urho3d/Source/Engine/Math/Plane.h

//
// Copyright (c) 2008-2014 the Urho3D project.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
//

#pragma once

#include "Matrix3x4.h"

namespace Urho3D
{

/// Surface in three-dimensional space.
class URHO3D_API Plane
{
public:
    /// Construct undefined.
    Plane()
    {
    }
    
    /// Copy-construct from another plane.
    Plane(const Plane& plane) :
        normal_(plane.normal_),
        absNormal_(plane.absNormal_),
        d_(plane.d_)
    {
    }
    
    /// Construct from 3 vertices.
    Plane(const Vector3& v0, const Vector3& v1, const Vector3& v2)
    {
        Define(v0, v1, v2);
    }
    
    /// Construct from a normal vector and a point on the plane.
    Plane(const Vector3& normal, const Vector3& point)
    {
        Define(normal, point);
    }
    
    /// Construct from a 4-dimensional vector, where the w coordinate is the plane parameter.
    Plane(const Vector4& plane)
    {
        Define(plane);
    }
    
    /// 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);
    
    /// 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;
};

}