mirror of
https://github.com/mii443/rust-openvr.git
synced 2025-08-22 16:25:36 +00:00
1 line
79 KiB
C
1 line
79 KiB
C
/************************************************************************************
|
|
|
|
PublicHeader: OVR.h
|
|
Filename : OVR_Math.h
|
|
Content : Implementation of 3D primitives such as vectors, matrices.
|
|
Created : September 4, 2012
|
|
Authors : Andrew Reisse, Michael Antonov, Steve LaValle,
|
|
Anna Yershova, Max Katsev, Dov Katz
|
|
|
|
Copyright : Copyright 2014 Oculus VR, Inc. All Rights reserved.
|
|
|
|
Licensed under the Oculus VR Rift SDK License Version 3.1 (the "License");
|
|
you may not use the Oculus VR Rift SDK except in compliance with the License,
|
|
which is provided at the time of installation or download, or which
|
|
otherwise accompanies this software in either electronic or hard copy form.
|
|
|
|
You may obtain a copy of the License at
|
|
|
|
http://www.oculusvr.com/licenses/LICENSE-3.1
|
|
|
|
Unless required by applicable law or agreed to in writing, the Oculus VR SDK
|
|
distributed under the License is distributed on an "AS IS" BASIS,
|
|
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
See the License for the specific language governing permissions and
|
|
limitations under the License.
|
|
|
|
*************************************************************************************/
|
|
|
|
#ifndef OVR_Math_h
|
|
#define OVR_Math_h
|
|
|
|
#include <assert.h>
|
|
#include <stdlib.h>
|
|
#include <math.h>
|
|
|
|
#include "OVR_Types.h"
|
|
#include "OVR_RefCount.h"
|
|
#include "OVR_Std.h"
|
|
#include "OVR_Alg.h"
|
|
|
|
|
|
namespace OVR {
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Constants for 3D world/axis definitions.
|
|
|
|
// Definitions of axes for coordinate and rotation conversions.
|
|
enum Axis
|
|
{
|
|
Axis_X = 0, Axis_Y = 1, Axis_Z = 2
|
|
};
|
|
|
|
// RotateDirection describes the rotation direction around an axis, interpreted as follows:
|
|
// CW - Clockwise while looking "down" from positive axis towards the origin.
|
|
// CCW - Counter-clockwise while looking from the positive axis towards the origin,
|
|
// which is in the negative axis direction.
|
|
// CCW is the default for the RHS coordinate system. Oculus standard RHS coordinate
|
|
// system defines Y up, X right, and Z back (pointing out from the screen). In this
|
|
// system Rotate_CCW around Z will specifies counter-clockwise rotation in XY plane.
|
|
enum RotateDirection
|
|
{
|
|
Rotate_CCW = 1,
|
|
Rotate_CW = -1
|
|
};
|
|
|
|
// Constants for right handed and left handed coordinate systems
|
|
enum HandedSystem
|
|
{
|
|
Handed_R = 1, Handed_L = -1
|
|
};
|
|
|
|
// AxisDirection describes which way the coordinate axis points. Used by WorldAxes.
|
|
enum AxisDirection
|
|
{
|
|
Axis_Up = 2,
|
|
Axis_Down = -2,
|
|
Axis_Right = 1,
|
|
Axis_Left = -1,
|
|
Axis_In = 3,
|
|
Axis_Out = -3
|
|
};
|
|
|
|
struct WorldAxes
|
|
{
|
|
AxisDirection XAxis, YAxis, ZAxis;
|
|
|
|
WorldAxes(AxisDirection x, AxisDirection y, AxisDirection z)
|
|
: XAxis(x), YAxis(y), ZAxis(z)
|
|
{ OVR_ASSERT(abs(x) != abs(y) && abs(y) != abs(z) && abs(z) != abs(x));}
|
|
};
|
|
|
|
} // namespace OVR
|
|
|
|
|
|
//------------------------------------------------------------------------------------//
|
|
// ***** C Compatibility Types
|
|
|
|
// These declarations are used to support conversion between C types used in
|
|
// LibOVR C interfaces and their C++ versions. As an example, they allow passing
|
|
// Vector3f into a function that expects ovrVector3f.
|
|
|
|
typedef struct ovrQuatf_ ovrQuatf;
|
|
typedef struct ovrQuatd_ ovrQuatd;
|
|
typedef struct ovrSizei_ ovrSizei;
|
|
typedef struct ovrSizef_ ovrSizef;
|
|
typedef struct ovrRecti_ ovrRecti;
|
|
typedef struct ovrVector2i_ ovrVector2i;
|
|
typedef struct ovrVector2f_ ovrVector2f;
|
|
typedef struct ovrVector3f_ ovrVector3f;
|
|
typedef struct ovrVector3d_ ovrVector3d;
|
|
typedef struct ovrMatrix3d_ ovrMatrix3d;
|
|
typedef struct ovrMatrix4f_ ovrMatrix4f;
|
|
typedef struct ovrPosef_ ovrPosef;
|
|
typedef struct ovrPosed_ ovrPosed;
|
|
typedef struct ovrPoseStatef_ ovrPoseStatef;
|
|
typedef struct ovrPoseStated_ ovrPoseStated;
|
|
|
|
namespace OVR {
|
|
|
|
// Forward-declare our templates.
|
|
template<class T> class Quat;
|
|
template<class T> class Size;
|
|
template<class T> class Rect;
|
|
template<class T> class Vector2;
|
|
template<class T> class Vector3;
|
|
template<class T> class Matrix3;
|
|
template<class T> class Matrix4;
|
|
template<class T> class Transform;
|
|
template<class T> class PoseState;
|
|
|
|
// CompatibleTypes::Type is used to lookup a compatible C-version of a C++ class.
|
|
template<class C>
|
|
struct CompatibleTypes
|
|
{
|
|
// Declaration here seems necessary for MSVC; specializations are
|
|
// used instead.
|
|
typedef float Type;
|
|
};
|
|
|
|
// Specializations providing CompatibleTypes::Type value.
|
|
template<> struct CompatibleTypes<Quat<float> > { typedef ovrQuatf Type; };
|
|
template<> struct CompatibleTypes<Quat<double> > { typedef ovrQuatd Type; };
|
|
template<> struct CompatibleTypes<Matrix3<double> > { typedef ovrMatrix3d Type; };
|
|
template<> struct CompatibleTypes<Matrix4<float> > { typedef ovrMatrix4f Type; };
|
|
template<> struct CompatibleTypes<Size<int> > { typedef ovrSizei Type; };
|
|
template<> struct CompatibleTypes<Size<float> > { typedef ovrSizef Type; };
|
|
template<> struct CompatibleTypes<Rect<int> > { typedef ovrRecti Type; };
|
|
template<> struct CompatibleTypes<Vector2<int> > { typedef ovrVector2i Type; };
|
|
template<> struct CompatibleTypes<Vector2<float> > { typedef ovrVector2f Type; };
|
|
template<> struct CompatibleTypes<Vector3<float> > { typedef ovrVector3f Type; };
|
|
template<> struct CompatibleTypes<Vector3<double> > { typedef ovrVector3d Type; };
|
|
|
|
template<> struct CompatibleTypes<Transform<float> > { typedef ovrPosef Type; };
|
|
template<> struct CompatibleTypes<PoseState<float> > { typedef ovrPoseStatef Type; };
|
|
|
|
template<> struct CompatibleTypes<Transform<double> > { typedef ovrPosed Type; };
|
|
template<> struct CompatibleTypes<PoseState<double> > { typedef ovrPoseStated Type; };
|
|
|
|
//------------------------------------------------------------------------------------//
|
|
// ***** Math
|
|
//
|
|
// Math class contains constants and functions. This class is a template specialized
|
|
// per type, with Math<float> and Math<double> being distinct.
|
|
template<class Type>
|
|
class Math
|
|
{
|
|
public:
|
|
// By default, support explicit conversion to float. This allows Vector2<int> to
|
|
// compile, for example.
|
|
typedef float OtherFloatType;
|
|
};
|
|
|
|
// Single-precision Math constants class.
|
|
template<>
|
|
class Math<float>
|
|
{
|
|
public:
|
|
static const float Pi;
|
|
static const float TwoPi;
|
|
static const float PiOver2;
|
|
static const float PiOver4;
|
|
static const float E;
|
|
|
|
static const float MaxValue; // Largest positive float Value
|
|
static const float MinPositiveValue; // Smallest possible positive value
|
|
|
|
static const float RadToDegreeFactor;
|
|
static const float DegreeToRadFactor;
|
|
|
|
static const float Tolerance; // 0.00001f;
|
|
static const float SingularityRadius; // 0.0000001f for Gimbal lock numerical problems
|
|
|
|
// Used to support direct conversions in template classes.
|
|
typedef double OtherFloatType;
|
|
};
|
|
|
|
// Double-precision Math constants class.
|
|
template<>
|
|
class Math<double>
|
|
{
|
|
public:
|
|
static const double Pi;
|
|
static const double TwoPi;
|
|
static const double PiOver2;
|
|
static const double PiOver4;
|
|
static const double E;
|
|
|
|
static const double MaxValue; // Largest positive double Value
|
|
static const double MinPositiveValue; // Smallest possible positive value
|
|
|
|
static const double RadToDegreeFactor;
|
|
static const double DegreeToRadFactor;
|
|
|
|
static const double Tolerance; // 0.00001;
|
|
static const double SingularityRadius; // 0.000000000001 for Gimbal lock numerical problems
|
|
|
|
typedef float OtherFloatType;
|
|
};
|
|
|
|
|
|
typedef Math<float> Mathf;
|
|
typedef Math<double> Mathd;
|
|
|
|
// Conversion functions between degrees and radians
|
|
template<class T>
|
|
T RadToDegree(T rads) { return rads * Math<T>::RadToDegreeFactor; }
|
|
template<class T>
|
|
T DegreeToRad(T rads) { return rads * Math<T>::DegreeToRadFactor; }
|
|
|
|
// Numerically stable acos function
|
|
template<class T>
|
|
T Acos(T val) {
|
|
if (val > T(1)) return T(0);
|
|
else if (val < T(-1)) return Math<T>::Pi;
|
|
else return acos(val);
|
|
};
|
|
|
|
// Numerically stable asin function
|
|
template<class T>
|
|
T Asin(T val) {
|
|
if (val > T(1)) return Math<T>::PiOver2;
|
|
else if (val < T(-1)) return Math<T>::PiOver2 * T(3);
|
|
else return asin(val);
|
|
};
|
|
|
|
#ifdef OVR_CC_MSVC
|
|
inline int isnan(double x) { return _isnan(x); };
|
|
#endif
|
|
|
|
template<class T>
|
|
class Quat;
|
|
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Vector2<>
|
|
|
|
// Vector2f (Vector2d) represents a 2-dimensional vector or point in space,
|
|
// consisting of coordinates x and y
|
|
|
|
template<class T>
|
|
class Vector2
|
|
{
|
|
public:
|
|
T x, y;
|
|
|
|
Vector2() : x(0), y(0) { }
|
|
Vector2(T x_, T y_) : x(x_), y(y_) { }
|
|
explicit Vector2(T s) : x(s), y(s) { }
|
|
explicit Vector2(const Vector2<typename Math<T>::OtherFloatType> &src)
|
|
: x((T)src.x), y((T)src.y) { }
|
|
|
|
|
|
// C-interop support.
|
|
typedef typename CompatibleTypes<Vector2<T> >::Type CompatibleType;
|
|
|
|
Vector2(const CompatibleType& s) : x(s.x), y(s.y) { }
|
|
|
|
operator const CompatibleType& () const
|
|
{
|
|
OVR_COMPILER_ASSERT(sizeof(Vector2<T>) == sizeof(CompatibleType));
|
|
return reinterpret_cast<const CompatibleType&>(*this);
|
|
}
|
|
|
|
|
|
bool operator== (const Vector2& b) const { return x == b.x && y == b.y; }
|
|
bool operator!= (const Vector2& b) const { return x != b.x || y != b.y; }
|
|
|
|
Vector2 operator+ (const Vector2& b) const { return Vector2(x + b.x, y + b.y); }
|
|
Vector2& operator+= (const Vector2& b) { x += b.x; y += b.y; return *this; }
|
|
Vector2 operator- (const Vector2& b) const { return Vector2(x - b.x, y - b.y); }
|
|
Vector2& operator-= (const Vector2& b) { x -= b.x; y -= b.y; return *this; }
|
|
Vector2 operator- () const { return Vector2(-x, -y); }
|
|
|
|
// Scalar multiplication/division scales vector.
|
|
Vector2 operator* (T s) const { return Vector2(x*s, y*s); }
|
|
Vector2& operator*= (T s) { x *= s; y *= s; return *this; }
|
|
|
|
Vector2 operator/ (T s) const { T rcp = T(1)/s;
|
|
return Vector2(x*rcp, y*rcp); }
|
|
Vector2& operator/= (T s) { T rcp = T(1)/s;
|
|
x *= rcp; y *= rcp;
|
|
return *this; }
|
|
|
|
static Vector2 Min(const Vector2& a, const Vector2& b) { return Vector2((a.x < b.x) ? a.x : b.x,
|
|
(a.y < b.y) ? a.y : b.y); }
|
|
static Vector2 Max(const Vector2& a, const Vector2& b) { return Vector2((a.x > b.x) ? a.x : b.x,
|
|
(a.y > b.y) ? a.y : b.y); }
|
|
|
|
// Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance.
|
|
bool Compare(const Vector2&b, T tolerance = Mathf::Tolerance)
|
|
{
|
|
return (fabs(b.x-x) < tolerance) && (fabs(b.y-y) < tolerance);
|
|
}
|
|
|
|
// Entrywise product of two vectors
|
|
Vector2 EntrywiseMultiply(const Vector2& b) const { return Vector2(x * b.x, y * b.y);}
|
|
|
|
|
|
// Multiply and divide operators do entry-wise math. Used Dot() for dot product.
