/// <summary>
/// Gets the tangent at a given point in the curve.
/// </summary>
protected VECTOR GetCenterTangent(int first, int last, int split)
{
using var _ = GetCenterTangentMarker.Auto();
List <VECTOR> pts = _pts;
List <FLOAT> arclen = _arclen;
// because we want to maintain C1 continuity on the spline, the tangents on either side must be inverses of one another
Debug.Assert(first < split && split < last);
FLOAT splitLen = arclen[split];
VECTOR pSplit = pts[split];
// left side
FLOAT firstLen = arclen[first];
FLOAT partLen = splitLen - firstLen;
VECTOR total = default(VECTOR);
FLOAT weightTotal = 0;
for (int i = Math.Max(first, split - MID_TANGENT_N_PTS); i < split; i++)
{
FLOAT t = (arclen[i] - firstLen) / partLen;
FLOAT weight = t * t * t;
VECTOR v = VectorHelper.Normalize(pts[i] - pSplit);
total += v * weight;
weightTotal += weight;
}
VECTOR tanL = VectorHelper.Length(total) > EPSILON && weightTotal > EPSILON?
VectorHelper.Normalize(total / weightTotal) :
VectorHelper.Normalize(pts[split - 1] - pSplit);
// right side
partLen = arclen[last] - splitLen;
int rMax = Math.Min(last, split + MID_TANGENT_N_PTS);
total = default(VECTOR);
weightTotal = 0;
for (int i = split + 1; i <= rMax; i++)
{
FLOAT ti = 1 - ((arclen[i] - splitLen) / partLen);
FLOAT weight = ti * ti * ti;
VECTOR v = VectorHelper.Normalize(pSplit - pts[i]);
total += v * weight;
weightTotal += weight;
}
VECTOR tanR = VectorHelper.Length(total) > EPSILON && weightTotal > EPSILON?
VectorHelper.Normalize(total / weightTotal) :
VectorHelper.Normalize(pSplit - pts[split + 1]);
// The reason we separate this into two halves is because we want the right and left tangents to be weighted
// equally no matter the weights of the individual parts of them, so that one of the curves doesn't get screwed
// for the pleasure of the other half
total = tanL + tanR;
// Since the points are never coincident, the vector between any two of them will be normalizable, however this can happen in some really
// odd cases when the points are going directly opposite directions (therefore the tangent is undefined)
if (VectorHelper.LengthSquared(total) < EPSILON)
{
// try one last time using only the three points at the center, otherwise just use one of the sides
tanL = VectorHelper.Normalize(pts[split - 1] - pSplit);
tanR = VectorHelper.Normalize(pSplit - pts[split + 1]);
total = tanL + tanR;
return(VectorHelper.LengthSquared(total) < EPSILON ? tanL : VectorHelper.Normalize(total / 2));
}
else
{
return(VectorHelper.Normalize(total / 2));
}
}