert>
#include "mtxlib.h"


////////////////////////////////////////////////////////////
// vector2 class
//

// Constructor with initializing float values
vector2::vector2(float inX, float inY) 
{
  x = inX;
  y = inY;
}

// Constructor with initializing vector2
vector2::vector2(const vector2 &v) 
{
  x = v.x;
  y = v.y;
}

// Array indexing
float &vector2::operator [] (unsigned int i) 
{
  assert (i<2);
  
  return *(&x+i);
}

// Array indexing
const float &vector2::operator [] (unsigned int i) const 
{
  assert (i<2);

  return *(&x+i);
}

// Assign 
vector2 &vector2::operator = (const vector2 &v) 
{
  x = v.x;
  y = v.y;

  return *this;
}

// Add a vector2 to this one
vector2 &vector2::operator += (const vector2 &v) 
{
  x += v.x;
  y += v.y;

  return *this;
}

// Subtract a vector2 from this one
vector2 &vector2::operator -= (const vector2 &v) 
{
  x -= v.x;
  y -= v.y;

  return *this;
}

// Multiply the vector2 by a float
vector2 &vector2::operator *= (float f) 
{
  x *= f;
  y *= f;

  return *this;
}

// Divide the vector2 by a float
vector2 &vector2::operator /= (float f) 
{
  x /= f;
  y /= f;

  return *this;
}

// Are these two vector2's equal?
bool operator == (const vector2 &a, const vector2 &b) 
{
  return ((a.x == b.x) && (a.y == b.y));
}

// Are these two vector2's not equal?
bool operator != (const vector2 &a, const vector2 &b) 
{
  return ((a.x != b.x) || (a.y != b.y));
}

// Add two vector2's
vector2 operator + (const vector2 &a, const vector2 &b) 
{
  vector2 ret(a);

  ret += b;

  return ret;
}

// Subtract one vector2 from another
vector2 operator - (const vector2 &a, const vector2 &b) 
{
  vector2 ret(a);

  ret -= b;

  return ret;
}

// Multiply vector2 by a float
vector2 operator * (const vector2 &v, float f) 
{
  return vector2(f * v.x, f * v.y);
}

// Multiply vector2 by a float
vector2 operator * (float f, const vector2 &v) 
{
  return vector2(f * v.x, f * v.y);
}

// Divide vector2 by a float
vector2 operator / (const vector2 &v, float f) 
{
  return vector2(v.x / f, v.y / f);
}

// Negate a vector2
vector2 operator - (const vector2 &a) 
{
  return vector2(-a.x, -a.y);
}

// Get length of a vector2
float vector2::length() const 
{
  return (float) sqrt(x*x + y*y);
}

// Get squared length of a vector2
float vector2::lengthSqr() const 
{
  return (x*x + y*y);
}

// Does vector2 equal (0, 0)?
bool vector2::isZero() const 
{
  return ((x == 0.0F) && (y == 0.0F));
}

// Normalize a vector2
vector2 &vector2::normalize() 
{
  float m = length();

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

  return *this;
}


////////////////////////////////////////////////////////////
// vector3 class
//

// Constructor with initializing float values
vector3::vector3(float inX, float inY, float inZ) 
{
  x = inX;
  y = inY;
  z = inZ;
}

// Constructor with initializing vector3
vector3::vector3(const vector3 &v) 
{
  x = v.x;
  y = v.y;
  z = v.z;
}

// Constructor with initializing vector2
vector3::vector3(const vector2 &v) 
{
  x = v.x;
  y = v.y;
  z = 0.0F;
}

// Array indexing
float &vector3::operator [] (unsigned int i) 
{
  assert (i<3);
        
  return *(&x+i);
}

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

  return *(&x+i);
}

// Assign
vector3 &vector3::operator = (const vector3 &v) 
{
  x = v.x;
  y = v.y;
  z = v.z;

  return *this;
}

// Assign from a vector2
vector3 &vector3::operator = (const vector2 &v) 
{
  x = v.x;
  y = v.y;
  z = 0.0F;

  return *this;
}

// Add a vector3 to this one
vector3 &vector3::operator += (const vector3 &v) 
{
  x += v.x;
  y += v.y;
  z += v.z;

  return *this;
}

// Subtract a vector3 from this one
vector3 &vector3::operator -= (const vector3 &v) 
{
  x -= v.x;
  y -= v.y;
  z -= v.z;

  return *this;
}

// Multiply the vector3 by a float
vector3 &vector3::operator *= (float f) 
{
  x *= f;
  y *= f;
  z *= f;

  return *this;
}

// Divide the vector3 by a float
vector3 &vector3::operator /= (float f) 
{
  x /= f;
  y /= f;
  z /= f;

  return *this;
}

// Are these two vector3's equal?
bool operator == (const vector3 &a, const vector3 &b) 
{
  return ((a.x == b.x) && (a.y == b.y) && (a.z == b.z));
}

// Are these two vector3's not equal?
bool operator != (const vector3 &a, const vector3 &b) 
{
  return ((a.x != b.x) || (a.y != b.y) || (a.z != b.z));
}