|
|
Vector2 operator* (const Vector2& b) const { return Vector2(x * b.x, y * b.y); }
|
|
Vector2 operator/ (const Vector2& b) const { return Vector2(x / b.x, y / b.y); }
|
|
|
|
// Dot product
|
|
// Used to calculate angle q between two vectors among other things,
|
|
// as (A dot B) = |a||b|cos(q).
|
|
T Dot(const Vector2& b) const { return x*b.x + y*b.y; }
|
|
|
|
// Returns the angle from this vector to b, in radians.
|
|
T Angle(const Vector2& b) const
|
|
{
|
|
T div = LengthSq()*b.LengthSq();
|
|
OVR_ASSERT(div != T(0));
|
|
T result = Acos((this->Dot(b))/sqrt(div));
|
|
return result;
|
|
}
|
|
|
|
// Return Length of the vector squared.
|
|
T LengthSq() const { return (x * x + y * y); }
|
|
|
|
// Return vector length.
|
|
T Length() const { return sqrt(LengthSq()); }
|
|
|
|
// Returns squared distance between two points represented by vectors.
|
|
T DistanceSq(Vector2& b) const { return (*this - b).LengthSq(); }
|
|
|
|
// Returns distance between two points represented by vectors.
|
|
T Distance(Vector2& b) const { return (*this - b).Length(); }
|
|
|
|
// Determine if this a unit vector.
|
|
bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance; }
|
|
|
|
// Normalize, convention vector length to 1.
|
|
void Normalize()
|
|
{
|
|
T l = Length();
|
|
OVR_ASSERT(l != T(0));
|
|
*this /= l;
|
|
}
|
|
// Returns normalized (unit) version of the vector without modifying itself.
|
|
Vector2 Normalized() const
|
|
{
|
|
T l = Length();
|
|
OVR_ASSERT(l != T(0));
|
|
return *this / l;
|
|
}
|
|
|
|
// Linearly interpolates from this vector to another.
|
|
// Factor should be between 0.0 and 1.0, with 0 giving full value to this.
|
|
Vector2 Lerp(const Vector2& b, T f) const { return *this*(T(1) - f) + b*f; }
|
|
|
|
// Projects this vector onto the argument; in other words,
|
|
// A.Project(B) returns projection of vector A onto B.
|
|
Vector2 ProjectTo(const Vector2& b) const
|
|
{
|
|
T l2 = b.LengthSq();
|
|
OVR_ASSERT(l2 != T(0));
|
|
return b * ( Dot(b) / l2 );
|
|
}
|
|
};
|
|
|
|
|
|
typedef Vector2<float> Vector2f;
|
|
typedef Vector2<double> Vector2d;
|
|
typedef Vector2<int> Vector2i;
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Vector3<> - 3D vector of {x, y, z}
|
|
|
|
//
|
|
// Vector3f (Vector3d) represents a 3-dimensional vector or point in space,
|
|
// consisting of coordinates x, y and z.
|
|
|
|
template<class T>
|
|
class Vector3
|
|
{
|
|
public:
|
|
T x, y, z;
|
|
|
|
Vector3() : x(0), y(0), z(0) { }
|
|
Vector3(T x_, T y_, T z_ = 0) : x(x_), y(y_), z(z_) { }
|
|
explicit Vector3(T s) : x(s), y(s), z(s) { }
|
|
explicit Vector3(const Vector3<typename Math<T>::OtherFloatType> &src)
|
|
: x((T)src.x), y((T)src.y), z((T)src.z) { }
|
|
|
|
|
|
// C-interop support.
|
|
typedef typename CompatibleTypes<Vector3<T> >::Type CompatibleType;
|
|
|
|
Vector3(const CompatibleType& s) : x(s.x), y(s.y), z(s.z) { }
|
|
|
|
operator const CompatibleType& () const
|
|
{
|
|
OVR_COMPILER_ASSERT(sizeof(Vector3<T>) == sizeof(CompatibleType));
|
|
return reinterpret_cast<const CompatibleType&>(*this);
|
|
}
|
|
|
|
bool operator== (const Vector3& b) const { return x == b.x && y == b.y && z == b.z; }
|
|
bool operator!= (const Vector3& b) const { return x != b.x || y != b.y || z != b.z; }
|
|
|
|
Vector3 operator+ (const Vector3& b) const { return Vector3(x + b.x, y + b.y, z + b.z); }
|
|
Vector3& operator+= (const Vector3& b) { x += b.x; y += b.y; z += b.z; return *this; }
|
|
Vector3 operator- (const Vector3& b) const { return Vector3(x - b.x, y - b.y, z - b.z); }
|
|
Vector3& operator-= (const Vector3& b) { x -= b.x; y -= b.y; z -= b.z; return *this; }
|
|
Vector3 operator- () const { return Vector3(-x, -y, -z); }
|
|
|
|
// Scalar multiplication/division scales vector.
|
|
Vector3 operator* (T s) const { return Vector3(x*s, y*s, z*s); }
|
|
Vector3& operator*= (T s) { x *= s; y *= s; z *= s; return *this; }
|
|
|
|
Vector3 operator/ (T s) const { T rcp = T(1)/s;
|
|
return Vector3(x*rcp, y*rcp, z*rcp); }
|
|
Vector3& operator/= (T s) { T rcp = T(1)/s;
|
|
x *= rcp; y *= rcp; z *= rcp;
|
|
return *this; }
|
|
|
|
static Vector3 Min(const Vector3& a, const Vector3& b)
|
|
{
|
|
return Vector3((a.x < b.x) ? a.x : b.x,
|
|
(a.y < b.y) ? a.y : b.y,
|
|
(a.z < b.z) ? a.z : b.z);
|
|
}
|
|
static Vector3 Max(const Vector3& a, const Vector3& b)
|
|
{
|
|
return Vector3((a.x > b.x) ? a.x : b.x,
|
|
(a.y > b.y) ? a.y : b.y,
|
|
(a.z > b.z) ? a.z : b.z);
|
|
}
|
|
|
|
// Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance.
|
|
bool Compare(const Vector3&b, T tolerance = Mathf::Tolerance)
|
|
{
|
|
return (fabs(b.x-x) < tolerance) &&
|
|
(fabs(b.y-y) < tolerance) &&
|
|
(fabs(b.z-z) < tolerance);
|
|
}
|
|
|
|
T& operator[] (int idx)
|
|
{
|
|
OVR_ASSERT(0 <= idx && idx < 3);
|
|
return *(&x + idx);
|
|
}
|
|
|
|
const T& operator[] (int idx) const
|
|
{
|
|
OVR_ASSERT(0 <= idx && idx < 3);
|
|
return *(&x + idx);
|
|
}
|
|
|
|
// Entrywise product of two vectors
|
|
Vector3 EntrywiseMultiply(const Vector3& b) const { return Vector3(x * b.x,
|
|
y * b.y,
|
|
z * b.z);}
|
|
|
|
// Multiply and divide operators do entry-wise math
|
|
Vector3 operator* (const Vector3& b) const { return Vector3(x * b.x,
|
|
y * b.y,
|
|
z * b.z); }
|
|
|
|
Vector3 operator/ (const Vector3& b) const { return Vector3(x / b.x,
|
|
y / b.y,
|
|
z / b.z); }
|
|
|
|
|
|
// Dot product
|
|
// Used to calculate angle q between two vectors among other things,
|
|
// as (A dot B) = |a||b|cos(q).
|
|
T Dot(const Vector3& b) const { return x*b.x + y*b.y + z*b.z; }
|
|
|
|
// Compute cross product, which generates a normal vector.
|
|
// Direction vector can be determined by right-hand rule: Pointing index finder in
|
|
// direction a and middle finger in direction b, thumb will point in a.Cross(b).
|
|
Vector3 Cross(const Vector3& b) const { return Vector3(y*b.z - z*b.y,
|
|
z*b.x - x*b.z,
|
|
x*b.y - y*b.x); }
|
|
|
|
// Returns the angle from this vector to b, in radians.
|
|
T Angle(const Vector3& b) const
|
|
{
|
|
T div = LengthSq()*b.LengthSq();
|
|
OVR_ASSERT(div != T(0));
|
|
T result = Acos((this->Dot(b))/sqrt(div));
|
|
return result;
|
|
}
|
|
|
|
// Return Length of the vector squared.
|
|
T LengthSq() const { return (x * x + y * y + z * z); }
|
|
|
|
// Return vector length.
|
|
T Length() const { return sqrt(LengthSq()); }
|
|
|
|
// Returns squared distance between two points represented by vectors.
|
|
T DistanceSq(Vector3 const& b) const { return (*this - b).LengthSq(); }
|
|
|
|
// Returns distance between two points represented by vectors.
|
|
T Distance(Vector3 const& b) const { return (*this - b).Length(); }
|
|
|
|
// Determine if this a unit vector.
|
|
bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance; }
|
|
|
|
// Normalize, convention vector length to 1.
|
|
void Normalize()
|
|
{
|
|
T l = Length();
|
|
OVR_ASSERT(l != T(0));
|
|
*this /= l;
|
|
}
|
|
|
|
// Returns normalized (unit) version of the vector without modifying itself.
|
|
Vector3 Normalized() const
|
|
{
|
|
T l = Length();
|
|
OVR_ASSERT(l != T(0));
|
|
return *this / l;
|
|
}
|
|
|
|
// Linearly interpolates from this vector to another.
|
|
// Factor should be between 0.0 and 1.0, with 0 giving full value to this.
|
|
Vector3 Lerp(const Vector3& b, T f) const { return *this*(T(1) - f) + b*f; }
|
|
|
|
// Projects this vector onto the argument; in other words,
|
|
// A.Project(B) returns projection of vector A onto B.
|
|
Vector3 ProjectTo(const Vector3& b) const
|
|
{
|
|
T l2 = b.LengthSq();
|
|
OVR_ASSERT(l2 != T(0));
|
|
return b * ( Dot(b) / l2 );
|
|
}
|
|
|
|
// Projects this vector onto a plane defined by a normal vector
|
|
Vector3 ProjectToPlane(const Vector3& normal) const { return *this - this->ProjectTo(normal); }
|
|
};
|
|
|
|
|
|
typedef Vector3<float> Vector3f;
|
|
typedef Vector3<double> Vector3d;
|
|
typedef Vector3<SInt32> Vector3i;
|
|
|
|
|
|
// JDC: this was defined in Render_Device.h, I moved it here, but it
|
|
// needs to be fleshed out like the other Vector types.
|
|
//
|
|
// A vector with a dummy w component for alignment in uniform buffers (and for float colors).
|
|
// The w component is not used in any calculations.
|
|
|
|
struct Vector4f : public Vector3f
|
|
{
|
|
float w;
|
|
|
|
Vector4f() : w(1) {}
|
|
Vector4f(const Vector3f& v) : Vector3f(v), w(1) {}
|
|
Vector4f(float r, float g, float b, float a) : Vector3f(r,g,b), w(a) {}
|
|
};
|
|
|
|
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Size
|
|
|
|
// Size class represents 2D size with Width, Height components.
|
|
// Used to describe distentions of render targets, etc.
|
|
|
|
template<class T>
|
|
class Size
|
|
{
|
|
public:
|
|
T w, h;
|
|
|
|
Size() : w(0), h(0) { }
|
|
Size(T w_, T h_) : w(w_), h(h_) { }
|
|
explicit Size(T s) : w(s), h(s) { }
|
|
explicit Size(const Size<typename Math<T>::OtherFloatType> &src)
|
|
: w((T)src.w), h((T)src.h) { }
|
|
|
|
// C-interop support.
|
|
typedef typename CompatibleTypes<Size<T> >::Type CompatibleType;
|
|
|
|
Size(const CompatibleType& s) : w(s.w), h(s.h) { }
|
|
|
|
operator const CompatibleType& () const
|
|
{
|
|
OVR_COMPILER_ASSERT(sizeof(Size<T>) == sizeof(CompatibleType));
|
|
return reinterpret_cast<const CompatibleType&>(*this);
|
|
}
|
|
|
|
bool operator== (const Size& b) const { return w == b.w && h == b.h; }
|
|
bool operator!= (const Size& b) const { return w != b.w || h != b.h; }
|
|
|
|
Size operator+ (const Size& b) const { return Size(w + b.w, h + b.h); }
|
|
Size& operator+= (const Size& b) { w += b.w; h += b.h; return *this; }
|
|
Size operator- (const Size& b) const { return Size(w - b.w, h - b.h); }
|
|
Size& operator-= (const Size& b) { w -= b.w; h -= b.h; return *this; }
|
|
Size operator- () const { return Size(-w, -h); }
|
|
Size operator* (const Size& b) const { return Size(w * b.w, h * b.h); }
|
|
Size& operator*= (const Size& b) { w *= b.w; h *= b.h; return *this; }
|
|
Size operator/ (const Size& b) const { return Size(w / b.w, h / b.h); }
|
|
Size& operator/= (const Size& b) { w /= b.w; h /= b.h; return *this; }
|
|
|
|
// Scalar multiplication/division scales both components.
