1684 lines
63 KiB
C++
1684 lines
63 KiB
C++
#include "StdAfx.h"
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/* Copyright (C) Dante Treglia II and Mark A. DeLoura, 2000.
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* All rights reserved worldwide.
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*
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* This software is provided "as is" without express or implied
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* warranties. You may freely copy and compile this source into
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* applications you distribute provided that the copyright text
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* below is included in the resulting source code, for example:
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* "Portions Copyright (C) Dante Treglia II and Mark A. DeLoura, 2000"
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*/
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//==========================================================
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// C++ Matrix Library
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// Version: 2.3 <FINAL>
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// Date: March 19, 2000
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// Authors: Dante Treglia II and Mark A. DeLoura
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// Thanks to: Miguel Gomez, Stan Melax, Pete Isensee,
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// Gabor Nagy, Scott Bilas, James Boer
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//==========================================================
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#include <cmath>
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#include <cstdio>
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#include <cassert>
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#include "mtxlib.h"
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#ifdef _DEBUG
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#define new new(_NORMAL_BLOCK,__FILE__,__LINE__)
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#endif
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////////////////////////////////////////////////////////////
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// vector2 class
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//
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// Constructor with initializing float values
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vector2::vector2(float inX, float inY)
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{
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x = inX;
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y = inY;
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}
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// Constructor with initializing vector2
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vector2::vector2(const vector2 &v)
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{
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x = v.x;
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y = v.y;
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}
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// Array indexing
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float &vector2::operator [] (unsigned int i)
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{
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assert (i<2);
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return *(&x+i);
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}
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// Array indexing
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const float &vector2::operator [] (unsigned int i) const
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{
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assert (i<2);
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return *(&x+i);
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}
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// Assign
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vector2 &vector2::operator = (const vector2 &v)
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{
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x = v.x;
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y = v.y;
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return *this;
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}
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// Add a vector2 to this one
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vector2 &vector2::operator += (const vector2 &v)
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{
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x += v.x;
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y += v.y;
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return *this;
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}
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// Subtract a vector2 from this one
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vector2 &vector2::operator -= (const vector2 &v)
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{
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x -= v.x;
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y -= v.y;
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return *this;
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}
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// Multiply the vector2 by a float
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vector2 &vector2::operator *= (float f)
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{
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x *= f;
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y *= f;
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return *this;
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}
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// Divide the vector2 by a float
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vector2 &vector2::operator /= (float f)
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{
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x /= f;
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y /= f;
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return *this;
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}
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// Are these two vector2's equal?
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bool operator == (const vector2 &a, const vector2 &b)
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{
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return ((a.x == b.x) && (a.y == b.y));
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}
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// Are these two vector2's not equal?
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bool operator != (const vector2 &a, const vector2 &b)
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{
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return ((a.x != b.x) || (a.y != b.y));
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}
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// Add two vector2's
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vector2 operator + (const vector2 &a, const vector2 &b)
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{
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vector2 ret(a);
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ret += b;
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return ret;
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}
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// Subtract one vector2 from another
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vector2 operator - (const vector2 &a, const vector2 &b)
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{
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vector2 ret(a);
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ret -= b;
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return ret;
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}
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// Multiply vector2 by a float
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vector2 operator * (const vector2 &v, float f)
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{
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return vector2(f * v.x, f * v.y);
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}
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// Multiply vector2 by a float
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vector2 operator * (float f, const vector2 &v)
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{
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return vector2(f * v.x, f * v.y);
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}
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// Divide vector2 by a float
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vector2 operator / (const vector2 &v, float f)
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{
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return vector2(v.x / f, v.y / f);
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}
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// Negate a vector2
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vector2 operator - (const vector2 &a)
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{
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return vector2(-a.x, -a.y);
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}
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// Get length of a vector2
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float vector2::length() const
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{
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return (float) sqrt(x*x + y*y);
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}
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// Get squared length of a vector2
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float vector2::lengthSqr() const
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{
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return (x*x + y*y);
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}
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// Does vector2 equal (0, 0)?
