SRL::Math::Types::Plane Class Reference

Detailed Description

Infinite plane in 3D space defined by normal and distance for efficient geometric calculations.

The Plane class represents an infinite mathematical plane in 3D space using the standard form of the plane equation: normal·X + d = 0, where:

• normal: Unit vector perpendicular to the plane (defines orientation)
• d: Signed distance from origin to plane along normal direction
• X: Any point on the plane

Key features:

• Memory-efficient representation (normal vector + distance scalar)
• Constant-time distance calculations to points
• Efficient intersection tests with rays, lines, and other geometric primitives
• Multiple construction methods (3 points, normal+point, normal+distance)
• Fixed-point arithmetic for consistent behavior across platforms

Mathematical properties:

• Distance to point P is calculated as: normal·P + d
  • Positive: Point is on same side as normal (in front of plane)
  • Zero: Point is exactly on the plane
  • Negative: Point is on opposite side from normal (behind plane)
• The normal vector should always be normalized (unit length) for correct distance calculations
• Planes can be used to define half-spaces for constructive solid geometry

Common applications:

• Collision detection and response
• View frustum culling (camera planes)
• Constructive solid geometry (CSG)
• Reflections and shadow calculations
• Clipping algorithms

Note

For optimal performance, ensure the normal vector is normalized. Non-normalized normals will result in incorrect distance calculations.

See also

Frustum For usage of planes in camera view frustums

AABB For intersection tests between planes and bounding boxes

#include <plane.hpp>

Public Member Functions
constexpr	Plane ()
	Default constructor. Creates XY plane at origin.
template<Precision P = Precision::Default>
	Plane (const Vector3D &a, const Vector3D &b, const Vector3D &c)
	Creates plane from three non-collinear points.
constexpr	Plane (const Vector3D &normal, const Vector3D &point)
	Creates plane from normal and point.
constexpr	Plane (const Vector3D &normal, Fxp d)
	Creates plane from normal and distance.
constexpr Fxp	Distance (const Vector3D &point) const
	Calculates signed distance from point to plane.
template<Precision P = Precision::Default>
constexpr Plane &	Normalize ()
	Normalizes the plane equation.
constexpr Vector3D	Project (const Vector3D &point) const
	Projects point onto plane.

Public Attributes
Fxp	d
Vector3D	normal