New class ray
Class ray who represents a ray in space and who can be used as a line. Support of classical intersections. Former-commit-id: 2ea5af0cf749dbefdd841f9b02bfab2af5058cdb
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@ -41,6 +41,7 @@
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#include <Nazara/Math/OrientedBox.hpp>
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#include <Nazara/Math/Plane.hpp>
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#include <Nazara/Math/Quaternion.hpp>
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#include <Nazara/Math/Ray.hpp>
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#include <Nazara/Math/Rect.hpp>
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#include <Nazara/Math/Sphere.hpp>
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#include <Nazara/Math/Vector2.hpp>
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@ -0,0 +1,71 @@
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// Copyright (C) 2014 Rémi Bèges - Jérôme Leclercq
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// This file is part of the "Nazara Engine - Mathematics module"
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// For conditions of distribution and use, see copyright notice in Config.hpp
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#pragma once
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#ifndef NAZARA_RAY_HPP
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#define NAZARA_RAY_HPP
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#include <Nazara/Core/String.hpp>
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#include <Nazara/Math/Box.hpp>
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#include <Nazara/Math/Frustum.hpp>
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#include <Nazara/Math/OrientedBox.hpp>
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#include <Nazara/Math/Plane.hpp>
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#include <Nazara/Math/Sphere.hpp>
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#include <Nazara/Math/Vector3.hpp>
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template<typename T> class NzRay
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{
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public:
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NzRay() = default;
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NzRay(T X, T Y, T Z, T directionX, T directionY, T directionZ);
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NzRay(const T origin[3], const T direction[3]);
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NzRay(const NzVector3<T>& origin, const NzVector3<T>& direction);
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NzRay(const NzPlane<T>& planeOne, const NzPlane<T>& planeTwo);
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template<typename U> explicit NzRay(const NzVector3<U>& origin, const NzVector3<U>& direction);
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template<typename U> explicit NzRay(const NzRay<U>& ray);
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NzRay(const NzRay<T>& ray) = default;
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~NzRay() = default;
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NzVector3<T> GetClosestPoint(const NzVector3<T>& point) const;
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NzVector3<T> GetDirection() const;
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NzVector3<T> GetOrigin() const;
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NzVector3<T> GetPoint(T lambda) const;
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bool Intersect(const NzBox<T>& box, NzVector3<T> * hitPoint = nullptr, NzVector3<T> * hitSecondPoint = nullptr) const;
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bool Intersect(const NzOrientedBox<T>& orientedBox, const NzMatrix4<T>& matrix, NzVector3<T> * hitPoint = nullptr, NzVector3<T> * hitSecondPoint = nullptr) const;
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bool Intersect(const NzPlane<T>& plane, NzVector3<T> * hitPoint = nullptr) const;
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bool Intersect(const NzSphere<T>& sphere, NzVector3<T> * hitPoint = nullptr, NzVector3<T> * hitSecondPoint = nullptr) const;
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NzVector3<T> operator*(T lambda) const;
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NzRay& Set(T X, T Y, T Z, T directionX, T directionY, T directionZ);
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NzRay& Set(const T origin[3], const T direction[3]);
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NzRay& Set(const NzVector3<T>& origin, const NzVector3<T>& direction);
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NzRay& Set(const NzPlane<T>& planeOne, const NzPlane<T>& planeTwo);
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template<typename U> NzRay& Set(const NzVector3<U>& origin, const NzVector3<U>& direction);
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template<typename U> NzRay& Set(const NzRay<U>& ray);
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NzRay& Set(const NzRay& ray);
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NzRay& SetDirection(const NzVector3<T>& direction);
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NzRay& SetOrigin(const NzVector3<T>& origin);
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NzString ToString() const;
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static NzRay Lerp(const NzRay& from, const NzRay& to, T interpolation);
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static NzRay UnitX();
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static NzRay UnitY();
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static NzRay UnitZ();
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NzVector3<T> direction, origin;
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};
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template<typename T> std::ostream& operator<<(std::ostream& out, const NzRay<T>& vec);
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typedef NzRay<double> NzRayd;
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typedef NzRay<float> NzRayf;
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#include <Nazara/Math/Ray.inl>
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#endif // NAZARA_RAY_HPP
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@ -0,0 +1,415 @@
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// Copyright (C) 2014 Jérôme Leclercq
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// This file is part of the "Nazara Engine - Mathematics module"
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// For conditions of distribution and use, see copyright notice in Config.hpp
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#include <Nazara/Core/StringStream.hpp>
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#include <Nazara/Core/Debug.hpp>
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#define F(a) static_cast<T>(a)
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template<typename T>
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NzRay<T>::NzRay(T X, T Y, T Z, T DirectionX, T DirectionY, T DirectionZ)
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{
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Set(X, Y, Z, DirectionX, DirectionY, DirectionZ);
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}
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template<typename T>
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NzRay<T>::NzRay(const T Origin[3], const T Direction[3])
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{
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Set(Origin, Direction);
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}
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template<typename T>
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NzRay<T>::NzRay(const NzVector3<T>& Origin, const NzVector3<T>& Direction)
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{
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Set(Origin, Direction);
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}
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template<typename T>