// Add two vector3's
vector3 operator + (const vector3 &a, const vector3 &b) 
{
  vector3 ret(a);

  ret += b;

  return ret;
}

// Subtract one vector3 from another
vector3 operator - (const vector3 &a, const vector3 &b) 
{
  vector3 ret(a);

  ret -= b;

  return ret;
}

// Multiply vector3 by a float
vector3 operator * (const vector3 &v, float f) 
{
  return vector3(f * v.x, f * v.y, f * v.z);
}

// Multiply vector3 by a float
vector3 operator * (float f, const vector3 &v) 
{
  return vector3(f * v.x, f * v.y, f * v.z);
}

// Divide vector3 by a float
vector3 operator / (const vector3 &v, float f) 
{
  return vector3(v.x / f, v.y / f, v.z / f);
}

// Negate a vector3
vector3 operator - (const vector3 &a) 
{
  return vector3(-a.x, -a.y, -a.z);
}

// Get length of a vector3
float vector3::length() const 
{
  return (float) sqrt(x*x + y*y + z*z);
}

// Get squared length of a vector3
float vector3::lengthSqr() const 
{
  return (x*x + y*y + z*z);
}

// Does vector3 equal (0, 0, 0)?
bool vector3::isZero() const 
{
  return ((x == 0.0F) && (y == 0.0F) && (z == 0.0F));
}

// Normalize a vector3
vector3 &vector3::normalize() 
{
  float m = length();

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

  return *this;
}


////////////////////////////////////////////////////////////
// vector4 class
//

// Constructor with initializing float values
vector4::vector4(float inX, float inY, float inZ, float inW) 
{
  x = inX;
  y = inY;
  z = inZ;
  w = inW;
}

// Constructor with initializing vector4
vector4::vector4(const vector4 &v) 
{
  x = v.x;
  y = v.y;
  z = v.z;
  w = v.w;
}

// Constructor with initializing vector3
vector4::vector4(const vector3 &v) 
{
  x = v.x;
  y = v.y;
  z = v.z;
  w = 0.0F;
}

// Constructor with initializing vector2
vector4::vector4(const vector2 &v) 
{
  x = v.x;
  y = v.y;
  z = 0.0F;
  w = 0.0F;
}

// Array indexing
float &vector4::operator [] (unsigned int i) 
{
  assert (i<4);
  
  return *(&x+i);
}

// Array indexing
const float &vector4::operator [] (unsigned int i) const 
{
  assert (i<4);
  
  return *(&x+i);
}

// Assign
vector4 &vector4::operator = (const vector4 &v) 
{
  x = v.x;
  y = v.y;
  z = v.z;
  w = v.w;

  return *this;
}

// Assign from a vector3
vector4 &vector4::operator = (const vector3 &v) 
{
  x = v.x;
  y = v.y;
  z = v.z;
  w = 0.0F;

  return *this;
}

// Assign from a vector2
vector4 &vector4::operator = (const vector2 &v) 
{
  x = v.x;
  y = v.y;
  z = 0.0F;
  w = 0.0F;

  return *this;
}

// Add a vector4 to this one
vector4 &vector4::operator += (const vector4 &v) 
{
  x += v.x;
  y += v.y;
  z += v.z;
  w += v.w;

  return *this;
}

// Subtract a vector4 from this one
vector4 &vector4::operator -= (const vector4 &v) 
{
  x -= v.x;
  y -= v.y;
  z -= v.z;
  w -= v.w;

  return *this;
}

// Multiply the vector4 by a float
vector4 &vector4::operator *= (float f) 
{
  x *= f;
  y *= f;
  z *= f;
  w *= f;

  return *this;
}

// Divide the vector4 by a float
vector4 &vector4::operator /= (float f) 
{
  x /= f;
  y /= f;
  z /= f;
  w /= f;

  return *this;
}

// Are these two vector4's equal?
bool operator == (const vector4 &a, const vector4 &b) 
{
  return ((a.x == b.x) && (a.y == b.y) &&
          (a.z == b.z) && (a.w == b.w));
}

// Are these two vector4's not equal?
bool operator != (const vector4 &a, const vector4 &b) 
{
  return ((a.x != b.x) || (a.y != b.y) ||
          (a.z != b.z) || (a.w != b.w));
}

// Add two vector4's
vector4 operator + (const vector4 &a, const vector4 &b) 
{
  vector4 ret(a);

  ret += b;

  return ret;
}

// Subtract one vector4 from another
vector4 operator - (const vector4 &a, const vector4 &b) 
{
  vector4 ret(a);

  ret -= b;

  return ret;
}

// Multiply vector4 by a float
vector4 operator * (const vector4 &v, float f) 
{
  return vector4(f * v.x, f * v.y, f * v.z, f * v.w);
}

// Multiply vector4 by a float
vector4 operator * (float f, const vector4 &v) 
{
  return vector4(f * v.x, f * v.y, f * v.z, f * v.w);
}

// Divide vector4 by a float
vector4 operator / (const vector4 &v, float f) 
{
  return vector4(v.x / f, v.y / f, v.z / f, v.w / f);
}

// Negate a vector4
vector4 operator - (const vector4 &a) 
{
  return vector4(-a.x, -a.y, -a.z, -a.w);
}

// 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
//

// 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 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)