# cee::Plane

class `Plane`

  Class defining a plane in space.

  The class describes a plane by the equation: Ax + By + Cz + Dx = 0 The plane’s normal is defined by the coefficients [A, B, C]

  Public Functions

  `Plane`()

    Constructs a plane.

  `Plane`(const Plane &other)

    Constructs a plane as a copy of other.

  `Plane`(double A, double B, double C, double D)

    Constructs a plane based on the equation: Ax + By + Cz + Dx = 0.

  Plane &`operator=`(const Plane &other)

    Assigns other to this plane and returns a reference to this plane.

  bool `operator==`(const Plane &rhs) const

    Returns true if rhs is equal to this plane; otherwise returns false.

  bool `operator!=`(const Plane &rhs) const

    Returns true if rhs is NOT equal to this plane; otherwise returns false.

  double `A`() const

    Returns the value A.

    Plane equation: Ax + By + Cz + Dx = 0

  double `B`() const

    Returns the value B.

    Plane equation: Ax + By + Cz + Dx = 0

  double `C`() const

    Returns the value C.

    Plane equation: Ax + By + Cz + Dx = 0

  double `D`() const

    Returns the value D.

    Plane equation: Ax + By + Cz + Dx = 0

  bool `isValid`() const

    Returns true if the plane is valid, otherwise returns false.

  double `distance`(const Vec3d &point) const

    Returns the distance between the give point and this plane.

  double `distanceSquared`(const Vec3d &point) const

    Returns the square of the distance from the point to the plane.

    The square of the distance is relatively fast to compute (no sqrt) and is useful for determine which side the point is on. To obtain the actual distance, divide by sqrt(A^2 + B^2 + C^2) or use the distance() function directly.

  Vec3d `normal`() const

    Returns the normal to this plane.

  Vec3d `pointInPlane`() const

    Gets a point located on the plane.

  void `set`(double A, double B, double C, double D)

    Sets A, B, C and D values for this plane.

    Plane equation: Ax + By + Cz + Dx = 0

  bool `setFromPointAndNormal`(const Vec3d &point, const Vec3d &normal)

    Sets the plane from a point and a normal.

  bool `setFromPoints`(const Vec3d &p1, const Vec3d &p2, const Vec3d &p3)

    Sets the plane from three points.

    The three points cannot be on a line as they need to define a plane. So (p2 - p1)*(p3 - p1) != 0

  void `transform`(const Mat4d &matrix)

    Transforms the plane with the given homogeneous transformation matrix.

  bool `rayIntersect`(const Ray &ray, Vec3d *intersectionPoint) const

    Calculates the intersection point between a ray and the plane.

    Returns true if an intersection point was found

  bool `rayIntersect`(const Ray &ray, double *distance) const

    Calculates the distance between a ray and the plane.

    Returns true if an intersection point was found

  bool `projectVector`(const Vec3d &vector, Vec3d *projectedVector) const

    Projects the given vector onto the plane.

    Returns true if successfully projected. false if the given vector is parallel with the plane’s normal

  Vec3d `projectPoint`(const Vec3d &point) const

    Projects the given point onto the plane.

  Public Static Functions

  static Plane `createFromPointAndNormal`(const Vec3d &point, const Vec3d &normal)

    Returns a plane created from a point and a normal.

  static Plane `createFromPoints`(const Vec3d &p1, const Vec3d &p2, const Vec3d &p3)

    Returns a plane created from three points.

    The three points cannot be on a line as they need to define a plane. So (p2 - p1)*(p3 - p1) != 0

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