|
|
Size operator* (T s) const { return Size(w*s, h*s); }
|
|
Size& operator*= (T s) { w *= s; h *= s; return *this; }
|
|
Size operator/ (T s) const { return Size(w/s, h/s); }
|
|
Size& operator/= (T s) { w /= s; h /= s; return *this; }
|
|
|
|
static Size Min(const Size& a, const Size& b) { return Size((a.w < b.w) ? a.w : b.w,
|
|
(a.h < b.h) ? a.h : b.h); }
|
|
static Size Max(const Size& a, const Size& b) { return Size((a.w > b.w) ? a.w : b.w,
|
|
(a.h > b.h) ? a.h : b.h); }
|
|
|
|
|
|
T Area() const { return w * h; }
|
|
|
|
inline Vector2<T> ToVector() const { return Vector2<T>(w, h); }
|
|
};
|
|
|
|
|
|
typedef Size<int> Sizei;
|
|
typedef Size<unsigned> Sizeu;
|
|
typedef Size<float> Sizef;
|
|
typedef Size<double> Sized;
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------------
|
|
// ***** Rect
|
|
|
|
// Rect describes a rectangular area for rendering, that includes position and size.
|
|
template<class T>
|
|
class Rect
|
|
{
|
|
public:
|
|
T x, y;
|
|
T w, h;
|
|
|
|
Rect() { }
|
|
Rect(T x1, T y1, T w1, T h1) : x(x1), y(y1), w(w1), h(h1) { }
|
|
Rect(const Vector2<T>& pos, const Size<T>& sz) : x(pos.x), y(pos.y), w(sz.w), h(sz.h) { }
|
|
Rect(const Size<T>& sz) : x(0), y(0), w(sz.w), h(sz.h) { }
|
|
|
|
// C-interop support.
|
|
typedef typename CompatibleTypes<Rect<T> >::Type CompatibleType;
|
|
|
|
Rect(const CompatibleType& s) : x(s.Pos.x), y(s.Pos.y), w(s.Size.w), h(s.Size.h) { }
|
|
|
|
operator const CompatibleType& () const
|
|
{
|
|
OVR_COMPILER_ASSERT(sizeof(Rect<T>) == sizeof(CompatibleType));
|
|
return reinterpret_cast<const CompatibleType&>(*this);
|
|
}
|
|
|
|
Vector2<T> GetPos() const { return Vector2<T>(x, y); }
|
|
Size<T> GetSize() const { return Size<T>(w, h); }
|
|
void SetPos(const Vector2<T>& pos) { x = pos.x; y = pos.y; }
|
|
void SetSize(const Size<T>& sz) { w = sz.w; h = sz.h; }
|
|
|
|
bool operator == (const Rect& vp) const
|
|
{ return (x == vp.x) && (y == vp.y) && (w == vp.w) && (h == vp.h); }
|
|
bool operator != (const Rect& vp) const
|
|
{ return !operator == (vp); }
|
|
};
|
|
|
|
typedef Rect<int> Recti;
|
|
|
|
|
|
//-------------------------------------------------------------------------------------//
|
|
// ***** Quat
|
|
//
|
|
// Quatf represents a quaternion class used for rotations.
|
|
//
|
|
// Quaternion multiplications are done in right-to-left order, to match the
|
|
// behavior of matrices.
|
|
|
|
|
|
template<class T>
|
|
class Quat
|
|
{
|
|
public:
|
|
// w + Xi + Yj + Zk
|
|
T x, y, z, w;
|
|
|
|
Quat() : x(0), y(0), z(0), w(1) { }
|
|
Quat(T x_, T y_, T z_, T w_) : x(x_), y(y_), z(z_), w(w_) { }
|
|
explicit Quat(const Quat<typename Math<T>::OtherFloatType> &src)
|
|
: x((T)src.x), y((T)src.y), z((T)src.z), w((T)src.w) { }
|
|
|
|
// C-interop support.
|
|
Quat(const typename CompatibleTypes<Quat<T> >::Type& s) : x(s.x), y(s.y), z(s.z), w(s.w) { }
|
|
|
|
operator typename CompatibleTypes<Quat<T> >::Type () const
|
|
{
|
|
typename CompatibleTypes<Quat<T> >::Type result;
|
|
result.x = x;
|
|
result.y = y;
|
|
result.z = z;
|
|
result.w = w;
|
|
return result;
|
|
}
|
|
|
|
// Constructs quaternion for rotation around the axis by an angle.
|
|
Quat(const Vector3<T>& axis, T angle)
|
|
{
|
|
// Make sure we don't divide by zero.
|
|
if (axis.LengthSq() == 0)
|
|
{
|
|
// Assert if the axis is zero, but the angle isn't
|
|
OVR_ASSERT(angle == 0);
|
|
x = 0; y = 0; z = 0; w = 1;
|
|
return;
|
|
}
|
|
|
|
Vector3<T> unitAxis = axis.Normalized();
|
|
T sinHalfAngle = sin(angle * T(0.5));
|
|
|
|
w = cos(angle * T(0.5));
|
|
x = unitAxis.x * sinHalfAngle;
|
|
y = unitAxis.y * sinHalfAngle;
|
|
z = unitAxis.z * sinHalfAngle;
|
|
}
|
|
|
|
// Constructs quaternion for rotation around one of the coordinate axis by an angle.
|
|
Quat(Axis A, T angle, RotateDirection d = Rotate_CCW, HandedSystem s = Handed_R)
|
|
{
|
|
T sinHalfAngle = s * d *sin(angle * T(0.5));
|
|
T v[3];
|
|
v[0] = v[1] = v[2] = T(0);
|
|
v[A] = sinHalfAngle;
|
|
|
|
w = cos(angle * T(0.5));
|
|
x = v[0];
|
|
y = v[1];
|
|
z = v[2];
|
|
}
|
|
|
|
// Compute axis and angle from quaternion
|
|
void GetAxisAngle(Vector3<T>* axis, T* angle) const
|
|
{
|
|
if ( x*x + y*y + z*z > Math<T>::Tolerance * Math<T>::Tolerance ) {
|
|
*axis = Vector3<T>(x, y, z).Normalized();
|
|
*angle = 2 * Acos(w);
|
|
if (*angle > Math<T>::Pi) // Reduce the magnitude of the angle, if necessary
|
|
{
|
|
*angle = Math<T>::TwoPi - *angle;
|
|
*axis = *axis * (-1);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
*axis = Vector3<T>(1, 0, 0);
|
|
*angle= 0;
|
|
}
|
|
}
|
|
|
|
// Constructs the quaternion from a rotation matrix
|
|
explicit Quat(const Matrix4<T>& m)
|
|
{
|
|
T trace = m.M[0][0] + m.M[1][1] + m.M[2][2];
|
|
|
|
// In almost all cases, the first part is executed.
|
|
// However, if the trace is not positive, the other
|
|
// cases arise.
|
|
if (trace > T(0))
|
|
{
|
|
T s = sqrt(trace + T(1)) * T(2); // s=4*qw
|
|
w = T(0.25) * s;
|
|
x = (m.M[2][1] - m.M[1][2]) / s;
|
|
y = (m.M[0][2] - m.M[2][0]) / s;
|
|
z = (m.M[1][0] - m.M[0][1]) / s;
|
|
}
|
|
else if ((m.M[0][0] > m.M[1][1])&&(m.M[0][0] > m.M[2][2]))
|
|
{
|
|
T s = sqrt(T(1) + m.M[0][0] - m.M[1][1] - m.M[2][2]) * T(2);
|
|
w = (m.M[2][1] - m.M[1][2]) / s;
|
|
x = T(0.25) * s;
|
|
y = (m.M[0][1] + m.M[1][0]) / s;
|
|
z = (m.M[2][0] + m.M[0][2]) / s;
|
|
}
|
|
else if (m.M[1][1] > m.M[2][2])
|
|
{
|
|
T s = sqrt(T(1) + m.M[1][1] - m.M[0][0] - m.M[2][2]) * T(2); // S=4*qy
|
|
w = (m.M[0][2] - m.M[2][0]) / s;
|
|
x = (m.M[0][1] + m.M[1][0]) / s;
|
|
y = T(0.25) * s;
|
|
z = (m.M[1][2] + m.M[2][1]) / s;
|
|
}
|
|
else
|
|
{
|
|
T s = sqrt(T(1) + m.M[2][2] - m.M[0][0] - m.M[1][1]) * T(2); // S=4*qz
|
|
w = (m.M[1][0] - m.M[0][1]) / s;
|
|
x = (m.M[0][2] + m.M[2][0]) / s;
|
|
y = (m.M[1][2] + m.M[2][1]) / s;
|
|
z = T(0.25) * s;
|
|
}
|
|
}
|
|
|
|
// Constructs the quaternion from a rotation matrix
|
|
explicit Quat(const Matrix3<T>& m)
|
|
{
|
|
T trace = m.M[0][0] + m.M[1][1] + m.M[2][2];
|
|
|
|
// In almost all cases, the first part is executed.
|
|
// However, if the trace is not positive, the other
|
|
// cases arise.
|
|
if (trace > T(0))
|
|
{
|
|
T s = sqrt(trace + T(1)) * T(2); // s=4*qw
|
|
w = T(0.25) * s;
|
|
x = (m.M[2][1] - m.M[1][2]) / s;
|
|
y = (m.M[0][2] - m.M[2][0]) / s;
|
|
z = (m.M[1][0] - m.M[0][1]) / s;
|
|
}
|
|
else if ((m.M[0][0] > m.M[1][1])&&(m.M[0][0] > m.M[2][2]))
|
|
{
|
|
T s = sqrt(T(1) + m.M[0][0] - m.M[1][1] - m.M[2][2]) * T(2);
|
|
w = (m.M[2][1] - m.M[1][2]) / s;
|
|
x = T(0.25) * s;
|
|
y = (m.M[0][1] + m.M[1][0]) / s;
|
|
z = (m.M[2][0] + m.M[0][2]) / s;
|
|
}
|
|
else if (m.M[1][1] > m.M[2][2])
|
|
{
|
|
T s = sqrt(T(1) + m.M[1][1] - m.M[0][0] - m.M[2][2]) * T(2); // S=4*qy
|
|
w = (m.M[0][2] - m.M[2][0]) / s;
|
|
x = (m.M[0][1] + m.M[1][0]) / s;
|
|
y = T(0.25) * s;
|
|
z = (m.M[1][2] + m.M[2][1]) / s;
|
|
}
|
|
else
|
|
{
|
|
T s = sqrt(T(1) + m.M[2][2] - m.M[0][0] - m.M[1][1]) * T(2); // S=4*qz
|
|
w = (m.M[1][0] - m.M[0][1]) / s;
|
|
x = (m.M[0][2] + m.M[2][0]) / s;
|
|
y = (m.M[1][2] + m.M[2][1]) / s;
|
|
z = T(0.25) * s;
|
|
}
|
|
}
|
|
|
|
bool operator== (const Quat& b) const { return x == b.x && y == b.y && z == b.z && w == b.w; }
|
|
bool operator!= (const Quat& b) const { return x != b.x || y != b.y || z != b.z || w != b.w; }
|
|
|
|
Quat operator+ (const Quat& b) const { return Quat(x + b.x, y + b.y, z + b.z, w + b.w); }
|
|
Quat& operator+= (const Quat& b) { w += b.w; x += b.x; y += b.y; z += b.z; return *this; }
|
|
Quat operator- (const Quat& b) const { return Quat(x - b.x, y - b.y, z - b.z, w - b.w); }
|
|
Quat& operator-= (const Quat& b) { w -= b.w; x -= b.x; y -= b.y; z -= b.z; return *this; }
|
|
|
|
Quat operator* (T s) const { return Quat(x * s, y * s, z * s, w * s); }
|
|
Quat& operator*= (T s) { w *= s; x *= s; y *= s; z *= s; return *this; }
|
|
Quat operator/ (T s) const { T rcp = T(1)/s; return Quat(x * rcp, y * rcp, z * rcp, w *rcp); }
|
|
Quat& operator/= (T s) { T rcp = T(1)/s; w *= rcp; x *= rcp; y *= rcp; z *= rcp; return *this; }
|
|
|
|
|
|
// Get Imaginary part vector
|
|
Vector3<T> Imag() const { return Vector3<T>(x,y,z); }
|
|
|
|
// Get quaternion length.
|
|
T Length() const { return sqrt(LengthSq()); }
|
|
|
|
// Get quaternion length squared.
|
|
T LengthSq() const { return (x * x + y * y + z * z + w * w); }
|
|
|
|
// Simple Euclidean distance in R^4 (not SLERP distance, but at least respects Haar measure)
|
|
T Distance(const Quat& q) const
|
|
{
|
|
T d1 = (*this - q).Length();
|
|
T d2 = (*this + q).Length(); // Antipodal point check
|
|
return (d1 < d2) ? d1 : d2;
|
|
}
|
|
|
|
T DistanceSq(const Quat& q) const
|
|
{
|
|
T d1 = (*this - q).LengthSq();
|
|
T d2 = (*this + q).LengthSq(); // Antipodal point check
|
|
return (d1 < d2) ? d1 : d2;
|
|
}
|
|
|
|
T Dot(const Quat& q) const
|
|
{
|
|
return x * q.x + y * q.y + z * q.z + w * q.w;
|
|
}
|
|
|
|
// Angle between two quaternions in radians
|
|
T Angle(const Quat& q) const
|
|
{
|
|
return 2 * Acos(Alg::Abs(Dot(q)));
|
|
}
|
|
|
|
// Normalize
|
|
bool IsNormalized() const { return fabs(LengthSq() - T(1)) < Math<T>::Tolerance; }
|
|
|
|
void Normalize()
|
|
{
|
|
T l = Length();
|
|
OVR_ASSERT(l != T(0));
|
|
*this /= l;
|
|
}
|
|
|
|
Quat Normalized() const
|
|
{
|
|
T l = Length();
|
|
OVR_ASSERT(l != T(0));
|
|
return *this / l;
|
|
}
|
|
|
|
// Returns conjugate of the quaternion. Produces inverse rotation if quaternion is normalized.
|
|
Quat Conj() const { return Quat(-x, -y, -z, w); }
|
|
|
|
// Quaternion multiplication. Combines quaternion rotations, performing the one on the
|
|
// right hand side first.
