lec1 - Geometric Constraints Introduction. OverOverView on...

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Geometric Constraints – Introduction. OverOverView on Geometric Constraints Orientation: Let’s consider a square box of side ‘a’ (2d). Now imagine that we want to draw 3 circles in this square without the circles overlapping each other or the boundaries of the square. A desirable configuration would be something like this. Basically what we want is to make these 3 circles as big as possible while still making them fit into the box. That would translate to saying maximize r i where r i denotes the radii of the circles. Generally: Pack(without overlapping) a disk D in 2-d with given radius d with disks D1,D2,. . Dn of radius x1,x2, . .,xn s.t. xi is maximized. Task 1: Can this be expressed as a LP problem in the xi? (You are allowed to add more variables.) Task 1’: If no (answer to Task 1), express as simply as possibly. (Please note “simply” here. We’ll discuss it in detail later. ) Task 1: Ideally we would like to capture all the constraints that have been implicitly expressed in the above diagram and description in the form of equations. Write out one such formulation. (Hint: Linear equations may not always work out). You are free to add as many variables as necessary.
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The problem that was just described is known as a packing problem. And it is an example of a geometric constraints problem. We have a lot of constraints and we would like to solve for a possible configuration within those constraints. This particular problem under
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This note was uploaded on 11/09/2011 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.

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lec1 - Geometric Constraints Introduction. OverOverView on...

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