public Vector3Variable(string name, CSP p, Interval x, Interval y, Interval z)
{
Name = name;
X = new FloatVariable(name + ".X", p, x);
Y = new FloatVariable(name + ".Y", p, y);
Z = new FloatVariable(name + ".Z", p, z);
}
public void IntegerPowerIntervalTest()
{
var neg = new Interval(-2, -1);
var pos = new Interval(1, 2);
var cross = new Interval(-2, 2);
Assert.AreEqual(new Interval(1, 1), neg ^ 0);
Assert.AreEqual(neg, neg ^ 1);
Assert.AreEqual(new Interval(1, 4), neg ^ 2);
Assert.AreEqual(new Interval(1, 4), pos ^ 2);
Assert.AreEqual(new Interval(0, 4), cross ^ 2);
Assert.AreEqual(new Interval(-8, -1), neg ^ 3);
Assert.AreEqual(new Interval(1, 8), pos ^ 3);
}
public bool Contains(Interval i)
{
return this.Lower <= i.Lower && this.Upper >= i.Upper;
}
public bool NearlyContains(Interval i, double epsilon)
{
return MathUtil.NearlyLE(this.Lower, i.Lower, epsilon) && MathUtil.NearlyGE(this.Upper, i.Upper, epsilon);
}
public static Interval UnionOfIntersections(Interval intersector, Interval a, Interval b)
{
return UnionBound(Intersection(intersector, a), Intersection(intersector, b));
}
public static Interval UnionBound(Interval a, Interval b)
{
if (a.Empty)
return b;
if (b.Empty)
return a;
return new Interval(Math.Min(a.Lower, b.Lower), Math.Max(a.Upper, b.Upper));
}
public static Interval PositiveSqrt(Interval a)
{
Debug.Assert(a.Lower >= 0, "Attempt to take square root of a negative interval");
return new Interval(Math.Sqrt(a.Lower), Math.Sqrt(a.Upper));
}
public static Interval InvPower(Interval a, uint exponent)
{
if (exponent == 1)
return a;
var invExponent = 1.0 / exponent;
if (exponent % 2 == 0)
{
// even exponent
var lower = Math.Pow(Math.Max(0, a.Lower), invExponent);
var upper = Math.Pow(Math.Max(0, a.Upper), invExponent);
return new Interval(lower, upper);
}
// odd exponent
return new Interval(NegativeTolerantPower(a.Lower, invExponent), NegativeTolerantPower(a.Upper, invExponent));
}
public static Interval Intersection(Interval a, Interval b)
{
return new Interval(Math.Max(a.Lower, b.Lower), Math.Min(a.Upper, b.Upper));
}
