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    <p>Generally, mutable-thing references should only be considered equivalent if they both refer to the same object. Only references to immutable things should use any other definition of equality. It would be helpful if <code>Object</code> included virtual functions to test for equivalence in the scenario where two references are held by separate objects, neither of which will expose its reference to anything that might mutate it. Unfortunately, even though the effectively-immutable-instance-of-mutable-type pattern is very common (nearly all immutable collections, for example, use one or more mutable-type objects such as arrays to hold their data) there's no standard pattern for equivalence testing with it.</p> <p>If you want to store vertices in a dictionary using <code>Object.Equals</code> for equality testing, it should be an immutable type. Alternatively, you could define a custom <code>IEqualityComparer&lt;T&gt;</code> for use with the dictionary, but you should be aware that <code>Dictionary</code> should only be used to find <em>perfect</em> matches. If you want to be able to find any point that's within <code>EPSILON</code> of a given point, you should use a which maps rounded values to lists of precise values (values should be rounded to a power of two that's at least twice as great as epsilon). If adding or subtracting EPSILON from some or all of the coordinates in a point would cause it to be rounded differently, the point should be included in the dictionary, rounded every such possible way.</p>
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