<frustum-matrix4> ( xy-dim near far -- matrix )
Extra matrix operations

Prev:	<vandermonde-matrix> ( u n -- matrix )
Next:	<ortho-matrix4> ( factors -- matrix )

Vocabulary
math.matrices.extras

Inputs

xy-dim	a pair
near	a number
far	a number

Outputs

matrix

a matrix

Word description
Make a 4 x 4 matrix suitable for representing an occlusion frustum. A viewing or occlusion frustum is the three-dimensional region of a three-dimensional object which is visible on the screen. See frustum on Wikipedia.

Notes
Only the first two values in xy-dim are used.

Examples

USING: math.matrices.extras prettyprint ; { 5 4 } 5 6 <frustum-matrix4> .
{ { 1.0 0.0 0.0 0.0 } { 0.0 1.25 0.0 0.0 } { 0.0 0.0 -11.0 -60.0 } { 0.0 0.0 -1.0 0.0 } }

See also
glFrustum

Definition

USING: math sequences ;

IN: math.matrices.extras

:: <frustum-matrix4> ( xy-dim near far -- matrix )
    xy-dim first2 :> ( x y ) near x /f :> xf near y /f
    :> yf near far + near far - /f :> zf 2 near far * *
    near far - /f :> wf {
        { xf 0.0 0.0 0.0 }
        { 0.0 yf 0.0 0.0 }
        { 0.0 0.0 zf wf }
        { 0.0 0.0 -1.0 0.0 }
    } ;