/// <summary>
/// Generate a 2D directional vector that is located in the middle of the largest angular extent
/// (i.e. has the most space). For example if we have a two vectors, one pointing up and one
/// pointing right we have to extents (.5π and 1.5π). The new vector would be pointing down and
/// to the left in the middle of the 1.5π extent.
/// </summary>
/// <param name="vectors">list of vectors</param>
/// <returns>the new vector</returns>
public static Vector2 NewVectorInLargestGap(IList <Vector2> vectors)
{
Debug.Assert(vectors.Count > 1);
double[] extents = VecmathUtil.Extents(vectors);
Array.Sort(extents);
// find and store the index of the largest extent
double max = -1;
int index = -1;
for (int i = 0; i < vectors.Count; i++)
{
double extent = extents[(i + 1) % vectors.Count] - extents[i];
if (extent < 0)
{
extent += TAU;
}
if (extent > max)
{
max = extent;
index = i;
}
}
Debug.Assert(index >= 0);
double mid = (max / 2);
double theta = extents[index] + mid;
return(new Vector2(Math.Cos(theta), Math.Sin(theta)));
}
/// <summary>
/// Using the angular extents of vectors, determine the best position for a hydrogen label. The
/// position with the most space is selected first. If multiple positions have the same amount of
/// space, the one where the hydrogen position is most centred is selected. If all position are
/// okay, the priority is Right > Left > Above > Below.
/// </summary>
/// <param name="vectors">directional vectors for each bond from an atom</param>
/// <returns>best hydrogen position</returns>
internal static HydrogenPosition UsingAngularExtent(IList <Vector2> vectors)
{
var extents = VecmathUtil.Extents(vectors);
Array.Sort(extents);
var extentMap = new Dictionary <HydrogenPosition, OffsetExtent>();
for (int i = 0; i < extents.Length; i++)
{
double before = extents[i];
double after = extents[(i + 1) % extents.Length];
foreach (var position in Values)
{
// adjust the extents such that this position is '0'
double bias = Tau - V[(int)position].Direction;
double afterBias = after + bias;
double beforeBias = before + bias;
// ensure values are 0 <= x < Tau
if (beforeBias >= Tau)
{
beforeBias -= Tau;
}
if (afterBias >= Tau)
{
afterBias -= Tau;
}
// we can now determine the extents before and after this
// hydrogen position
double afterExtent = afterBias;
double beforeExtent = Tau - beforeBias;
// the total extent is amount of space between these two bonds
// when sweeping round. The offset is how close this hydrogen
// position is to the center of the extent.
double totalExtent = afterExtent + beforeExtent;
double offset = Math.Abs(totalExtent / 2 - beforeExtent);
// for each position keep the one with the smallest extent this is
// the most space available without another bond getting in the way
if (!extentMap.TryGetValue(position, out OffsetExtent offsetExtent) || totalExtent < offsetExtent.Extent)
{
extentMap[position] = new OffsetExtent(totalExtent, offset);
}
}
}
// we now have the offset extent for each position that we can sort and prioritise
var extentEntries = extentMap;
KeyValuePair <HydrogenPosition, OffsetExtent>?best = null;
foreach (var e in extentEntries)
{
if (best == null || ExtentPriority.Instance.Compare(e, best.Value) < 0)
{
best = e;
}
}
Debug.Assert(best != null);
return(best.Value.Key);
}