597 lines
20 KiB
C++
597 lines
20 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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// Sources:
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// http://www.crownandcutlass.com/features/technicaldetails/frustum.html
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// http://www.lighthouse3d.com/tutorials/view-frustum-culling/
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#include <Nazara/Core/Algorithm.hpp>
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#include <NazaraUtils/EnumArray.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::Frustum
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* \brief Math class that represents a frustum in the three dimensional vector space
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*
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* Frustums are used to determine what is inside the camera's field of view. They help speed up the rendering process
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*/
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/*!
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* \brief Constructs a Frustum by specifying its planes
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*
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* \param corners Corners
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* \param planes Frustum of type U to convert to type T
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*/
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template<typename T>
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constexpr Frustum<T>::Frustum(const EnumArray<FrustumPlane, Plane<T>>& planes) :
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m_planes(planes)
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{
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}
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/*!
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* \brief Constructs a Frustum object from another type of Frustum
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*
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* \param frustum Frustum 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 Frustum<T>::Frustum(const Frustum<U>& frustum)
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{
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for (auto&& [planeEnum, plane] : m_planes.iter_kv())
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plane = Frustum(frustum.GetPlane(planeEnum));
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}
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template<typename T>
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constexpr bool Frustum<T>::ApproxEqual(const Frustum& frustum, T maxDifference) const
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{
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for (auto&& [planeEnum, plane] : m_planes.iter_kv())
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{
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if (!plane.ApproxEqual(frustum.GetPlane(planeEnum)))
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return false;
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}
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return true;
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}
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/*!
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* \brief Computes the position of a frustum corner
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* \return The corner position
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*
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* \param corner Which corner to compute
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*/
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template<typename T>
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constexpr Vector3<T> Frustum<T>::ComputeCorner(BoxCorner corner) const
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{
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switch (corner)
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{
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case BoxCorner::FarLeftBottom: return Plane<T>::Intersect(GetPlane(FrustumPlane::Far), GetPlane(FrustumPlane::Left), GetPlane(FrustumPlane::Bottom));
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case BoxCorner::FarLeftTop: return Plane<T>::Intersect(GetPlane(FrustumPlane::Far), GetPlane(FrustumPlane::Left), GetPlane(FrustumPlane::Top));
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case BoxCorner::FarRightBottom: return Plane<T>::Intersect(GetPlane(FrustumPlane::Far), GetPlane(FrustumPlane::Right), GetPlane(FrustumPlane::Bottom));
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case BoxCorner::FarRightTop: return Plane<T>::Intersect(GetPlane(FrustumPlane::Far), GetPlane(FrustumPlane::Right), GetPlane(FrustumPlane::Top));
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case BoxCorner::NearLeftBottom: return Plane<T>::Intersect(GetPlane(FrustumPlane::Near), GetPlane(FrustumPlane::Left), GetPlane(FrustumPlane::Bottom));
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case BoxCorner::NearLeftTop: return Plane<T>::Intersect(GetPlane(FrustumPlane::Near), GetPlane(FrustumPlane::Left), GetPlane(FrustumPlane::Top));
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case BoxCorner::NearRightBottom: return Plane<T>::Intersect(GetPlane(FrustumPlane::Near), GetPlane(FrustumPlane::Right), GetPlane(FrustumPlane::Bottom));
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case BoxCorner::NearRightTop: return Plane<T>::Intersect(GetPlane(FrustumPlane::Near), GetPlane(FrustumPlane::Right), GetPlane(FrustumPlane::Top));
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}
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NazaraError("invalid frustum corner");
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return Vector3<T>();
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}
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/*!
