Improve math module (#396)
* Improve math module - Mark almost everything constexpr - Equality (a == b) is now exact, down to the bit level. If you want approximate equality use the new ApproxEqual method/static method - Rename Nz::Extend to Nz::Extent - Removed Make[] and Set[] methods in favor of their static counterpart and operator=
This commit is contained in:
Jérôme Leclercq
GitHub
@@ -26,11 +26,11 @@ namespace Nz
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* \param normalZ Z component of the normal
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* \param D Distance to origin
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*/
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template<typename T>
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Plane<T>::Plane(T normalX, T normalY, T normalZ, T D)
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constexpr Plane<T>::Plane(T normalX, T normalY, T normalZ, T D) :
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normal(normalX, normalY, normalZ),
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distance(D)
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{
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Set(normalX, normalY, normalZ, D);
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}
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/*!
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@@ -38,11 +38,11 @@ namespace Nz
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*
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* \param plane[4] plane[0] is X component, plane[1] is Y component, plane[2] is Z component and plane[3] is D
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*/
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template<typename T>
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Plane<T>::Plane(const T plane[4])
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constexpr Plane<T>::Plane(const T plane[4]) :
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normal(plane[0], plane[1], plane[2]),
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distance(plane[3])
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{
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Set(plane);
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}
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/*!
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@@ -51,11 +51,11 @@ namespace Nz
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* \param Normal normal of the vector
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* \param D Distance to origin
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*/
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template<typename T>
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Plane<T>::Plane(const Vector3<T>& Normal, T D)
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constexpr Plane<T>::Plane(const Vector3<T>& Normal, T D) :
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normal(Normal),
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distance(D)
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{
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Set(Normal, D);
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}
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/*!
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@@ -64,11 +64,11 @@ namespace Nz
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* \param Normal Normal of the plane
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* \param point Point which verifies the equation of the plane
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*/
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template<typename T>
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Plane<T>::Plane(const Vector3<T>& Normal, const Vector3<T>& point)
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constexpr Plane<T>::Plane(const Vector3<T>& Normal, const Vector3<T>& point) :
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normal(Normal),
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distance(-Normal.DotProduct(point))
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{
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Set(Normal, point);
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}
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/*!
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@@ -80,11 +80,15 @@ namespace Nz
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*
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* \remark They are expected not to be colinear
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*/
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template<typename T>
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Plane<T>::Plane(const Vector3<T>& point1, const Vector3<T>& point2, const Vector3<T>& point3)
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{
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Set(point1, point2, point3);
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Vector3<T> edge1 = point2 - point1;
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Vector3<T> edge2 = point3 - point1;
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normal = edge1.CrossProduct(edge2);
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normal.Normalize();
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distance = normal.DotProduct(point3);
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}
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/*!
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@@ -92,12 +96,21 @@ namespace Nz
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*
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* \param plane Plane of type U to convert to type T
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*/
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template<typename T>
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template<typename U>
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Plane<T>::Plane(const Plane<U>& plane)
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constexpr Plane<T>::Plane(const Plane<U>& plane) :
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normal(Vector3<T>(plane.normal)),
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distance(T(plane.distance))
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{
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Set(plane);
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}
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template<typename T>
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constexpr bool Plane<T>::ApproxEqual(const Plane& plane, T maxDifference) const
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{
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if (!normal.ApproxEqual(plane.normal, maxDifference))
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return false;
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return NumberEquals(distance, plane.distance, maxDifference);
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}
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/*!
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@@ -112,9 +125,8 @@ namespace Nz
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*
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* \see Distance
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*/
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template<typename T>
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T Plane<T>::Distance(T x, T y, T z) const
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constexpr T Plane<T>::Distance(T x, T y, T z) const
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{
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return Distance(Vector3<T>(x, y, z));
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}
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@@ -129,162 +141,12 @@ namespace Nz
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*
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* \see Distance
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*/
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template<typename T>
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T Plane<T>::Distance(const Vector3<T>& point) const
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constexpr T Plane<T>::Distance(const Vector3<T>& point) const
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{
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return normal.DotProduct(point) - distance; // ax + by + cd - d = 0.