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NzRay<T>::NzRay(const NzPlane<T>& planeOne, const NzPlane<T>& planeTwo)
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{
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Set(planeOne, planeTwo);
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}
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template<typename T>
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template<typename U>
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NzRay<T>::NzRay(const NzVector3<U>& Origin, const NzVector3<U>& Direction)
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{
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Set(Origin, Direction);
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}
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template<typename T>
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template<typename U>
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NzRay<T>::NzRay(const NzRay<U>& ray)
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{
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Set(ray);
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}
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template<typename T>
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NzVector3<T> NzRay<T>::GetClosestPoint(const NzVector3<T>& point) const
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{
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NzVector3<T> delta = point - origin;
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T vsq = direction.GetSquaredLength();
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T proj = delta.DotProduct(direction);
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return GetPoint(proj/vsq);
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}
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template<typename T>
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NzVector3<T> NzRay<T>::GetDirection() const
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{
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return direction;
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}
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template<typename T>
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NzVector3<T> NzRay<T>::GetOrigin() const
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{
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return origin;
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}
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template<typename T>
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NzVector3<T> NzRay<T>::GetPoint(T lambda) const
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{
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return NzVector3<T>(origin + direction * lambda);
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}
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template<typename T>
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bool NzRay<T>::Intersect(const NzBox<T>& box, NzVector3<T> * hitPoint, NzVector3<T> * hitSecondPoint) const
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{
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// Slab method
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#if NAZARA_MATH_SAFE
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if (NzNumberEquals(direction.x, F(0.0)) || NzNumberEquals(direction.y, F(0.0)) || NzNumberEquals(direction.z, F(0.0)))
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{
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NazaraWarning("Division by zero !"); // The algorithm is still correct.
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}
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#endif
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T tx1 = (box.x - origin.x) / direction.x;
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T tx2 = (box.x + box.width - origin.x) / direction.x;
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T tmin = std::min(tx1, tx2);
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T tmax = std::max(tx1, tx2);
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T ty1 = (box.y - origin.y) / direction.y;
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T ty2 = (box.y + box.height - origin.y) / direction.y;
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tmin = std::max(tmin, std::min(ty1, ty2));
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tmax = std::min(tmax, std::max(ty1, ty2));
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T tz1 = (box.z - origin.z) / direction.z;
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T tz2 = (box.z + box.depth - origin.z) / direction.z;
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tmin = std::max(tmin, std::min(tz1, tz2));
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tmax = std::min(tmax, std::max(tz1, tz2));
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if (hitPoint)
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hitPoint->Set(GetPoint(tmin));
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if (hitSecondPoint)
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hitSecondPoint->Set(GetPoint(tmax));
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return tmax >= std::max(F(0.0), tmin) && tmin < INFINITY;
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}
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template<typename T>
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bool NzRay<T>::Intersect(const NzOrientedBox<T>& orientedBox, const NzMatrix4<T>& matrix, NzVector3<T> * hitPoint, NzVector3<T> * hitSecondPoint) const
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{
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// Intersection method from Real-Time Rendering and Essential Mathematics for Games
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T tMin = F(0.0);
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T tMax = INFINITY;
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NzVector3<T> OBBposition_worldspace(matrix[3].x, matrix[3].y, matrix[3].z);
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NzVector3<T> delta = OBBposition_worldspace - origin;
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// Test intersection with the 2 planes perpendicular to the OBB's X axis
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NzVector3<T> xaxis(matrix[0].x, matrix[0].y, matrix[0].z);
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T e = xaxis.DotProduct(delta);
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T f = direction.DotProduct(xaxis);
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if (std::abs(f) > F(0.0))
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{ // Standard case
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T t1 = (e + orientedBox.localBox.x) / f; // Intersection with the "left" plane
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T t2 = (e + (orientedBox.localBox.x + orientedBox.localBox.width)) / f; // Intersection with the "right" plane
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// t1 and t2 now contain distances betwen ray origin and ray-plane intersections
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// We want t1 to represent the nearest intersection,
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// so if it's not the case, invert t1 and t2
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if (t1 > t2)
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{ T w = t1; t1 = t2; t2 = w; } // swap t1 and t2
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// tMax is the nearest "far" intersection (amongst the X,Y and Z planes pairs)
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if (t2 < tMax)
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tMax = t2;
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// tMin is the farthest "near" intersection (amongst the X,Y and Z planes pairs)
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if (t1 > tMin)
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tMin = t1;
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// And here's the trick :
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// If "far" is closer than "near", then there is NO intersection.