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bool vector2::isZero() const
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{
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return ((x == 0.0F) && (y == 0.0F));
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}
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// Normalize a vector2
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vector2 &vector2::normalize()
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{
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float m = length();
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if (m > 0.0F)
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m = 1.0F / m;
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else
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m = 0.0F;
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x *= m;
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y *= m;
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return *this;
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}
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////////////////////////////////////////////////////////////
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// vector3 class
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//
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// Constructor with initializing float values
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vector3::vector3(float inX, float inY, float inZ)
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{
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x = inX;
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y = inY;
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z = inZ;
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}
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// Constructor with initializing vector3
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vector3::vector3(const vector3 &v)
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{
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x = v.x;
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y = v.y;
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z = v.z;
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}
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// Constructor with initializing vector2
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vector3::vector3(const vector2 &v)
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{
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x = v.x;
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y = v.y;
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z = 0.0F;
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}
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// Array indexing
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float &vector3::operator [] (unsigned int i)
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{
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assert (i<3);
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return *(&x+i);
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}
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// Array indexing
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const float &vector3::operator [] (unsigned int i) const
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{
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assert (i<3);
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return *(&x+i);
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}
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// Assign
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vector3 &vector3::operator = (const vector3 &v)
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{
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x = v.x;
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y = v.y;
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z = v.z;
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return *this;
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}
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// Assign from a vector2
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vector3 &vector3::operator = (const vector2 &v)
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{
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x = v.x;
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y = v.y;
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z = 0.0F;
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return *this;
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}
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// Add a vector3 to this one
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vector3 &vector3::operator += (const vector3 &v)
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{
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x += v.x;
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y += v.y;
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z += v.z;
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return *this;
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}
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// Subtract a vector3 from this one
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vector3 &vector3::operator -= (const vector3 &v)
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{
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x -= v.x;
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y -= v.y;
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z -= v.z;
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return *this;
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}
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// Multiply the vector3 by a float
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vector3 &vector3::operator *= (float f)
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{
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x *= f;
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y *= f;
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z *= f;
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return *this;
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}
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// Divide the vector3 by a float
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vector3 &vector3::operator /= (float f)
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{
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x /= f;
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y /= f;
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z /= f;
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return *this;
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}
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// Are these two vector3's equal?
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bool operator == (const vector3 &a, const vector3 &b)
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{
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return ((a.x == b.x) && (a.y == b.y) && (a.z == b.z));
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}
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// Are these two vector3's not equal?
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bool operator != (const vector3 &a, const vector3 &b)
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{
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return ((a.x != b.x) || (a.y != b.y) || (a.z != b.z));
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}
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// Add two vector3's
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vector3 operator + (const vector3 &a, const vector3 &b)
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{
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vector3 ret(a);
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ret += b;
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return ret;
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}
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// Subtract one vector3 from another
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vector3 operator - (const vector3 &a, const vector3 &b)
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{
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vector3 ret(a);
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ret -= b;
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return ret;
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}
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// Multiply vector3 by a float
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vector3 operator * (const vector3 &v, float f)
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{
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return vector3(f * v.x, f * v.y, f * v.z);
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}
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// Multiply vector3 by a float
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vector3 operator * (float f, const vector3 &v)
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{
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return vector3(f * v.x, f * v.y, f * v.z);
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}
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// Divide vector3 by a float
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vector3 operator / (const vector3 &v, float f)
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{
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return vector3(v.x / f, v.y / f, v.z / f);
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}
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// Negate a vector3
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vector3 operator - (const vector3 &a)
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{
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return vector3(-a.x, -a.y, -a.z);
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}
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// Get length of a vector3
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float vector3::length() const
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{
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return (float) sqrt(x*x + y*y + z*z);
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}
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// Get squared length of a vector3
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float vector3::lengthSqr() const
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{
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return (x*x + y*y + z*z);
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}
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// Does vector3 equal (0, 0, 0)?