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}
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/*!
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* \brief Makes the plane (0, 0, 1, 0)
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* \return A reference to this plane with components (0, 0, 1, 0)
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*
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* \see XY
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*/
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template<typename T>
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Plane<T>& Plane<T>::MakeXY()
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{
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return Set(T(0.0), T(0.0), T(1.0), T(0.0));
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}
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/*!
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* \brief Makes the plane (0, 1, 0, 0)
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* \return A reference to this plane with components (0, 1, 0, 0)
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*
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* \see XZ
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*/
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template<typename T>
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Plane<T>& Plane<T>::MakeXZ()
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{
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return Set(T(0.0), T(1.0), T(0.0), T(0.0));
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}
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/*!
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* \brief Makes the plane (1, 0, 0, 0)
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* \return A reference to this plane with components (1, 0, 0, 0)
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*
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* \see YZ
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*/
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template<typename T>
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Plane<T>& Plane<T>::MakeYZ()
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{
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return Set(T(1.0), T(0.0), T(0.0), T(0.0));
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}
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/*!
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* \brief Sets the components of the plane
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* \return A reference to this plane
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*
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* \param normalX X component of the normal
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* \param normalY Y component of the normal
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* \param normalZ Z component of the normal
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* \param D Distance to origin
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*/
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template<typename T>
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Plane<T>& Plane<T>::Set(T normalX, T normalY, T normalZ, T D)
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{
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distance = D;
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normal.Set(normalX, normalY, normalZ);
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return *this;
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}
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/*!
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* \brief Sets the components of the plane from an array of four elements
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* \return A reference to this plane
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*
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* \param plane[4] plane[0] is X component, plane[1] is Y component, plane[2] is Z component and plane[3] is D
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*/
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template<typename T>
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Plane<T>& Plane<T>::Set(const T plane[4])
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{
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normal.Set(plane[0], plane[1], plane[2]);
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distance = plane[3];
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return *this;
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}
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/*!
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* \brief Sets the components of the plane from a normal and a distance
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* \return A reference to this plane
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*
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* \param Normal Normal of the vector
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* \param D Distance to origin
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*/
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template<typename T>
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Plane<T>& Plane<T>::Set(const Vector3<T>& Normal, T D)
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{
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distance = D;
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normal = Normal;
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return *this;
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}
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/*!
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* \brief Sets the components of the plane from a normal and a point
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* \return A reference to this plane
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*
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* \param Normal Normal of the plane
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* \param point Point which verifies the equation of the plane
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*/
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template<typename T>
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Plane<T>& Plane<T>::Set(const Vector3<T>& Normal, const Vector3<T>& point)
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{
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normal = Normal;
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distance = -normal.DotProduct(point);
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return *this;
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}
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/*!
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* \brief Sets the components of the plane from three points
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* \return A reference to this plane
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*
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* \param point1 First point
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* \param point2 Second point
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* \param point3 Third point
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*
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* \remark They are expected not to be colinear
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*/
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template<typename T>
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Plane<T>& Plane<T>::Set(const Vector3<T>& point1, const Vector3<T>& point2, const Vector3<T>& point3)
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{
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Vector3<T> edge1 = point2 - point1;
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Vector3<T> edge2 = point3 - point1;
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normal = edge1.CrossProduct(edge2);
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normal.Normalize();
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distance = normal.DotProduct(point3);
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return *this;
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}
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/*!
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* \brief Sets the components of the plane from another type of Plane
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* \return A reference to this plane
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*
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* \param plane Plane of type U to convert its components
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*/
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template<typename T>
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template<typename U>
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Plane<T>& Plane<T>::Set(const Plane<U>& plane)
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{
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normal.Set(plane.normal);
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distance = T(plane.distance);
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return *this;
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}
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/*!