|
|
Quat operator* (const Quat& b) const { return Quat(w * b.x + x * b.w + y * b.z - z * b.y,
|
|
w * b.y - x * b.z + y * b.w + z * b.x,
|
|
w * b.z + x * b.y - y * b.x + z * b.w,
|
|
w * b.w - x * b.x - y * b.y - z * b.z); }
|
|
|
|
//
|
|
// this^p normalized; same as rotating by this p times.
|
|
Quat PowNormalized(T p) const
|
|
{
|
|
Vector3<T> v;
|
|
T a;
|
|
GetAxisAngle(&v, &a);
|
|
return Quat(v, a * p);
|
|
}
|
|
|
|
// Normalized linear interpolation of quaternions
|
|
Quat Nlerp(const Quat& other, T a)
|
|
{
|
|
T sign = (Dot(other) >= 0) ? 1 : -1;
|
|
return (*this * sign * a + other * (1-a)).Normalized();
|
|
}
|
|
|
|
// Rotate transforms vector in a manner that matches Matrix rotations (counter-clockwise,
|
|
// assuming negative direction of the axis). Standard formula: q(t) * V * q(t)^-1.
|
|
Vector3<T> Rotate(const Vector3<T>& v) const
|
|
{
|
|
return ((*this * Quat<T>(v.x, v.y, v.z, T(0))) * Inverted()).Imag();
|
|
}
|
|
|
|
// Inversed quaternion rotates in the opposite direction.
|
|
Quat Inverted() const
|
|
{
|
|
return Quat(-x, -y, -z, w);
|
|
}
|
|
|
|
// Sets this quaternion to the one rotates in the opposite direction.
|
|
void Invert()
|
|
{
|
|
*this = Quat(-x, -y, -z, w);
|
|
}
|
|
|
|
// GetEulerAngles extracts Euler angles from the quaternion, in the specified order of
|
|
// axis rotations and the specified coordinate system. Right-handed coordinate system
|
|
// is the default, with CCW rotations while looking in the negative axis direction.
|
|
// Here a,b,c, are the Yaw/Pitch/Roll angles to be returned.
|
|
// rotation a around axis A1
|
|
// is followed by rotation b around axis A2
|
|
// is followed by rotation c around axis A3
|
|
// rotations are CCW or CW (D) in LH or RH coordinate system (S)
|
|
template <Axis A1, Axis A2, Axis A3, RotateDirection D, HandedSystem S>
|
|
void GetEulerAngles(T *a, T *b, T *c) const
|
|
{
|
|
OVR_COMPILER_ASSERT((A1 != A2) && (A2 != A3) && (A1 != A3));
|
|
|
|
T Q[3] = { x, y, z }; //Quaternion components x,y,z
|
|
|
|
T ww = w*w;
|
|
T Q11 = Q[A1]*Q[A1];
|
|
T Q22 = Q[A2]*Q[A2];
|
|
T Q33 = Q[A3]*Q[A3];
|
|
|
|
T psign = T(-1);
|
|
// Determine whether even permutation
|
|
if (((A1 + 1) % 3 == A2) && ((A2 + 1) % 3 == A3))
|
|
psign = T(1);
|
|
|
|
T s2 = psign * T(2) * (psign*w*Q[A2] + Q[A1]*Q[A3]);
|
|
|
|
if (s2 < T(-1) + Math<T>::SingularityRadius)
|
|
{ // South pole singularity
|
|
*a = T(0);
|
|
*b = -S*D*Math<T>::PiOver2;
|
|
*c = S*D*atan2(T(2)*(psign*Q[A1]*Q[A2] + w*Q[A3]),
|
|
ww + Q22 - Q11 - Q33 );
|
|
}
|
|
else if (s2 > T(1) - Math<T>::SingularityRadius)
|
|
{ // North pole singularity
|
|
*a = T(0);
|
|
*b = S*D*Math<T>::PiOver2;
|
|
*c = S*D*atan2(T(2)*(psign*Q[A1]*Q[A2] + w*Q[A3]),
|
|
ww + Q22 - Q11 - Q33);
|
|
}
|
|
else
|
|
{
|
|
*a = -S*D*atan2(T(-2)*(w*Q[A1] - psign*Q[A2]*Q[A3]),
|
|
ww + Q33 - Q11 - Q22);
|
|
*b = S*D*asin(s2);
|
|
*c = S*D*atan2(T(2)*(w*Q[A3] - psign*Q[A1]*Q[A2]),
|
|
ww + Q11 - Q22 - Q33);
|
|
}
|
|
return;
|
|
}
|
|
|
|
template <Axis A1, Axis A2, Axis A3, RotateDirection D>
|
|
void GetEulerAngles(T *a, T *b, T *c) const
|
|
{ GetEulerAngles<A1, A2, A3, D, Handed_R>(a, b, c); }
|
|
|
|
template <Axis A1, Axis A2, Axis A3>
|
|
void GetEulerAngles(T *a, T *b, T *c) const
|
|
{ GetEulerAngles<A1, A2, A3, Rotate_CCW, Handed_R>(a, b, c); }
|
|
|
|
|
|
// GetEulerAnglesABA extracts Euler angles from the quaternion, in the specified order of
|
|
// axis rotations and the specified coordinate system. Right-handed coordinate system
|
|
// is the default, with CCW rotations while looking in the negative axis direction.
|
|
// Here a,b,c, are the Yaw/Pitch/Roll angles to be returned.
|
|
// rotation a around axis A1
|
|
// is followed by rotation b around axis A2
|
|
// is followed by rotation c around axis A1
|
|
// Rotations are CCW or CW (D) in LH or RH coordinate system (S)
|
|
template <Axis A1, Axis A2, RotateDirection D, HandedSystem S>
|
|
void GetEulerAnglesABA(T *a, T *b, T *c) const
|
|
{
|
|
OVR_COMPILER_ASSERT(A1 != A2);
|
|
|
|
T Q[3] = {x, y, z}; // Quaternion components
|
|
|
|
// Determine the missing axis that was not supplied
|
|
int m = 3 - A1 - A2;
|
|
|
|
T ww = w*w;
|
|
T Q11 = Q[A1]*Q[A1];
|
|
T Q22 = Q[A2]*Q[A2];
|
|
T Qmm = Q[m]*Q[m];
|
|
|
|
T psign = T(-1);
|
|
if ((A1 + 1) % 3 == A2) // Determine whether even permutation
|
|
{
|
|
psign = T(1);
|
|
}
|
|
|
|
T c2 = ww + Q11 - Q22 - Qmm;
|
|
if (c2 < T(-1) + Math<T>::SingularityRadius)
|
|
{ // South pole singularity
|
|
*a = T(0);
|
|
*b = S*D*Math<T>::Pi;
|
|
*c = S*D*atan2( T(2)*(w*Q[A1] - psign*Q[A2]*Q[m]),
|
|
ww + Q22 - Q11 - Qmm);
|
|
}
|
|
else if (c2 > T(1) - Math<T>::SingularityRadius)
|
|
{ // North pole singularity
|
|
*a = T(0);
|
|
*b = T(0);
|
|
*c = S*D*atan2( T(2)*(w*Q[A1] - psign*Q[A2]*Q[m]),
|
|
ww + Q22 - Q11 - Qmm);
|
|
}
|
|
else
|
|
{
|
|
*a = S*D*atan2( psign*w*Q[m] + Q[A1]*Q[A2],
|
|
w*Q[A2] -psign*Q[A1]*Q[m]);
|
|
*b = S*D*acos(c2);
|
|
*c = S*D*atan2( -psign*w*Q[m] + Q[A1]*Q[A2],
|
|
w*Q[A2] + psign*Q[A1]*Q[m]);
|
|
}
|
|
return;
|
|
}
|
|
};
|
|
|
|
typedef Quat<float> Quatf;
|
|
typedef Quat<double> Quatd;
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Pose
|
|
|
|
// Position and orientation combined.
|
|
|
|
template<class T>
|
|
class Transform
|
|
{
|
|
public:
|
|
|
|
typedef typename CompatibleTypes<Transform<T> >::Type CompatibleType;
|
|
|
|
Transform() { }
|
|
Transform(const Quat<T>& orientation, const Vector3<T>& pos)
|
|
: Rotation(orientation), Translation(pos) { }
|
|
Transform(const Transform& s)
|
|
: Rotation(s.Rotation), Translation(s.Translation) { }
|
|
Transform(const CompatibleType& s)
|
|
: Rotation(s.Orientation), Translation(s.Position) { }
|
|
explicit Transform(const Transform<typename Math<T>::OtherFloatType> &s)
|
|
: Rotation(s.Rotation), Translation(s.Translation) { }
|
|
|
|
operator typename CompatibleTypes<Transform<T> >::Type () const
|
|
{
|
|
typename CompatibleTypes<Transform<T> >::Type result;
|
|
result.Orientation = Rotation;
|
|
result.Position = Translation;
|
|
return result;
|
|
}
|
|
|
|
Quat<T> Rotation;
|
|
Vector3<T> Translation;
|
|
|
|
Vector3<T> Rotate(const Vector3<T>& v) const
|
|
{
|
|
return Rotation.Rotate(v);
|
|
}
|
|
|
|
Vector3<T> Translate(const Vector3<T>& v) const
|
|
{
|
|
return v + Translation;
|
|
}
|
|
|
|
Vector3<T> Apply(const Vector3<T>& v) const
|
|
{
|
|
return Translate(Rotate(v));
|
|
}
|
|
|
|
Transform operator*(const Transform& other) const
|
|
{
|
|
return Transform(Rotation * other.Rotation, Apply(other.Translation));
|
|
}
|
|
|
|
PoseState<T> operator*(const PoseState<T>& poseState) const
|
|
{
|
|
PoseState<T> result;
|
|
result.Pose = (*this) * poseState.Pose;
|
|
result.LinearVelocity = this->Rotate(poseState.LinearVelocity);
|
|
result.LinearAcceleration = this->Rotate(poseState.LinearAcceleration);
|
|
result.AngularVelocity = this->Rotate(poseState.AngularVelocity);
|
|
result.AngularAcceleration = this->Rotate(poseState.AngularAcceleration);
|
|
return result;
|
|
}
|
|
|
|
Transform Inverted() const
|
|
{
|
|
Quat<T> inv = Rotation.Inverted();
|
|
return Transform(inv, inv.Rotate(-Translation));
|
|
}
|
|
};
|
|
|
|
typedef Transform<float> Transformf;
|
|
typedef Transform<double> Transformd;
|
|
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Matrix4
|
|
//
|
|
// Matrix4 is a 4x4 matrix used for 3d transformations and projections.
|
|
// Translation stored in the last column.
|
|
// The matrix is stored in row-major order in memory, meaning that values
|
|
// of the first row are stored before the next one.
|
|
//
|
|
// The arrangement of the matrix is chosen to be in Right-Handed
|
|
// coordinate system and counterclockwise rotations when looking down
|
|
// the axis
|
|
//
|
|
// Transformation Order:
|
|
// - Transformations are applied from right to left, so the expression
|
|
// M1 * M2 * M3 * V means that the vector V is transformed by M3 first,
|
|
// followed by M2 and M1.
|
|
//
|
|
// Coordinate system: Right Handed
|
|
//
|
|
// Rotations: Counterclockwise when looking down the axis. All angles are in radians.
|
|
//
|
|
// | sx 01 02 tx | // First column (sx, 10, 20): Axis X basis vector.
|
|
// | 10 sy 12 ty | // Second column (01, sy, 21): Axis Y basis vector.
|
|
// | 20 21 sz tz | // Third columnt (02, 12, sz): Axis Z basis vector.
|
|
// | 30 31 32 33 |
|
|
//
|
|
// The basis vectors are first three columns.
|
|
|
|
template<class T>
|
|
class Matrix4
|
|
{
|
|
static const Matrix4 IdentityValue;
|
|
|
|
public:
|
|
T M[4][4];
|
|
|
|
enum NoInitType { NoInit };
|
|
|
|
// Construct with no memory initialization.
|
|
Matrix4(NoInitType) { }
|
|
|
|
// By default, we construct identity matrix.
|
|
Matrix4()
|
|
{
|
|
SetIdentity();
|
|
}
|
|
|
|
Matrix4(T m11, T m12, T m13, T m14,
|
|
T m21, T m22, T m23, T m24,
|
|
T m31, T m32, T m33, T m34,
|
|
T m41, T m42, T m43, T m44)
|
|
{
|
|
M[0][0] = m11; M[0][1] = m12; M[0][2] = m13; M[0][3] = m14;
|
|
M[1][0] = m21; M[1][1] = m22; M[1][2] = m23; M[1][3] = m24;
|
|
M[2][0] = m31; M[2][1] = m32; M[2][2] = m33; M[2][3] = m34;
|
|
M[3][0] = m41; M[3][1] = m42; M[3][2] = m43; M[3][3] = m44;
|
|
}
|
|
|
|
Matrix4(T m11, T m12, T m13,
|
|
T m21, T m22, T m23,
|
|
T m31, T m32, T m33)
|
|
{
|
|
M[0][0] = m11; M[0][1] = m12; M[0][2] = m13; M[0][3] = 0;
|
|
M[1][0] = m21; M[1][1] = m22; M[1][2] = m23; M[1][3] = 0;
|
|
M[2][0] = m31; M[2][1] = m32; M[2][2] = m33; M[2][3] = 0;
|
|
M[3][0] = 0; M[3][1] = 0; M[3][2] = 0; M[3][3] = 1;
|
|
}
|
|
|
|
explicit Matrix4(const Quat<T>& q)
|
|
{
|
|
T ww = q.w*q.w;
|
|
T xx = q.x*q.x;
|
|
T yy = q.y*q.y;
|
|
T zz = q.z*q.z;
|
|
|
|
M[0][0] = ww + xx - yy - zz; M[0][1] = 2 * (q.x*q.y - q.w*q.z); M[0][2] = 2 * (q.x*q.z + q.w*q.y); M[0][3] = 0;
|
|
M[1][0] = 2 * (q.x*q.y + q.w*q.z); M[1][1] = ww - xx + yy - zz; M[1][2] = 2 * (q.y*q.z - q.w*q.x); M[1][3] = 0;
|
|
M[2][0] = 2 * (q.x*q.z - q.w*q.y); M[2][1] = 2 * (q.y*q.z + q.w*q.x); M[2][2] = ww - xx - yy + zz; M[2][3] = 0;
|
|
M[3][0] = 0; M[3][1] = 0; M[3][2] = 0; M[3][3] = 1;
|
|
}
|
|
|
|
explicit Matrix4(const Transform<T>& p)
|
|
{
|
|
Matrix4 result(p.Rotation);
|
|
result.SetTranslation(p.Translation);
|
|
*this = result;
|
|
}
|
|
|
|
// C-interop support
|
|
explicit Matrix4(const Matrix4<typename Math<T>::OtherFloatType> &src)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
for (int j = 0; j < 4; j++)
|
|
M[i][j] = (T)src.M[i][j];
|
|
}
|
|
|
|
// C-interop support.
