337 lines
8.5 KiB
C++
337 lines
8.5 KiB
C++
// Copyright (C) 2023 Jérôme "Lynix" Leclercq (lynix680@gmail.com)
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// This file is part of the "Nazara Engine - Math module"
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// For conditions of distribution and use, see copyright notice in Config.hpp
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#include <Nazara/Core/Algorithm.hpp>
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#include <cstring>
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#include <sstream>
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#include <Nazara/Core/Debug.hpp>
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namespace Nz
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{
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/*!
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* \ingroup math
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* \class Nz::Plane
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* \brief Math class that represents a plane in 3D
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*
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* \remark The convention used in this class is: If you ask for plane with normal (0, 1, 0) and distance 1, you will get 0 * X + 1 * Y + 0 * Z - 1 = 0 or Y = 1. Notice the sign minus before the distance on the left side of the equation
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*/
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/*!
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* \brief Constructs a Plane object from its components
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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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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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}
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/*!
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* \brief Constructs a Plane object from an array of four elements
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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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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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}
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/*!
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* \brief Constructs a Plane object from a normal and a distance
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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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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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}
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/*!
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* \brief Constructs a Plane object from a normal and a point
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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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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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}
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/*!
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* \brief Constructs a Plane object from three points
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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(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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}
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/*!
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* \brief Constructs a Plane object from another type of Plane
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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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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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}
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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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* \brief Returns the distance from the plane to the point
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* \return Distance to the point
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*
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* \param x X position of the point
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* \param y Y position of the point
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* \param z Z position of the point
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*
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* \remark If T is negative, it means that the point is in the opposite direction of the normal
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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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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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/*!
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* \brief Returns the distance from the plane to the point
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* \return Distance to the point
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*
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* \param point Position of the point
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*
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* \remark If T is negative, it means that the point is in the opposite direction of the normal
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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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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 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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*/
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template<typename T>
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std::string Plane<T>::ToString() const
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{
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std::ostringstream ss;
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ss << *this;
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return ss.str();
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}
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/*!
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* \brief Compares the plane to other one
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* \return true if the planes are the same
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*
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* \param plane Other vector to compare with
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*
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* \remark Plane with normal N and distance D is the same than with normal -N et distance -D
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*/
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template<typename T>
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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 && distance == plane.distance;
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}
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/*!
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* \brief Compares the plane to other one
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* \return false if the planes are the same
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*
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* \param plane Other plane to compare with
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*
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* \remark Plane with normal N and distance D is the same than with normal -N et distance -D
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*/
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template<typename T>
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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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*
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* \param p0 First plane
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* \param p1 Second plane
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* \param p2 Third plane
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*
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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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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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Vector3f cxa = Vector3f::CrossProduct(p2.normal, p0.normal);
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Vector3f axb = Vector3f::CrossProduct(p0.normal, p1.normal);
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Vector3f r = -p0.distance * bxc - p1.distance * cxa - p2.distance * axb;
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return r * (T(1.0) / Vector3f::DotProduct(p0.normal, bxc));
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}
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/*!
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* \brief Interpolates the plane to other one with a factor of interpolation
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* \return A new plane which is the interpolation of two planes
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*
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* \param from Initial plane
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* \param to Target plane
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* \param interpolation Factor of interpolation
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*
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* \remark interpolation is meant to be between 0 and 1, other values are potentially undefined behavior
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* \remark With NAZARA_DEBUG, a NazaraError is thrown and Plane() is returned
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*
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* \see Lerp
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*/
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template<typename T>
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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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{
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NazaraError("Interpolation must be in range [0..1] (Got " + NumberToString(interpolation) + ')');
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return Plane();
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}
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#endif
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Plane plane;
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plane.distance = Nz::Lerp(from.distance, to.distance, interpolation);
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plane.normal = Vector3<T>::Lerp(from.normal, to.normal, interpolation);
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plane.normal.Normalize();
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return plane;
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}
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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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template<typename T>
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constexpr Plane<T> Plane<T>::XY()
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{
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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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template<typename T>
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constexpr Plane<T> Plane<T>::XZ()
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{
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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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template<typename T>
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constexpr Plane<T> Plane<T>::YZ()
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{
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return Plane(Vector3<T>::UnitX(), 0);
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}
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/*!
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* \brief Serializes a Vector2
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* \return true if successfully serialized
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*
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* \param context Serialization context
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* \param plane Input Vector2
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*/
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template<typename T>
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bool Serialize(SerializationContext& context, const Plane<T>& plane, TypeTag<Plane<T>>)
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{
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if (!Serialize(context, plane.normal))
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return false;
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if (!Serialize(context, plane.distance))
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return false;
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return true;
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}
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/*!
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* \brief Unserializes a Plane
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* \return true if successfully unserialized
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*
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* \param context Serialization context
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* \param plane Output Plane
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*/
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template<typename T>
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bool Unserialize(SerializationContext& context, Plane<T>* plane, TypeTag<Plane<T>>)
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{
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if (!Unserialize(context, &plane->normal))
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return false;
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if (!Unserialize(context, &plane->distance))
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return false;
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return true;
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}
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/*!
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* \brief Output operator
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* \return The stream
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*
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* \param out The stream
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* \param plane The plane to output
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*/
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template<typename T>
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std::ostream& operator<<(std::ostream& out, const Nz::Plane<T>& plane)
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{
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return out << "Plane(Normal: " << plane.normal << "; Distance: " << plane.distance << ')';
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}
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}
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#include <Nazara/Core/DebugOff.hpp>
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#include "Plane.hpp"
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