Mathematical Prerequisites - Introduction to 3D Game Programming with DirectX 9.0 - page 26

In Figure 12 we see that the graph of a plane is all the points p that sat-
isfy the equation.

0

(7) n p p

0

Figure 12: If p 0 is a point on the plane, then
the point p is also on the plane if the vector
formed from ( p - p 0 ) is orthogonal to the
plane's normal vector.

When describing a particular plane, the normal n and a known point on
the plane p 0 are fixed, so it is typical to write equation (7) as:

n p d 0

(8)

where d =- n p 0 .

Note: If the plane's normal vector n is of unit length, d =- n p 0

gives the shortest signed distance from the origin to the plane.

D3DXPLANE
When representing a plane in code, it suffices to store only the normal
vector n and the constant d . It is useful to think of this as a 4D vector,
which we denote as ( n , d ). The D3DX library uses the following struc-
ture for a plane:
typedef struct D3DXPLANE
{
#ifdef __cplusplus
public:
D3DXPLANE() {}
D3DXPLANE( CONST FLOAT* );
D3DXPLANE( CONST D3DXFLOAT16* );
D3DXPLANE( FLOAT a, FLOAT b, FLOAT c, FLOAT d );

// casting
operator FLOAT* ();
operator CONST FLOAT* () const;

// unary operators
D3DXPLANE operator + () const;
D3DXPLANE operator - () const;

// binary operators
BOOL operator == ( CONST D3DXPLANE& ) const;
BOOL operator != ( CONST D3DXPLANE& ) const;