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// See the images in the tutorials for the visual explanation.
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if (tMax < tMin)
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return false;
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}
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else
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// Rare case : the ray is almost parallel to the planes, so they don't have any "intersection"
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if (-e + orientedBox.localBox.x > F(0.0) || -e + (orientedBox.localBox.x + orientedBox.localBox.width) < F(0.0))
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return false;
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// Test intersection with the 2 planes perpendicular to the OBB's Y axis
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// Exactly the same thing than above.
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NzVector3<T> yaxis(matrix[1].x, matrix[1].y, matrix[1].z);
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e = yaxis.DotProduct(delta);
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f = direction.DotProduct(yaxis);
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if (std::abs(f) > F(0.0))
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{
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T t1 = (e + orientedBox.localBox.y) / f;
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T t2 = (e + (orientedBox.localBox.y + orientedBox.localBox.height)) / f;
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if (t1 > t2)
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{ T w = t1; t1 = t2; t2 = w; } // swap t1 and t2
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if (t2 < tMax)
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tMax = t2;
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if (t1 > tMin)
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tMin = t1;
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if (tMin > tMax)
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return false;
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}
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else
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if (-e + orientedBox.localBox.y > F(0.0) || -e + (orientedBox.localBox.y + orientedBox.localBox.height) < F(0.0))
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return false;
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// Test intersection with the 2 planes perpendicular to the OBB's Z axis
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// Exactly the same thing than above.
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NzVector3<T> zaxis(matrix[2].x, matrix[2].y, matrix[2].z);
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e = zaxis.DotProduct(delta);
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f = direction.DotProduct(zaxis);
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if (std::abs(f) > F(0.0))
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{
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T t1 = (e + orientedBox.localBox.z) / f;
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T t2 = (e + (orientedBox.localBox.z + orientedBox.localBox.depth)) / f;
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if (t1 > t2)
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{ T w = t1; t1 = t2; t2 = w; } // swap t1 and t2
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if (t2 < tMax)
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tMax = t2;
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if (t1 > tMin)
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tMin = t1;
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if (tMin > tMax)
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return false;
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}
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else
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if (-e + orientedBox.localBox.z > F(0.0) || -e + (orientedBox.localBox.z + orientedBox.localBox.depth) < F(0.0))
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return false;
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if (hitPoint)
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hitPoint->Set(GetPoint(tMin));
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if (hitSecondPoint)
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hitSecondPoint->Set(GetPoint(tMax));
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return true;
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}
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template<typename T>
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bool NzRay<T>::Intersect(const NzPlane<T>& plane, NzVector3<T> * hitPoint) const
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{
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T divisor = plane.normal.DotProduct(direction);
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if (NzNumberEquals(divisor, F(0.0)))
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return false; // perpendicular
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if (!hitPoint)
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return true;
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T lambda = - (plane.normal.DotProduct(origin) - plane.distance) / divisor; // The plane is ax+by+cz=d
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hitPoint->Set(GetPoint(lambda));
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return true;
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}
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template<typename T>
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bool NzRay<T>::Intersect(const NzSphere<T>& sphere, NzVector3<T> * hitPoint, NzVector3<T> * hitSecondPoint) const
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{
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NzVector3<T> distanceCenterOrigin = sphere.GetPosition() - origin;
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T length = distanceCenterOrigin.DotProduct(direction);
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if (length < F(0.0))
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return false; // ray is perpendicular to the vector origin - center
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T squaredDistance = distanceCenterOrigin.GetSquaredLength() - length * length;
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T squaredRadius = sphere.GetRadius() * sphere.GetRadius();
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if (squaredDistance > squaredRadius)
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return false; // if the ray is further than the radius
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if (!hitPoint)
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return true;
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T deltaLambda = std::sqrt(squaredRadius - squaredDistance);
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if (hitPoint)
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hitPoint->Set(GetPoint(length - deltaLambda));
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if (hitSecondPoint)
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hitSecondPoint->Set(GetPoint(length + deltaLambda));
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return true;
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}
