Code:
/ Dotnetfx_Vista_SP2 / Dotnetfx_Vista_SP2 / 8.0.50727.4016 / DEVDIV / depot / DevDiv / releases / Orcas / QFE / wpf / src / Core / CSharp / MS / Internal / Ink / Lasso.cs / 1 / Lasso.cs
//------------------------------------------------------------------------
//
// Copyright (c) Microsoft Corporation. All rights reserved.
//
//-----------------------------------------------------------------------
//#define TRACE
using System;
using System.Windows;
using System.Windows.Ink;
using System.Windows.Media;
using System.Collections.Generic;
using System.Globalization;
namespace MS.Internal.Ink
{
#region Lasso
///
/// Represents a lasso for selecting/cutting ink strokes with.
/// Lasso is a sequence of points defining a complex region (polygon)
///
internal class Lasso
{
#region Constructors
///
/// Default c-tor. Used in incremental hit-testing.
///
internal Lasso()
{
_points = new List();
}
#endregion
#region API
///
/// Returns the bounds of the lasso
///
internal Rect Bounds
{
get { return _bounds; }
set { _bounds = value;}
}
///
/// Tells whether the lasso captures any area
///
internal bool IsEmpty
{
get
{
System.Diagnostics.Debug.Assert(_points != null);
// The value is based on the assumption that the lasso is normalized
// i.e. it has no duplicate points or collinear sibling segments.
return (_points.Count < 3);
}
}
///
/// Returns the count of points in the lasso
///
internal int PointCount
{
get
{
System.Diagnostics.Debug.Assert(_points != null);
return _points.Count;
}
}
///
/// Index-based read-only accessor to lasso points
///
/// index of the point to return
/// a point in the lasso
internal Point this[int index]
{
get
{
System.Diagnostics.Debug.Assert(_points != null);
System.Diagnostics.Debug.Assert((0 <= index) && (index < _points.Count));
return _points[index];
}
}
///
/// Extends the lasso by appending more points
///
/// new points
internal void AddPoints(IEnumerable points)
{
System.Diagnostics.Debug.Assert(null != points);
foreach (Point point in points)
{
AddPoint(point);
}
}
///
/// Appends a point to the lasso
///
/// new lasso point
internal void AddPoint(Point point)
{
System.Diagnostics.Debug.Assert(_points != null);
if (!Filter(point))
{
// The point is not filtered, add it to the lasso
AddPointImpl(point);
}
}
///
/// This method implement the core algorithm to check whether a point is within a polygon
/// that are formed by the lasso points.
///
///
/// true if the point is contained within the lasso; false otherwise
internal bool Contains(Point point)
{
System.Diagnostics.Debug.Assert(_points != null);
if (false == _bounds.Contains(point))
{
return false;
}
bool isHigher = false;
int last = _points.Count;
while (--last >= 0)
{
if (!DoubleUtil.AreClose(_points[last].Y,point.Y))
{
isHigher = (point.Y < _points[last].Y);
break;
}
}
bool isInside = false;
Point prevLassoPoint = _points[_points.Count - 1];
for (int i = 0; i < _points.Count; i++)
{
Point lassoPoint = _points[i];
if (DoubleUtil.AreClose(lassoPoint.Y, point.Y))
{
if (DoubleUtil.AreClose(lassoPoint.X, point.X))
{
isInside = true;
break;
}
if ((0 != i) && DoubleUtil.AreClose(prevLassoPoint.Y, point.Y) &&
DoubleUtil.GreaterThanOrClose(point.X, Math.Min(prevLassoPoint.X, lassoPoint.X)) &&
DoubleUtil.LessThanOrClose(point.X, Math.Max(prevLassoPoint.X, lassoPoint.X)))
{
isInside = true;
break;
}
}
else if (isHigher != (point.Y < lassoPoint.Y))
{
isHigher = !isHigher;
if (DoubleUtil.GreaterThanOrClose(point.X, Math.Max(prevLassoPoint.X, lassoPoint.X)))
{
// there certainly is an intersection on the left
isInside = !isInside;
}
else if (DoubleUtil.GreaterThanOrClose(point.X, Math.Min(prevLassoPoint.X, lassoPoint.X)))
{
// The X of the point lies within the x ranges for the segment.
// Calculate the x value of the point where the segment intersects with the line.
