I found this topic and i was wondering, as the third method is by far the easiest, why i always see people using using the cartesian equation? Is this because it is faster when using static planes (is it?) or for another reason? The topic Thanks

if you are using the plane for intersection tests (or in cases when you have to decide of a point is on the plane) use the explicit form of the plane (cartesian equation, hope its the same in english as in hungarian). Use it simply becouse you get simpler algorithms, with simpler expressions. But if you use the plane for bounding something, so you need only to tell whether a point is behind or front of the plane, you should use the parametric form (the one with the normal and an arbitrary point on the plane given).
so you should always use the best suitable. (sometimes the implicit form is good too, but i can tell no example for that right now )

"Knowledge is no more expensive than ignorance, and at least as satisfying." -Barrin

One question on cartesian equations:

for ray-plane intersection testing you need the plane origin, is this the vertex (a*d,b*d,c*d)?

Thanks

Someone, please !