Is there a mathmatician in the house?

[MortalMonkey]

I just can't figure it out:
How on earth does one calculate the base point of a normal (N) from a point (P) to a line (AB) in 3d space?

[Lurox]

Ask Ordinator, he made a nice tutorial on UEd to real scale.

[LaughingRat]

Adjust your coordinate axes so that P and AB are co-planar, and solve as for 2D?

[ElJoelio]

I sez: http://www.netcomuk.co.uk/~jenolive/vect8.html

Dalai sez: http://physics.syr.edu/courses/java-suite/crosspro.html

[Thebos]

Been a while, but I believe it goes like this:

Consider points A,B,P,Q.

Points A and B form vector AB (ie vec(AB)).

Point P is a known point in space. It also forms (with point A) vec(AP).

Point Q exist on line AB and line PQ is perpendicular to to line AB

1) Find the dot product [(vec(AP))*(vec(AB))]. Result is a scalar.

2) Find the distance of point Q from point A by dividing the magnitude of vec(AB) by the dot product just obtained. (ie { (vec(AP))*(vec(AB)) } / { |vec(AB)| } ).

Hope that helps.

<Edited because I made a mistake>

[Thebos]

Not sure how the cross-product references above are to be applied (unless I misunderstood the intial question). Apply the definitions from my first comment and add plane(ABP) as the plane defined by points A,B and P. { Vec(AB) X vec(AP) } results in a vector perpendicular to plane(ABP) that intersects plane(ABP) at point A. Not sure how that helps find point Q on line(AB) such that line(PQ) is perpendicular to line(AB). If it does, please elaborate as I am curious. Thanks.

[ElJoelio]

Hmm.. maybe I misunderstood the question - I thought he was looking for the normal of the plane created by the 3 points.

[MortalMonkey]

Thanks everyone.

If I know the distance from A to Q, it's really easy:

Q = A + Normal( B - A ) * distance

So the whole formula in UScript would be:

Q = A + Normal( B - A ) * ((( B - A ) dot ( P - A )) / VSize( A - B ));

Would that be correct?

[MortalMonkey]

w00t!
Thanks Thebos, it's working perfectly!
Methinks me might have to script you a funny mutator with this...

[Yenzarill]

I flew a plane in 3D space once.

Normal? what? ohh... me? hell no.