Non mathematical description of a plane
Author
Hi all,
I'm struggling to get to grasp what a plane is ? I know the equation of a plane is :
Ax + By + Cz + D = 0
Where A,B,C make up the normal of the plane and D is the distance.
If I have an object whose position is 10,100,-30 how do I know if this is in front or behind the plane ? Where do A,B,C come from ?
Any help is much appreciated.
Steve
At this level, the best for you is to learn how to learn. I'd start with the FAQ. See the linky in the math forum ? You'll find links for neophytes in 3D algebra. Try to find the relation between 3 points (a triplet) and a plane. Understand that there is only a dot product involved. The duality between a planr and an axis ... That's straightforward to picture it all.
If you still don't find enough to understand, come back here.
If you still don't find enough to understand, come back here.
It's a flat surface that stretchs on forever. You can draw a straight line from any point in the plane to any other point in the plane without leaving the plane. The direction from any point in the plane to any other point in the plane is orthogonal (perpendicular) to the normal.
Oh yes, and if 10A+100b-30C+D<0 you are on one side of the plane, if 10A+100b-30C+D>0 then you are on the other side and if 10A+100b-30C+D=0 then you are in the plane. Which is infront or behind is a matter of opinion.
Oh yes, and if 10A+100b-30C+D<0 you are on one side of the plane, if 10A+100b-30C+D>0 then you are on the other side and if 10A+100b-30C+D=0 then you are in the plane. Which is infront or behind is a matter of opinion.
if the dot product of the planes normal and your position plus the D value in the plane equation is positive then the position is in front of the plane, if it's 0 it's on the plane and if it's smaller then it's behind the plane. This number is actually the distance to the plane.
so:
point: P.x, P.y, P.z
plane: A,B,C,D (where A,B,C equals X,Y,Z of the normal)
P.x*A + P.y*B + P.z*C + D = distance to plane (positive is in front and negative behind of the plane)
Good luck,
Marty
so:
point: P.x, P.y, P.z
plane: A,B,C,D (where A,B,C equals X,Y,Z of the normal)
P.x*A + P.y*B + P.z*C + D = distance to plane (positive is in front and negative behind of the plane)
Good luck,
Marty
This topic is closed to new replies.
Advertisement
Popular Topics
Advertisement
