TIGSource Forums

Hey Guys,
       Can anyone explain what is perp product and when we use perp product?

Thanks in advance

Perp product? Are you perhaps talking about a vector cross product, which generates a vector perpendicular to the two in the equation? Or are you taking about the results of a perpetrator who is committing a felony?

I came through this when i was searching for intersection of two vectors. In one article it says that perp product is similar to dot product in which instead of the first vector, the normal of the first vector will be used. I couldn't understand why we should take normal and when we should go for perp product and when for dot product?

Never heard of this before, and as far as I can tell, "A perp B" is just the same as "C dot B, where C is perpendicular to A".

Incidentally, it's not quite right to call a perpendicular vector "the normal of a vector". I guess in 2D, that definition might work, but in 3D, there are infinite vectors perpendicular to any given vector, so which one is the normal?

The perpendicular dot product is just that - the dot product of a vector and the perpendicular vector to another vector. Whereas the ordinary dot product would be (A . B = (A.x * B.x + A.y * B.y), the perpendicular dot product is ( A.x * -B.y + A.y * B.x ).

The relation to the cross product is a bit tricky. A cross product between two 3D vectors is a vector perpendicular to both whose magnitude is relative to the angle between the vectors (that is, parallel vectors yield a zero-length cross product etc), but in 2D you only need one vector for a perpendicular so the perpendicular dot product is simply the magnitude, the cosine of the vectors' projection on each others perpendiculars ( considering the dot product rule; A . B = |A| * |B| * cos(a) )

It's really nothing more fancy than that. You can use it to find out if two lines are parallel (that is, the perpendicular dot product is 0), and some calculations (like the impulse calculation) that require the cross product in 3D can be simplified to 2D with the perpendicular dot product - but it's really just a dot product of a perpendicular vector.

Did that help?

This is the first time I'd ever heard of this. A quick search turned up this bit (http://books.google.com/books?id=CCqzMm_-WucC&pg=PA138&lpg=PA138&dq=the+pleasures+of+perp+dot+products&source=bl&ots=mrly48IHjm&sig=C5mSIKr68FaUG7KVvZOn8KIKHUU&hl=en&ei=FfKfS6axNpmsMpHM_d0M&sa=X&oi=book_result&ct=result&resnum=9&ved=0CDEQ6AEwCA#v=onepage&q=the%20pleasures%20of%20perp%20dot%20products&f=false) from Graphical Gems

It's a 2D concept.

Mathworld's definition is here: http://mathworld.wolfram.com/PerpDotProduct.html

this helps a lot....

Might be useful here aswell.