# PlaneReference

The `plane`

primitive is a simple way to define an infinite
flat surface. The plane is not a thin boundary or can be compared to a sheet
of paper. A plane is a solid object of infinite size that divides POV-space
in two parts, inside and outside the plane. The plane is specified as follows:

PLANE: plane { <Normal>, Distance [OBJECT_MODIFIERS...] }

The * <Normal>* vector defines the surface normal
of the plane. A surface normal is a vector which points up from the surface
at a 90 degree angle. This is followed by a float value that gives the
distance along the normal that the plane is from the origin (that is only
true if the normal vector has unit length; see below). For example:

plane { <0, 1, 0>, 4 }

This is a plane where straight up is defined in the positive y-direction.
The plane is 4 units in that direction away from the origin. Because most
planes are defined with surface normals in the direction of an axis you will
often see planes defined using the `x`

, `y`

or ```
z
```

built-in vector identifiers. The example above could be specified
as:

plane { y, 4 }

The plane extends infinitely in the x- and z-directions. It effectively
divides the world into two pieces. By definition the normal vector points to
the outside of the plane while any points away from the vector are defined as
inside. This inside/outside distinction is important when using planes in CSG
and `clipped_by`

. It is also important when using fog or
atmospheric media. If you place a camera on the "inside" half of
the world, then the fog or media will not appear. Such issues arise in any
solid object but it is more common with planes. Users typically know when
they have accidentally placed a camera inside a sphere or box but
"inside a plane" is an unusual concept. In general you can reverse the
inside/outside properties of an object by adding the object modifier ```
inverse
```

. See Inverse and Empty and Solid Objects for details.

A plane is called a *polynomial* shape because it is defined by a
first order polynomial equation. Given a plane:

plane { <A, B, C>, D }

it can be represented by the equation * A*x + B*y + C*z - D*sqrt(A^2 + B^2 + C^2) = 0*.

Therefore our example `plane{y,4}`

is actually the polynomial
equation y=4. You can think of this as a set of all x, y, z points where all
have y values equal to 4, regardless of the x or z values.

This equation is a first order polynomial because each term contains only single powers of x, y or z. A second order equation has terms like x^2, y^2, z^2, xy, xz and yz. Another name for a 2nd order equation is a quadric equation. Third order polys are called cubics. A 4th order equation is a quartic. Such shapes are described in the sections below.