|
|
Matrix4(const typename CompatibleTypes<Matrix4<T> >::Type& s)
|
|
{
|
|
OVR_COMPILER_ASSERT(sizeof(s) == sizeof(Matrix4));
|
|
memcpy(M, s.M, sizeof(M));
|
|
}
|
|
|
|
operator typename CompatibleTypes<Matrix4<T> >::Type () const
|
|
{
|
|
typename CompatibleTypes<Matrix4<T> >::Type result;
|
|
OVR_COMPILER_ASSERT(sizeof(result) == sizeof(Matrix4));
|
|
memcpy(result.M, M, sizeof(M));
|
|
return result;
|
|
}
|
|
|
|
void ToString(char* dest, UPInt destsize) const
|
|
{
|
|
UPInt pos = 0;
|
|
for (int r=0; r<4; r++)
|
|
for (int c=0; c<4; c++)
|
|
pos += OVR_sprintf(dest+pos, destsize-pos, "%g ", M[r][c]);
|
|
}
|
|
|
|
static Matrix4 FromString(const char* src)
|
|
{
|
|
Matrix4 result;
|
|
for (int r=0; r<4; r++)
|
|
for (int c=0; c<4; c++)
|
|
{
|
|
result.M[r][c] = (T)atof(src);
|
|
while (src && *src != ' ')
|
|
src++;
|
|
while (src && *src == ' ')
|
|
src++;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
static const Matrix4& Identity() { return IdentityValue; }
|
|
|
|
void SetIdentity()
|
|
{
|
|
M[0][0] = M[1][1] = M[2][2] = M[3][3] = 1;
|
|
M[0][1] = M[1][0] = M[2][3] = M[3][1] = 0;
|
|
M[0][2] = M[1][2] = M[2][0] = M[3][2] = 0;
|
|
M[0][3] = M[1][3] = M[2][1] = M[3][0] = 0;
|
|
}
|
|
|
|
bool operator== (const Matrix4& b) const
|
|
{
|
|
bool isEqual = true;
|
|
for (int i = 0; i < 4; i++)
|
|
for (int j = 0; j < 4; j++)
|
|
isEqual &= (M[i][j] == b.M[i][j]);
|
|
|
|
return isEqual;
|
|
}
|
|
|
|
Matrix4 operator+ (const Matrix4& b) const
|
|
{
|
|
Matrix4 result(*this);
|
|
result += b;
|
|
return result;
|
|
}
|
|
|
|
Matrix4& operator+= (const Matrix4& b)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
for (int j = 0; j < 4; j++)
|
|
M[i][j] += b.M[i][j];
|
|
return *this;
|
|
}
|
|
|
|
Matrix4 operator- (const Matrix4& b) const
|
|
{
|
|
Matrix4 result(*this);
|
|
result -= b;
|
|
return result;
|
|
}
|
|
|
|
Matrix4& operator-= (const Matrix4& b)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
for (int j = 0; j < 4; j++)
|
|
M[i][j] -= b.M[i][j];
|
|
return *this;
|
|
}
|
|
|
|
// Multiplies two matrices into destination with minimum copying.
|
|
static Matrix4& Multiply(Matrix4* d, const Matrix4& a, const Matrix4& b)
|
|
{
|
|
OVR_ASSERT((d != &a) && (d != &b));
|
|
int i = 0;
|
|
do {
|
|
d->M[i][0] = a.M[i][0] * b.M[0][0] + a.M[i][1] * b.M[1][0] + a.M[i][2] * b.M[2][0] + a.M[i][3] * b.M[3][0];
|
|
d->M[i][1] = a.M[i][0] * b.M[0][1] + a.M[i][1] * b.M[1][1] + a.M[i][2] * b.M[2][1] + a.M[i][3] * b.M[3][1];
|
|
d->M[i][2] = a.M[i][0] * b.M[0][2] + a.M[i][1] * b.M[1][2] + a.M[i][2] * b.M[2][2] + a.M[i][3] * b.M[3][2];
|
|
d->M[i][3] = a.M[i][0] * b.M[0][3] + a.M[i][1] * b.M[1][3] + a.M[i][2] * b.M[2][3] + a.M[i][3] * b.M[3][3];
|
|
} while((++i) < 4);
|
|
|
|
return *d;
|
|
}
|
|
|
|
Matrix4 operator* (const Matrix4& b) const
|
|
{
|
|
Matrix4 result(Matrix4::NoInit);
|
|
Multiply(&result, *this, b);
|
|
return result;
|
|
}
|
|
|
|
Matrix4& operator*= (const Matrix4& b)
|
|
{
|
|
return Multiply(this, Matrix4(*this), b);
|
|
}
|
|
|
|
Matrix4 operator* (T s) const
|
|
{
|
|
Matrix4 result(*this);
|
|
result *= s;
|
|
return result;
|
|
}
|
|
|
|
Matrix4& operator*= (T s)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
for (int j = 0; j < 4; j++)
|
|
M[i][j] *= s;
|
|
return *this;
|
|
}
|
|
|
|
|
|
Matrix4 operator/ (T s) const
|
|
{
|
|
Matrix4 result(*this);
|
|
result /= s;
|
|
return result;
|
|
}
|
|
|
|
Matrix4& operator/= (T s)
|
|
{
|
|
for (int i = 0; i < 4; i++)
|
|
for (int j = 0; j < 4; j++)
|
|
M[i][j] /= s;
|
|
return *this;
|
|
}
|
|
|
|
Vector3<T> Transform(const Vector3<T>& v) const
|
|
{
|
|
return Vector3<T>(M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z + M[0][3],
|
|
M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z + M[1][3],
|
|
M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z + M[2][3]);
|
|
}
|
|
|
|
Matrix4 Transposed() const
|
|
{
|
|
return Matrix4(M[0][0], M[1][0], M[2][0], M[3][0],
|
|
M[0][1], M[1][1], M[2][1], M[3][1],
|
|
M[0][2], M[1][2], M[2][2], M[3][2],
|
|
M[0][3], M[1][3], M[2][3], M[3][3]);
|
|
}
|
|
|
|
void Transpose()
|
|
{
|
|
*this = Transposed();
|
|
}
|
|
|
|
|
|
T SubDet (const UPInt* rows, const UPInt* cols) const
|
|
{
|
|
return M[rows[0]][cols[0]] * (M[rows[1]][cols[1]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[1]])
|
|
- M[rows[0]][cols[1]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[0]])
|
|
+ M[rows[0]][cols[2]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[1]] - M[rows[1]][cols[1]] * M[rows[2]][cols[0]]);
|
|
}
|
|
|
|
T Cofactor(UPInt I, UPInt J) const
|
|
{
|
|
const UPInt indices[4][3] = {{1,2,3},{0,2,3},{0,1,3},{0,1,2}};
|
|
return ((I+J)&1) ? -SubDet(indices[I],indices[J]) : SubDet(indices[I],indices[J]);
|
|
}
|
|
|
|
T Determinant() const
|
|
{
|
|
return M[0][0] * Cofactor(0,0) + M[0][1] * Cofactor(0,1) + M[0][2] * Cofactor(0,2) + M[0][3] * Cofactor(0,3);
|
|
}
|
|
|
|
Matrix4 Adjugated() const
|
|
{
|
|
return Matrix4(Cofactor(0,0), Cofactor(1,0), Cofactor(2,0), Cofactor(3,0),
|
|
Cofactor(0,1), Cofactor(1,1), Cofactor(2,1), Cofactor(3,1),
|
|
Cofactor(0,2), Cofactor(1,2), Cofactor(2,2), Cofactor(3,2),
|
|
Cofactor(0,3), Cofactor(1,3), Cofactor(2,3), Cofactor(3,3));
|
|
}
|
|
|
|
Matrix4 Inverted() const
|
|
{
|
|
T det = Determinant();
|
|
assert(det != 0);
|
|
return Adjugated() * (1.0f/det);
|
|
}
|
|
|
|
void Invert()
|
|
{
|
|
*this = Inverted();
|
|
}
|
|
|
|
// This is more efficient than general inverse, but ONLY works
|
|
// correctly if it is a homogeneous transform matrix (rot + trans)
|
|
Matrix4 InvertedHomogeneousTransform() const
|
|
{
|
|
// Make the inverse rotation matrix
|
|
Matrix4 rinv = this->Transposed();
|
|
rinv.M[3][0] = rinv.M[3][1] = rinv.M[3][2] = 0.0f;
|
|
// Make the inverse translation matrix
|
|
Vector3<T> tvinv(-M[0][3],-M[1][3],-M[2][3]);
|
|
Matrix4 tinv = Matrix4::Translation(tvinv);
|
|
return rinv * tinv; // "untranslate", then "unrotate"
|
|
}
|
|
|
|
// This is more efficient than general inverse, but ONLY works
|
|
// correctly if it is a homogeneous transform matrix (rot + trans)
|
|
void InvertHomogeneousTransform()
|
|
{
|
|
*this = InvertedHomogeneousTransform();
|
|
}
|
|
|
|
// Matrix to Euler Angles conversion
|
|
// a,b,c, are the YawPitchRoll angles to be returned
|
|
// rotation a around axis A1
|
|
// is followed by rotation b around axis A2
|
|
// is followed by rotation c around axis A3
|
|
// rotations are CCW or CW (D) in LH or RH coordinate system (S)
|
|
template <Axis A1, Axis A2, Axis A3, RotateDirection D, HandedSystem S>
|
|
void ToEulerAngles(T *a, T *b, T *c)
|
|
{
|
|
OVR_COMPILER_ASSERT((A1 != A2) && (A2 != A3) && (A1 != A3));
|
|
|
|
T psign = -1;
|
|
if (((A1 + 1) % 3 == A2) && ((A2 + 1) % 3 == A3)) // Determine whether even permutation
|
|
psign = 1;
|
|
|
|
T pm = psign*M[A1][A3];
|
|
if (pm < -1.0f + Math<T>::SingularityRadius)
|
|
{ // South pole singularity
|
|
*a = 0;
|
|
*b = -S*D*Math<T>::PiOver2;
|
|
*c = S*D*atan2( psign*M[A2][A1], M[A2][A2] );
|
|
}
|
|
else if (pm > 1.0f - Math<T>::SingularityRadius)
|
|
{ // North pole singularity
|
|
*a = 0;
|
|
*b = S*D*Math<T>::PiOver2;
|
|
*c = S*D*atan2( psign*M[A2][A1], M[A2][A2] );
|
|
}
|
|
else
|
|
{ // Normal case (nonsingular)
|
|
*a = S*D*atan2( -psign*M[A2][A3], M[A3][A3] );
|
|
*b = S*D*asin(pm);
|
|
*c = S*D*atan2( -psign*M[A1][A2], M[A1][A1] );
|
|
}
|
|
|
|
return;
|
|
}
|
|
|
|
// Matrix to Euler Angles conversion
|
|
// a,b,c, are the YawPitchRoll angles to be returned
|
|
// rotation a around axis A1
|
|
// is followed by rotation b around axis A2
|
|
// is followed by rotation c around axis A1
|
|
// rotations are CCW or CW (D) in LH or RH coordinate system (S)
|
|
template <Axis A1, Axis A2, RotateDirection D, HandedSystem S>
|
|
void ToEulerAnglesABA(T *a, T *b, T *c)
|
|
{
|
|
OVR_COMPILER_ASSERT(A1 != A2);
|
|
|
|
// Determine the axis that was not supplied
|
|
int m = 3 - A1 - A2;
|
|
|
|
T psign = -1;
|
|
if ((A1 + 1) % 3 == A2) // Determine whether even permutation
|
|
psign = 1.0f;
|
|
|
|
T c2 = M[A1][A1];
|
|
if (c2 < -1 + Math<T>::SingularityRadius)
|
|
{ // South pole singularity
|
|
*a = 0;
|
|
*b = S*D*Math<T>::Pi;
|
|
*c = S*D*atan2( -psign*M[A2][m],M[A2][A2]);
|
|
}
|
|
else if (c2 > 1.0f - Math<T>::SingularityRadius)
|
|
{ // North pole singularity
|
|
*a = 0;
|
|
*b = 0;
|
|
*c = S*D*atan2( -psign*M[A2][m],M[A2][A2]);
|
|
}
|
|
else
|
|
{ // Normal case (nonsingular)
|
|
*a = S*D*atan2( M[A2][A1],-psign*M[m][A1]);
|
|
*b = S*D*acos(c2);
|
|
*c = S*D*atan2( M[A1][A2],psign*M[A1][m]);
|
|
}
|
|
return;
|
|
}
|
|
|
|
// Creates a matrix that converts the vertices from one coordinate system
|
|
// to another.
