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// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: t -*-
// Copyright 2010 Michael Smith, all rights reserved.
// This library is free software; you can redistribute it and / or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// Derived closely from:
/****************************************
* 3D Vector Classes
* By Bill Perone (billperone@yahoo.com)
* Original: 9-16-2002
* Revised: 19-11-2003
* 11-12-2003
* 18-12-2003
* 06-06-2004
*
* � 2003, This code is provided "as is" and you can use it freely as long as
* credit is given to Bill Perone in the application it is used in
*
* Notes:
* if a*b = 0 then a & b are orthogonal
* a%b = -b%a
* a*(b%c) = (a%b)*c
* a%b = a(cast to matrix)*b
* (a%b).length() = area of parallelogram formed by a & b
* (a%b).length() = a.length()*b.length() * sin(angle between a & b)
* (a%b).length() = 0 if angle between a & b = 0 or a.length() = 0 or b.length() = 0
* a * (b%c) = volume of parallelpiped formed by a, b, c
* vector triple product: a%(b%c) = b*(a*c) - c*(a*b)
* scalar triple product: a*(b%c) = c*(a%b) = b*(c%a)
* vector quadruple product: (a%b)*(c%d) = (a*c)*(b*d) - (a*d)*(b*c)
* if a is unit vector along b then a%b = -b%a = -b(cast to matrix)*a = 0
* vectors a1...an are linearly dependant if there exists a vector of scalars (b) where a1*b1 + ... + an*bn = 0
* or if the matrix (A) * b = 0
*
****************************************/
#ifndef VECTOR3_H
#define VECTOR3_H
#include <math.h>
#include <string.h>
#include "Constants.h"
#include "Vector3.h"
template <typename T>
class Vector3
{
public:
T x, y, z;
// trivial ctor
Vector3<T>() { x = y = z = 0; }
// setting ctor
Vector3<T>(const T x0, const T y0, const T z0): x(x0), y(y0), z(z0) {}
// function call operator
void operator ()(const T x0, const T y0, const T z0)
{ x= x0; y= y0; z= z0; }
// indexing operator
T operator [](uint8_t i)
{ switch(i) {
case 0: return x;
case 1: return y;
case 2: return z;
default: return 0;
}
}
// test for equality
bool operator==(const Vector3<T> &v)
{ return (x==v.x && y==v.y && z==v.z); }
// test for inequality
bool operator!=(const Vector3<T> &v)
{ return (x!=v.x || y!=v.y || z!=v.z); }
// negation
Vector3<T> operator -(void) const
{ return Vector3<T>(-x,-y,-z); }
// addition
Vector3<T> operator +(const Vector3<T> &v) const
{ return Vector3<T>(x+v.x, y+v.y, z+v.z); }
// subtraction
Vector3<T> operator -(const Vector3<T> &v) const
{ return Vector3<T>(x-v.x, y-v.y, z-v.z); }
// uniform scaling
Vector3<T> operator *(const T num) const
{
Vector3<T> temp(*this);
return temp*=num;
}
// uniform scaling
Vector3<T> operator /(const T num) const
{
Vector3<T> temp(*this);
return temp/=num;
}
// addition
Vector3<T> &operator +=(const Vector3<T> &v)
{
x+=v.x; y+=v.y; z+=v.z;
return *this;
}
// subtraction
Vector3<T> &operator -=(const Vector3<T> &v)
{
x-=v.x; y-=v.y; z-=v.z;
return *this;
}
// uniform scaling
Vector3<T> &operator *=(const T num)
{
x*=num; y*=num; z*=num;
return *this;
}
// uniform scaling
Vector3<T> &operator /=(const T num)
{
x/=num; y/=num; z/=num;
return *this;
}
// dot product
T operator *(const Vector3<T> &v) const
{ return x*v.x + y*v.y + z*v.z; }
// cross product
Vector3<T> operator %(const Vector3<T> &v) const
{
Vector3<T> temp(y*v.z - z*v.y, z*v.x - x*v.z, x*v.y - y*v.x);
return temp;
}
// gets the length of this vector squared
T length_squared() const
{ return (T)(*this * *this); }
// gets the length of this vector
float length() const
{ return (T)sqrt(*this * *this); }
// normalizes this vector
void normalize()
{ *this/=length(); }
// zero the vector
void zero()
{ x = y = z = 0.0; }
// returns the normalized version of this vector
Vector3<T> normalized() const
{ return *this/length(); }
// reflects this vector about n
void reflect(const Vector3<T> &n)
{
Vector3<T> orig(*this);
project(n);
*this= *this*2 - orig;
}
// projects this vector onto v
void project(const Vector3<T> &v)
{ *this= v * (*this * v)/(v*v); }
// returns this vector projected onto v
Vector3<T> projected(const Vector3<T> &v)
{ return v * (*this * v)/(v*v); }
// computes the angle between 2 arbitrary vectors
T angle(const Vector3<T> &v1, const Vector3<T> &v2)
{ return (T)acosf((v1*v2) / (v1.length()*v2.length())); }
// computes the angle between 2 arbitrary normalized vectors
T angle_normalized(const Vector3<T> &v1, const Vector3<T> &v2)
{ return (T)acosf(v1*v2); }
// check if any elements are NAN
bool is_nan(void)
{ return isnan(x) || isnan(y) || isnan(z); }
// check if any elements are infinity
bool is_inf(void)
{ return isinf(x) || isinf(y) || isinf(z); }
// rotate by a standard rotation
void rotate(enum Rotation rotation);
};
typedef Vector3<int16_t> Vector3i;
typedef Vector3<uint16_t> Vector3ui;
typedef Vector3<int32_t> Vector3l;
typedef Vector3<uint32_t> Vector3ul;
typedef Vector3<float> Vector3f;
#endif // VECTOR3_H