Maths - Projections of lines on planes

Maths - Projections of lines on planes - Forum Discussion

By: Nobody/Anonymous - nobody
Correction on Projections of lines on planes
2004-05-21 12:56

Here:
http://www.euclideanspace.com/maths/geometry/elements/plane/lineOnPlane/

It is stated that:
"So the direction is:

(A x B) x B"

It should be:
B x (A x B)
or:
(B x A) x B

(B x A) is indeed out of the page as the text says but (A x B) x B has opposite direction to A || B.

I've also tried to implement the "Alternative using Matrix representation" without success. Since I'm pressed for time, I didn't try to find out why.

By: Martin Baker - martinbaker
RE: Correction on Projections of lines on planes
2004-05-24 16:18

Thanks very much for this, Im away from my main computer at the moment but as soon as I get back I will work through this and update the webpage.

Martin

By: Martin Baker - martinbaker
RE: Correction on Projections of lines on planes
2004-06-07 14:58

Thanks very much, I have updated the page now. Sorry it took so long but I underestimated all the work waiting for me when I got back to base.

Martin

By: Nobody/Anonymous - nobody
RE: Correction on Projections of lines ...
2004-09-01 14:12

Hello,

Some typos :

paragraph : Calculation of the projection on the plane
But from this page we know that: ...
_ _ _
A || B = |A| xB x A x B <- unit vectors A,B should be separated ?

paragraph : Calculation of the perpendicular component
Therefore combining these equations gives:

A | B <- instead of A || B
---

grouping terms,

Alternative using Matrix representation

(A B)x = (Az * Bx* Bz - Bz * Ax* Bz - @ Ax * By* By + Bx * Ay* By) / (Bx2 + By2 + Bz2)
@ missing a minus sign here

Thanks for popularizing so complex stuffs !

Nop

By: Martin Baker - martinbaker
RE: Correction on Projections of lines on pla
2004-09-02 14:09

Thanks very much, I have fixed this page as you suggested.

Martin

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Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

New Foundations for Classical Mechanics (Fundamental Theories of Physics). This is very good on the geometric interpretation of this algebra. It has lots of insights into the mechanics of solid bodies. I still cant work out if the position, velocity, etc. of solid bodies can be represented by a 3D multivector or if 4 or 5D multivectors are required to represent translation and rotation.

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Can you help?

Please send me any improvements to here. I would appreciate ideas to make the pages more useful including error correction, ideas for new pages, improvements to wording. It helps if you quote the full URL of the page.

Are the signs of the terms correct? see error heading above

Is there a simpler derivation?

progam

I am working on a project which uses these principles, if you would like to help me with this you are welcome to join in, here:

http://sourceforge.net/projects/mjbworld/

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