Explain how to get a parametric equation from |x| + |y| = 1

Question

anonymous · Answer

OK, I've never done parameteric equations before,
but I think I get it from the wikipedia page.

How about we try something with a unit circle, that has an inscribed square like this:

|dw:1316430463001:dw|

anonymous · Answer

so the free variable will be alpha ?

anonymous · Answer

Hmmm...but how to get equatios for x and y in terms of t?

anonymous · Answer

I don't know if it's possible, I'm thinking about it. It might not be the right direction.

anonymous · Answer

The reason is that I'm trying to solve a line integral and I'm given just this eqatuion |x| + |y| = 1. My guess is that from this I need to get parametric equation. But since it's not a cirlce, elipse I don't know how.

anonymous · Answer

will it be any help to create a piecewise  parameteric equation ?

for example:

for 0<=a<=1

y=a
x=1-a

And define 3 additional similar pieces ?

It sounds kinda useless to me, but asking - just in case :)

anonymous · Answer

Does this help ? http://www.physicsforums.com/archive/index.php/t-245401.html