Finding the map between two images

Thread starter king vitamin
Start date Mar 29, 2009
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SUMMARY

The discussion focuses on finding a transformation T that maps the parallelogram D* with vertices at (-1,3), (0,0), (2,-1), and (1,2) to the rectangle D defined as D = [0,1] X [0,1]. The key equation is T(D*) = D, indicating that the transformation must effectively convert the shape and dimensions of D* into those of D. The participants express confusion over the method to derive such a transformation, particularly whether to connect vertices or transform sides.

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Understanding of vector calculus principles
Familiarity with geometric transformations
Knowledge of mapping techniques in mathematics
Ability to work with coordinate systems

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Mar 29, 2009

king vitamin

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Homework Statement

Let D* be the parallelogram with vertices at (-1,3), (0,0), (2,-1), and (1,2), and let D be the rectangle D = [0,1] X [0,1]. Find a T such that D is the image set of D8 under T.

Homework Equations

Not much to say other than T(D*) = D

The Attempt at a Solution

This section of the book is on mapping, and the book does not give any clues on how to find maps given images, so I'm pretty stumped. This is a vector calculus text, by the way, in case you're wondering about context.

Should I try to find a map that connects the vertices? Or one that transforms the sides? (I've tried both of these with no luck) Or is there a general method for solving this?