769 lines
24 KiB
C
769 lines
24 KiB
C
|
/*
|
||
|
|
-----------------------------------------------------------------------------
|
||
|
|
This source file is part of OGRE
|
||
|
|
(Object-oriented Graphics Rendering Engine)
|
||
|
|
For the latest info, see http://www.ogre3d.org/
|
||
|
|
|
||
|
|
Copyright (c) 2000-2009 Torus Knot Software Ltd
|
||
|
|
|
||
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||
|
|
of this software and associated documentation files (the "Software"), to deal
|
||
|
|
in the Software without restriction, including without limitation the rights
|
||
|
|
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||
|
|
copies of the Software, and to permit persons to whom the Software is
|
||
|
|
furnished to do so, subject to the following conditions:
|
||
|
|
|
||
|
|
The above copyright notice and this permission notice shall be included in
|
||
|
|
all copies or substantial portions of the Software.
|
||
|
|
|
||
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||
|
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||
|
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
||
|
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||
|
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
||
|
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
|
||
|
|
THE SOFTWARE.
|
||
|
|
-----------------------------------------------------------------------------
|
||
|
|
*/
|
||
|
|
#ifndef __Vector3_H__
|
||
|
|
#define __Vector3_H__
|
||
|
|
|
||
|
|
#include "OgrePrerequisites.h"
|
||
|
|
#include "OgreMath.h"
|
||
|
|
#include "OgreQuaternion.h"
|
||
|
|
|
||
|
|
namespace Ogre
|
||
|
|
{
|
||
|
|
|
||
|
|
/** \addtogroup Core
|
||
|
|
* @{
|
||
|
|
*/
|
||
|
|
/** \addtogroup Math
|
||
|
|
* @{
|
||
|
|
*/
|
||
|
|
/** Standard 3-dimensional vector.
|
||
|
|
@remarks
|
||
|
|
A direction in 3D space represented as distances along the 3
|
||
|
|
orthogonal axes (x, y, z). Note that positions, directions and
|
||
|
|
scaling factors can be represented by a vector, depending on how
|
||
|
|
you interpret the values.
|
||
|
|
*/
|
||
|
|
class Vector3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
Real x, y, z;
|
||
|
|
|
||
|
|
public:
|
||
|
|
inline Vector3()
|
||
|
|
{
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3( const Real fX, const Real fY, const Real fZ )
|
||
|
|
: x( fX ), y( fY ), z( fZ )
|
||
|
|
{
|
||
|
|
}
|
||
|
|
|
||
|
|
inline explicit Vector3( const Real afCoordinate[3] )
|
||
|
|
: x( afCoordinate[0] ),
|
||
|
|
y( afCoordinate[1] ),
|
||
|
|
z( afCoordinate[2] )
|
||
|
|
{
|
||
|
|
}
|
||
|
|
|
||
|
|
inline explicit Vector3( const int afCoordinate[3] )
|
||
|
|
{
|
||
|
|
x = (Real)afCoordinate[0];
|
||
|
|
y = (Real)afCoordinate[1];
|
||
|
|
z = (Real)afCoordinate[2];
|
||
|
|
}
|
||
|
|
|
||
|
|
inline explicit Vector3( Real* const r )
|
||
|
|
: x( r[0] ), y( r[1] ), z( r[2] )
|
||
|
|
{
|
||
|
|
}
|
||
|
|
|
||
|
|
inline explicit Vector3( const Real scaler )
|
||
|
|
: x( scaler )
|
||
|
|
, y( scaler )
|
||
|
|
, z( scaler )
|
||
|
|
{
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/** Exchange the contents of this vector with another.
|
||
|
|
*/
|
||
|
|
inline void swap(Vector3& other)
|
||
|
|
{
|
||
|
|
std::swap(x, other.x);
|
||
|
|
std::swap(y, other.y);
|
||
|
|
std::swap(z, other.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Real operator [] ( const size_t i ) const
|
||
|
|
{
|
||
|
|
assert( i < 3 );
|
||
|
|
|
||
|
|
return *(&x+i);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Real& operator [] ( const size_t i )
|
||
|
|
{
|
||
|
|
assert( i < 3 );
|
||
|
|
|
||
|
|
return *(&x+i);
|
||
|
|
}
|
||
|
|
/// Pointer accessor for direct copying
|
||
|
|
inline Real* ptr()
|
||
|
|
{
|
||
|
|
return &x;
|
||
|
|
}
|
||
|
|
/// Pointer accessor for direct copying
|
||
|
|
inline const Real* ptr() const
|
||
|
|
{
|
||
|
|
return &x;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Assigns the value of the other vector.
