Practical Algorithms for 3D Computer Graphics, 2nd Edition

180 5. Realistic visualization

i f p

1z

− p

0z

< ǫ {

return no intersection line does not cross plane

}

Let µ =

z

0

− p

0z

p

1z

− p

0z

and α = p

0x

+ µ(p

1x

− p

0x

)

Then i f α ≤ X

min

or α ≥ X

max

{

return no intersection cro s s es plane outside box

}

Let β = p

0y

+ µ(p

1y

− p

0y

)

i f β ≤ Y

min

or β ≥ Y

max

{

return no intersection cro s s es plane outside box

}

return intersection

5. The 12 edges are ch ecked against the polygon using the lin e triangle inter-

section algorithm described in section 2.11.1.

Even though the above s tep s have been describ ed for triangular polygon s

there is no reason why the procedu r e could not be applied to any convex planar

polygon.

5.3.5 A simple o