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* \brief Checks whether or not a bounding volume is contained in the frustum
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* \return true if the bounding volume is entirely in the frustum
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*
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* \param volume Volume to check
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*
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* \remark If volume is infinite, true is returned
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* \remark If volume is null, false is returned
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* \remark If enumeration of the volume is not defined in Extent, a NazaraError is thrown and false is returned
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* \remark If enumeration of the intersection is not defined in IntersectionSide, a NazaraError is thrown and false is returned. This should not never happen for a user of the library
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*/
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template<typename T>
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constexpr bool Frustum<T>::Contains(const BoundingVolume<T>& volume) const
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{
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switch (volume.extent)
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{
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case Extent::Finite:
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{
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IntersectionSide side = Intersect(volume.aabb);
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switch (side)
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{
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case IntersectionSide::Inside:
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return true;
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case IntersectionSide::Intersecting:
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return Contains(volume.obb);
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case IntersectionSide::Outside:
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return false;
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}
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NazaraError("Invalid intersection side (0x" + NumberToString(UnderlyingCast(side), 16) + ')');
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return false;
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}
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case Extent::Infinite:
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return true;
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case Extent::Null:
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return false;
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}
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NazaraError("Invalid extent type (0x" + NumberToString(UnderlyingCast(volume.extent), 16) + ')');
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return false;
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}
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/*!
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* \brief Checks whether or not a box is contained in the frustum
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* \return true if the box is entirely in the frustum
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*
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* \param box Box to check
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*/
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template<typename T>
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constexpr bool Frustum<T>::Contains(const Box<T>& box) const
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{
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// https://gdbooks.gitbooks.io/3dcollisions/content/Chapter2/static_aabb_plane.html
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// https://learnopengl.com/Guest-Articles/2021/Scene/Frustum-Culling
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Vector3<T> center = box.GetCenter();
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Vector3<T> extents = box.GetLengths() * T(0.5);
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for (const auto& plane : m_planes)
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{
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Vector3<T> projectedExtents = extents * plane.normal.GetAbs();
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float radius = projectedExtents.x + projectedExtents.y + projectedExtents.z;
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float distance = plane.SignedDistance(center);
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if (distance < T(radius))
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return false;
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}
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return true;
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}
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/*!
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* \brief Checks whether or not an oriented box is contained in the frustum
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* \return true if the oriented box is entirely in the frustum
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*
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* \param orientedbox Oriented box to check
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*/
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template<typename T>
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constexpr bool Frustum<T>::Contains(const OrientedBox<T>& orientedbox) const
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{
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return Contains(orientedbox.GetCorners(), 8);
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}
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/*!
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* \brief Checks whether or not a sphere is contained in the frustum
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* \return true if the sphere is entirely in the frustum
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*
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* \param sphere Sphere to check
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*/
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template<typename T>
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constexpr bool Frustum<T>::Contains(const Sphere<T>& sphere) const
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{
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for (const auto& plane : m_planes)
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{
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if (plane.SignedDistance(sphere.GetPosition()) < -sphere.radius)
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return false;
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}
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return true;
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}
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/*!
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* \brief Checks whether or not a Vector3 is contained in the frustum
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* \return true if the Vector3 is in the frustum
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*
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* \param point Vector3 which represents a point in the space
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*/
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template<typename T>
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constexpr bool Frustum<T>::Contains(const Vector3<T>& point) const
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{
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for (const auto& plane : m_planes)
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{
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if (plane.SignedDistance(point) < T(0.0))
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return false;
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}
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return true;
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}
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/*!
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* \brief Checks whether or not a set of Vector3 is contained in the frustum
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* \return true if the set of Vector3 is in the frustum
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*
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* \param points Pointer to Vector3 which represents a set of points in the space
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* \param pointCount Number of points to check
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*/
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template<typename T>
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constexpr bool Frustum<T>::Contains(const Vector3<T>* points, std::size_t pointCount) const
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{
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for (const auto& plane : m_planes)
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{
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for (std::size_t i = 0; i < pointCount; ++i)
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{
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if (plane.SignedDistance(points[i]) < T(0.0))
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return false;
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}
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}
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return true;
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}
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/*!