Vector lassoSegment = lassoPoint - prevLassoPoint;
System.Diagnostics.Debug.Assert(lassoSegment.Y != 0);
double x = prevLassoPoint.X + (lassoSegment.X / lassoSegment.Y) * (point.Y - prevLassoPoint.Y);
if (DoubleUtil.GreaterThanOrClose(point.X, x))
{
isInside = !isInside;
}
}
}
prevLassoPoint = lassoPoint;
}
return isInside;
}
internal StrokeIntersection[] HitTest(StrokeNodeIterator iterator)
{
System.Diagnostics.Debug.Assert(_points != null);
System.Diagnostics.Debug.Assert(iterator != null);
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("Lasso: start lasso histtesing a new stroke ..."));
#endif
if (_points.Count < 3)
{
//
// it takes at least 3 points to create a lasso
//
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("Lasso:.............. done. Nothing hit because lasso lasso has only {0} points", _points.Count));
#endif
return new StrokeIntersection[0];
}
//
// We're about to perform hit testing with a lasso.
// To do so we need to iterate through each StrokeNode.
// As we do, we calculate the bounding rect between it
// and the previous StrokeNode and store this in 'currentStrokeSegmentBounds'
//
// Next, we check to see if that StrokeNode pair's bounding box intersects
// with the bounding box of the Lasso points. If not, we continue iterating through
// StrokeNode pairs.
//
// If it does, we do a more granular hit test by pairing points in the Lasso, getting
// their bounding box and seeing if that bounding box intersects our current StrokeNode
// pair
//
Point lastNodePosition = new Point();
Point lassoLastPoint = _points[_points.Count - 1];
Rect currentStrokeSegmentBounds = Rect.Empty;
// Initilize the current crossing to be an empty one
LassoCrossing currentCrossing = LassoCrossing.EmptyCrossing;
// Creat a list to hold all the crossings
List crossingList = new List();
for (int i = 0; i < iterator.Count; i++)
{
StrokeNode strokeNode = iterator[i];
Rect nodeBounds = strokeNode.GetBounds();
currentStrokeSegmentBounds.Union(nodeBounds);
// Skip the node if it's outside of the lasso's bounds
if (currentStrokeSegmentBounds.IntersectsWith(_bounds) == true)
{
// currentStrokeSegmentBounds, made up of the bounding box of
// this StrokeNode unioned with the last StrokeNode,
// intersects the lasso bounding box.
//
// Now we need to iterate through the lasso points and find out where they cross
//
Point lastPoint = lassoLastPoint;
foreach (Point point in _points)
{
//
// calculate a segment of the lasso from the last point
// to the current point
//
Rect lassoSegmentBounds = new Rect(lastPoint, point);
//
// see if this lasso segment intersects with the current stroke segment
//
if (!currentStrokeSegmentBounds.IntersectsWith(lassoSegmentBounds))
{
lastPoint = point;
continue;
}
//
// the lasso segment DOES intersect with the current stroke segment
// find out precisely where
//
StrokeFIndices strokeFIndices = strokeNode.CutTest(lastPoint, point);
#if TRACE
if (!strokeFIndices.IsEmpty)
{
System.Diagnostics.Debug.WriteLine (String.Format("\t\tLasso: found nonempty StrokeFIndices {0} with points [{1}] and [{2}] for strokeNode at {3}", strokeFIndices, lastPoint, point,strokeNode.Position));
}
#endif
lastPoint = point;
if (strokeFIndices.IsEmpty)
{
// current lasso segment does not hit the stroke segment, continue with the next lasso point
continue;
}
// Create a potentially new crossing for the current hit testing result.
LassoCrossing potentialNewCrossing = new LassoCrossing(strokeFIndices, strokeNode);
// Try to merge with the current crossing. If the merge is succussful (return true), the new crossing is actually
// continueing the current crossing, so do not start a new crossing. Otherwise, start a new one and add the existing
// one to the list.
