Three- and two-dimensional plane.

• Two-dimensional plane is a line defined by its normal and a point on the line. Normal is computed by rotating the line by 90 degrees clockwise.
• Three-dimensional plane is a plane define by its normal and a point on the plane.
• See line_normal and surface_normal global functions.

Types

• using const_reference = const value_type &
• using reference = value_type &
• using value_type = Vertex< T, N >
• using scalar_type = T

Fields

• constexpr const int dimensions

Methods

• coordinate_system() const -> vtb::geometry::Coordinate_system< T, 3 >
• basis() const -> vtb::geometry::Basis< T, 3 >
• redundant_dimension() const -> int
• Plane(const_reference a, const_reference b, const_reference c)
• gnuplot(std::ostream & out) const -> void
• clear() -> void
• coordinate_system() const -> Coordinate_system< T, N >

  Coordinate system defined by the normal and the origin. This system can be used to project arbitrary points on the plane and then "unproject" them back. After projecting the point on the plane one of its coordinates becomes redundant. The redundant dimension is returned by redundant_dimension method. See puncture and restore global functions that reduce and add dimensions to a vertex.

  Date

  2019-04-09

  Author

  Ivan Gankevich

• basis() const -> Basis< T, N >

  Vector basis for the coordinate system defined by the normal and the origin.

  Date

  2019-04-09

  Author

  Ivan Gankevich

• redundant_dimension() const -> int

  The index of dimension that has nought basis vector. Method basis still returns unit vector instead of nought for this dimension.

  Date

  2019-04-09

  Author

  Ivan Gankevich

• project_vector(const_reference vector) const -> value_type

  Project vector on the plane.

  Date

  2019-11-06

• project(const_reference point) const -> value_type

  Project point on the plane.

  Date

  2019-04-09

  Author

  Ivan Gankevich

• operator()() const -> T

  Substitute nought into the plane equation to get $d$.

  Date

  2019-04-09

  Author

  Ivan Gankevich

  Return

  $d$

• operator()(const_reference point) const -> T

  Substitute point p to the plane equation.

  • If the result is less than nought, then point p lies behind the plane.
  • If the result is greater than nought, then point p lies in front of the plane.
  • If the result is nought, then point p lies on the plane.

  Date

  2019-04-05

  Author

  Ivan Gankevich

• invert() -> void

  Invert plane orientation (the direction of the normal).

• origin() const -> const_reference

  A point on the plane.

• normal() const -> const_reference

  A vector that is orthogonal to the plane.

• Plane(const_reference a, const_reference b, const_reference c)explicit

  Construct plane from plane equation. The plane is defined by equation $ax+by+cz+d=0$, where $(a,b,c)$ is plane normal and $d$ is a normal multiplied by any point lying on the plane.

  Date

  2019-04-05

  Author

  Ivan Gankevich

• Plane(const_reference normal)explicit
• Plane(const_reference normal, const_reference origin)explicit
• Plane()

Returns intersection point of ray and plane. Edge cases are ignored.