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* \brief Gets the Plane for the face
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* \return The face of the frustum according to enum FrustumPlane
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*
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* \param plane Enumeration of type FrustumPlane
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*
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* \remark If enumeration is not defined in FrustumPlane and NAZARA_DEBUG defined, a NazaraError is thrown and a Plane uninitialised is returned
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*/
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template<typename T>
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constexpr const Plane<T>& Frustum<T>::GetPlane(FrustumPlane plane) const
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{
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NazaraAssert(plane <= FrustumPlane::Max, "invalid plane");
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return m_planes[plane];
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}
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template<typename T>
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constexpr const EnumArray<FrustumPlane, Plane<T>>& Frustum<T>::GetPlanes() const
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{
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return m_planes;
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}
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/*!
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* \brief Checks whether or not a bounding volume intersects with the frustum
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* \return IntersectionSide How the bounding volume is intersecting with the frustum
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*
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* \param volume Volume to check
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*
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* \remark If volume is infinite, IntersectionSide::Intersecting is returned
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* \remark If volume is null, IntersectionSide::Outside is returned
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* \remark If enumeration of the volume is not defined in Extent, a NazaraError is thrown and IntersectionSide::Outside is returned
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* \remark If enumeration of the intersection is not defined in IntersectionSide, a NazaraError is thrown and IntersectionSide::Outside is returned. This should not never happen for a user of the library
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*/
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template<typename T>
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constexpr IntersectionSide Frustum<T>::Intersect(const BoundingVolume<T>& volume) const
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{
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switch (volume.extent)
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{
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case Extent::Finite:
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{
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IntersectionSide side = Intersect(volume.aabb);
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switch (side)
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{
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case IntersectionSide::Inside:
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return IntersectionSide::Inside;
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case IntersectionSide::Intersecting:
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return Intersect(volume.obb);
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case IntersectionSide::Outside:
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return IntersectionSide::Outside;
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}
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NazaraError("Invalid intersection side (0x" + NumberToString(UnderlyingCast(side), 16) + ')');
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return IntersectionSide::Outside;
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}
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case Extent::Infinite:
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return IntersectionSide::Intersecting; // We can not contain infinity
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case Extent::Null:
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return IntersectionSide::Outside;
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}
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NazaraError("Invalid extent type (0x" + NumberToString(UnderlyingCast(volume.extent), 16) + ')');
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return IntersectionSide::Outside;
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}
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/*!
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* \brief Checks whether or not a box intersects with the frustum
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* \return IntersectionSide How the box is intersecting with the frustum
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*
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* \param box Box to check
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*/
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template<typename T>
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constexpr IntersectionSide Frustum<T>::Intersect(const Box<T>& box) const
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{
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// https://gdbooks.gitbooks.io/3dcollisions/content/Chapter2/static_aabb_plane.html
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// https://learnopengl.com/Guest-Articles/2021/Scene/Frustum-Culling
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IntersectionSide side = IntersectionSide::Inside;
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Vector3<T> center = box.GetCenter();
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Vector3<T> extents = box.GetLengths() * T(0.5);
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for (const auto& plane : m_planes)
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{
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Vector3<T> projectedExtents = extents * plane.normal.GetAbs();
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float radius = projectedExtents.x + projectedExtents.y + projectedExtents.z;
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float distance = plane.SignedDistance(center);
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if (distance < T(-radius))
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return IntersectionSide::Outside;
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else if (distance < T(radius))
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side = IntersectionSide::Intersecting;
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}
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return side;
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}
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/*!
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* \brief Checks whether or not an oriented box intersects with the frustum
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* \return IntersectionSide How the oriented box is intersecting with the frustum
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*
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* \param oriented box OrientedBox to check
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*/
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template<typename T>
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constexpr IntersectionSide Frustum<T>::Intersect(const OrientedBox<T>& orientedbox) const
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{
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return Intersect(orientedbox.GetCorners(), 8);
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}
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/*!
