Serious Math Help Needed

[WhoIsThat]

Argh, I have no idea how to do this problem. I think I understand conceptually what an affine transformation is, and what this question is asking, but my brain is completely blank on how to do this question, and have been staring at it for hours.

Click for the question.

Help!

 

[crt1530]

Get a Schaum's Outline.

 

[Spencer278]

Yeah you need a lot of help

 

[HonkeyDonk]

i think maybe 1 person on this msg board can answer that.

 

[WhoIsThat]

Help!

 

[BigJ]

Is that russian? Cause I don't understand what the hell that question is asking. What level Math is this?

 

[WhoIsThat]

help

 

[Stealth1024]

is this for real variables?

 

[GtPrOjEcTX]

Briefly understand it. The 3space is Calc 3 and above level for those interested.

Not quite sure how to approach it though.

I think I understand conceptually what an affine transformation is

Then you've got some on me then. GL

 

[agnitrate]

It's worded poorly, but also hard to read your handwriting for certain words.

-silver

 

[WhoIsThat]

Well, it's not my handwriting. This is a theoritical calculus class that's about three classes after Cal III.

We are only learning background information for the main subject, and this is a question on some of the background stuff we must know.

 

[GtPrOjEcTX]

This is a theoritical calculus class that's about three classes after Cal III.

Nice. I stopped at Calc. III

 

[FFactory0x]

I suck at Math and stat

 

[Fatalist]

This is just calculating a 3 x 3 matrix to change the coordinate basis from [(1,0) (0,1)] to [P1, P2]

Edit:
I guess this could be just a 2x2 matrix composed of rotation, scaling, and shearing.

http://www.css.tayloru.edu/~btoll/s99/424/res/mtu/Notes/geometry/geo-tran.htm#affine

 

[WhoIsThat]

I think the part that really throws me off is the inequality part. How do I deal with the inequality part?

 

[Fatalist]

I'm thinking that the inequality just means that P0, P1, and P2 are not colinear, but I could be wrong.

 

[TuxDave]

Soo.... this is what I get (minus all the mumbo jumbo in the paragraph)

You need a transformation matrix that will:

Decompose your vector of (xo,yo)-(x,y) into components of (xo,yo)-(x1,y1) and (xo,yo)-(x2,y2) and set the magnitudes of those components as your new x and y coordinate?

 

[TuxDave]

Originally posted by: Fatalist
I'm thinking that the inequality just means that P0, P1, and P2 are not colinear, but I could be wrong.

Yes... that's exactly what I think it means. Otherwise you cannot make a clear cut transformation.

 

[TuxDave]

nm... it's all kinda screwy.

 

[bigalt]

I'm stumped.

it should be

[x'] = [a1 a2] [x] + [b1 b2]
[y'] = [a3 a4] [y] + [b3 b4]

but you have 8 unknowns, and 3 points gives you 6 equations. no idea how to solve it.

 

[Fatalist]

Change of basis just uses P1 and P2 as the rows or columns of M, IIRC.
Use a linear algebra textbook.