|
||
|
|
@param
|
||
|
|
rkVector The other vector
|
||
|
|
*/
|
||
|
|
inline Vector3& operator = ( const Vector3& rkVector )
|
||
|
|
{
|
||
|
|
x = rkVector.x;
|
||
|
|
y = rkVector.y;
|
||
|
|
z = rkVector.z;
|
||
|
|
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3& operator = ( const Real fScaler )
|
||
|
|
{
|
||
|
|
x = fScaler;
|
||
|
|
y = fScaler;
|
||
|
|
z = fScaler;
|
||
|
|
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline bool operator == ( const Vector3& rkVector ) const
|
||
|
|
{
|
||
|
|
return ( x == rkVector.x && y == rkVector.y && z == rkVector.z );
|
||
|
|
}
|
||
|
|
|
||
|
|
inline bool operator != ( const Vector3& rkVector ) const
|
||
|
|
{
|
||
|
|
return ( x != rkVector.x || y != rkVector.y || z != rkVector.z );
|
||
|
|
}
|
||
|
|
|
||
|
|
// arithmetic operations
|
||
|
|
inline Vector3 operator + ( const Vector3& rkVector ) const
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
x + rkVector.x,
|
||
|
|
y + rkVector.y,
|
||
|
|
z + rkVector.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3 operator - ( const Vector3& rkVector ) const
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
x - rkVector.x,
|
||
|
|
y - rkVector.y,
|
||
|
|
z - rkVector.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3 operator * ( const Real fScalar ) const
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
x * fScalar,
|
||
|
|
y * fScalar,
|
||
|
|
z * fScalar);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3 operator * ( const Vector3& rhs) const
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
x * rhs.x,
|
||
|
|
y * rhs.y,
|
||
|
|
z * rhs.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3 operator / ( const Real fScalar ) const
|
||
|
|
{
|
||
|
|
assert( fScalar != 0.0 );
|
||
|
|
|
||
|
|
Real fInv = 1.0f / fScalar;
|
||
|
|
|
||
|
|
return Vector3(
|
||
|
|
x * fInv,
|
||
|
|
y * fInv,
|
||
|
|
z * fInv);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3 operator / ( const Vector3& rhs) const
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
x / rhs.x,
|
||
|
|
y / rhs.y,
|
||
|
|
z / rhs.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline const Vector3& operator + () const
|
||
|
|
{
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3 operator - () const
|
||
|
|
{
|
||
|
|
return Vector3(-x, -y, -z);
|
||
|
|
}
|
||
|
|
|
||
|
|
// overloaded operators to help Vector3
|
||
|
|
inline friend Vector3 operator * ( const Real fScalar, const Vector3& rkVector )
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
fScalar * rkVector.x,
|
||
|
|
fScalar * rkVector.y,
|
||
|
|
fScalar * rkVector.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline friend Vector3 operator / ( const Real fScalar, const Vector3& rkVector )
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
fScalar / rkVector.x,
|
||
|
|
fScalar / rkVector.y,
|
||
|
|
fScalar / rkVector.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline friend Vector3 operator + (const Vector3& lhs, const Real rhs)
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
lhs.x + rhs,
|
||
|
|
lhs.y + rhs,
|
||
|
|
lhs.z + rhs);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline friend Vector3 operator + (const Real lhs, const Vector3& rhs)
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
lhs + rhs.x,
|
||
|
|
lhs + rhs.y,
|
||
|
|
lhs + rhs.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline friend Vector3 operator - (const Vector3& lhs, const Real rhs)
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
lhs.x - rhs,
|
||
|
|
lhs.y - rhs,
|
||
|
|
lhs.z - rhs);
|
||
|
|
}
|
||
|
|
|
||
|
|
inline friend Vector3 operator - (const Real lhs, const Vector3& rhs)
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
lhs - rhs.x,
|
||
|
|
lhs - rhs.y,
|
||