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* \brief Checks whether or not a sphere intersects with the frustum
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* \return IntersectionSide How the sphere is intersecting with the frustum
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*
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* \param sphere Sphere to check
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*/
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template<typename T>
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constexpr IntersectionSide Frustum<T>::Intersect(const Sphere<T>& sphere) const
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{
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// http://www.lighthouse3d.com/tutorials/view-frustum-culling/geometric-approach-testing-points-and-spheres/
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IntersectionSide side = IntersectionSide::Inside;
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for (const auto& plane : m_planes)
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{
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T distance = plane.SignedDistance(sphere.GetPosition());
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if (distance < -sphere.radius)
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return IntersectionSide::Outside;
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else if (distance < sphere.radius)
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side = IntersectionSide::Intersecting;
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}
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return side;
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}
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/*!
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* \brief Checks whether or not a set of Vector3 intersects with the frustum
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* \return IntersectionSide How the set of Vector3 is intersecting with the frustum
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*
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* \param points Pointer to Vector3 which represents a set of points in the space
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* \param pointCount Number of points to check
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*/
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template<typename T>
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constexpr IntersectionSide Frustum<T>::Intersect(const Vector3<T>* points, std::size_t pointCount) const
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{
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IntersectionSide side = IntersectionSide::Inside;
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for (const auto& plane : m_planes)
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{
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bool outside = true;
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for (std::size_t i = 0; i < pointCount; ++i)
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{
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// If at least one point is outside of the frustum, we're intersecting
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if (plane.SignedDistance(points[i]) < T(0.0))
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side = IntersectionSide::Intersecting;
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else
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outside = false;
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}
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// But if no point is intersecting on this plane, then it's outside
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if (outside)
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return IntersectionSide::Outside;
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}
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return side;
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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: "Frustum(Plane ...)"
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*/
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template<typename T>
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std::string Frustum<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 Builds the frustum object
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* \return A reference to this frustum which is the build up camera's field of view
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*
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* \param angle FOV angle
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* \param ratio Rendering ratio (typically 16/9 or 4/3)
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* \param zNear Distance where 'vision' begins
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* \param zFar Distance where 'vision' ends
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* \param eye Position of the camera
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* \param target Position of the target of the camera
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* \param up Direction of up vector according to the orientation of camera
