//returns whether to go left or right in the BST, given a certain point and certain target normal
//informally this predicate aims to find the point whose adjacent edges e1, e2 have normals n1, n2 such that
//n1 <= normal <= n2
protected int NormalBSTPredicate(TPoint2D point, double normal)
{
TPoint2D leftNeighbor, rightNeighbor;
Points.TryGetPredecessor(point, out leftNeighbor);
Points.TryGetSuccessor(point, out rightNeighbor);
//when at the start, pick left normal to point straight left
var leftNormal = leftNeighbor != null?Normal(leftNeighbor, point, IsUpper) : ConvertToHullAngle(Math.PI);
//when at the end, pick right normal to point straight right
var rightNormal = rightNeighbor != null?Normal(point, rightNeighbor, IsUpper) : ConvertToHullAngle(0.0);
var leftSign = Math.Sign(IsUpper ? normal - rightNormal : rightNormal - normal);
var rightSign = Math.Sign(IsUpper ? normal - leftNormal : leftNormal - normal);
//point was found
if (leftSign == -rightSign || leftSign == 0 || rightSign == 0)
{
return(0);
}
//go left
if (leftSign == rightSign && leftSign == 1)
{
return(-1);
}
//go right
if (leftSign == rightSign && leftSign == -1)
{
return(1);
}
throw new InvalidOperationException("Illegal case detected");
}