|
|
lhs - rhs.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
// arithmetic updates
|
||
|
|
inline Vector3& operator += ( const Vector3& rkVector )
|
||
|
|
{
|
||
|
|
x += rkVector.x;
|
||
|
|
y += rkVector.y;
|
||
|
|
z += rkVector.z;
|
||
|
|
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3& operator += ( const Real fScalar )
|
||
|
|
{
|
||
|
|
x += fScalar;
|
||
|
|
y += fScalar;
|
||
|
|
z += fScalar;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3& operator -= ( const Vector3& rkVector )
|
||
|
|
{
|
||
|
|
x -= rkVector.x;
|
||
|
|
y -= rkVector.y;
|
||
|
|
z -= rkVector.z;
|
||
|
|
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3& operator -= ( const Real fScalar )
|
||
|
|
{
|
||
|
|
x -= fScalar;
|
||
|
|
y -= fScalar;
|
||
|
|
z -= fScalar;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3& operator *= ( const Real fScalar )
|
||
|
|
{
|
||
|
|
x *= fScalar;
|
||
|
|
y *= fScalar;
|
||
|
|
z *= fScalar;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3& operator *= ( const Vector3& rkVector )
|
||
|
|
{
|
||
|
|
x *= rkVector.x;
|
||
|
|
y *= rkVector.y;
|
||
|
|
z *= rkVector.z;
|
||
|
|
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3& operator /= ( const Real fScalar )
|
||
|
|
{
|
||
|
|
assert( fScalar != 0.0 );
|
||
|
|
|
||
|
|
Real fInv = 1.0f / fScalar;
|
||
|
|
|
||
|
|
x *= fInv;
|
||
|
|
y *= fInv;
|
||
|
|
z *= fInv;
|
||
|
|
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
inline Vector3& operator /= ( const Vector3& rkVector )
|
||
|
|
{
|
||
|
|
x /= rkVector.x;
|
||
|
|
y /= rkVector.y;
|
||
|
|
z /= rkVector.z;
|
||
|
|
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/** Returns the length (magnitude) of the vector.
|
||
|
|
@warning
|
||
|
|
This operation requires a square root and is expensive in
|
||
|
|
terms of CPU operations. If you don't need to know the exact
|
||
|
|
length (e.g. for just comparing lengths) use squaredLength()
|
||
|
|
instead.
|
||
|
|
*/
|
||
|
|
inline Real length () const
|
||
|
|
{
|
||
|
|
return Math::Sqrt( x * x + y * y + z * z );
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns the square of the length(magnitude) of the vector.
|
||
|
|
@remarks
|
||
|
|
This method is for efficiency - calculating the actual
|
||
|
|
length of a vector requires a square root, which is expensive
|
||
|
|
in terms of the operations required. This method returns the
|
||
|
|
square of the length of the vector, i.e. the same as the
|
||
|
|
length but before the square root is taken. Use this if you
|
||
|
|
want to find the longest / shortest vector without incurring
|
||
|
|
the square root.
|
||
|
|
*/
|
||
|
|
inline Real squaredLength () const
|
||
|
|
{
|
||
|
|
return x * x + y * y + z * z;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns the distance to another vector.
|
||
|
|
@warning
|
||
|
|
This operation requires a square root and is expensive in
|
||
|
|
terms of CPU operations. If you don't need to know the exact
|
||
|
|
distance (e.g. for just comparing distances) use squaredDistance()
|
||
|
|
instead.
|
||
|
|
*/
|
||
|
|
inline Real distance(const Vector3& rhs) const
|
||
|
|
{
|
||
|
|
return (*this - rhs).length();
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns the square of the distance to another vector.
|
||
|
|
@remarks
|
||
|
|
This method is for efficiency - calculating the actual
|
||
|
|
distance to another vector requires a square root, which is
|
||
|
|
expensive in terms of the operations required. This method
|
||
|
|
returns the square of the distance to another vector, i.e.
|
||
|
|
the same as the distance but before the square root is taken.
|
||
|
|
Use this if you want to find the longest / shortest distance
|
||
|
|
without incurring the square root.