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bool vector3::isZero() const
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{
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return ((x == 0.0F) && (y == 0.0F) && (z == 0.0F));
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}
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// Normalize a vector3
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vector3 &vector3::normalize()
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{
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float m = length();
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if (m > 0.0F)
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m = 1.0F / m;
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else
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m = 0.0F;
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x *= m;
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y *= m;
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z *= m;
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return *this;
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}
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////////////////////////////////////////////////////////////
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// vector4 class
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//
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// Constructor with initializing float values
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vector4::vector4(float inX, float inY, float inZ, float inW)
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{
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x = inX;
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y = inY;
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z = inZ;
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w = inW;
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}
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// Constructor with initializing vector4
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vector4::vector4(const vector4 &v)
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{
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x = v.x;
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y = v.y;
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z = v.z;
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w = v.w;
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}
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// Constructor with initializing vector3
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vector4::vector4(const vector3 &v)
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{
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x = v.x;
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y = v.y;
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z = v.z;
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w = 0.0F;
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}
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// Constructor with initializing vector2
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vector4::vector4(const vector2 &v)
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{
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x = v.x;
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y = v.y;
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z = 0.0F;
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w = 0.0F;
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}
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// Array indexing
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float &vector4::operator [] (unsigned int i)
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{
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assert (i<4);
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return *(&x+i);
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}
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// Array indexing
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const float &vector4::operator [] (unsigned int i) const
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{
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assert (i<4);
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return *(&x+i);
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}
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// Assign
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vector4 &vector4::operator = (const vector4 &v)
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{
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x = v.x;
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y = v.y;
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z = v.z;
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w = v.w;
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return *this;
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}
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// Assign from a vector3
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vector4 &vector4::operator = (const vector3 &v)
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{
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x = v.x;
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y = v.y;
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z = v.z;
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w = 0.0F;
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||
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return *this;
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}
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||
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// Assign from a vector2
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vector4 &vector4::operator = (const vector2 &v)
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{
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x = v.x;
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y = v.y;
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z = 0.0F;
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w = 0.0F;
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return *this;
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}
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// Add a vector4 to this one
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vector4 &vector4::operator += (const vector4 &v)
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{
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x += v.x;
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y += v.y;
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z += v.z;
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w += v.w;
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return *this;
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}
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|
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// Subtract a vector4 from this one
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vector4 &vector4::operator -= (const vector4 &v)
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{
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x -= v.x;
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y -= v.y;
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z -= v.z;
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w -= v.w;
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return *this;
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}
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|
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// Multiply the vector4 by a float
|
||
vector4 &vector4::operator *= (float f)
|
||
{
|
||
x *= f;
|
||
y *= f;
|
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z *= f;
|
||
w *= f;
|
||
|
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return *this;
|
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}
|
||
|
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// 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)
|
||
{
|
||
vector3 ret;
|
||
matrix33 pose(TransposeMatrix33(m));
|
||
|
||
ret.x = DotProduct(pose[0], v);
|
||
ret.y = DotProduct(pose[1], v);
|
||
ret.z = DotProduct(pose[2], v);
|
||
|
||
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 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)
|
||
{
|
||
col[0] -= m[0];
|
||
col[1] -= m[1];
|
||
col[2] -= m[2];
|
||
col[3] -= m[3];
|
||
|
||
return *this;
|
||
}
|
||
|
||
// Multiply the matrix44 by another matrix44
|
||
matrix44 &matrix44::operator *= (const matrix44 &m)
|
||
{
|
||
matrix44 t;
|
||
|
||
for (unsigned int r = 0; r < 4; r++)
|
||
{
|
||
for (unsigned int c = 0; c < 4; 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];
|
||
f += col[3][r] * m[c][3];
|
||
|
||
t[c][r] = f;
|
||
}
|
||
}
|
||
|
||
*this = t;
|
||
|
||
return *this;
|
||
}
|
||
|
||
// Multiply the matrix44 by a float
|
||
matrix44 &matrix44::operator *= (float f)
|
||
{
|
||
col[0] *= f;
|
||
col[1] *= f;
|
||
col[2] *= f;
|
||
col[3] *= f;
|
||
|
||
return *this;
|
||
}
|
||
|
||
// Are these two matrix44's equal?