|
|
static Matrix4 AxisConversion(const WorldAxes& to, const WorldAxes& from)
|
|
{
|
|
// Holds axis values from the 'to' structure
|
|
int toArray[3] = { to.XAxis, to.YAxis, to.ZAxis };
|
|
|
|
// The inverse of the toArray
|
|
int inv[4];
|
|
inv[0] = inv[abs(to.XAxis)] = 0;
|
|
inv[abs(to.YAxis)] = 1;
|
|
inv[abs(to.ZAxis)] = 2;
|
|
|
|
Matrix4 m(0, 0, 0,
|
|
0, 0, 0,
|
|
0, 0, 0);
|
|
|
|
// Only three values in the matrix need to be changed to 1 or -1.
|
|
m.M[inv[abs(from.XAxis)]][0] = T(from.XAxis/toArray[inv[abs(from.XAxis)]]);
|
|
m.M[inv[abs(from.YAxis)]][1] = T(from.YAxis/toArray[inv[abs(from.YAxis)]]);
|
|
m.M[inv[abs(from.ZAxis)]][2] = T(from.ZAxis/toArray[inv[abs(from.ZAxis)]]);
|
|
return m;
|
|
}
|
|
|
|
|
|
// Creates a matrix for translation by vector
|
|
static Matrix4 Translation(const Vector3<T>& v)
|
|
{
|
|
Matrix4 t;
|
|
t.M[0][3] = v.x;
|
|
t.M[1][3] = v.y;
|
|
t.M[2][3] = v.z;
|
|
return t;
|
|
}
|
|
|
|
// Creates a matrix for translation by vector
|
|
static Matrix4 Translation(T x, T y, T z = 0.0f)
|
|
{
|
|
Matrix4 t;
|
|
t.M[0][3] = x;
|
|
t.M[1][3] = y;
|
|
t.M[2][3] = z;
|
|
return t;
|
|
}
|
|
|
|
// Sets the translation part
|
|
void SetTranslation(const Vector3<T>& v)
|
|
{
|
|
M[0][3] = v.x;
|
|
M[1][3] = v.y;
|
|
M[2][3] = v.z;
|
|
}
|
|
|
|
Vector3<T> GetTranslation() const
|
|
{
|
|
return Vector3<T>( M[0][3], M[1][3], M[2][3] );
|
|
}
|
|
|
|
// Creates a matrix for scaling by vector
|
|
static Matrix4 Scaling(const Vector3<T>& v)
|
|
{
|
|
Matrix4 t;
|
|
t.M[0][0] = v.x;
|
|
t.M[1][1] = v.y;
|
|
t.M[2][2] = v.z;
|
|
return t;
|
|
}
|
|
|
|
// Creates a matrix for scaling by vector
|
|
static Matrix4 Scaling(T x, T y, T z)
|
|
{
|
|
Matrix4 t;
|
|
t.M[0][0] = x;
|
|
t.M[1][1] = y;
|
|
t.M[2][2] = z;
|
|
return t;
|
|
}
|
|
|
|
// Creates a matrix for scaling by constant
|
|
static Matrix4 Scaling(T s)
|
|
{
|
|
Matrix4 t;
|
|
t.M[0][0] = s;
|
|
t.M[1][1] = s;
|
|
t.M[2][2] = s;
|
|
return t;
|
|
}
|
|
|
|
// Simple L1 distance in R^12
|
|
T Distance(const Matrix4& m2) const
|
|
{
|
|
T d = fabs(M[0][0] - m2.M[0][0]) + fabs(M[0][1] - m2.M[0][1]);
|
|
d += fabs(M[0][2] - m2.M[0][2]) + fabs(M[0][3] - m2.M[0][3]);
|
|
d += fabs(M[1][0] - m2.M[1][0]) + fabs(M[1][1] - m2.M[1][1]);
|
|
d += fabs(M[1][2] - m2.M[1][2]) + fabs(M[1][3] - m2.M[1][3]);
|
|
d += fabs(M[2][0] - m2.M[2][0]) + fabs(M[2][1] - m2.M[2][1]);
|
|
d += fabs(M[2][2] - m2.M[2][2]) + fabs(M[2][3] - m2.M[2][3]);
|
|
d += fabs(M[3][0] - m2.M[3][0]) + fabs(M[3][1] - m2.M[3][1]);
|
|
d += fabs(M[3][2] - m2.M[3][2]) + fabs(M[3][3] - m2.M[3][3]);
|
|
return d;
|
|
}
|
|
|
|
// Creates a rotation matrix rotating around the X axis by 'angle' radians.
|
|
// Just for quick testing. Not for final API. Need to remove case.
|
|
static Matrix4 RotationAxis(Axis A, T angle, RotateDirection d, HandedSystem s)
|
|
{
|
|
T sina = s * d *sin(angle);
|
|
T cosa = cos(angle);
|
|
|
|
switch(A)
|
|
{
|
|
case Axis_X:
|
|
return Matrix4(1, 0, 0,
|
|
0, cosa, -sina,
|
|
0, sina, cosa);
|
|
case Axis_Y:
|
|
return Matrix4(cosa, 0, sina,
|
|
0, 1, 0,
|
|
-sina, 0, cosa);
|
|
case Axis_Z:
|
|
return Matrix4(cosa, -sina, 0,
|
|
sina, cosa, 0,
|
|
0, 0, 1);
|
|
}
|
|
}
|
|
|
|
|
|
// Creates a rotation matrix rotating around the X axis by 'angle' radians.
|
|
// Rotation direction is depends on the coordinate system:
|
|
// RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
|
|
// while looking in the negative axis direction. This is the
|
|
// same as looking down from positive axis values towards origin.
|
|
// LHS: Positive angle values rotate clock-wise (CW), while looking in the
|
|
// negative axis direction.
|
|
static Matrix4 RotationX(T angle)
|
|
{
|
|
T sina = sin(angle);
|
|
T cosa = cos(angle);
|
|
return Matrix4(1, 0, 0,
|
|
0, cosa, -sina,
|
|
0, sina, cosa);
|
|
}
|
|
|
|
// Creates a rotation matrix rotating around the Y axis by 'angle' radians.
|
|
// Rotation direction is depends on the coordinate system:
|
|
// RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
|
|
// while looking in the negative axis direction. This is the
|
|
// same as looking down from positive axis values towards origin.
|
|
// LHS: Positive angle values rotate clock-wise (CW), while looking in the
|
|
// negative axis direction.
|
|
static Matrix4 RotationY(T angle)
|
|
{
|
|
T sina = sin(angle);
|
|
T cosa = cos(angle);
|
|
return Matrix4(cosa, 0, sina,
|
|
0, 1, 0,
|
|
-sina, 0, cosa);
|
|
}
|
|
|
|
// Creates a rotation matrix rotating around the Z axis by 'angle' radians.
|
|
// Rotation direction is depends on the coordinate system:
|
|
// RHS (Oculus default): Positive angle values rotate Counter-clockwise (CCW),
|
|
// while looking in the negative axis direction. This is the
|
|
// same as looking down from positive axis values towards origin.
|
|
// LHS: Positive angle values rotate clock-wise (CW), while looking in the
|
|
// negative axis direction.
|
|
static Matrix4 RotationZ(T angle)
|
|
{
|
|
T sina = sin(angle);
|
|
T cosa = cos(angle);
|
|
return Matrix4(cosa, -sina, 0,
|
|
sina, cosa, 0,
|
|
0, 0, 1);
|
|
}
|
|
|
|
// LookAtRH creates a View transformation matrix for right-handed coordinate system.
|
|
// The resulting matrix points camera from 'eye' towards 'at' direction, with 'up'
|
|
// specifying the up vector. The resulting matrix should be used with PerspectiveRH
|
|
// projection.
|
|
static Matrix4 LookAtRH(const Vector3<T>& eye, const Vector3<T>& at, const Vector3<T>& up)
|
|
{
|
|
Vector3<T> z = (eye - at).Normalized(); // Forward
|
|
Vector3<T> x = up.Cross(z).Normalized(); // Right
|
|
Vector3<T> y = z.Cross(x);
|
|
|
|
Matrix4 m(x.x, x.y, x.z, -(x.Dot(eye)),
|
|
y.x, y.y, y.z, -(y.Dot(eye)),
|
|
z.x, z.y, z.z, -(z.Dot(eye)),
|
|
0, 0, 0, 1 );
|
|
return m;
|
|
}
|
|
|
|
// LookAtLH creates a View transformation matrix for left-handed coordinate system.
|
|
// The resulting matrix points camera from 'eye' towards 'at' direction, with 'up'
|
|
// specifying the up vector.
|
|
static Matrix4 LookAtLH(const Vector3<T>& eye, const Vector3<T>& at, const Vector3<T>& up)
|
|
{
|
|
Vector3<T> z = (at - eye).Normalized(); // Forward
|
|
Vector3<T> x = up.Cross(z).Normalized(); // Right
|
|
Vector3<T> y = z.Cross(x);
|
|
|
|
Matrix4 m(x.x, x.y, x.z, -(x.Dot(eye)),
|
|
y.x, y.y, y.z, -(y.Dot(eye)),
|
|
z.x, z.y, z.z, -(z.Dot(eye)),
|
|
0, 0, 0, 1 );
|
|
return m;
|
|
}
|
|
|
|
// PerspectiveRH creates a right-handed perspective projection matrix that can be
|
|
// used with the Oculus sample renderer.
|
|
// yfov - Specifies vertical field of view in radians.
|
|
// aspect - Screen aspect ration, which is usually width/height for square pixels.
|
|
// Note that xfov = yfov * aspect.
|
|
// znear - Absolute value of near Z clipping clipping range.
|
|
// zfar - Absolute value of far Z clipping clipping range (larger then near).
|
|
// Even though RHS usually looks in the direction of negative Z, positive values
|
|
// are expected for znear and zfar.
|
|
static Matrix4 PerspectiveRH(T yfov, T aspect, T znear, T zfar)
|
|
{
|
|
Matrix4 m;
|
|
T tanHalfFov = tan(yfov * 0.5f);
|
|
|
|
m.M[0][0] = 1 / (aspect * tanHalfFov);
|
|
m.M[1][1] = 1 / tanHalfFov;
|
|
m.M[2][2] = zfar / (zfar - znear);
|
|
m.M[3][2] = 1;
|
|
m.M[2][3] = (zfar * znear) / (znear - zfar);
|
|
m.M[3][3] = 0;
|
|
|
|
// Note: Post-projection matrix result assumes Left-Handed coordinate system,
|
|
// with Y up, X right and Z forward. This supports positive z-buffer values.
|
|
return m;
|
|
}
|
|
|
|
// PerspectiveRH creates a left-handed perspective projection matrix that can be
|
|
// used with the Oculus sample renderer.
|
|
// yfov - Specifies vertical field of view in radians.
|
|
// aspect - Screen aspect ration, which is usually width/height for square pixels.
|
|
// Note that xfov = yfov * aspect.
|
|
// znear - Absolute value of near Z clipping clipping range.
|
|
// zfar - Absolute value of far Z clipping clipping range (larger then near).
|
|
static Matrix4 PerspectiveLH(T yfov, T aspect, T znear, T zfar)
|
|
{
|
|
Matrix4 m;
|
|
T tanHalfFov = tan(yfov * 0.5f);
|
|
|
|
m.M[0][0] = 1.0 / (aspect * tanHalfFov);
|
|
m.M[1][1] = 1.0 / tanHalfFov;
|
|
m.M[2][2] = zfar / (znear - zfar);
|
|
// m.M[2][2] = zfar / (zfar - znear);
|
|
m.M[3][2] = -1.0;
|
|
m.M[2][3] = (zfar * znear) / (znear - zfar);
|
|
m.M[3][3] = 0.0;
|
|
|
|
// Note: Post-projection matrix result assumes Left-Handed coordinate system,
|
|
// with Y up, X right and Z forward. This supports positive z-buffer values.
|
|
// This is the case even for RHS cooridnate input.
|
|
return m;
|
|
}
|
|
|
|
static Matrix4 Ortho2D(T w, T h)
|
|
{
|
|
Matrix4 m;
|
|
m.M[0][0] = 2.0/w;
|
|
m.M[1][1] = -2.0/h;
|
|
m.M[0][3] = -1.0;
|
|
m.M[1][3] = 1.0;
|
|
m.M[2][2] = 0;
|
|
return m;
|
|
}
|
|
};
|
|
|
|
typedef Matrix4<float> Matrix4f;
|
|
typedef Matrix4<double> Matrix4d;
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Matrix3
|
|
//
|
|
// Matrix3 is a 3x3 matrix used for representing a rotation matrix.
|
|
// The matrix is stored in row-major order in memory, meaning that values
|
|
// of the first row are stored before the next one.
|
|
//
|
|
// The arrangement of the matrix is chosen to be in Right-Handed
|
|
// coordinate system and counterclockwise rotations when looking down
|
|
// the axis
|
|
//
|
|
// Transformation Order:
|
|
// - Transformations are applied from right to left, so the expression
|
|
// M1 * M2 * M3 * V means that the vector V is transformed by M3 first,
|
|
// followed by M2 and M1.
|
|
//
|
|
// Coordinate system: Right Handed
|
|
//
|
|
// Rotations: Counterclockwise when looking down the axis. All angles are in radians.
|
|
|
|
template<typename T>
|
|
class SymMat3;
|
|
|
|
template<class T>
|
|
class Matrix3
|
|
{
|
|
static const Matrix3 IdentityValue;
|
|
|
|
public:
|
|
T M[3][3];
|
|
|
|
enum NoInitType { NoInit };
|
|
|
|
// Construct with no memory initialization.