|
||
|
|
*/
|
||
|
|
inline Real squaredDistance(const Vector3& rhs) const
|
||
|
|
{
|
||
|
|
return (*this - rhs).squaredLength();
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Calculates the dot (scalar) product of this vector with another.
|
||
|
|
@remarks
|
||
|
|
The dot product can be used to calculate the angle between 2
|
||
|
|
vectors. If both are unit vectors, the dot product is the
|
||
|
|
cosine of the angle; otherwise the dot product must be
|
||
|
|
divided by the product of the lengths of both vectors to get
|
||
|
|
the cosine of the angle. This result can further be used to
|
||
|
|
calculate the distance of a point from a plane.
|
||
|
|
@param
|
||
|
|
vec Vector with which to calculate the dot product (together
|
||
|
|
with this one).
|
||
|
|
@returns
|
||
|
|
A float representing the dot product value.
|
||
|
|
*/
|
||
|
|
inline Real dotProduct(const Vector3& vec) const
|
||
|
|
{
|
||
|
|
return x * vec.x + y * vec.y + z * vec.z;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Calculates the absolute dot (scalar) product of this vector with another.
|
||
|
|
@remarks
|
||
|
|
This function work similar dotProduct, except it use absolute value
|
||
|
|
of each component of the vector to computing.
|
||
|
|
@param
|
||
|
|
vec Vector with which to calculate the absolute dot product (together
|
||
|
|
with this one).
|
||
|
|
@returns
|
||
|
|
A Real representing the absolute dot product value.
|
||
|
|
*/
|
||
|
|
inline Real absDotProduct(const Vector3& vec) const
|
||
|
|
{
|
||
|
|
return Math::Abs(x * vec.x) + Math::Abs(y * vec.y) + Math::Abs(z * vec.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Normalises the vector.
|
||
|
|
@remarks
|
||
|
|
This method normalises the vector such that it's
|
||
|
|
length / magnitude is 1. The result is called a unit vector.
|
||
|
|
@note
|
||
|
|
This function will not crash for zero-sized vectors, but there
|
||
|
|
will be no changes made to their components.
|
||
|
|
@returns The previous length of the vector.
|
||
|
|
*/
|
||
|
|
inline Real normalise()
|
||
|
|
{
|
||
|
|
Real fLength = Math::Sqrt( x * x + y * y + z * z );
|
||
|
|
|
||
|
|
// Will also work for zero-sized vectors, but will change nothing
|
||
|
|
if ( fLength > 1e-08 )
|
||
|
|
{
|
||
|
|
Real fInvLength = 1.0f / fLength;
|
||
|
|
x *= fInvLength;
|
||
|
|
y *= fInvLength;
|
||
|
|
z *= fInvLength;
|
||
|
|
}
|
||
|
|
|
||
|
|
return fLength;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Calculates the cross-product of 2 vectors, i.e. the vector that
|
||
|
|
lies perpendicular to them both.
|
||
|
|
@remarks
|
||
|
|
The cross-product is normally used to calculate the normal
|
||
|
|
vector of a plane, by calculating the cross-product of 2
|
||
|
|
non-equivalent vectors which lie on the plane (e.g. 2 edges
|
||
|
|
of a triangle).
|
||
|
|
@param
|
||
|
|
vec Vector which, together with this one, will be used to
|
||
|
|
calculate the cross-product.
|
||
|
|
@returns
|
||
|
|
A vector which is the result of the cross-product. This
|
||
|
|
vector will <b>NOT</b> be normalised, to maximise efficiency
|
||
|
|
- call Vector3::normalise on the result if you wish this to
|
||
|
|
be done. As for which side the resultant vector will be on, the
|
||
|
|
returned vector will be on the side from which the arc from 'this'
|
||
|
|
to rkVector is anticlockwise, e.g. UNIT_Y.crossProduct(UNIT_Z)
|
||
|
|
= UNIT_X, whilst UNIT_Z.crossProduct(UNIT_Y) = -UNIT_X.
|
||
|
|
This is because OGRE uses a right-handed coordinate system.
|
||
|
|
@par
|
||
|
|
For a clearer explanation, look a the left and the bottom edges
|
||
|
|
of your monitor's screen. Assume that the first vector is the
|
||
|
|
left edge and the second vector is the bottom edge, both of
|
||
|
|
them starting from the lower-left corner of the screen. The
|
||
|
|
resulting vector is going to be perpendicular to both of them
|
||
|
|
and will go <i>inside</i> the screen, towards the cathode tube
|
||
|
|
(assuming you're using a CRT monitor, of course).