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* \brief Gives a string representation
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* \return A string representation of the object: "Plane(Normal: Vector3(x, y, z); Distance: w)"
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@@ -309,9 +171,9 @@ namespace Nz
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*/
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template<typename T>
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bool Plane<T>::operator==(const Plane& plane) const
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constexpr bool Plane<T>::operator==(const Plane& plane) const
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{
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return (normal == plane.normal && NumberEquals(distance, plane.distance)) || (normal == -plane.normal && NumberEquals(distance, -plane.distance));
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return normal == plane.normal && distance == plane.distance;
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}
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/*!
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@@ -324,11 +186,17 @@ namespace Nz
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*/
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template<typename T>
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bool Plane<T>::operator!=(const Plane& plane) const
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constexpr bool Plane<T>::operator!=(const Plane& plane) const
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{
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return !operator==(plane);
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}
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template<typename T>
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constexpr bool Plane<T>::ApproxEqual(const Plane& lhs, const Plane& rhs, T maxDifference)
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{
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return lhs.ApproxEqual(rhs, maxDifference);
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}
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/*!
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* \brief Intersects three planes to retrieve a single intersection point
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* \return The intersection point
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@@ -340,7 +208,7 @@ namespace Nz
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* \remark All three planes must have differents normals otherwise result is undefined
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*/
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template<typename T>
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Vector3<T> Plane<T>::Intersect(const Plane& p0, const Plane& p1, const Plane& p2)
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constexpr Vector3<T> Plane<T>::Intersect(const Plane& p0, const Plane& p1, const Plane& p2)
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{
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// From https://donw.io/post/frustum-point-extraction/
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Vector3f bxc = Vector3f::CrossProduct(p1.normal, p2.normal);
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@@ -365,7 +233,7 @@ namespace Nz
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* \see Lerp
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*/
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template<typename T>
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Plane<T> Plane<T>::Lerp(const Plane& from, const Plane& to, T interpolation)
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constexpr Plane<T> Plane<T>::Lerp(const Plane& from, const Plane& to, T interpolation)
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{
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#ifdef NAZARA_DEBUG
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if (interpolation < T(0.0) || interpolation > T(1.0))
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@@ -386,49 +254,31 @@ namespace Nz
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/*!
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* \brief Shorthand for the plane (0, 0, 1, 0)
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* \return A plane with components (0, 0, 1, 0)
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*
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* \see MakeXY
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*/
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template<typename T>
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Plane<T> Plane<T>::XY()
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constexpr Plane<T> Plane<T>::XY()
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{
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Plane plane;
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plane.MakeXY();
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return plane;
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return Plane(Vector3<T>::UnitZ(), 0);
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}
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/*!
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* \brief Shorthand for the plane (0, 1, 0, 0)
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* \return A plane with components (0, 1, 0, 0)
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*
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* \see MakeXZ
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*/
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template<typename T>
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Plane<T> Plane<T>::XZ()
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constexpr Plane<T> Plane<T>::XZ()
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{
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Plane plane;
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plane.MakeXZ();
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return plane;
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return Plane(Vector3<T>::UnitY(), 0);
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}
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/*!
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* \brief Shorthand for the plane (1, 0, 0, 0)
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* \return A plane with components (1, 0, 0, 0)
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*
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* \see MakeYZ
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*/
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template<typename T>
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Plane<T> Plane<T>::YZ()
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constexpr Plane<T> Plane<T>::YZ()
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{
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Plane plane;
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plane.MakeYZ();
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return plane;
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return Plane(Vector3<T>::UnitX(), 0);
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}
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/*!
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@@ -484,3 +334,4 @@ namespace Nz
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}
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#include <Nazara/Core/DebugOff.hpp>
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#include "Plane.hpp"
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