Planes are ax+by+cz=d
Planes are changed to ax+by+cz=d, so the plane with normal (0, 1, 0) and distance 1 is y=1. Operators == and !=. Former-commit-id: 5267a183a9e6fb490de099d536ea2f64558f674d
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#include <Nazara/Math/Plane.hpp>
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#include <catch.hpp>
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SCENARIO("Plane", "[MATH][PLANE]")
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{
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GIVEN("Two planes normal(1, 1, 1), distance 1")
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{
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NzPlanef firstPlane(NzVector3f::Unit().Normalize(), 1.f);
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NzPlanef secondPlane(NzPlaned(NzVector3d::Unit().Normalize(), 1.0));
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WHEN("We compare them")
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{
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THEN("They are equal")
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{
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REQUIRE(firstPlane == secondPlane);
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}
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AND_THEN("We compare with normal(-1, -1, -1), distance -1")
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{
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REQUIRE(firstPlane == NzPlanef(-NzVector3f::Unit().Normalize(), -1.f));
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}
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AND_THEN("They have the same distance from the same point")
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{
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NzVector3f point(-2.f, 3.f, 1.f);
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REQUIRE(firstPlane.Distance(point) == Approx(secondPlane.Distance(point)));
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REQUIRE(firstPlane.Distance(-2.f, 3.f, 1.f) == Approx(0.1547f));
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}
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AND_THEN("Distance between Plane (0, 1, 0), distance 1 and point (0, 2, 0) should be 1")
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{
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REQUIRE(NzPlanef(NzVector3f::UnitY(), 1.f).Distance(NzVector3f::UnitY() * 2.f) == Approx(1.f));
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}
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AND_THEN("Distance between Plane (0, 1, 0), distance 5 and point (0, 2, 0) should be -3")
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{
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REQUIRE(NzPlanef(NzVector3f::UnitY(), 5.f).Distance(NzVector3f::UnitY() * 2.f) == Approx(-3.f));
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}
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AND_THEN("Distance between Plane (0, 1, 0), distance 1000 and point (0, 500, 0) and (0, 1500, 0)")
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{
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REQUIRE(NzPlanef(NzVector3f::UnitY(), 1000.f).Distance(NzVector3f::UnitY() * 500.f) == Approx(-500.f));
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REQUIRE(NzPlanef(NzVector3f::UnitY(), 1000.f).Distance(NzVector3f::UnitY() * 1500.f) == Approx(500.f));
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}
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AND_THEN("Distance between Plane (0, -1, 0), distance -1000 and point (0, 500, 0) and (0, 1500, 0)")
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{
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REQUIRE(NzPlanef(-NzVector3f::UnitY(), -1000.f).Distance(NzVector3f::UnitY() * 500.f) == Approx(500.f));
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REQUIRE(NzPlanef(-NzVector3f::UnitY(), -1000.f).Distance(NzVector3f::UnitY() * 1500.f) == Approx(-500.f));
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}
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}
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}
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GIVEN("The plane XZ, distance 1 with 3 points (0, 1, 0), (1, 1, 1), (-1, 1, 0)")
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{
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WHEN("We do a positive plane")
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{
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NzPlanef xy(NzVector3f(2.f, 1.f, 0.f), NzVector3f(-1.f, 1.f, -1.f), NzVector3f(-1.f, 1.f, 0.f));
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THEN("It must be equal to XZ distance 1")
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{
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REQUIRE(xy == NzPlanef(NzVector3f::UnitY(), 1.f));
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}
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}
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WHEN("We do a negative plane")
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{
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NzPlanef xy(NzVector3f(0.f, 1.f, 0.f), NzVector3f(1.f, 1.f, 1.f), NzVector3f(-1.f, 1.f, 0.f));
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THEN("It must be equal to XZ distance 1")
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{
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REQUIRE(xy == NzPlanef(-NzVector3f::UnitY(), -1.f));
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}
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}
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}
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}
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@ -0,0 +1,60 @@
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// Copyright (C) 2015 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_PLANE_HPP
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#define NAZARA_PLANE_HPP
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#include <Nazara/Core/String.hpp>
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#include <Nazara/Math/Vector3.hpp>
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template<typename T>
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class NzPlane
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{
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public:
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NzPlane() = default;
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NzPlane(T normalX, T normalY, T normalZ, T Distance);
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NzPlane(const T plane[4]);
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NzPlane(const NzVector3<T>& Normal, T Distance);
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NzPlane(const NzVector3<T>& Normal, const NzVector3<T>& point);
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NzPlane(const NzVector3<T>& point1, const NzVector3<T>& point2, const NzVector3<T>& point3);
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template<typename U> explicit NzPlane(const NzPlane<U>& plane);
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NzPlane(const NzPlane& plane) = default;
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~NzPlane() = default;
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T Distance(const NzVector3<T>& point) const;
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T Distance(T x, T y, T z) const;
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NzPlane& Set(T normalX, T normalY, T normalZ, T Distance);
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NzPlane& Set(const T plane[4]);
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NzPlane& Set(const NzPlane& plane);
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NzPlane& Set(const NzVector3<T>& Normal, T Distance);
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NzPlane& Set(const NzVector3<T>& Normal, const NzVector3<T>& point);
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NzPlane& Set(const NzVector3<T>& point1, const NzVector3<T>& point2, const NzVector3<T>& point3);
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template<typename U> NzPlane& Set(const NzPlane<U>& plane);
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NzString ToString() const;
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bool operator==(const NzPlane& plane) const;
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bool operator!=(const NzPlane& plane) const;
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static NzPlane Lerp(const NzPlane& from, const NzPlane& to, T interpolation);
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static NzPlane XY();
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static NzPlane XZ();
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static NzPlane YZ();
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NzVector3<T> normal;
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T distance;
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};
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template<typename T>
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std::ostream& operator<<(std::ostream& out, const NzPlane<T>& plane);
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typedef NzPlane<double> NzPlaned;
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typedef NzPlane<float> NzPlanef;
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#include <Nazara/Math/Plane.inl>
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#endif // NAZARA_PLANE_HPP
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@ -0,0 +1,193 @@
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// Copyright (C) 2015 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/Math/Algorithm.hpp>
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#include <cstring>
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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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NzPlane<T>::NzPlane(T normalX, T normalY, T normalZ, T D)
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{
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Set(normalX, normalY, normalZ, D);
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}
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template<typename T>
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NzPlane<T>::NzPlane(const T plane[4])
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{
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Set(plane);
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}
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template<typename T>
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NzPlane<T>::NzPlane(const NzVector3<T>& Normal, T D)
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{
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Set(Normal, D);
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}
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template<typename T>
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NzPlane<T>::NzPlane(const NzVector3<T>& Normal, const NzVector3<T>& point)
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{
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Set(Normal, point);
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}
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template<typename T>
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NzPlane<T>::NzPlane(const NzVector3<T>& point1, const NzVector3<T>& point2, const NzVector3<T>& point3)
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{
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Set(point1, point2, point3);
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}
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template<typename T>
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template<typename U>
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NzPlane<T>::NzPlane(const NzPlane<U>& plane)
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{
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Set(plane);
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}
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template<typename T>
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T NzPlane<T>::Distance(const NzVector3<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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template<typename T>
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T NzPlane<T>::Distance(T x, T y, T z) const
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{
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return Distance(NzVector3<T>(x, y, z));
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}
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template<typename T>
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NzPlane<T>& NzPlane<T>::Set(T normalX, T normalY, T normalZ, T D)
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{
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distance = D;
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normal.Set(normalX, normalY, normalZ);
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return *this;
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}
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template<typename T>
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NzPlane<T>& NzPlane<T>::Set(const T plane[4])
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{
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normal.Set(plane[0], plane[1], plane[2]);
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distance = plane[3];
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return *this;
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}
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template<typename T>
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NzPlane<T>& NzPlane<T>::Set(const NzPlane& plane)
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{
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std::memcpy(this, &plane, sizeof(NzPlane));
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return *this;
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}
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template<typename T>
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NzPlane<T>& NzPlane<T>::Set(const NzVector3<T>& Normal, T D)
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{
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distance = D;
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normal = Normal;
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return *this;
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}
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template<typename T>
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NzPlane<T>& NzPlane<T>::Set(const NzVector3<T>& Normal, const NzVector3<T>& point)
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{
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normal = Normal;
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distance = -normal.DotProduct(point);
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return *this;
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}
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template<typename T>
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NzPlane<T>& NzPlane<T>::Set(const NzVector3<T>& point1, const NzVector3<T>& point2, const NzVector3<T>& point3)
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{
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NzVector3<T> edge1 = point2 - point1;
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NzVector3<T> edge2 = point3 - point1;
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normal = edge1.CrossProduct(edge2);
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normal.Normalize();
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distance = normal.DotProduct(point3);
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return *this;
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}
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template<typename T>
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template<typename U>
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NzPlane<T>& NzPlane<T>::Set(const NzPlane<U>& plane)
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{
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normal.Set(plane.normal);
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distance = F(plane.distance);
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return *this;
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}
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template<typename T>
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NzString NzPlane<T>::ToString() const
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{
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NzStringStream ss;
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return ss << "Plane(Normal: " << normal.ToString() << "; Distance: " << distance << ')';
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}
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template<typename T>
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bool NzPlane<T>::operator==(const NzPlane& plane) const
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{
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return (normal == plane.normal && NzNumberEquals(distance, plane.distance)) || (normal == -plane.normal && NzNumberEquals(distance, -plane.distance));
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}
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template<typename T>
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bool NzPlane<T>::operator!=(const NzPlane& 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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NzPlane<T> NzPlane<T>::Lerp(const NzPlane& from, const NzPlane& to, T interpolation)
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{
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#ifdef NAZARA_DEBUG
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if (interpolation < F(0.0) || interpolation > F(1.0))
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{
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NazaraError("Interpolation must be in range [0..1] (Got " + NzString::Number(interpolation) + ')');
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return NzPlane();
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}
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#endif
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NzPlane plane;
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plane.distance = NzLerp(from.distance, to.distance, interpolation);
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plane.normal = NzVector3<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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template<typename T>
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NzPlane<T> NzPlane<T>::XY()
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{
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return NzPlane<T>(F(0.0), F(0.0), F(1.0), F(0.0));
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}
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template<typename T>
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NzPlane<T> NzPlane<T>::XZ()
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{
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return NzPlane<T>(F(0.0), F(1.0), F(0.0), F(0.0));
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}
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template<typename T>
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NzPlane<T> NzPlane<T>::YZ()
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{
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return NzPlane<T>(F(1.0), F(0.0), F(0.0), F(0.0));
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}
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template<typename T>
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std::ostream& operator<<(std::ostream& out, const NzPlane<T>& plane)
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{
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return out << plane.ToString();
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}
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#undef F
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#include <Nazara/Core/DebugOff.hpp>
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