|
||
|
|
*/
|
||
|
|
inline Vector3 crossProduct( const Vector3& rkVector ) const
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
y * rkVector.z - z * rkVector.y,
|
||
|
|
z * rkVector.x - x * rkVector.z,
|
||
|
|
x * rkVector.y - y * rkVector.x);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns a vector at a point half way between this and the passed
|
||
|
|
in vector.
|
||
|
|
*/
|
||
|
|
inline Vector3 midPoint( const Vector3& vec ) const
|
||
|
|
{
|
||
|
|
return Vector3(
|
||
|
|
( x + vec.x ) * 0.5f,
|
||
|
|
( y + vec.y ) * 0.5f,
|
||
|
|
( z + vec.z ) * 0.5f );
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns true if the vector's scalar components are all greater
|
||
|
|
that the ones of the vector it is compared against.
|
||
|
|
*/
|
||
|
|
inline bool operator < ( const Vector3& rhs ) const
|
||
|
|
{
|
||
|
|
if( x < rhs.x && y < rhs.y && z < rhs.z )
|
||
|
|
return true;
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns true if the vector's scalar components are all smaller
|
||
|
|
that the ones of the vector it is compared against.
|
||
|
|
*/
|
||
|
|
inline bool operator > ( const Vector3& rhs ) const
|
||
|
|
{
|
||
|
|
if( x > rhs.x && y > rhs.y && z > rhs.z )
|
||
|
|
return true;
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Sets this vector's components to the minimum of its own and the
|
||
|
|
ones of the passed in vector.
|
||
|
|
@remarks
|
||
|
|
'Minimum' in this case means the combination of the lowest
|
||
|
|
value of x, y and z from both vectors. Lowest is taken just
|
||
|
|
numerically, not magnitude, so -1 < 0.
|
||
|
|
*/
|
||
|
|
inline void makeFloor( const Vector3& cmp )
|
||
|
|
{
|
||
|
|
if( cmp.x < x ) x = cmp.x;
|
||
|
|
if( cmp.y < y ) y = cmp.y;
|
||
|
|
if( cmp.z < z ) z = cmp.z;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Sets this vector's components to the maximum of its own and the
|
||
|
|
ones of the passed in vector.
|
||
|
|
@remarks
|
||
|
|
'Maximum' in this case means the combination of the highest
|
||
|
|
value of x, y and z from both vectors. Highest is taken just
|
||
|
|
numerically, not magnitude, so 1 > -3.
|
||
|
|
*/
|
||
|
|
inline void makeCeil( const Vector3& cmp )
|
||
|
|
{
|
||
|
|
if( cmp.x > x ) x = cmp.x;
|
||
|
|
if( cmp.y > y ) y = cmp.y;
|
||
|
|
if( cmp.z > z ) z = cmp.z;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Generates a vector perpendicular to this vector (eg an 'up' vector).
|
||
|
|
@remarks
|
||
|
|
This method will return a vector which is perpendicular to this
|
||
|
|
vector. There are an infinite number of possibilities but this
|
||
|
|
method will guarantee to generate one of them. If you need more
|
||
|
|
control you should use the Quaternion class.
|
||
|
|
*/
|
||
|
|
inline Vector3 perpendicular(void) const
|
||
|
|
{
|
||
|
|
static const Real fSquareZero = (Real)(1e-06 * 1e-06);
|
||
|
|
|
||
|
|
Vector3 perp = this->crossProduct( Vector3::UNIT_X );
|
||
|
|
|
||
|
|
// Check length
|
||
|
|
if( perp.squaredLength() < fSquareZero )
|
||
|
|
{
|
||
|
|
/* This vector is the Y axis multiplied by a scalar, so we have
|
||
|
|
to use another axis.
|
||
|
|
*/
|
||
|
|
perp = this->crossProduct( Vector3::UNIT_Y );
|
||
|
|
}
|
||
|
|
perp.normalise();
|
||
|
|
|
||
|
|
return perp;
|
||
|
|
}
|
||
|
|
/** Generates a new random vector which deviates from this vector by a
|
||
|
|
given angle in a random direction.
