//public Z3Point3D GetApproximateNormalized()
//{
// Z3Point3D result = this.GetManhattanNormalized();
// result.X = CalcApproximateCoordFromManhattanToEuclidianSystem(result.X, result.Y, result.Z);
// result.Y = CalcApproximateCoordFromManhattanToEuclidianSystem(result.Y, result.X, result.Z);
// result.Z = CalcApproximateCoordFromManhattanToEuclidianSystem(result.Z, result.Y, result.X);
// return result;
//}
public ArithExpr Norm()
{
ArithExpr result =
Z3Math.Max(
Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(this.X, this.Y, this.Z)),
Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(this.Y, this.X, this.Z)),
Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(this.Z, this.Y, this.X)));
return(result);
}
public static void Run()
{
Z3Point3D constPoint = Z3Point3D.MkZ3Const("const"); // ("const X", "const Y", "const Z")
Z3Point3D normalized = new Z3Point3D();
ArithExpr higherCoord =
Z3Math.Max(
Z3Math.Max(
Z3Math.Abs(constPoint.X),
Z3Math.Abs(constPoint.Y)),
Z3Math.Abs(constPoint.Z));
normalized.X = Z3.Context.MkDiv(constPoint.X, constPoint.Y);
normalized.Y = Z3Math.One;//Z3.Context.MkDiv(constPoint.Y, higherCoord);
normalized.Z = Z3.Context.MkDiv(constPoint.Z, constPoint.Y);
normalized.X = CalcApproximateCoordFromManhattanToEuclidianSystem(normalized.X, normalized.Y, normalized.Z);
normalized.Y = CalcApproximateCoordFromManhattanToEuclidianSystem(normalized.Y, normalized.X, normalized.Z);
normalized.Z = CalcApproximateCoordFromManhattanToEuclidianSystem(normalized.Z, normalized.Y, normalized.X);
Z3Point3D up = Z3Point3D.DirectionPoint(Direction.Up); // (0, 1, 0)
Z3Point3D distVec = normalized - up;
ArithExpr distance =
Max(
Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.X, distVec.Y, distVec.Z)),
Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.Y, distVec.X, distVec.Z)),
Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.Z, distVec.Y, distVec.X)));
BoolExpr expr = Z3.Context.MkLt(distance, Z3.Context.MkReal(1, 2));
Solver solver = Z3.Context.MkSolver();
solver.Assert(expr);
Status status = solver.Check();
Statistics stats = solver.Statistics;
switch (status)
{
case Status.UNKNOWN:
Console.WriteLine("Solver check for witness returned Status.UNKNOWN because: " + solver.ReasonUnknown);
throw new ArgumentException("Test Failed Expception");
case Status.UNSATISFIABLE:
Console.WriteLine("There is no valid witness for " + expr);
throw new ArgumentException("Test Failed Expception");
case Status.SATISFIABLE:
Console.WriteLine("OK, model: " + solver.Model);
break;
}
}
public Z3Point3D GetManhattanNormalized()
{
Z3Point3D result = new Z3Point3D();
ArithExpr higherCoord =
Z3Math.Max(
Z3Math.Max(
Z3Math.Abs(this.X),
Z3Math.Abs(this.Y)),
Z3Math.Abs(this.Z));
result.X = Z3Math.Div(this.X, higherCoord);
result.Y = Z3Math.Div(this.Y, higherCoord);
result.Z = Z3Math.Div(this.Z, higherCoord);
return(result);
}
public ArithExpr CalcApproximateDistance(Z3Point3D that)
{
// Manhattan distance vector
Z3Point3D distVec = this.GrabDistancePoint3D(that);
//ArithExpr result =
// Z3Math.Add(
// Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.X, distVec.Y, distVec.Z)),
// Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.Y, distVec.X, distVec.Z)),
// Z3Math.Abs(CalcApproximateCoordFromManhattanToEuclidianSystem(distVec.Z, distVec.Y, distVec.X)));
ArithExpr result =
Z3Math.Max(
Z3Math.Abs(distVec.X),
Z3Math.Abs(distVec.Y),
Z3Math.Abs(distVec.Z));
return(result);
}
ArithExpr CalcApproximateCoordFromManhattanToEuclidianSystem(
ArithExpr firstCoord,
ArithExpr secondCoord,
ArithExpr thirdCoord)
{
// Work only with values length
// Values sign will be assigned again in the end
ArithExpr firstCoordLength = Z3Math.Abs(firstCoord);
ArithExpr secondCoordLength = Z3Math.Abs(secondCoord);
ArithExpr thirdCoordLength = Z3Math.Abs(thirdCoord);
// The all common length will be weighted by this
// This way for example a (1, 1, 1) vector will become
// A (0.57, 0.57, 0.57) with norm near to 1
//ArithExpr sqrt1div3 = Z3Math.Real(0.57735026918962576450914878050196);
ArithExpr sqrt1div3 = Z3Math.Real(0.577);
// The remaining common length will be weighted by this
// This way for example a (1, 1, 0) vector will become
// A (0.7, 0.7, 0.7) with norm near to 1
//ArithExpr sin45 = Z3Math.Real(0.70710678118654752440084436210485)
ArithExpr sin45 = Z3Math.Real(0.707);
// Calc common length between x, y, z
ArithExpr allCommonLength =
Z3Math.Min(
firstCoordLength,
secondCoordLength,
thirdCoordLength);
// Calc the common length between the target coord (firstCoord)
// and the higher coord between the second and third coords
ArithExpr lastTwoCommonLength =
Z3Math.Max(
Z3Math.Min(secondCoordLength, firstCoordLength),
Z3Math.Min(thirdCoordLength, firstCoordLength));
// Calc exclusevely common length with the remaining coordinate
ArithExpr lastTwoExclusiveCommonLength =
Z3Math.Sub(
lastTwoCommonLength,
allCommonLength);
// Calc remaining length
ArithExpr especificLength =
Z3Math.Sub(firstCoordLength,
Z3Math.Add(lastTwoExclusiveCommonLength, allCommonLength));
// Calc weighted lengths
ArithExpr weigthedLength1 = Z3Math.Mul(lastTwoExclusiveCommonLength, sin45);
ArithExpr weigthedLength2 = Z3Math.Mul(allCommonLength, sqrt1div3);
// Calc weighted result length
ArithExpr resultLength =
Z3Math.Add(
especificLength,
weigthedLength1,
weigthedLength2);
// The transform doesn't change the sign of the coordinate
// Recover it from original data
Expr result =
Z3.Context.MkITE(
Z3.Context.MkGe(firstCoord, Z3Math.Zero),
resultLength,
Z3Math.Neg(resultLength));
return(result as ArithExpr);
}
public static ArithExpr Max(ArithExpr expr1, ArithExpr expr2, ArithExpr expr3)
{
return(Z3Math.Max(Z3Math.Max(expr1, expr2), expr3));
}