|
|
Matrix3(NoInitType) { }
|
|
|
|
// By default, we construct identity matrix.
|
|
Matrix3()
|
|
{
|
|
SetIdentity();
|
|
}
|
|
|
|
Matrix3(T m11, T m12, T m13,
|
|
T m21, T m22, T m23,
|
|
T m31, T m32, T m33)
|
|
{
|
|
M[0][0] = m11; M[0][1] = m12; M[0][2] = m13;
|
|
M[1][0] = m21; M[1][1] = m22; M[1][2] = m23;
|
|
M[2][0] = m31; M[2][1] = m32; M[2][2] = m33;
|
|
}
|
|
|
|
/*
|
|
explicit Matrix3(const Quat<T>& q)
|
|
{
|
|
T ww = q.w*q.w;
|
|
T xx = q.x*q.x;
|
|
T yy = q.y*q.y;
|
|
T zz = q.z*q.z;
|
|
|
|
M[0][0] = ww + xx - yy - zz; M[0][1] = 2 * (q.x*q.y - q.w*q.z); M[0][2] = 2 * (q.x*q.z + q.w*q.y);
|
|
M[1][0] = 2 * (q.x*q.y + q.w*q.z); M[1][1] = ww - xx + yy - zz; M[1][2] = 2 * (q.y*q.z - q.w*q.x);
|
|
M[2][0] = 2 * (q.x*q.z - q.w*q.y); M[2][1] = 2 * (q.y*q.z + q.w*q.x); M[2][2] = ww - xx - yy + zz;
|
|
}
|
|
*/
|
|
|
|
explicit Matrix3(const Quat<T>& q)
|
|
{
|
|
const T tx = q.x+q.x, ty = q.y+q.y, tz = q.z+q.z;
|
|
const T twx = q.w*tx, twy = q.w*ty, twz = q.w*tz;
|
|
const T txx = q.x*tx, txy = q.x*ty, txz = q.x*tz;
|
|
const T tyy = q.y*ty, tyz = q.y*tz, tzz = q.z*tz;
|
|
M[0][0] = T(1) - (tyy + tzz); M[0][1] = txy - twz; M[0][2] = txz + twy;
|
|
M[1][0] = txy + twz; M[1][1] = T(1) - (txx + tzz); M[1][2] = tyz - twx;
|
|
M[2][0] = txz - twy; M[2][1] = tyz + twx; M[2][2] = T(1) - (txx + tyy);
|
|
}
|
|
|
|
inline explicit Matrix3(T s)
|
|
{
|
|
M[0][0] = M[1][1] = M[2][2] = s;
|
|
M[0][1] = M[0][2] = M[1][0] = M[1][2] = M[2][0] = M[2][1] = 0;
|
|
}
|
|
|
|
explicit Matrix3(const Transform<T>& p)
|
|
{
|
|
Matrix3 result(p.Rotation);
|
|
result.SetTranslation(p.Translation);
|
|
*this = result;
|
|
}
|
|
|
|
// C-interop support
|
|
explicit Matrix3(const Matrix4<typename Math<T>::OtherFloatType> &src)
|
|
{
|
|
for (int i = 0; i < 3; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
M[i][j] = (T)src.M[i][j];
|
|
}
|
|
|
|
// C-interop support.
|
|
Matrix3(const typename CompatibleTypes<Matrix3<T> >::Type& s)
|
|
{
|
|
OVR_COMPILER_ASSERT(sizeof(s) == sizeof(Matrix3));
|
|
memcpy(M, s.M, sizeof(M));
|
|
}
|
|
|
|
operator typename CompatibleTypes<Matrix3<T> >::Type () const
|
|
{
|
|
typename CompatibleTypes<Matrix3<T> >::Type result;
|
|
OVR_COMPILER_ASSERT(sizeof(result) == sizeof(Matrix3));
|
|
memcpy(result.M, M, sizeof(M));
|
|
return result;
|
|
}
|
|
|
|
void ToString(char* dest, UPInt destsize) const
|
|
{
|
|
UPInt pos = 0;
|
|
for (int r=0; r<3; r++)
|
|
for (int c=0; c<3; c++)
|
|
pos += OVR_sprintf(dest+pos, destsize-pos, "%g ", M[r][c]);
|
|
}
|
|
|
|
static Matrix3 FromString(const char* src)
|
|
{
|
|
Matrix3 result;
|
|
for (int r=0; r<3; r++)
|
|
for (int c=0; c<3; c++)
|
|
{
|
|
result.M[r][c] = (T)atof(src);
|
|
while (src && *src != ' ')
|
|
src++;
|
|
while (src && *src == ' ')
|
|
src++;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
static const Matrix3& Identity() { return IdentityValue; }
|
|
|
|
void SetIdentity()
|
|
{
|
|
M[0][0] = M[1][1] = M[2][2] = 1;
|
|
M[0][1] = M[1][0] = M[2][0] = 0;
|
|
M[0][2] = M[1][2] = M[2][1] = 0;
|
|
}
|
|
|
|
bool operator== (const Matrix3& b) const
|
|
{
|
|
bool isEqual = true;
|
|
for (int i = 0; i < 3; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
isEqual &= (M[i][j] == b.M[i][j]);
|
|
|
|
return isEqual;
|
|
}
|
|
|
|
Matrix3 operator+ (const Matrix3& b) const
|
|
{
|
|
Matrix4<T> result(*this);
|
|
result += b;
|
|
return result;
|
|
}
|
|
|
|
Matrix3& operator+= (const Matrix3& b)
|
|
{
|
|
for (int i = 0; i < 3; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
M[i][j] += b.M[i][j];
|
|
return *this;
|
|
}
|
|
|
|
void operator= (const Matrix3& b)
|
|
{
|
|
for (int i = 0; i < 3; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
M[i][j] = b.M[i][j];
|
|
return;
|
|
}
|
|
|
|
void operator= (const SymMat3<T>& b)
|
|
{
|
|
for (int i = 0; i < 3; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
M[i][j] = 0;
|
|
|
|
M[0][0] = b.v[0];
|
|
M[0][1] = b.v[1];
|
|
M[0][2] = b.v[2];
|
|
M[1][1] = b.v[3];
|
|
M[1][2] = b.v[4];
|
|
M[2][2] = b.v[5];
|
|
|
|
return;
|
|
}
|
|
|
|
Matrix3 operator- (const Matrix3& b) const
|
|
{
|
|
Matrix3 result(*this);
|
|
result -= b;
|
|
return result;
|
|
}
|
|
|
|
Matrix3& operator-= (const Matrix3& b)
|
|
{
|
|
for (int i = 0; i < 3; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
M[i][j] -= b.M[i][j];
|
|
return *this;
|
|
}
|
|
|
|
// Multiplies two matrices into destination with minimum copying.
|
|
static Matrix3& Multiply(Matrix3* d, const Matrix3& a, const Matrix3& b)
|
|
{
|
|
OVR_ASSERT((d != &a) && (d != &b));
|
|
int i = 0;
|
|
do {
|
|
d->M[i][0] = a.M[i][0] * b.M[0][0] + a.M[i][1] * b.M[1][0] + a.M[i][2] * b.M[2][0];
|
|
d->M[i][1] = a.M[i][0] * b.M[0][1] + a.M[i][1] * b.M[1][1] + a.M[i][2] * b.M[2][1];
|
|
d->M[i][2] = a.M[i][0] * b.M[0][2] + a.M[i][1] * b.M[1][2] + a.M[i][2] * b.M[2][2];
|
|
} while((++i) < 3);
|
|
|
|
return *d;
|
|
}
|
|
|
|
Matrix3 operator* (const Matrix3& b) const
|
|
{
|
|
Matrix3 result(Matrix3::NoInit);
|
|
Multiply(&result, *this, b);
|
|
return result;
|
|
}
|
|
|
|
Matrix3& operator*= (const Matrix3& b)
|
|
{
|
|
return Multiply(this, Matrix3(*this), b);
|
|
}
|
|
|
|
Matrix3 operator* (T s) const
|
|
{
|
|
Matrix3 result(*this);
|
|
result *= s;
|
|
return result;
|
|
}
|
|
|
|
Matrix3& operator*= (T s)
|
|
{
|
|
for (int i = 0; i < 3; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
M[i][j] *= s;
|
|
return *this;
|
|
}
|
|
|
|
Vector3<T> operator* (const Vector3<T> &b) const
|
|
{
|
|
Vector3<T> result;
|
|
result.x = M[0][0]*b.x + M[0][1]*b.y + M[0][2]*b.z;
|
|
result.y = M[1][0]*b.x + M[1][1]*b.y + M[1][2]*b.z;
|
|
result.z = M[2][0]*b.x + M[2][1]*b.y + M[2][2]*b.z;
|
|
|
|
return result;
|
|
}
|
|
|
|
Matrix3 operator/ (T s) const
|
|
{
|
|
Matrix3 result(*this);
|
|
result /= s;
|
|
return result;
|
|
}
|
|
|
|
Matrix3& operator/= (T s)
|
|
{
|
|
for (int i = 0; i < 3; i++)
|
|
for (int j = 0; j < 3; j++)
|
|
M[i][j] /= s;
|
|
return *this;
|
|
}
|
|
|
|
Vector3<T> Transform(const Vector3<T>& v) const
|
|
{
|
|
return Vector3<T>(M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z,
|
|
M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z,
|
|
M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z);
|
|
}
|
|
|
|
Matrix3 Transposed() const
|
|
{
|
|
return Matrix3(M[0][0], M[1][0], M[2][0],
|
|
M[0][1], M[1][1], M[2][1],
|
|
M[0][2], M[1][2], M[2][2]);
|
|
}
|
|
|
|
void Transpose()
|
|
{
|
|
*this = Transposed();
|
|
}
|
|
|
|
|
|
T SubDet (const UPInt* rows, const UPInt* cols) const
|
|
{
|
|
return M[rows[0]][cols[0]] * (M[rows[1]][cols[1]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[1]])
|
|
- M[rows[0]][cols[1]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[2]] - M[rows[1]][cols[2]] * M[rows[2]][cols[0]])
|
|
+ M[rows[0]][cols[2]] * (M[rows[1]][cols[0]] * M[rows[2]][cols[1]] - M[rows[1]][cols[1]] * M[rows[2]][cols[0]]);
|
|
}
|
|
|
|
// M += a*b.t()
|
|
inline void Rank1Add(const Vector3<T> &a, const Vector3<T> &b)
|
|
{
|
|
M[0][0] += a.x*b.x; M[0][1] += a.x*b.y; M[0][2] += a.x*b.z;
|
|
M[1][0] += a.y*b.x; M[1][1] += a.y*b.y; M[1][2] += a.y*b.z;
|
|
M[2][0] += a.z*b.x; M[2][1] += a.z*b.y; M[2][2] += a.z*b.z;
|
|
}
|
|
|
|
// M -= a*b.t()
|
|
inline void Rank1Sub(const Vector3<T> &a, const Vector3<T> &b)
|
|
{
|
|
M[0][0] -= a.x*b.x; M[0][1] -= a.x*b.y; M[0][2] -= a.x*b.z;
|
|
M[1][0] -= a.y*b.x; M[1][1] -= a.y*b.y; M[1][2] -= a.y*b.z;
|
|
M[2][0] -= a.z*b.x; M[2][1] -= a.z*b.y; M[2][2] -= a.z*b.z;
|
|
}
|
|
|
|
inline Vector3<T> Col(int c) const
|
|
{
|
|
return Vector3<T>(M[0][c], M[1][c], M[2][c]);
|
|
}
|
|
|
|
inline Vector3<T> Row(int r) const
|
|
{
|
|
return Vector3<T>(M[r][0], M[r][1], M[r][2]);
|
|
}
|
|
|
|
inline T Determinant() const
|
|
{
|
|
const Matrix3<T>& m = *this;
|
|
T d;
|
|
|
|
d = m.M[0][0] * (m.M[1][1]*m.M[2][2] - m.M[1][2] * m.M[2][1]);
|
|
d -= m.M[0][1] * (m.M[1][0]*m.M[2][2] - m.M[1][2] * m.M[2][0]);
|
|
d += m.M[0][2] * (m.M[1][0]*m.M[2][1] - m.M[1][1] * m.M[2][0]);
|
|
|
|
return d;
|
|
}
|
|
|
|
inline Matrix3<T> Inverse() const
|
|
{
|
|
Matrix3<T> a;
|
|
const Matrix3<T>& m = *this;
|
|
T d = Determinant();
|
|
|
|
assert(d != 0);
|
|
T s = T(1)/d;
|
|
|
|
a.M[0][0] = s * (m.M[1][1] * m.M[2][2] - m.M[1][2] * m.M[2][1]);
|
|
a.M[1][0] = s * (m.M[1][2] * m.M[2][0] - m.M[1][0] * m.M[2][2]);
|
|
a.M[2][0] = s * (m.M[1][0] * m.M[2][1] - m.M[1][1] * m.M[2][0]);
|
|
|
|
a.M[0][1] = s * (m.M[0][2] * m.M[2][1] - m.M[0][1] * m.M[2][2]);
|
|
a.M[1][1] = s * (m.M[0][0] * m.M[2][2] - m.M[0][2] * m.M[2][0]);
|
|
a.M[2][1] = s * (m.M[0][1] * m.M[2][0] - m.M[0][0] * m.M[2][1]);
|
|
|
|
a.M[0][2] = s * (m.M[0][1] * m.M[1][2] - m.M[0][2] * m.M[1][1]);
|
|
a.M[1][2] = s * (m.M[0][2] * m.M[1][0] - m.M[0][0] * m.M[1][2]);
|
|
a.M[2][2] = s * (m.M[0][0] * m.M[1][1] - m.M[0][1] * m.M[1][0]);
|
|
|
|
return a;
|
|
}
|
|
|
|
};
|
|
|
|
typedef Matrix3<float> Matrix3f;
|
|
typedef Matrix3<double> Matrix3d;
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
|
|
template<typename T>
|
|
class SymMat3
|
|
{
|
|
private:
|
|
typedef SymMat3<T> this_type;
|
|
|
|
public:
|
|
typedef T Value_t;
|
|
// Upper symmetric
|
|
T v[6]; // _00 _01 _02 _11 _12 _22
|
|
|
|
inline SymMat3() {}
|
|
|
|
inline explicit SymMat3(T s)
|
|
{
|
|
v[0] = v[3] = v[5] = s;
|
|
v[1] = v[2] = v[4] = 0;
|
|
}
|
|
|
|
inline explicit SymMat3(T a00, T a01, T a02, T a11, T a12, T a22)
|
|
{
|
|
v[0] = a00; v[1] = a01; v[2] = a02;
|
|
v[3] = a11; v[4] = a12;
|
|
v[5] = a22;
|
|
}
|
|
|
|
static inline int Index(unsigned int i, unsigned int j)
|
|
{
|
|
return (i <= j) ? (3*i - i*(i+1)/2 + j) : (3*j - j*(j+1)/2 + i);
|
|
}
|
|
|
|
inline T operator()(int i, int j) const { return v[Index(i,j)]; }
|
|
|
|
inline T &operator()(int i, int j) { return v[Index(i,j)]; }
|
|
|
|
template<typename U>
|
|
inline SymMat3<U> CastTo() const
|
|
{
|
|
return SymMat3<U>(static_cast<U>(v[0]), static_cast<U>(v[1]), static_cast<U>(v[2]),
|
|
static_cast<U>(v[3]), static_cast<U>(v[4]), static_cast<U>(v[5]));
|
|
}
|
|
|
|
inline this_type& operator+=(const this_type& b)
|
|
{
|
|
v[0]+=b.v[0];
|
|
v[1]+=b.v[1];
|
|
v[2]+=b.v[2];
|
|
v[3]+=b.v[3];
|
|
v[4]+=b.v[4];
|
|
v[5]+=b.v[5];
|
|
return *this;
|
|
}
|
|
|
|
inline this_type& operator-=(const this_type& b)
|
|
{
|
|
v[0]-=b.v[0];
|
|
v[1]-=b.v[1];
|
|
v[2]-=b.v[2];
|
|
v[3]-=b.v[3];
|
|
v[4]-=b.v[4];
|
|
v[5]-=b.v[5];
|
|
|
|
return *this;
|
|
}
|
|
|
|
inline this_type& operator*=(T s)
|
|
{
|
|
v[0]*=s;
|
|
v[1]*=s;
|
|
v[2]*=s;
|
|
v[3]*=s;
|
|
v[4]*=s;
|
|
v[5]*=s;
|
|
|
|
return *this;
|
|
}
|
|
|
|
inline SymMat3 operator*(T s) const
|
|
{
|
|
SymMat3 d;
|
|
d.v[0] = v[0]*s;
|
|
d.v[1] = v[1]*s;
|
|
d.v[2] = v[2]*s;
|
|
d.v[3] = v[3]*s;
|
|
d.v[4] = v[4]*s;
|
|
d.v[5] = v[5]*s;
|
|
|
|
return d;
|
|
}
|
|
|
|
// Multiplies two matrices into destination with minimum copying.