|
||
|
|
@remarks
|
||
|
|
This method assumes that the random number generator has already
|
||
|
|
been seeded appropriately.
|
||
|
|
@param
|
||
|
|
angle The angle at which to deviate
|
||
|
|
@param
|
||
|
|
up Any vector perpendicular to this one (which could generated
|
||
|
|
by cross-product of this vector and any other non-colinear
|
||
|
|
vector). If you choose not to provide this the function will
|
||
|
|
derive one on it's own, however if you provide one yourself the
|
||
|
|
function will be faster (this allows you to reuse up vectors if
|
||
|
|
you call this method more than once)
|
||
|
|
@returns
|
||
|
|
A random vector which deviates from this vector by angle. This
|
||
|
|
vector will not be normalised, normalise it if you wish
|
||
|
|
afterwards.
|
||
|
|
*/
|
||
|
|
inline Vector3 randomDeviant(
|
||
|
|
const Radian& angle,
|
||
|
|
const Vector3& up = Vector3::ZERO ) const
|
||
|
|
{
|
||
|
|
Vector3 newUp;
|
||
|
|
|
||
|
|
if (up == Vector3::ZERO)
|
||
|
|
{
|
||
|
|
// Generate an up vector
|
||
|
|
newUp = this->perpendicular();
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
newUp = up;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Rotate up vector by random amount around this
|
||
|
|
Quaternion q;
|
||
|
|
q.FromAngleAxis( Radian(Math::UnitRandom() * Math::TWO_PI), *this );
|
||
|
|
newUp = q * newUp;
|
||
|
|
|
||
|
|
// Finally rotate this by given angle around randomised up
|
||
|
|
q.FromAngleAxis( angle, newUp );
|
||
|
|
return q * (*this);
|
||
|
|
}
|
||
|
|
/** Gets the shortest arc quaternion to rotate this vector to the destination
|
||
|
|
vector.
|
||
|
|
@remarks
|
||
|
|
If you call this with a dest vector that is close to the inverse
|
||
|
|
of this vector, we will rotate 180 degrees around the 'fallbackAxis'
|
||
|
|
(if specified, or a generated axis if not) since in this case
|
||
|
|
ANY axis of rotation is valid.
|
||
|
|
*/
|
||
|
|
Quaternion getRotationTo(const Vector3& dest,
|
||
|
|
const Vector3& fallbackAxis = Vector3::ZERO) const
|
||
|
|
{
|
||
|
|
// Based on Stan Melax's article in Game Programming Gems
|
||
|
|
Quaternion q;
|
||
|
|
// Copy, since cannot modify local
|
||
|
|
Vector3 v0 = *this;
|
||
|
|
Vector3 v1 = dest;
|
||
|
|
v0.normalise();
|
||
|
|
v1.normalise();
|
||
|
|
|
||
|
|
Real d = v0.dotProduct(v1);
|
||
|
|
// If dot == 1, vectors are the same
|
||
|
|
if (d >= 1.0f)
|
||
|
|
{
|
||
|
|
return Quaternion::IDENTITY;
|
||
|
|
}
|
||
|
|
if (d < (1e-6f - 1.0f))
|
||
|
|
{
|
||
|
|
if (fallbackAxis != Vector3::ZERO)
|
||
|
|
{
|
||
|
|
// rotate 180 degrees about the fallback axis
|
||
|
|
q.FromAngleAxis(Radian(Math::OGRE_PI), fallbackAxis);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// Generate an axis
|
||
|
|
Vector3 axis = Vector3::UNIT_X.crossProduct(*this);
|
||
|
|
if (axis.isZeroLength()) // pick another if colinear
|
||
|
|
axis = Vector3::UNIT_Y.crossProduct(*this);
|
||
|
|
axis.normalise();
|
||
|
|
q.FromAngleAxis(Radian(Math::OGRE_PI), axis);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
Real s = Math::Sqrt( (1+d)*2 );
|
||
|
|
Real invs = 1 / s;
|
||
|
|
|
||
|
|
Vector3 c = v0.crossProduct(v1);
|
||
|
|
|
||
|
|
q.x = c.x * invs;
|
||
|
|
q.y = c.y * invs;
|
||
|
|
q.z = c.z * invs;
|
||
|
|
q.w = s * 0.5f;
|
||
|
|
q.normalise();
|
||
|
|
}
|
||
|
|
return q;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns true if this vector is zero length. */
|
||
|
|
inline bool isZeroLength(void) const
|
||
|
|
{
|
||
|
|
Real sqlen = (x * x) + (y * y) + (z * z);
|
||
|
|
return (sqlen < (1e-06 * 1e-06));
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
/** As normalise, except that this vector is unaffected and the
|
||
|
|
normalised vector is returned as a copy. */
|
||
|
|
inline Vector3 normalisedCopy(void) const
|
||
|
|
{
|
||
|
|
Vector3 ret = *this;
|
||
|
|
ret.normalise();
|
||
|
|
return ret;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Calculates a reflection vector to the plane with the given normal .
