Mathematical Prerequisites - Introduction to 3D Game Programming with DirectX 9.0 - page 27

#endif //__cplusplus
FLOAT a, b, c, d;
} D3DXPLANE, *LPD3DXPLANE;
where a , b , and c form the components of the plane's normal vector n
and d is the constant d , from equation (8).

Point and Plane Spatial Relation
Equation (8) is primarily useful for testing the location of points relative
to the plane. For example, given the plane ( n , d ), we can test how a par-
ticular point p is in relation with the plane:
If n p + d = 0, then p is coplanar with the plane.
If n p + d > 0, then p is in front of the plane and in the plane's
positive half-space.
If n p + d < 0, then p is in back of the plane and in the plane's
negative half-space.

Note: If the plane's normal vector n is of unit length, then n p + d

gives the shortest signed distance from the plane to the point p .
This next D3DX function evaluates n p + d for a particular plane and
point:
FLOAT D3DXPlaneDotCoord(
CONST D3DXPLANE *pP,

// plane.

CONST D3DXVECTOR3 *pV // point.

);

// Test the locality of a point relative to a plane.
D3DXPLANE p(0.0f, 1.0f, 0.0f, 0.0f);

D3DXVECTOR3 v(3.0f, 5.0f, 2.0f);

float x = D3DXPlaneDotCoord( &p, &v );

if( x approximately equals 0.0f ) // v is coplanar to the plane.

if(x>0) //visinpositive half-space.

if(x<0) //visinnegative half-space.

Note: We say “approximately equals” due to floating-point impreci-
sion. See the note in the section titled “Vector Equality.”

Note: Methods similar to D3DXPlaneDotCoord are D3DXPlaneDot
and D3DXPlaneDotNormal . See the DirectX documentation for details.

Construction
Besides directly specifying the normal and signed distance of a plane,
we can calculate these two components in two ways. Given the normal
n and a known point on the plane p 0 , we can solve for the d component: