hashtable - Check Uniqueness of a Java Object, within some epsilon -

i'm trying prune 3d mesh checking vertices uniqueness. because each vertex has sort of error associated it, 2 "similar" verts same. e.g.

<1.9999999, 1, 3> same vertex <2.000001, 1, 3>

i have millions of vertices need check, going put of objects hash table , query see if unique. overriding isequal easy: take abs of difference between 2 coordinates , divide magnitude of one. example:

if (math.abs((x2-x2)/x1) < 0.0000001) return true;

but how come hashcode return same 2 equal, not equal vertices?

i thought quantizing space, i.e. taking floor decimal place entire set. but, in example above round <1.999, 1, 3> , <2.000, 1, 3> example.

but how come hashcode return same 2 equal, not equal vertices?

in short, that's not possible.

if hashcode(x) == hashcode(x + eps) x, it's true hashcode(x + eps) == hashcode(x + 2*eps) , on.

the way satisfy int hashcode() { return constant; }, of limited use...

---

as corollary, equals() method flawed too. contract equals() requires transitive, i.e. if a.equals(b) , b.equals(c), a.equals(c), any a, b, c. not case definition.

this going lead sorts of subtle hell, many of standard java collections, etc. rely on this.