public Z3Point3D GetInverted()
{
ArithExpr invertedX = Z3Math.Neg(this.X);
ArithExpr invertedY = Z3Math.Neg(this.Y);
ArithExpr invertedZ = Z3Math.Neg(this.Z);
return(new Z3Point3D(invertedX, invertedY, invertedZ));
}
// Arithmetic helpers
public static ArithExpr Abs(ArithExpr expr)
{
Expr result = Z3.Context.MkITE(
Z3.Context.MkGe(expr, Z3Math.Zero),
expr,
Z3Math.Neg(expr));
return(result as ArithExpr);
}
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);
}