diff options
Diffstat (limited to 'LibOVR/Src/Kernel/OVR_Math.h')
| -rw-r--r-- | LibOVR/Src/Kernel/OVR_Math.h | 2791 |
1 files changed, 0 insertions, 2791 deletions
diff --git a/LibOVR/Src/Kernel/OVR_Math.h b/LibOVR/Src/Kernel/OVR_Math.h deleted file mode 100644 index c187cda..0000000 --- a/LibOVR/Src/Kernel/OVR_Math.h +++ /dev/null @@ -1,2791 +0,0 @@ -/************************************************************************************ - -PublicHeader: OVR_Kernel.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, LLC All Rights reserved. - -Licensed under the Oculus VR Rift SDK License Version 3.2 (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-3.2 - -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 Pose; -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 struct {} 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<Pose<float> > { typedef ovrPosef Type; }; -template<> struct CompatibleTypes<Pose<double> > { typedef ovrPosed 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; -}; - - -#define MATH_FLOAT_PI (3.1415926f) -#define MATH_FLOAT_TWOPI (2.0f *MATH_FLOAT_PI) -#define MATH_FLOAT_PIOVER2 (0.5f *MATH_FLOAT_PI) -#define MATH_FLOAT_PIOVER4 (0.25f*MATH_FLOAT_PI) -#define MATH_FLOAT_E (2.7182818f) -#define MATH_FLOAT_MAXVALUE (FLT_MAX) -#define MATH_FLOAT MINPOSITIVEVALUE (FLT_MIN) -#define MATH_FLOAT_RADTODEGREEFACTOR (360.0f / MATH_FLOAT_TWOPI) -#define MATH_FLOAT_DEGREETORADFACTOR (MATH_FLOAT_TWOPI / 360.0f) -#define MATH_FLOAT_TOLERANCE (0.00001f) -#define MATH_FLOAT_SINGULARITYRADIUS (0.0000001f) // Use for Gimbal lock numerical problems - -#define MATH_DOUBLE_PI (3.14159265358979) -#define MATH_DOUBLE_TWOPI (2.0f *MATH_DOUBLE_PI) -#define MATH_DOUBLE_PIOVER2 (0.5f *MATH_DOUBLE_PI) -#define MATH_DOUBLE_PIOVER4 (0.25f*MATH_DOUBLE_PI) -#define MATH_DOUBLE_E (2.71828182845905) -#define MATH_DOUBLE_MAXVALUE (DBL_MAX) -#define MATH_DOUBLE MINPOSITIVEVALUE (DBL_MIN) -#define MATH_DOUBLE_RADTODEGREEFACTOR (360.0f / MATH_DOUBLE_TWOPI) -#define MATH_DOUBLE_DEGREETORADFACTOR (MATH_DOUBLE_TWOPI / 360.0f) -#define MATH_DOUBLE_TOLERANCE (0.00001) -#define MATH_DOUBLE_SINGULARITYRADIUS (0.000000000001) // Use for Gimbal lock numerical problems - - - - -// Single-precision Math constants class. -template<> -class Math<float> -{ -public: - typedef double OtherFloatType; -}; - -// Double-precision Math constants class. -template<> -class Math<double> -{ -public: - 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 * ((T)MATH_DOUBLE_RADTODEGREEFACTOR); } -template<class T> -T DegreeToRad(T rads) { return rads * ((T)MATH_DOUBLE_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 ((T)MATH_DOUBLE_PI); - else return acos(val); -}; - -// Numerically stable asin function -template<class T> -T Asin(T val) { - if (val > T(1)) return ((T)MATH_DOUBLE_PIOVER2); - else if (val < T(-1)) return ((T)MATH_DOUBLE_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 - { - static_assert(sizeof(Vector2<T>) == sizeof(CompatibleType), "sizeof(Vector2<T>) failure"); - 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 = ((T)MATH_DOUBLE_TOLERANCE)) - { - return (fabs(b.x-x) < tolerance) && (fabs(b.y-y) < tolerance); - } - - // Access element by index - T& operator[] (int idx) - { - OVR_ASSERT(0 <= idx && idx < 2); - return *(&x + idx); - } - const T& operator[] (int idx) const - { - OVR_ASSERT(0 <= idx && idx < 2); - return *(&x + idx); - } - - // Entry-wise 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(const Vector2& b) const { return (*this - b).LengthSq(); } - - // Returns distance between two points represented by vectors. - T Distance(const Vector2& b) const { return (*this - b).Length(); } - - // Determine if this a unit vector. - bool IsNormalized() const { return fabs(LengthSq() - T(1)) < ((T)MATH_DOUBLE_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; - -typedef Vector2<float> Point2f; -typedef Vector2<double> Point2d; -typedef