Handle Ambiguity in RotatedRectangleDemo Positions

[dwmunster]

Overview

Since the RotatedRectangleDemo is underspecified and used across the tests for several solvers, this PR adds a method that will check for the four possible outcomes and test their positions to the desired tolerance.

Details

The RotatedRectangleDemo has 7 constraints (for the rectangle):

• Fix A at the origin
• Line AB and BC are perpendicular
• Line BC and CD are perpendicular
• Line CD and DA are perpendicular
• || AB || = 2
• || BC || = 3
• Line AB has an angle with the x-axis of 45 degrees

This leaves two choices for the line segment AB: above the x-axis or below the x-axis. Each of those options has two sub-options corresponding to the two orthogonal directions to the line segment AB. E.g., if AB is above the x-axis, point C can be up-and-left or down-and-right of point B.

This leaves four cases to test for, which this PR adds.

Alternatives

We could consider adding additional constraints to fully specify the rectangle. However, I think have an underconstrained example is valuable, as it helped catch an erroneous assumption of mine while working on the GaussNewtonSolver.