# Plane3¶

```#include <Imath/ImathPlane.h>
```

The `Plane3` class template represents a plane in 3D space, with predefined typedefs for planes of type `float` and `double`.

Example:

```#include <Imath/ImathPlane.h>

void
plane3_example()
{
Imath::V3f a (1.0f, 0.0f, 0.0f);
Imath::V3f b (0.0f, 1.0f, 0.0f);
Imath::V3f c (0.0f, 0.0f, 1.0f);

Imath::Plane3f p (a, b, c);

Imath::V3f n (1.0f,  1.0f,  1.0f);
n.normalize();

assert (p.normal == n);

Imath::V3f o (0.0f, 0.0f, 0.0f);
float d = p.distanceTo (o);
assert (Imath::equalWithAbsError (d, -0.57735f, 1e-6f));
}
```
typedef Plane3<float> Imath::Plane3f

Plane of type float.

typedef Plane3<double> Imath::Plane3d

Plane of type double.

template<class T>
class Imath::Plane3

The `Plane3` class represents a half space in 3D, so the normal may point either towards or away from origin.

The plane `P` can be represented by Plane3 as either `p` or `-p` corresponding to the two half-spaces on either side of the plane. Any function which computes a distance will return either negative or positive values for the distance indicating which half-space the point is in. Note that reflection, and intersection functions will operate as expected.

Vec3<T> normal

The normal to the plane.

T distance

The distance from the origin to the plane.

Constructors

inline Plane3() noexcept

Uninitialized by default.

inline constexpr Plane3(const Vec3<T> &normal, T distance) noexcept

Initialize with a normal and distance.

inline constexpr Plane3(const Vec3<T> &point, const Vec3<T> &normal) noexcept

Initialize with a point and a normal.

inline constexpr Plane3(const Vec3<T> &point1, const Vec3<T> &point2, const Vec3<T> &point3) noexcept

Initialize with three points.

Manipulation

inline void set(const Vec3<T> &normal, T distance) noexcept

Set via a given normal and distance.

inline void set(const Vec3<T> &point, const Vec3<T> &normal) noexcept

Set via a given point and normal.

inline void set(const Vec3<T> &point1, const Vec3<T> &point2, const Vec3<T> &point3) noexcept

Set via three points.

Utility Methods

inline constexpr bool intersect(const Line3<T> &line, Vec3<T> &intersection) const noexcept

Determine if a line intersects the plane.

Parameters
• line – The line

• intersection[out] The point of intersection

Returns

True if the line intersects the plane.

inline constexpr bool intersectT(const Line3<T> &line, T &parameter) const noexcept

Determine if a line intersects the plane.

Parameters
• line – The line

• parameter[out] The parametric value of the point of intersection

Returns

True if the line intersects the plane.

inline constexpr T distanceTo(const Vec3<T> &point) const noexcept

Return the distance from a point to the plane.

inline constexpr Vec3<T> reflectPoint(const Vec3<T> &point) const noexcept

Reflect the given point around the plane.

inline constexpr Vec3<T> reflectVector(const Vec3<T> &vec) const noexcept

Reflect the direction vector around the plane.

template<class T>
std::ostream &Imath::operator<<(std::ostream &o, const Plane3<T> &plane)

Stream output, as “(normal distance)”.