View Full Version : point intersection?

04-14-2001, 09:49 PM
Its been a couple of years since I had my advanced calc, so I don't remember this, and I've been trying to figure it out but this is easier...

okay, I have points A and B, and a plane in between them, how do I calculate the point along the vector defined from A to B that intersects the plane?

If you can give me general formulas I would be most appreciative.

For example lets say we have A=(-5, 2, -15); C=(15,4,-25) and a plane defined by x=5;

Obviously by hand we can see that it intersects at B=(5, 3, -20), but what is the general formula?

Michael Steinberg
04-14-2001, 10:07 PM
int LinePlaneIntersect( CVector& a, CVector& b, CPlane& plane, CVector& result ){
double quot, t;
t = (plane.place-a)*plane.normal;
quot = b*plane.normal;

if( DOUBLE_EQ( quot, 0.0 ) ) {
if( DOUBLE_EQ( t, 0.0 ) )
return LPI_INSIDE;
else return LPI_PARALLEL;
t = t/quot;
result = a+b*t;
return LPI_CUT;

a is the place vector of the line, b the direction vector.
DOUBLE_EQ checks wether two doubles are about the same (with a little delta due to imprecision).
Returns LPI_INSIDE if the line is inside the plane. LPI_PARALLEL if the line is parallel to the plane. LPI_CUT otherwise.

I have a vector class, that's why I can simply calculate with these vectors. The theory stays the same however, even if you haven't it (yeah... sorry.)

[This message has been edited by Michael Steinberg (edited 04-15-2001).]

04-15-2001, 10:57 PM

No code, but 2 ways to tackle the problem. It's also simple to turn into code.

Thanks again Paul Bourke! Great site. Always helps me when I'm too lazy to pick up a textbook.

[This message has been edited by ffish (edited 04-16-2001).]

Michael Steinberg
04-16-2001, 03:36 AM
Has my code not been good?

04-16-2001, 05:49 AM
actually I feel stupid that I didn't come back and close the discussion; about 5 minutes after I posted that I figured it out, so though I didn't end up using your code, I'm sure that its good, however given my own datatypes and such and the fact that I figured it out before I had a chance to read your post, I didn't end up using them. Sorry, but thanks.

04-16-2001, 10:46 PM
Your code was good Michael. I just posted a reference that I use fairly often for lots of different geometry related problems.