|
||
|
|
@remarks NB assumes 'this' is pointing AWAY FROM the plane, invert if it is not.
|
||
|
|
*/
|
||
|
|
inline Vector3 reflect(const Vector3& normal) const
|
||
|
|
{
|
||
|
|
return Vector3( *this - ( 2 * this->dotProduct(normal) * normal ) );
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns whether this vector is within a positional tolerance
|
||
|
|
of another vector.
|
||
|
|
@param rhs The vector to compare with
|
||
|
|
@param tolerance The amount that each element of the vector may vary by
|
||
|
|
and still be considered equal
|
||
|
|
*/
|
||
|
|
inline bool positionEquals(const Vector3& rhs, Real tolerance = 1e-03) const
|
||
|
|
{
|
||
|
|
return Math::RealEqual(x, rhs.x, tolerance) &&
|
||
|
|
Math::RealEqual(y, rhs.y, tolerance) &&
|
||
|
|
Math::RealEqual(z, rhs.z, tolerance);
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns whether this vector is within a positional tolerance
|
||
|
|
of another vector, also take scale of the vectors into account.
|
||
|
|
@param rhs The vector to compare with
|
||
|
|
@param tolerance The amount (related to the scale of vectors) that distance
|
||
|
|
of the vector may vary by and still be considered close
|
||
|
|
*/
|
||
|
|
inline bool positionCloses(const Vector3& rhs, Real tolerance = 1e-03f) const
|
||
|
|
{
|
||
|
|
return squaredDistance(rhs) <=
|
||
|
|
(squaredLength() + rhs.squaredLength()) * tolerance;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Returns whether this vector is within a directional tolerance
|
||
|
|
of another vector.
|
||
|
|
@param rhs The vector to compare with
|
||
|
|
@param tolerance The maximum angle by which the vectors may vary and
|
||
|
|
still be considered equal
|
||
|
|
@note Both vectors should be normalised.
|
||
|
|
*/
|
||
|
|
inline bool directionEquals(const Vector3& rhs,
|
||
|
|
const Radian& tolerance) const
|
||
|
|
{
|
||
|
|
Real dot = dotProduct(rhs);
|
||
|
|
Radian angle = Math::ACos(dot);
|
||
|
|
|
||
|
|
return Math::Abs(angle.valueRadians()) <= tolerance.valueRadians();
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
/// Check whether this vector contains valid values
|
||
|
|
inline bool isNaN() const
|
||
|
|
{
|
||
|
|
return Math::isNaN(x) || Math::isNaN(y) || Math::isNaN(z);
|
||
|
|
}
|
||
|
|
|
||
|
|
// special points
|
||
|
|
static const Vector3 ZERO;
|
||
|
|
static const Vector3 UNIT_X;
|
||
|
|
static const Vector3 UNIT_Y;
|
||
|
|
static const Vector3 UNIT_Z;
|
||
|
|
static const Vector3 NEGATIVE_UNIT_X;
|
||
|
|
static const Vector3 NEGATIVE_UNIT_Y;
|
||
|
|
static const Vector3 NEGATIVE_UNIT_Z;
|
||
|
|
static const Vector3 UNIT_SCALE;
|
||
|
|
};
|
||
|
|
/** @} */
|
||
|
|
/** @} */
|
||
|
|
|
||
|
|
}
|
||
|
|
#endif
|