|
|
static SymMat3& Multiply(SymMat3* d, const SymMat3& a, const SymMat3& b)
|
|
{
|
|
// _00 _01 _02 _11 _12 _22
|
|
|
|
d->v[0] = a.v[0] * b.v[0];
|
|
d->v[1] = a.v[0] * b.v[1] + a.v[1] * b.v[3];
|
|
d->v[2] = a.v[0] * b.v[2] + a.v[1] * b.v[4];
|
|
|
|
d->v[3] = a.v[3] * b.v[3];
|
|
d->v[4] = a.v[3] * b.v[4] + a.v[4] * b.v[5];
|
|
|
|
d->v[5] = a.v[5] * b.v[5];
|
|
|
|
return *d;
|
|
}
|
|
|
|
inline T Determinant() const
|
|
{
|
|
const this_type& m = *this;
|
|
T d;
|
|
|
|
d = m(0,0) * (m(1,1)*m(2,2) - m(1,2) * m(2,1));
|
|
d -= m(0,1) * (m(1,0)*m(2,2) - m(1,2) * m(2,0));
|
|
d += m(0,2) * (m(1,0)*m(2,1) - m(1,1) * m(2,0));
|
|
|
|
return d;
|
|
}
|
|
|
|
inline this_type Inverse() const
|
|
{
|
|
this_type a;
|
|
const this_type& m = *this;
|
|
T d = Determinant();
|
|
|
|
assert(d != 0);
|
|
T s = T(1)/d;
|
|
|
|
a(0,0) = s * (m(1,1) * m(2,2) - m(1,2) * m(2,1));
|
|
|
|
a(0,1) = s * (m(0,2) * m(2,1) - m(0,1) * m(2,2));
|
|
a(1,1) = s * (m(0,0) * m(2,2) - m(0,2) * m(2,0));
|
|
|
|
a(0,2) = s * (m(0,1) * m(1,2) - m(0,2) * m(1,1));
|
|
a(1,2) = s * (m(0,2) * m(1,0) - m(0,0) * m(1,2));
|
|
a(2,2) = s * (m(0,0) * m(1,1) - m(0,1) * m(1,0));
|
|
|
|
return a;
|
|
}
|
|
|
|
inline T Trace() const { return v[0] + v[3] + v[5]; }
|
|
|
|
// M = a*a.t()
|
|
inline void Rank1(const Vector3<T> &a)
|
|
{
|
|
v[0] = a.x*a.x; v[1] = a.x*a.y; v[2] = a.x*a.z;
|
|
v[3] = a.y*a.y; v[4] = a.y*a.z;
|
|
v[5] = a.z*a.z;
|
|
}
|
|
|
|
// M += a*a.t()
|
|
inline void Rank1Add(const Vector3<T> &a)
|
|
{
|
|
v[0] += a.x*a.x; v[1] += a.x*a.y; v[2] += a.x*a.z;
|
|
v[3] += a.y*a.y; v[4] += a.y*a.z;
|
|
v[5] += a.z*a.z;
|
|
}
|
|
|
|
// M -= a*a.t()
|
|
inline void Rank1Sub(const Vector3<T> &a)
|
|
{
|
|
v[0] -= a.x*a.x; v[1] -= a.x*a.y; v[2] -= a.x*a.z;
|
|
v[3] -= a.y*a.y; v[4] -= a.y*a.z;
|
|
v[5] -= a.z*a.z;
|
|
}
|
|
};
|
|
|
|
typedef SymMat3<float> SymMat3f;
|
|
typedef SymMat3<double> SymMat3d;
|
|
|
|
template<typename T>
|
|
inline Matrix3<T> operator*(const SymMat3<T>& a, const SymMat3<T>& b)
|
|
{
|
|
#define AJB_ARBC(r,c) (a(r,0)*b(0,c)+a(r,1)*b(1,c)+a(r,2)*b(2,c))
|
|
return Matrix3<T>(
|
|
AJB_ARBC(0,0), AJB_ARBC(0,1), AJB_ARBC(0,2),
|
|
AJB_ARBC(1,0), AJB_ARBC(1,1), AJB_ARBC(1,2),
|
|
AJB_ARBC(2,0), AJB_ARBC(2,1), AJB_ARBC(2,2));
|
|
#undef AJB_ARBC
|
|
}
|
|
|
|
template<typename T>
|
|
inline Matrix3<T> operator*(const Matrix3<T>& a, const SymMat3<T>& b)
|
|
{
|
|
#define AJB_ARBC(r,c) (a(r,0)*b(0,c)+a(r,1)*b(1,c)+a(r,2)*b(2,c))
|
|
return Matrix3<T>(
|
|
AJB_ARBC(0,0), AJB_ARBC(0,1), AJB_ARBC(0,2),
|
|
AJB_ARBC(1,0), AJB_ARBC(1,1), AJB_ARBC(1,2),
|
|
AJB_ARBC(2,0), AJB_ARBC(2,1), AJB_ARBC(2,2));
|
|
#undef AJB_ARBC
|
|
}
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Angle
|
|
|
|
// Cleanly representing the algebra of 2D rotations.
|
|
// The operations maintain the angle between -Pi and Pi, the same range as atan2.
|
|
|
|
template<class T>
|
|
class Angle
|
|
{
|
|
public:
|
|
enum AngularUnits
|
|
{
|
|
Radians = 0,
|
|
Degrees = 1
|
|
};
|
|
|
|
Angle() : a(0) {}
|
|
|
|
// Fix the range to be between -Pi and Pi
|
|
Angle(T a_, AngularUnits u = Radians) : a((u == Radians) ? a_ : a_*Math<T>::DegreeToRadFactor) { FixRange(); }
|
|
|
|
T Get(AngularUnits u = Radians) const { return (u == Radians) ? a : a*Math<T>::RadToDegreeFactor; }
|
|
void Set(const T& x, AngularUnits u = Radians) { a = (u == Radians) ? x : x*Math<T>::DegreeToRadFactor; FixRange(); }
|
|
int Sign() const { if (a == 0) return 0; else return (a > 0) ? 1 : -1; }
|
|
T Abs() const { return (a > 0) ? a : -a; }
|
|
|
|
bool operator== (const Angle& b) const { return a == b.a; }
|
|
bool operator!= (const Angle& b) const { return a != b.a; }
|
|
// bool operator< (const Angle& b) const { return a < a.b; }
|
|
// bool operator> (const Angle& b) const { return a > a.b; }
|
|
// bool operator<= (const Angle& b) const { return a <= a.b; }
|
|
// bool operator>= (const Angle& b) const { return a >= a.b; }
|
|
// bool operator= (const T& x) { a = x; FixRange(); }
|
|
|
|
// These operations assume a is already between -Pi and Pi.
|
|
Angle& operator+= (const Angle& b) { a = a + b.a; FastFixRange(); return *this; }
|
|
Angle& operator+= (const T& x) { a = a + x; FixRange(); return *this; }
|
|
Angle operator+ (const Angle& b) const { Angle res = *this; res += b; return res; }
|
|
Angle operator+ (const T& x) const { Angle res = *this; res += x; return res; }
|
|
Angle& operator-= (const Angle& b) { a = a - b.a; FastFixRange(); return *this; }
|
|
Angle& operator-= (const T& x) { a = a - x; FixRange(); return *this; }
|
|
Angle operator- (const Angle& b) const { Angle res = *this; res -= b; return res; }
|
|
Angle operator- (const T& x) const { Angle res = *this; res -= x; return res; }
|
|
|
|
T Distance(const Angle& b) { T c = fabs(a - b.a); return (c <= Math<T>::Pi) ? c : Math<T>::TwoPi - c; }
|
|
|
|
private:
|
|
|
|
// The stored angle, which should be maintained between -Pi and Pi
|
|
T a;
|
|
|
|
// Fixes the angle range to [-Pi,Pi], but assumes no more than 2Pi away on either side
|
|
inline void FastFixRange()
|
|
{
|
|
if (a < -Math<T>::Pi)
|
|
a += Math<T>::TwoPi;
|
|
else if (a > Math<T>::Pi)
|
|
a -= Math<T>::TwoPi;
|
|
}
|
|
|
|
// Fixes the angle range to [-Pi,Pi] for any given range, but slower then the fast method
|
|
inline void FixRange()
|
|
{
|
|
// do nothing if the value is already in the correct range, since fmod call is expensive
|
|
if (a >= -Math<T>::Pi && a <= Math<T>::Pi)
|
|
return;
|
|
a = fmod(a,Math<T>::TwoPi);
|
|
if (a < -Math<T>::Pi)
|
|
a += Math<T>::TwoPi;
|
|
else if (a > Math<T>::Pi)
|
|
a -= Math<T>::TwoPi;
|
|
}
|
|
};
|
|
|
|
|
|
typedef Angle<float> Anglef;
|
|
typedef Angle<double> Angled;
|
|
|
|
|
|
//-------------------------------------------------------------------------------------
|
|
// ***** Plane
|
|
|
|
// Consists of a normal vector and distance from the origin where the plane is located.
|
|
|
|
template<class T>
|
|
class Plane : public RefCountBase<Plane<T> >
|
|
{
|
|
public:
|
|
Vector3<T> N;
|
|
T D;
|
|
|
|
Plane() : D(0) {}
|
|
|
|
// Normals must already be normalized
|
|
Plane(const Vector3<T>& n, T d) : N(n), D(d) {}
|
|
Plane(T x, T y, T z, T d) : N(x,y,z), D(d) {}
|
|
|
|
// construct from a point on the plane and the normal
|
|
Plane(const Vector3<T>& p, const Vector3<T>& n) : N(n), D(-(p * n)) {}
|
|
|
|
// Find the point to plane distance. The sign indicates what side of the plane the point is on (0 = point on plane).
|
|
T TestSide(const Vector3<T>& p) const
|
|
{
|
|
return (N.Dot(p)) + D;
|
|
}
|
|
|
|
Plane<T> Flipped() const
|
|
{
|
|
return Plane(-N, -D);
|
|
}
|
|
|
|
void Flip()
|
|
{
|
|
N = -N;
|
|
D = -D;
|
|
}
|
|
|
|
bool operator==(const Plane<T>& rhs) const
|
|
{
|
|
return (this->D == rhs.D && this->N == rhs.N);
|
|
}
|
|
};
|
|
|
|
typedef Plane<float> Planef;
|
|
|
|
} // Namespace OVR
|
|
|
|
#endif
|