I need a good linear algebra tutorial

[Chaotic42]

Hey folks.

I've been assigned the task of finding a rectangle that will describe an arbitrarily large set of 3D points. The rectangle needs to be as efficient as possible (highest point density), and of course can't be infintely small or large or what have you.

I'm only in Calc I, and I've studied up to Calc 2, but I'm not sure how to go about finding this rectangle. I posted about this in Software, but I need some direction (No, this isn't homework).

Can anyone point me in the right direction here?

 

[OutHouse]

im trying to teach my daughter simple math. ill get back to you in 6 years when she is in high school.

 

[Gibson486]

I really do not get what you mean by"needs to be as efficient as possible (highest point density)", but since you are talking 3 space, you will need some matrix/vector algebra....

 

[Kyteland]

I remember doing something similar to this in an algorithms class a few years ago. I'll see if I still have those notes when I get home from work tonight.

Edit: http://compgeom.cs.uiuc.edu/~jeffe/compgeom/
That is a web page by my prof from that class. You can probably find something to help you there.

This problem is probably related to finding the convex hull of a set of points. Take a look at a few of the algorithms for doing that to get a picture of how to go about doing this.

 

[eLiu]

if you want linalg, this may be useful.

 

[Mo0o]

Originally posted by: Citrix
im trying to teach my daughter simple math. ill get back to you in 6 years when she is in high school.

If you're teaching your daughter linear albegra at the high school level i will be impressed beyond belief.

 

[EvilYoda]

Originally posted by: Mo0o

Originally posted by: Citrix
im trying to teach my daughter simple math. ill get back to you in 6 years when she is in high school.

If you're teaching your daughter linear albegra at the high school level i will be impressed beyond belief.

yah...she'll be like that girl in the article that was linked to a few days ago. 🙂

 

[Chaotic42]

Thanks guys, I'll check these out this weekend.

 

[Ameesh]

am i missing something? wouldn't you just iterate over the set of coordinates and find the bounds of the rectangle that way? whatever the left most point is you add one and that is your -x boundry, the rightmost is your =x boundry and you do the same for , y and z

😕 sorry if ia m not understanding your question properly.

 

[Ameesh]

Originally posted by: Mo0o

Originally posted by: Citrix
im trying to teach my daughter simple math. ill get back to you in 6 years when she is in high school.

If you're teaching your daughter linear albegra at the high school level i will be impressed beyond belief.

linear algebra isnt that hard. in my opinion it should be taught right after you learn algebra then you can learn calculas.

 

[Goosemaster]

"augmented matrix"

 

[Chaotic42]

Originally posted by: Ameesh
am i missing something? wouldn't you just iterate over the set of coordinates and find the bounds of the rectangle that way? whatever the left most point is you add one and that is your -x boundry, the rightmost is your =x boundry and you do the same for , y and z

😕 sorry if ia m not understanding your question properly.

Some of the data will be erroneous.

The best analogy that I can come up with is a cloud. Imagine that you have a random cloud. I need a rectangle that will describe that cloud in the best way. There may be small water droplets around the cloud, and those would need to be thrown out or moved down in their importance.

I'm freaking exhausted now, maybe I can give a better description of what I need this weekend.

Thanks for the replies, everyone.

 

[Ameesh]

Originally posted by: Chaotic42

Originally posted by: Ameesh
am i missing something? wouldn't you just iterate over the set of coordinates and find the bounds of the rectangle that way? whatever the left most point is you add one and that is your -x boundry, the rightmost is your =x boundry and you do the same for , y and z

😕 sorry if ia m not understanding your question properly.

Some of the data will be erroneous.

The best analogy that I can come up with is a cloud. Imagine that you have a random cloud. I need a rectangle that will describe that cloud in the best way. There may be small water droplets around the cloud, and those would need to be thrown out or moved down in their importance.

I'm freaking exhausted now, maybe I can give a better description of what I need this weekend.

Thanks for the replies, everyone.

if it were me i would figure out an algorithm to get rid of the errouneous data points and then run my simple algorithm above.