|
||
bool operator == (const matrix44 &a, const matrix44 &b)
|
||
{
|
||
return ((a[0] == b[0]) && (a[1] == b[1]) &&
|
||
(a[2] == b[2]) && (a[3] == b[3]));
|
||
}
|
||
|
||
// Are these two matrix44's not equal?
|
||
bool operator != (const matrix44 &a, const matrix44 &b)
|
||
{
|
||
return ((a[0] != b[0]) || (a[1] != b[1]) ||
|
||
(a[2] != b[2]) || (a[3] != b[3]));
|
||
}
|
||
|
||
// Add two matrix44's
|
||
matrix44 operator + (const matrix44 &a, const matrix44 &b)
|
||
{
|
||
matrix44 ret(a);
|
||
|
||
ret += b;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Subtract one matrix44 from another
|
||
matrix44 operator - (const matrix44 &a, const matrix44 &b)
|
||
{
|
||
matrix44 ret(a);
|
||
|
||
ret -= b;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Multiply matrix44 by another matrix44
|
||
matrix44 operator * (const matrix44 &a, const matrix44 &b)
|
||
{
|
||
matrix44 ret(a);
|
||
|
||
ret *= b;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Multiply a vector4 by this matrix44
|
||
vector4 operator * (const matrix44 &m, const vector4 &v)
|
||
{
|
||
vector4 ret;
|
||
matrix44 pose(TransposeMatrix44(m));
|
||
|
||
ret.x = DotProduct(pose[0], v);
|
||
ret.y = DotProduct(pose[1], v);
|
||
ret.z = DotProduct(pose[2], v);
|
||
ret.w = DotProduct(pose[3], v);
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Multiply a vector4 by this matrix44
|
||
vector4 operator * (const vector4 &v, const matrix44 &m)
|
||
{
|
||
vector4 ret;
|
||
|
||
ret.x = DotProduct(m[0], v);
|
||
ret.y = DotProduct(m[1], v);
|
||
ret.z = DotProduct(m[2], v);
|
||
ret.w = DotProduct(m[3], v);
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Multiply matrix44 by a float
|
||
matrix44 operator * (float f, const matrix44 &m)
|
||
{
|
||
matrix44 ret(m);
|
||
|
||
ret *= f;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Set matrix44 to the identity matrix
|
||
matrix44 &matrix44::identity()
|
||
{
|
||
for (unsigned int c = 0; c < 4; c++)
|
||
{
|
||
for (unsigned int r = 0; r < 4; r++)
|
||
{
|
||
if (c == r)
|
||
col[c][r] = 1.0F;
|
||
else
|
||
col[c][r] = 0.0F;
|
||
}
|
||
}
|
||
|
||
return *this;
|
||
}
|
||
|
||
// Transpose the matrix44
|
||
matrix44 &matrix44::transpose()
|
||
{
|
||
float t;
|
||
|
||
for (unsigned int c = 0; c < 4; c++)
|
||
{
|
||
for (unsigned int r = c + 1; r < 4; r++)
|
||
{
|
||
t = col[c][r];
|
||
col[c][r] = col[r][c];
|
||
col[r][c] = t;
|
||
}
|
||
}
|
||
|
||
return *this;
|
||
}
|
||
|
||
// Invert the matrix44
|
||
matrix44 &matrix44::invert()
|
||
{
|
||
matrix44 a(*this);
|
||
matrix44 b(IdentityMatrix44());
|
||
|
||
unsigned int r, c;
|
||
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<4; c++)
|
||
{
|
||
|
||
// Find the row with max value in this column
|
||
rowMax = c;
|
||
for (r=c+1; r<4; 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<4; 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<4; 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 < 4; row++)
|
||
{
|
||
if (row != c)
|
||
{
|
||
tmp = a[c][row];
|
||
for (cc=0; cc<4; cc++)
|
||
{
|
||
a[cc][row] -= a[cc][c] * tmp;
|
||
b[cc][row] -= b[cc][c] * tmp;
|
||
}
|
||
}
|
||
}
|
||
|
||
}
|
||
|
||
*this = b;
|
||
|
||
return *this;
|
||
}
|
||
|
||
// Return a matrix44 set to the identity matrix
|
||
matrix44 IdentityMatrix44()
|
||
{
|
||
matrix44 ret;
|
||
|
||
return ret.identity();
|
||
}
|
||
|
||
// Return the transpose of the matrix44
|
||
matrix44 TransposeMatrix44(const matrix44 &m)
|
||
{
|
||
matrix44 ret(m);
|
||
|
||
return ret.transpose();
|
||
}
|
||
|
||
// Return the inverted matrix44
|
||
matrix44 InvertMatrix44(const matrix44 &m)
|
||
{
|
||
matrix44 ret(m);
|
||
|
||
return ret.invert();
|
||
}
|
||
|
||
// Return a 3D axis-rotation matrix44
|
||
// Pass in 'x', 'y', or 'z' for the axis.