Vector2<int> Point2i; - -//------------------------------------------------------------------------------------- -// ***** 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; - - // FIXME: default initialization of a vector class can be very expensive in a full-blown - // application. A few hundred thousand vector constructions is not unlikely and can add - // up to milliseconds of time on processors like the PS3 PPU. - 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) { } - - static const Vector3 ZERO; - - // 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 - { - static_assert(sizeof(Vector3<T>) == sizeof(CompatibleType), "sizeof(Vector3<T>) failure"); - 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 = ((T)MATH_DOUBLE_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)) < ((T)MATH_DOUBLE_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<int32_t> Vector3i; - -static_assert((sizeof(Vector3f) == 3*sizeof(float)), "sizeof(Vector3f) failure"); -static_assert((sizeof(Vector3d) == 3*sizeof(double)), "sizeof(Vector3d) failure"); -static_assert((sizeof(Vector3i) == 3*sizeof(int32_t)), "sizeof(Vector3i) failure"); - -typedef Vector3<float> Point3f; -typedef Vector3<double> Point3d; -typedef Vector3<int32_t> Point3i; - - -//------------------------------------------------------------------------------------- -// ***** Vector4<> - 4D vector of {x, y, z, w} - -// -// Vector4f (Vector4d) represents a 3-dimensional vector or point in space, -// consisting of coordinates x, y, z and w. - -template<class T> -class Vector4 -{ -public: - T x, y, z, w; - - // FIXME: default initialization of a vector class can be very expensive in a full-blown - // application. A few hundred thousand vector constructions is not unlikely and can add - // up to milliseconds of time on processors like the PS3 PPU. - Vector4() : x(0), y(0), z(0), w(0) { } - Vector4(T x_, T y_, T z_, T w_) : x(x_), y(y_), z(z_), w(w_) { } - explicit Vector4(T s) : x(s), y(s), z(s), w(s) { } - explicit Vector4(const Vector3<T>& v, const float w_=1) : x(v.x), y(v.y), z(v.z), w(w_) { } - explicit Vector4(const Vector4<typename Math<T>::OtherFloatType> &src) - : x((T)src.x), y((T)src.y), z((T)src.z), w((T)src.w) { } - - static const Vector4 ZERO; - - // C-interop support. - typedef typename CompatibleTypes< Vector4<T> >::Type CompatibleType; - - Vector4(const CompatibleType& s) : x(s.x), y(s.y), z(s.z), w(s.w) { } - - operator const CompatibleType& () const - { - static_assert(sizeof(Vector4<T>) == sizeof(CompatibleType), "sizeof(Vector4<T>) failure"); - return reinterpret_cast<const CompatibleType&>(*this); - } - - Vector4& operator= (const Vector3<T>& other) { x=other.x; y=other.y; z=other.z; w=1; return *this; } - bool operator== (const Vector4& b) const { return x == b.x && y == b.y && z == b.z && w == b.w; } - bool operator!= (const Vector4& b) const { return x != b.x || y != b.y || z != b.z || w != b.w; } - - Vector4 operator+ (const Vector4& b) const { return Vector4(x + b.x, y + b.y, z + b.z, w + b.w); } - Vector4& operator+= (const Vector4& b) { x += b.x; y += b.y; z += b.z; w += b.w; return *this; } - Vector4 operator- (const Vector4& b) const { return Vector4(x - b.x, y - b.y, z - b.z, w - b.w); } - Vector4& operator-= (const Vector4& b) { x -= b.x; y -= b.y; z -= b.z; w -= b.w; return *this; } - Vector4 operator- () const { return Vector4(-x, -y, -z, -w); } - - // Scalar multiplication/division scales vector. - Vector4 operator* (T s) const { return Vector4(x*s, y*s, z*s, w*s); } - Vector4& operator*= (T s) { x *= s; y *= s; z *= s; w *= s;return *this; } - - Vector4 operator/ (T s) const { T rcp = T(1)/s; - return Vector4(x*rcp, y*rcp, z*rcp, w*rcp); } - Vector4& operator/= (T s) { T rcp = T(1)/s; - x *= rcp; y *= rcp; z *= rcp; w *= rcp; - return *this; } - - static Vector4 Min(const Vector4& a, const Vector4& b) - { - return Vector4((a.x < b.x) ? a.x : b.x, - (a.y < b.y) ? a.y : b.y, - (a.z < b.z) ? a.z : b.z, - (a.w < b.w) ? a.w : b.w); - } - static Vector4 Max(const Vector4& a, const Vector4& b) - { - return Vector4((a.x > b.x) ? a.x : b.x, - (a.y > b.y) ? a.y : b.y, - (a.z > b.z) ? a.z : b.z, - (a.w > b.w) ? a.w : b.w); - } - - // Compare two vectors for equality with tolerance. Returns true if vectors match withing tolerance. - bool Compare(const Vector4&b, T tolerance = ((T)MATH_DOUBLE_TOLERANCE)) - { - return (fabs(b.x-x) < tolerance) && - (fabs(b.y-y) < tolerance) && - (fabs(b.z-z) < tolerance) && - (fabs(b.w-w) < tolerance); - } - - T& operator[] (int idx) - { - OVR_ASSERT(0 <= idx && idx < 4); - return *(&x + idx); - } - - const T& operator[] (int idx) const - { - OVR_ASSERT(0 <= idx && idx < 4); - return *(&x + idx); - } - - // Entry wise product of two vectors - Vector4 EntrywiseMultiply(const Vector4& b) const { return Vector4(x * b.x, - y * b.y, - z * b.z);} - - // Multiply and divide operators do entry-wise math - Vector4 operator* (const Vector4& b) const { return Vector4(x * b.x, - y * b.y, - z * b.z, - w * b.w); } - - Vector4 operator/ (const Vector4& b) const { return Vector4(x / b.x, - y / b.y, - z / b.z, - w / b.w); } - - - // Dot product - T Dot(const Vector4& b) const { return x*b.x + y*b.y + z*b.z + w*b.w; } - - // Return Length of the vector squared. - T LengthSq() const { return (x * x + y * y + z * z + w * w); } - - // Return vector length. - T Length() const { return sqrt(LengthSq()); } - - // 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. - Vector4 Normalized() const - { - T l = Length(); - OVR_ASSERT(l != T(0)); - return *this / l; - } -}; - -typedef Vector4<float> Vector4f; -typedef Vector4<double> Vector4d; -typedef Vector4<int> Vector4i; - - -//------------------------------------------------------------------------------------- -// ***** Bounds3 - -// Bounds class used to describe a 3D axis aligned bounding box. - -template<class T> -class Bounds3 -{ -public: - Vector3<T> b[2]; - - Bounds3() - { - } - - Bounds3( const Vector3<T> & mins, const Vector3<T> & maxs ) -{ - b[0] = mins; - b[1] = maxs; - } - - void Clear() - { - b[0].x = b[0].y = b[0].z = Math<T>::MaxValue; - b[1].x = b[1].y = b[1].z = -Math<T>::MaxValue; - } - - void AddPoint( const Vector3<T> & v ) - { - b[0].x = Alg::Min( b[0].x, v.x ); - b[0].y = Alg::Min( b[0].y, v.y ); - b[0].z = Alg::Min( b[0].z, v.z ); - b[1].x = Alg::Max( b[1].x, v.x ); - b[1].y = Alg::Max( b[1].y, v.y ); - b[1].z = Alg::Max( b[1].z, v.z ); - } - - const Vector3<T> & GetMins() const { return b[0]; } - const Vector3<T> & GetMaxs() const { return b[1]; } - - Vector3<T> & GetMins() { return b[0]; } - Vector3<T> & GetMaxs() { return b[1]; } -}; - -typedef Bounds3<float> Bounds3f; -typedef Bounds3<double> Bounds3d; - - -//------------------------------------------------------------------------------------- -// ***** 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 - { - static_assert(sizeof(Size<T>) == sizeof(CompatibleType), "sizeof(Size<T>) failure"); - 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 - { - static_assert(sizeof(Rect<T>) == sizeof(CompatibleType), "sizeof(Rect<T>) failure"); - 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) { } - - typedef typename CompatibleTypes<Quat<T> >::Type CompatibleType; - - // C-interop support. - Quat(const CompatibleType& s) : x(s.x), y(s.y), z(s.z), w(s.w) { } - - operator CompatibleType () const - { - CompatibleType 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 > ((T)MATH_DOUBLE_TOLERANCE) * ((T)MATH_DOUBLE_TOLERANCE) ) { - *axis = Vector3<T>(x, y, z).Normalized(); - *angle = 2 * Acos(w); - if (*angle > ((T)MATH_DOUBLE_PI)) // Reduce the magnitude of the angle, if necessary - { - *angle = ((T)MATH_DOUBLE_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)) < ((T)MATH_DOUBLE_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 - { - static_assert((A1 != A2) && (A2 != A3) && (A1 != A3), "(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) + ((T)MATH_DOUBLE_SINGULARITYRADIUS)) - { // South pole singularity - *a = T(0); - *b = -S*D*((T)MATH_DOUBLE_PIOVER2); - *c = S*D*atan2(T(2)*(psign*Q[A1]*Q[A2] + w*Q[A3]), - ww + Q22 - Q11 - Q33 ); - } - else if (s2 > T(1) - ((T)MATH_DOUBLE_SINGULARITYRADIUS)) - { // North pole singularity - *a = T(0); - *b = S*D*((T)MATH_DOUBLE_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 - { - static_assert(A1 != A2, "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*((T)MATH_DOUBLE_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; - -static_assert((sizeof(Quatf) == 4*sizeof(float)), "sizeof(Quatf) failure"); -static_assert((sizeof(Quatd) == 4*sizeof(double)), "sizeof(Quatd) failure"); - -//------------------------------------------------------------------------------------- -// ***** Pose - -// Position and orientation combined. - -template<class T> -class Pose -{ -public: - typedef typename CompatibleTypes<Pose<T> >::Type CompatibleType; - - Pose() { } - Pose(const Quat<T>& orientation, const Vector3<T>& pos) - : Rotation(orientation), Translation(pos) { } - Pose(const Pose& s) - : Rotation(s.Rotation), Translation(s.Translation) { } - Pose(const CompatibleType& s) - : Rotation(s.Orientation), Translation(s.Position) { } - explicit Pose(const Pose<typename Math<T>::OtherFloatType> &s) - : Rotation(s.Rotation), Translation(s.Translation) { } - - operator typename CompatibleTypes<Pose<T> >::Type () const - { - typename CompatibleTypes<Pose<T> >::Type result; - result.Orientation = Rotation; - result.Position = Translation; - return result; - } - - Quat<T> Rotation; - Vector3<T> Translation; - - static_assert((sizeof(T) == sizeof(double) || sizeof(T) == sizeof(float)), "(sizeof(T) == sizeof(double) || sizeof(T) == sizeof(float))"); - - void ToArray(T* arr) const - { - T temp[7] = { Rotation.x, Rotation.y, Rotation.z, Rotation.w, Translation.x, Translation.y, Translation.z }; - for (int i = 0; i < 7; i++) arr[i] = temp[i]; - } - - static Pose<T> FromArray(const T* v) - { - Quat<T> rotation(v[0], v[1], v[2], v[3]); - Vector3<T> translation(v[4], v[5], v[6]); - return Pose<T>(rotation, 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)); - } - - Pose operator*(const Pose& other) const - { - return Pose(Rotation * other.Rotation, Apply(other.Translation)); - } - - Pose Inverted() const - { - Quat<T> inv = Rotation.Inverted(); - return Pose(inv, inv.Rotate(-Translation)); - } -}; - -typedef Pose<float> Posef; -typedef Pose<double> Posed; - -static_assert((sizeof(Posed) == sizeof(Quatd) + sizeof(Vector3d)), "sizeof(Posed) failure"); -static_assert((sizeof(Posef) == sizeof(Quatf) + sizeof(Vector3f)), "sizeof(Posef) failure"); - - -//------------------------------------------------------------------------------------- -// ***** 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 Pose<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) - { - static_assert(sizeof(s) == sizeof(Matrix4), "sizeof(s) == sizeof(Matrix4)"); - memcpy(M, s.M, sizeof(M)); - } - - operator typename CompatibleTypes<Matrix4<T> >::Type () const - { - typename CompatibleTypes<Matrix4<T> >::Type result; - static_assert(sizeof(result) == sizeof(Matrix4), "sizeof(result) == sizeof(Matrix4)"); - memcpy(result.M, M, sizeof(M)); - return result; - } - - void ToString(char* dest, size_t destsize) const - { - size_t 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; - if (src) - { - 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; - } - - void SetXBasis(const Vector3f & v) - { - M[0][0] = v.x; - M[1][0] = v.y; - M[2][0] = v.z; - } - Vector3f GetXBasis() const - { - return Vector3f(M[0][0], M[1][0], M[2][0]); - } - - void SetYBasis(const Vector3f & v) - { - M[0][1] = v.x; - M[1][1] = v.y; - M[2][1] = v.z; - } - Vector3f GetYBasis() const - { - return Vector3f(M[0][1], M[1][1], M[2][1]); - } - - void SetZBasis(const Vector3f & v) - { - M[0][2] = v.x; - M[1][2] = v.y; - M[2][2] = v.z; - } - Vector3f