/// <summary>
/// Clip-Testing a circular inking segment again a hitting point.
///
/// What need to find out a doulbe value s, which is between 0 and 1, such that
/// DistanceOf(hit - s*spine) = beginRadius + s * (endRadius - beginRadius)
/// That is
/// (hit.X-s*spine.X)^2 + (hit.Y-s*spine.Y)^2 = [beginRadius + s*(endRadius-beginRadius)]^2
/// Rearrange
/// A*s^2 + B*s + C = 0
/// where the value of A, B and C are described in the source code.
/// Solving for s:
/// s = (-B + sqrt(B^2-4A*C))/(2A) or s = (-B - sqrt(B^2-4A*C))/(2A)
/// The smaller value between 0 and 1 is the one we want and discard the other one.
/// </summary>
/// <param name="spine">Represent the spine of the inking segment pointing from the beginNode to endNode</param>
/// <param name="beginRadius">Radius of the beginNode</param>
/// <param name="endRadius">Radius of the endNode</param>
/// <param name="hit">The hitting point</param>
/// <returns>A double which represents the location for cutting</returns>
private static double ClipTest(Vector spine, double beginRadius, double endRadius, Vector hit)
{
double radDiff = endRadius - beginRadius;
double A = spine.X * spine.X + spine.Y * spine.Y - radDiff * radDiff;
double B = -2.0f * (hit.X * spine.X + hit.Y * spine.Y + beginRadius * radDiff);
double C = hit.X * hit.X + hit.Y * hit.Y - beginRadius * beginRadius;
// There checks are here since if either fail no real solution can be caculated and we may
// as well bail out now and save the caculations that are below.
if (DoubleUtil.IsZero(A) || !DoubleUtil.GreaterThanOrClose(B * B, 4.0f * A * C))
{
return(1d);
}
double tmp = Math.Sqrt(B * B - 4.0f * A * C);
double s1 = (-B + tmp) / (2.0f * A);
double s2 = (-B - tmp) / (2.0f * A);
double findex;
if (DoubleUtil.IsBetweenZeroAndOne(s1) && DoubleUtil.IsBetweenZeroAndOne(s1))
{
findex = Math.Min(s1, s2);
}
else if (DoubleUtil.IsBetweenZeroAndOne(s1))
{
findex = s1;
}
else if (DoubleUtil.IsBetweenZeroAndOne(s2))
{
findex = s2;
}
else
{
// There is still possiblity that value like 1.0000000000000402 is not considered
// as "IsOne" by DoubleUtil class. We should be at either one of the following two cases:
// 1. s1/s2 around 0 but not close enough (say -0.0000000000001)
// 2. s1/s2 around 1 but not close enought (say 1.0000000000000402)
if (s1 > 1d && s2 > 1d)
{
findex = 1d;
}
else if (s1 < 0d && s2 < 0d)
{
findex = 0d;
}
else
{
findex = Math.Abs(Math.Min(s1, s2) - 0d) < Math.Abs(Math.Max(s1, s2) - 1d) ? 0d : 1d;
}
}
return(AdjustFIndex(findex));
}
/// <summary>
/// Clip-Testing a circluar inking segment against a linear segment.
/// See http://tabletpc/longhorn/Specs/Rendering%20and%20Hit-Testing%20Ink%20in%20Avalon%20M11.doc section
/// 5.4.4.14 Clip-Testing a Circular Inking Segment against a Linear Segment for details of the algorithm
/// </summary>
/// <param name="spineVector">Represent the spine of the inking segment pointing from the beginNode to endNode</param>
/// <param name="beginRadius">Radius of the beginNode</param>
/// <param name="endRadius">Radius of the endNode</param>
/// <param name="hitBegin">Hitting segment start point</param>
/// <param name="hitEnd">Hitting segment end point</param>
/// <returns>A double which represents the location for cutting</returns>
private static double ClipTest(Vector spineVector, double beginRadius, double endRadius, Vector hitBegin, Vector hitEnd)
{
// First handle the special case when the spineVector is (0,0). In other words, this is the case
// when the stylus stays at the the location but pressure changes.
if (DoubleUtil.IsZero(spineVector.X) && DoubleUtil.IsZero(spineVector.Y))
{
System.Diagnostics.Debug.Assert(DoubleUtil.AreClose(beginRadius, endRadius) == false);
Vector nearest = GetNearest(hitBegin, hitEnd);
double radius;
if (nearest.X == 0)
{
radius = Math.Abs(nearest.Y);
}
else if (nearest.Y == 0)
{
radius = Math.Abs(nearest.X);
}
else
{
radius = nearest.Length;
}
return(AdjustFIndex((radius - beginRadius) / (endRadius - beginRadius)));
}
// This change to ClipTest with a point if the two hitting segment are close enough.