|
||
matrix44 RotateRadMatrix44(char axis, float rad)
|
||
{
|
||
matrix44 ret;
|
||
float sinA, cosA;
|
||
|
||
sinA = (float)sin(rad);
|
||
cosA = (float)cos(rad);
|
||
|
||
switch(axis)
|
||
{
|
||
case 'x':
|
||
case 'X':
|
||
ret[0][0] = 1.0F; ret[1][0] = 0.0F; ret[2][0] = 0.0F;
|
||
ret[0][1] = 0.0F; ret[1][1] = cosA; ret[2][1] = -sinA;
|
||
ret[0][2] = 0.0F; ret[1][2] = sinA; ret[2][2] = cosA;
|
||
break;
|
||
|
||
case 'y':
|
||
case 'Y':
|
||
ret[0][0] = cosA; ret[1][0] = 0.0F; ret[2][0] = sinA;
|
||
ret[0][1] = 0.0F; ret[1][1] = 1.0F; ret[2][1] = 0.0F;
|
||
ret[0][2] = -sinA; ret[1][2] = 0.0F; ret[2][2] = cosA;
|
||
break;
|
||
|
||
case 'z':
|
||
case 'Z':
|
||
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;
|
||
break;
|
||
}
|
||
|
||
ret[0][3] = 0.0F; ret[1][3] = 0.0F; ret[2][3] = 0.0F;
|
||
ret[3][0] = 0.0F;
|
||
ret[3][1] = 0.0F;
|
||
ret[3][2] = 0.0F;
|
||
ret[3][3] = 1.0F;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Return a 3D axis-rotation matrix44
|
||
// Pass in an arbitrary vector3 axis.