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*/
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template<typename T>
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constexpr bool Frustum<T>::operator==(const Frustum& frustum) const
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{
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for (auto&& [planeEnum, plane] : m_planes.iter_kv())
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{
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if (!plane != frustum.GetPlane(planeEnum))
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return false;
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}
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return true;
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}
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template<typename T>
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constexpr bool Frustum<T>::operator!=(const Frustum& frustum) const
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{
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return !operator==(frustum);
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}
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template<typename T>
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constexpr bool Frustum<T>::ApproxEqual(const Frustum& lhs, const Frustum& rhs, T maxDifference)
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{
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return lhs.ApproxEqual(rhs, maxDifference);
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}
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template<typename T>
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Frustum<T> Frustum<T>::Build(RadianAngle<T> angle, T ratio, T zNear, T zFar, const Vector3<T>& eye, const Vector3<T>& target, const Vector3<T>& up)
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{
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angle /= T(2.0);
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T tangent = angle.GetTan();
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T nearH = zNear * tangent;
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T nearW = nearH * ratio;
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T farH = zFar * tangent;
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T farW = farH * ratio;
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Vector3<T> f = Vector3<T>::Normalize(target - eye);
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Vector3<T> u = Vector3<T>::Normalize(up);
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Vector3<T> s = Vector3<T>::Normalize(f.CrossProduct(u));
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u = s.CrossProduct(f);
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Vector3<T> nc = eye + f * zNear;
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Vector3<T> fc = eye + f * zFar;
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// Computing the frustum
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EnumArray<BoxCorner, Vector3<T>> corners;
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corners[BoxCorner::FarLeftBottom] = fc - u * farH - s * farW;
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corners[BoxCorner::FarLeftTop] = fc + u * farH - s * farW;
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corners[BoxCorner::FarRightTop] = fc + u * farH + s * farW;
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corners[BoxCorner::FarRightBottom] = fc - u * farH + s * farW;
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corners[BoxCorner::NearLeftBottom] = nc - u * nearH - s * nearW;
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corners[BoxCorner::NearLeftTop] = nc + u * nearH - s * nearW;
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corners[BoxCorner::NearRightTop] = nc + u * nearH + s * nearW;
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corners[BoxCorner::NearRightBottom] = nc - u * nearH + s * nearW;
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// Construction of frustum's planes
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EnumArray<FrustumPlane, Plane<T>> planes;
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planes[FrustumPlane::Bottom] = Plane(corners[BoxCorner::NearLeftBottom], corners[BoxCorner::NearRightBottom], corners[BoxCorner::FarRightBottom]);
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planes[FrustumPlane::Far] = Plane(corners[BoxCorner::FarRightTop], corners[BoxCorner::FarLeftTop], corners[BoxCorner::FarLeftBottom]);
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planes[FrustumPlane::Left] = Plane(corners[BoxCorner::NearLeftTop], corners[BoxCorner::NearLeftBottom], corners[BoxCorner::FarLeftBottom]);
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planes[FrustumPlane::Near] = Plane(corners[BoxCorner::NearLeftTop], corners[BoxCorner::NearRightTop], corners[BoxCorner::NearRightBottom]);
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planes[FrustumPlane::Right] = Plane(corners[BoxCorner::NearRightBottom], corners[BoxCorner::NearRightTop], corners[BoxCorner::FarRightBottom]);
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planes[FrustumPlane::Top] = Plane(corners[BoxCorner::NearRightTop], corners[BoxCorner::NearLeftTop], corners[BoxCorner::FarLeftTop]);