if (DoubleUtil.AreClose(hitBegin, hitEnd))
{
return(ClipTest(spineVector, beginRadius, endRadius, hitBegin));
}
double findex;
Vector hitVector = hitEnd - hitBegin;
if (DoubleUtil.IsZero(Vector.Determinant(spineVector, hitVector)))
{
// hitVector and spineVector are parallel
findex = ClipTest(spineVector, beginRadius, endRadius, GetNearest(hitBegin, hitEnd));
System.Diagnostics.Debug.Assert(!double.IsNaN(findex));
}
else
{
// On the line defined by the segment find point P1Xp, the nearest to the beginNode.Position
double x = GetProjectionFIndex(hitBegin, hitEnd);
Vector P1Xp = hitBegin + (hitVector * x);
if (P1Xp.LengthSquared < (beginRadius * beginRadius))
{
System.Diagnostics.Debug.Assert(DoubleUtil.IsBetweenZeroAndOne(x) == false);
findex = ClipTest(spineVector, beginRadius, endRadius, (0 > x) ? hitBegin : hitEnd);
System.Diagnostics.Debug.Assert(!double.IsNaN(findex));
}
else
{
// Find the projection point P of endNode.Position to the line (beginNode.Position, B).
Vector P1P2p = spineVector + GetProjection(-spineVector, P1Xp - spineVector);
//System.Diagnostics.Debug.Assert(false == DoubleUtil.IsZero(P1P2p.LengthSquared));
//System.Diagnostics.Debug.Assert(false == DoubleUtil.IsZero(endRadius - beginRadius + P1P2p.Length));
// There checks are here since if either fail no real solution can be caculated and we may
// as well bail out now and save the caculations that are below.
if (DoubleUtil.IsZero(P1P2p.LengthSquared) || DoubleUtil.IsZero(endRadius - beginRadius + P1P2p.Length))
{
return(1d);
}
// Calculate the findex of the point to split the ink segment at.
findex = (P1Xp.Length - beginRadius) / (endRadius - beginRadius + P1P2p.Length);
System.Diagnostics.Debug.Assert(!double.IsNaN(findex));
// Find the projection of the split point to the line of this segment.
Vector S = spineVector * findex;
double r = GetProjectionFIndex(hitBegin - S, hitEnd - S);
// If the nearest point misses the segment, then find the findex
// of the node nearest to the segment.
if (false == DoubleUtil.IsBetweenZeroAndOne(r))
{
findex = ClipTest(spineVector, beginRadius, endRadius, (0 > r) ? hitBegin : hitEnd);
System.Diagnostics.Debug.Assert(!double.IsNaN(findex));
}
}
}
return(AdjustFIndex(findex));
}
private Point[] FilterPoints(Point[] path)
{
System.Diagnostics.Debug.Assert(path.Length > 1);
Point back2, back1;
int i;
List <Point> newPath = new List <Point>();
if (_nodeIterator.Count == 0)
{
newPath.Add(path[0]);
newPath.Add(path[1]);
back2 = path[0];
back1 = path[1];
i = 2;
}
else
{
newPath.Add(path[0]);
back2 = _nodeIterator[_nodeIterator.Count - 1].Position;
back1 = path[0];
i = 1;
}
while (i < path.Length)
{
if (DoubleUtil.AreClose(back1, path[i]))
{
// Filter out duplicate points
i++;
continue;
}
Vector begin = back2 - back1;
Vector end = path[i] - back1;
//On a line defined by begin & end, finds the findex of the point nearest to the origin (0,0).
double findex = StrokeNodeOperations.GetProjectionFIndex(begin, end);
if (DoubleUtil.IsBetweenZeroAndOne(findex))
{
Vector v = (begin + (end - begin) * findex);
if (v.LengthSquared < CollinearTolerance)
{
// The point back1 can be considered as on the line from back2 to the toTest StrokeNode.
// Modify the previous point.
newPath[newPath.Count - 1] = path[i];
back1 = path[i];
i++;
#if POINTS_FILTER_TRACE
_collinearPointsScreened++;
#endif
continue;
}
}
// Add the surviving point into the list.
newPath.Add(path[i]);
back2 = back1;
back1 = path[i];
i++;
}
#if POINTS_FILTER_TRACE
_totalPointsScreened += path.Length - newPath.Count;
#endif
return(newPath.ToArray());
}