|
||
matrix44 RotateRadMatrix44(const vector3 &axis, float rad)
|
||
{
|
||
matrix44 ret;
|
||
float sinA, cosA;
|
||
float invCosA;
|
||
vector3 nrm = axis;
|
||
float x, y, z;
|
||
float xSq, ySq, zSq;
|
||
|
||
nrm.normalize();
|
||
sinA = (float)sin(rad);
|
||
cosA = (float)cos(rad);
|
||
invCosA = 1.0F - cosA;
|
||
|
||
x = nrm.x;
|
||
y = nrm.y;
|
||
z = nrm.z;
|
||
|
||
xSq = x * x;
|
||
ySq = y * y;
|
||
zSq = z * z;
|
||
|
||
ret[0][0] = (invCosA * xSq) + (cosA);
|
||
ret[1][0] = (invCosA * x * y) - (sinA * z );
|
||
ret[2][0] = (invCosA * x * z) + (sinA * y );
|
||
ret[3][0] = 0.0F;
|
||
|
||
ret[0][1] = (invCosA * x * y) + (sinA * z);
|
||
ret[1][1] = (invCosA * ySq) + (cosA);
|
||
ret[2][1] = (invCosA * y * z) - (sinA * x);
|
||
ret[3][1] = 0.0F;
|
||
|
||
ret[0][2] = (invCosA * x * z) - (sinA * y);
|
||
ret[1][2] = (invCosA * y * z) + (sinA * x);
|
||
ret[2][2] = (invCosA * zSq) + (cosA);
|
||
ret[3][2] = 0.0F;
|
||
|
||
ret[0][3] = 0.0F;
|
||
ret[1][3] = 0.0F;
|
||
ret[2][3] = 0.0F;
|
||
ret[3][3] = 1.0F;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Return a 3D translation matrix44
|
||
matrix44 TranslateMatrix44(float x, float y, float z)
|
||
{
|
||
matrix44 ret;
|
||
|
||
ret.identity();
|
||
ret[3][0] = x;
|
||
ret[3][1] = y;
|
||
ret[3][2] = z;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Return a 3D/4D scale matrix44
|
||
matrix44 ScaleMatrix44(float x, float y, float z, float w)
|
||
{
|
||
matrix44 ret;
|
||
|
||
ret.identity();
|
||
ret[0][0] = x;
|
||
ret[1][1] = y;
|
||
ret[2][2] = z;
|
||
ret[3][3] = w;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Return a "lookat" matrix44 given the current camera position (vector3),
|
||
// camera-up vector3, and camera-target vector3.
|
||
matrix44 LookAtMatrix44(const vector3 &camPos, const vector3 &camUp,
|
||
const vector3 &target )
|
||
{
|
||
matrix44 ret;
|
||
|
||
vector3 F = target - camPos;
|
||
F.normalize();
|
||
|
||
vector3 upNorm = camUp;
|
||
upNorm.normalize();
|
||
|
||
vector3 s = CrossProduct(F, upNorm);
|
||
vector3 u = CrossProduct(s, F);
|
||
|
||
ret[0][0] = s[0]; ret[1][0] = s[1]; ret[2][0] = s[2]; ret[3][0] = 0.0F;
|
||
ret[0][1] = u[0]; ret[1][1] = u[1]; ret[2][1] = u[2]; ret[3][1] = 0.0F;
|
||
ret[0][2] =-F[0]; ret[1][2] =-F[1]; ret[2][2] =-F[2]; ret[3][2] = 0.0F;
|
||
ret[0][3] = 0.0F; ret[1][3] = 0.0F; ret[2][3] = 0.0F; ret[3][3] = 1.0F;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Return a frustum matrix44 given the left, right, bottom, top,
|
||
// near, and far values for the frustum boundaries.
|
||
matrix44 FrustumMatrix44(float l, float r,
|
||
float b, float t, float n, float f)
|
||
{
|
||
matrix44 ret;
|
||
float width = r-l;
|
||
float height = t-b;
|
||
float depth = f-n;
|
||
|
||
ret[0][0] = (2*n) / width;
|
||
ret[0][1] = 0.0F;
|
||
ret[0][2] = 0.0F;
|
||
ret[0][3] = 0.0F;
|
||
|
||
ret[1][0] = 0.0F;
|
||
ret[1][1] = (2*n) / height;
|
||
ret[1][2] = 0.0F;
|
||
ret[1][3] = 0.0F;
|
||
|
||
ret[2][0] = (r + l) / width;
|
||
ret[2][1] = (t + b) / height;
|
||
ret[2][2] = -(f + n) / depth;
|
||
ret[2][3] = -1.0F;
|
||
|
||
ret[3][0] = 0.0F;
|
||
ret[3][1] = 0.0F;
|
||
ret[3][2] = -(2*f*n) / depth;
|
||
ret[3][3] = 0.0F;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Return a perspective matrix44 given the field-of-view in the Y
|
||
// direction in degrees, the aspect ratio of Y/X, and near and
|
||
// far plane distances.