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|
|
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return Frustum(planes);
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|
}
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|
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/*!
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|
* \brief Constructs the frustum from a Matrix4
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* \return A reference to this frustum which is the build up of projective matrix
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*
|
|
* \param viewProjMatrix Matrix which represents the transformation of the frustum
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*/
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template<typename T>
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Frustum<T> Frustum<T>::Extract(const Matrix4<T>& viewProjMatrix)
|
|
{
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EnumArray<FrustumPlane, Plane<T>> planes;
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planes[FrustumPlane::Left].normal.x = viewProjMatrix(3, 0) + viewProjMatrix(0, 0);
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planes[FrustumPlane::Left].normal.y = viewProjMatrix(3, 1) + viewProjMatrix(0, 1);
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planes[FrustumPlane::Left].normal.z = viewProjMatrix(3, 2) + viewProjMatrix(0, 2);
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planes[FrustumPlane::Left].distance = viewProjMatrix(3, 3) + viewProjMatrix(0, 3);
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|
|
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planes[FrustumPlane::Right].normal.x = viewProjMatrix(3, 0) - viewProjMatrix(0, 0);
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|
planes[FrustumPlane::Right].normal.y = viewProjMatrix(3, 1) - viewProjMatrix(0, 1);
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|
planes[FrustumPlane::Right].normal.z = viewProjMatrix(3, 2) - viewProjMatrix(0, 2);
|
|
planes[FrustumPlane::Right].distance = viewProjMatrix(3, 3) - viewProjMatrix(0, 3);
|
|
|
|
planes[FrustumPlane::Bottom].normal.x = viewProjMatrix(3, 0) - viewProjMatrix(1, 0);
|
|
planes[FrustumPlane::Bottom].normal.y = viewProjMatrix(3, 1) - viewProjMatrix(1, 1);
|
|
planes[FrustumPlane::Bottom].normal.z = viewProjMatrix(3, 2) - viewProjMatrix(1, 2);
|
|
planes[FrustumPlane::Bottom].distance = viewProjMatrix(3, 3) - viewProjMatrix(1, 3);
|
|
|
|
planes[FrustumPlane::Top].normal.x = viewProjMatrix(3, 0) + viewProjMatrix(1, 0);
|
|
planes[FrustumPlane::Top].normal.y = viewProjMatrix(3, 1) + viewProjMatrix(1, 1);
|
|
planes[FrustumPlane::Top].normal.z = viewProjMatrix(3, 2) + viewProjMatrix(1, 2);
|
|
planes[FrustumPlane::Top].distance = viewProjMatrix(3, 3) + viewProjMatrix(1, 3);
|
|
|
|
planes[FrustumPlane::Far].normal.x = viewProjMatrix(3, 0) + viewProjMatrix(2, 0);
|
|
planes[FrustumPlane::Far].normal.y = viewProjMatrix(3, 1) + viewProjMatrix(2, 1);
|
|
planes[FrustumPlane::Far].normal.z = viewProjMatrix(3, 2) + viewProjMatrix(2, 2);
|
|
planes[FrustumPlane::Far].distance = viewProjMatrix(3, 3) + viewProjMatrix(2, 3);
|
|
|
|
planes[FrustumPlane::Near].normal.x = viewProjMatrix(3, 0) - viewProjMatrix(2, 0);
|
|
planes[FrustumPlane::Near].normal.y = viewProjMatrix(3, 1) - viewProjMatrix(2, 1);
|
|
planes[FrustumPlane::Near].normal.z = viewProjMatrix(3, 2) - viewProjMatrix(2, 2);
|
|
planes[FrustumPlane::Near].distance = viewProjMatrix(3, 3) - viewProjMatrix(2, 3);
|
|
|
|
for (auto& plane : planes)
|
|
plane.Normalize();
|
|
|
|
return Frustum(planes);
|
|
}
|
|
|
|
/*!
|
|
* \brief Serializes a Frustum
|
|
* \return true if successfully serialized
|
|
*
|
|
* \param context Serialization context
|
|
* \param matrix Input frustum
|
|
*/
|
|
template<typename T>
|
|
bool Serialize(SerializationContext& context, const Frustum<T>& frustum, TypeTag<Frustum<T>>)
|
|
{
|
|
for (const auto& plane : frustum.m_planes)
|
|
{
|
|
if (!Serialize(context, plane))
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
/*!
|
|
* \brief Unserializes a Frustum
|
|
* \return true if successfully unserialized
|
|
*
|
|
* \param context Serialization context
|
|
* \param matrix Output frustum
|
|
*/
|
|
template<typename T>
|
|
bool Unserialize(SerializationContext& context, Frustum<T>* frustum, TypeTag<Frustum<T>>)
|
|
{
|
|
for (auto& plane : frustum->m_planes)
|
|
{
|
|
if (!Unserialize(context, &plane))
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
/*!
|
|
* \brief Output operator
|
|
* \return The stream
|
|
*
|
|
* \param out The stream
|
|
* \param frustum The frustum to output
|
|
*/
|
|
template<typename T>
|
|
std::ostream& operator<<(std::ostream& out, const Nz::Frustum<T>& frustum)
|
|
{
|
|
return out << "Frustum(Bottom: " << frustum.GetPlane(Nz::FrustumPlane::Bottom) << ",\n"
|
|
<< " Far: " << frustum.GetPlane(Nz::FrustumPlane::Far) << ",\n"
|
|
<< " Left: " << frustum.GetPlane(Nz::FrustumPlane::Left) << ",\n"
|
|
<< " Near: " << frustum.GetPlane(Nz::FrustumPlane::Near) << ",\n"
|
|
<< " Right: " << frustum.GetPlane(Nz::FrustumPlane::Right) << ",\n"
|
|
<< " Top: " << frustum.GetPlane(Nz::FrustumPlane::Top) << ")\n";
|
|
}
|
|
}
|
|
|
|
#include <Nazara/Core/DebugOff.hpp>
|