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template<typename T>
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NzVector3<T> NzRay<T>::operator*(T lambda) const
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{
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return GetPoint(lambda);
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}
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template<typename T>
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NzRay<T>& NzRay<T>::Set(T X, T Y, T Z, T directionX, T directionY, T directionZ)
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{
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direction = NzVector3<T>(directionX, directionY, directionZ);
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origin = NzVector3<T>(X, Y, Z);
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return *this;
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}
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template<typename T>
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NzRay<T>& NzRay<T>::Set(const T Origin[3], const T Direction[3])
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{
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direction = NzVector3<T>(Direction);
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origin = NzVector3<T>(Origin);
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return *this;
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}
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template<typename T>
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NzRay<T>& NzRay<T>::Set(const NzVector3<T>& Origin, const NzVector3<T>& Direction)
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{
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direction = Direction;
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origin = Origin;
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return *this;
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}
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template<typename T>
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NzRay<T>& NzRay<T>::Set(const NzPlane<T>& planeOne, const NzPlane<T>& planeTwo)
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{
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T termOne = planeOne.normal.GetLength();
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T termTwo = planeOne.normal.DotProduct(planeTwo.normal);
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T termFour = planeTwo.normal.GetLength();
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T det = termOne * termFour - termTwo * termTwo;
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#if NAZARA_MATH_SAFE
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if (NzNumberEquals(det, F(0.0)))
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{
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NzString error("Planes are parallel.");
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NazaraError(error);
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throw std::domain_error(error);
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}
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#endif
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T invdet = F(1.0) / det;
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T fc0 = (termFour * -planeOne.distance + termTwo * planeTwo.distance) * invdet;
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T fc1 = (termOne * -planeTwo.distance + termTwo * planeOne.distance) * invdet;
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direction = planeOne.normal.CrossProduct(planeTwo.normal);
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origin = planeOne.normal * fc0 + planeTwo.normal * fc1;
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return *this;
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}
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template<typename T>
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template<typename U>
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NzRay<T>& NzRay<T>::Set(const NzVector3<U>& Origin, const NzVector3<U>& Direction)
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{
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direction = NzVector3<T>(Direction);
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origin = NzVector3<T>(Origin);
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return *this;
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}
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template<typename T>
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template<typename U>
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NzRay<T>& NzRay<T>::Set(const NzRay<U>& ray)
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{
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direction = NzVector3<T>(ray.direction);
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origin = NzVector3<T>(ray.origin);
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return *this;
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}
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template<typename T>
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NzRay<T>& NzRay<T>::Set(const NzRay& ray)
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{
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std::memcpy(this, &ray, sizeof(NzRay));
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return *this;
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}
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template<typename T>
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NzRay<T>& NzRay<T>::SetDirection(const NzVector3<T>& Direction)
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{
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direction = Direction;
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return *this;
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}
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template<typename T>
|
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NzRay<T>& NzRay<T>::SetOrigin(const NzVector3<T>& Origin)
|
||||
{
|
||||
origin = Origin;
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
NzString NzRay<T>::ToString() const
|
||||
{
|
||||
NzStringStream ss;
|
||||
|
||||
return ss << "Ray(" << origin.x << ", " << origin.y << ", " << origin.z << " | direction: " << direction.x << ", " << direction.y << ", " << direction.z << ')';
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
NzRay<T> NzRay<T>::Lerp(const NzRay& from, const NzRay& to, T interpolation)
|
||||
{
|
||||
return NzRay<T>(from.origin.Lerp(to.origin, interpolation), from.direction.Lerp(to.direction, interpolation));
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
NzRay<T> NzRay<T>::UnitX()
|
||||
{
|
||||
return NzRay(NzVector3<T>::Zero(), NzVector3<T>::UnitX());
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
NzRay<T> NzRay<T>::UnitY()
|
||||
{
|
||||
return NzRay(NzVector3<T>::Zero(), NzVector3<T>::UnitY());
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
NzRay<T> NzRay<T>::UnitZ()
|
||||
{
|
||||
return NzRay(NzVector3<T>::Zero(), NzVector3<T>::UnitZ());
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
std::ostream& operator<<(std::ostream& out, const NzRay<T>& ray)
|
||||
{
|
||||
return out << ray.ToString();
|
||||
}
|
||||
|
||||
#undef F
|
||||
|
||||
#include <Nazara/Core/DebugOff.hpp>
|
||||
Loading…
Reference in New Issue