urho3d/Source/Urho3D/Math/Plane.h

//
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#pragma once

#include "../Math/Matrix3x4.h"

namespace Urho3D
{

/// Surface in three-dimensional space.
class URHO3D_API Plane
{
public:
    /// Construct a degenerate plane with zero normal and parameter.
    Plane() noexcept :
        d_(0.0f)
    {
    }

    /// Copy-construct from another plane.
    Plane(const Plane& plane) noexcept = default;

    /// Construct from 3 vertices.
    Plane(const Vector3& v0, const Vector3& v1, const Vector3& v2) noexcept
    {
        Define(v0, v1, v2);
    }

    /// Construct from a normal vector and a point on the plane.
    Plane(const Vector3& normal, const Vector3& point) noexcept
    {
        Define(normal, point);
    }

    /// Construct from a 4-dimensional vector, where the w coordinate is the plane parameter.
    explicit Plane(const Vector4& plane) noexcept
    {
        Define(plane);
    }

    /// Assign from another plane.
    Plane& operator =(const Plane& rhs) noexcept = default;

    /// Define from 3 vertices.
    void Define(const Vector3& v0, const Vector3& v1, const Vector3& v2)
    {
        Vector3 dist1 = v1 - v0;
        Vector3 dist2 = v2 - v0;

        Define(dist1.CrossProduct(dist2), v0);
    }

    /// Define from a normal vector and a point on the plane.
    void Define(const Vector3& normal, const Vector3& point)
    {
        normal_ = normal.Normalized();
        absNormal_ = normal_.Abs();
        d_ = -normal_.DotProduct(point);
    }

    /// Define from a 4-dimensional vector, where the w coordinate is the plane parameter.
    void Define(const Vector4& plane)
    {
        normal_ = Vector3(plane.x_, plane.y_, plane.z_);
        absNormal_ = normal_.Abs();
        d_ = plane.w_;
    }

    /// Transform with a 3x3 matrix.
    void Transform(const Matrix3& transform);
    /// Transform with a 3x4 matrix.
    void Transform(const Matrix3x4& transform);
    /// Transform with a 4x4 matrix.
    void Transform(const Matrix4& transform);

    /// Project a point on the plane.
    Vector3 Project(const Vector3& point) const { return point - normal_ * (normal_.DotProduct(point) + d_); }

    /// Return signed distance to a point.
    float Distance(const Vector3& point) const { return normal_.DotProduct(point) + d_; }

    /// Reflect a normalized direction vector.
    Vector3 Reflect(const Vector3& direction) const { return direction - (2.0f * normal_.DotProduct(direction) * normal_); }

    /// Return a reflection matrix.
    Matrix3x4 ReflectionMatrix() const;
    /// Return transformed by a 3x3 matrix.
    Plane Transformed(const Matrix3& transform) const;
    /// Return transformed by a 3x4 matrix.
    Plane Transformed(const Matrix3x4& transform) const;
    /// Return transformed by a 4x4 matrix.
    Plane Transformed(const Matrix4& transform) const;

    /// Return as a vector.
    Vector4 ToVector4() const { return Vector4(normal_, d_); }

    /// Plane normal.
    Vector3 normal_;
    /// Plane absolute normal.
    Vector3 absNormal_;
    /// Plane constant.
    float d_{};

    /// Plane at origin with normal pointing up.
    static const Plane UP;
};

}