GetZBasis() const - { - return Vector3f(M[0][2], M[1][2], M[2][2]); - } - - 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 - { - const T rcpW = 1.0f / (M[3][0] * v.x + M[3][1] * v.y + M[3][2] * v.z + M[3][3]); - return Vector3<T>((M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z + M[0][3]) * rcpW, - (M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z + M[1][3]) * rcpW, - (M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z + M[2][3]) * rcpW); - } - - Vector4<T> Transform(const Vector4<T>& v) const - { - return Vector4<T>(M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z + M[0][3] * v.w, - M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z + M[1][3] * v.w, - M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z + M[2][3] * v.w, - M[3][0] * v.x + M[3][1] * v.y + M[3][2] * v.z + M[3][3] * v.w); - } - - 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 size_t* rows, const size_t* 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(size_t I, size_t J) const - { - const size_t 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) const - { - static_assert((A1 != A2) && (A2 != A3) && (A1 != A3), "(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*((T)MATH_DOUBLE_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*((T)MATH_DOUBLE_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) const - { - static_assert(A1 != A2, "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*((T)MATH_DOUBLE_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 / (znear - zfar); - 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. - // This is the case even for RHS coordinate input. - return m; - } - - // PerspectiveLH 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. / (aspect * tanHalfFov); - m.M[1][1] = 1. / tanHalfFov; - //m.M[2][2] = zfar / (znear - zfar); - 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. - // This is the case even for RHS coordinate 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 Pose<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) - { - static_assert(sizeof(s) == sizeof(Matrix3), "sizeof(s) == sizeof(Matrix3)"); - memcpy(M, s.M, sizeof(M)); - } - - operator const typename CompatibleTypes<Matrix3<T> >::Type () const - { - typename CompatibleTypes<Matrix3<T> >::Type result; - static_assert(sizeof(result) == sizeof(Matrix3), "sizeof(result) == sizeof(Matrix3)"); - memcpy(result.M, M, sizeof(M)); - return result; - } - - void ToString(char* dest, size_t destsize) const - { - size_t 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; - } - - Vector2<T> Transform(const Vector2<T>& v) const - { - const float rcpZ = 1.0f / (M[2][0] * v.x + M[2][1] * v.y + M[2][2]); - return Vector2<T>((M[0][0] * v.x + M[0][1] * v.y + M[0][2]) * rcpZ, - (M[1][0] * v.x + M[1][1] * v.y + M[1][2]) * rcpZ); - } - - 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 size_t* rows, const size_t* 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_*((T)MATH_DOUBLE_DEGREETORADFACTOR)) { FixRange(); } - - T Get(AngularUnits u = Radians) const { return (u == Radians) ? a : a*((T)MATH_DOUBLE_RADTODEGREEFACTOR); } - void Set(const T& x, AngularUnits u = Radians) { a = (u == Radians) ? x : x*((T)MATH_DOUBLE_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 <= ((T)MATH_DOUBLE_PI)) ? c : ((T)MATH_DOUBLE_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 < -((T)MATH_DOUBLE_PI)) - a += ((T)MATH_DOUBLE_TWOPI); - else if (a > ((T)MATH_DOUBLE_PI)) - a -= ((T)MATH_DOUBLE_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 >= -((T)MATH_DOUBLE_PI) && a <= ((T)MATH_DOUBLE_PI)) - return; - a = fmod(a,((T)MATH_DOUBLE_TWOPI)); - if (a < -((T)MATH_DOUBLE_PI)) - a += ((T)MATH_DOUBLE_TWOPI); - else if (a > ((T)MATH_DOUBLE_PI)) - a -= ((T)MATH_DOUBLE_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: - 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; -typedef Plane<double> Planed; - - -} // Namespace OVR - -#endif |