|
||
matrix44 PerspectiveMatrix44(float fovY, float aspect, float n, float f)
|
||
{
|
||
matrix44 ret;
|
||
float angle;
|
||
float cot;
|
||
|
||
angle = fovY / 2.0F;
|
||
angle = DegToRad( angle );
|
||
|
||
cot = (float) cos(angle) / (float) sin(angle);
|
||
|
||
ret[0][0] = cot / aspect;
|
||
ret[0][1] = 0.0F;
|
||
ret[0][2] = 0.0F;
|
||
ret[0][3] = 0.0F;
|
||
|
||
ret[1][0] = 0.0F;
|
||
ret[1][1] = cot;
|
||
ret[1][2] = 0.0F;
|
||
ret[1][3] = 0.0F;
|
||
|
||
ret[2][0] = 0.0F;
|
||
ret[2][1] = 0.0F;
|
||
ret[2][2] = -(f + n) / (f - n);
|
||
ret[2][3] = -1.0F;
|
||
|
||
|
||
ret[3][0] = 0.0F;
|
||
ret[3][1] = 0.0F;
|
||
ret[3][2] = -(2*f*n) / (f - n);
|
||
ret[3][3] = 0.0F;
|
||
|
||
return ret;
|
||
}
|
||
|
||
// Return an orthographic matrix44 given the left, right, bottom, top,
|
||
// near, and far values for the frustum boundaries.
|
||
matrix44 OrthoMatrix44(float l, float r,
|
||
float b, float t, float n, float f)
|
||
{
|
||
matrix44 ret;
|
||
float width = r-l;
|
||
float height = t-b;
|
||
float depth = f-n;
|
||
|
||
ret[0][0] = 2.0F / width;
|
||
ret[0][1] = 0.0F;
|
||
ret[0][2] = 0.0F;
|
||
ret[0][3] = 0.0F;
|
||
|
||
ret[1][0] = 0.0F;
|
||
ret[1][1] = 2.0F / height;
|
||
ret[1][2] = 0.0F;
|
||
ret[1][3] = 0.0F;
|
||
|
||
ret[2][0] = 0.0F;
|
||
ret[2][1] = 0.0F;
|
||
ret[2][2] = -(2.0F) / depth;
|
||
ret[2][3] = 0.0F;
|
||
|
||
ret[3][0] = -(r + l) / width;
|
||
ret[1][3] = -(t + b) / height;
|
||
ret[3][2] = -(f + n) / depth;
|
||
ret[3][3] = 1.0F;
|
||
|
||
return ret;
|
||
}
|
||
|
||
|
||
////////////////////////////////////////////////////////////
|
||
// Debug functions
|
||
//
|
||
|
||
// Print a vector2 to a file
|
||
void vector2::fprint(FILE* file, char* str) const
|
||
{
|
||
fprintf(file, "%svector2: <%f, %f>\n", str, x, y);
|
||
}
|
||
|
||
// Print a vector3 to a file
|
||
void vector3::fprint(FILE* file, char* str) const
|
||
{
|
||
fprintf(file, "%svector3: <%f, %f, %f>\n", str, x, y, z);
|
||
}
|
||
|
||
// Print a vector4 to a file
|
||
void vector4::fprint(FILE* file, char* str) const
|
||
{
|
||
fprintf(file, "%svector4: <%f, %f, %f, %f>\n", str, x, y, z, w);
|
||
}
|
||
|
||
// Print a matrix33 to a file
|
||
void matrix33::fprint(FILE* file, char * str) const
|
||
{
|
||
fprintf(file, "%smatrix33:\n", str);
|
||
col[0].fprint(file, "\t");
|
||
col[1].fprint(file, "\t");
|
||
col[2].fprint(file, "\t");
|
||
}
|
||
|
||
// Print a matrix44 to a file
|
||
void matrix44::fprint(FILE* file, char* str) const
|
||
{
|
||
fprintf(file, "%smatrix44:\n", str);
|
||
col[0].fprint(file, "\t");
|
||
col[1].fprint(file, "\t");
|
||
col[2].fprint(file, "\t");
|
||
col[3].fprint(file, "\t");
|
||
}
|