if (!currentCrossing.Merge(potentialNewCrossing))
{
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("\tLasso: adding {0} to crossingList and starting a new crossing {1}", currentCrossing, potentialNewCrossing));
#endif
// start a new crossing and add the existing on to the list
crossingList.Add(currentCrossing);
currentCrossing = potentialNewCrossing;
}
}
}
// Continue with the next node
currentStrokeSegmentBounds = nodeBounds;
lastNodePosition = strokeNode.Position;
}
// Adding the last crossing to the list, if valid
if (!currentCrossing.IsEmpty)
{
crossingList.Add(currentCrossing);
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("\tLasso: adding the last crossing {0} to crossingList", currentCrossing));
#endif
}
// Handle the special case of no intersection at all
if (crossingList.Count == 0)
{
// the stroke was either completely inside the lasso
// or outside the lasso
if (this.Contains(lastNodePosition))
{
StrokeIntersection[] strokeIntersections = new StrokeIntersection[1];
strokeIntersections[0] = StrokeIntersection.Full;
return strokeIntersections;
}
else
{
return new StrokeIntersection[0];
}
}
// It is still possible that the current crossing list is not sorted or overlapping.
// Sort the list and merge the overlapping ones.
SortAndMerge(ref crossingList);
// Produce the hit test results and store them in a list
List strokeIntersectionList = new List();
ProduceHitTestResults(crossingList, strokeIntersectionList);
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("Lasso:.............. done. Lasso hit {0} segments", strokeIntersectionList.Count));
#endif
return strokeIntersectionList.ToArray();
}
///
/// Sort and merge the crossing list
///
/// The crossing list to sort/merge
private static void SortAndMerge(ref List crossingList)
{
// Sort the crossings based on the BeginFIndex values
crossingList.Sort();
List mergedList = new List();
LassoCrossing mcrossing = LassoCrossing.EmptyCrossing;
foreach (LassoCrossing crossing in crossingList)
{
System.Diagnostics.Debug.Assert(!crossing.IsEmpty && crossing.StartNode.IsValid && crossing.EndNode.IsValid);
if (!mcrossing.Merge(crossing))
{
System.Diagnostics.Debug.Assert(!mcrossing.IsEmpty && mcrossing.StartNode.IsValid && mcrossing.EndNode.IsValid);
mergedList.Add(mcrossing);
mcrossing = crossing;
}
}
if (!mcrossing.IsEmpty)
{
System.Diagnostics.Debug.Assert(!mcrossing.IsEmpty && mcrossing.StartNode.IsValid && mcrossing.EndNode.IsValid);
mergedList.Add(mcrossing);
}
crossingList = mergedList;
}
///
/// Helper function to find out whether a point is inside the lasso
///
private bool SegmentWithinLasso(StrokeNode strokeNode, double fIndex)
{
bool currentSegmentWithinLasso;
if (DoubleUtil.AreClose(fIndex, StrokeFIndices.BeforeFirst))
{
// This should check against the very first stroke node
currentSegmentWithinLasso = this.Contains(strokeNode.GetPointAt(0f));
}
else if (DoubleUtil.AreClose(fIndex, StrokeFIndices.AfterLast))
{
// This should check against the last stroke node
currentSegmentWithinLasso = this.Contains(strokeNode.Position);
}
else
{
currentSegmentWithinLasso = this.Contains(strokeNode.GetPointAt(fIndex));
}
return currentSegmentWithinLasso;
}
///
/// Helper function to find out the hit test result
///
private void ProduceHitTestResults(
List crossingList, List strokeIntersections)
{
bool previousSegmentInsideLasso = false;
for (int x = 0; x <= crossingList.Count; x++)
{
bool currentSegmentWithinLasso = false;
bool canMerge = true;
StrokeIntersection si = new StrokeIntersection();
if (x == 0)
{
si.HitBegin = StrokeFIndices.BeforeFirst;
si.InBegin = StrokeFIndices.BeforeFirst;
}
else
{
si.InBegin = crossingList[x - 1].FIndices.EndFIndex;
si.HitBegin = crossingList[x - 1].FIndices.BeginFIndex;
currentSegmentWithinLasso = SegmentWithinLasso(crossingList[x - 1].EndNode, si.InBegin);
}
if (x == crossingList.Count)
{
// NTRAID#WINOS-1132904-2005/04/27-XIAOTU: For a special case when the last intersection is something like (1.2, AL).
// As a result the last InSegment should be empty.
if (DoubleUtil.AreClose(si.InBegin, StrokeFIndices.AfterLast))
{
si.InEnd = StrokeFIndices.BeforeFirst;
}
else
{
si.InEnd = StrokeFIndices.AfterLast;
}
si.HitEnd = StrokeFIndices.AfterLast;
}
else
{
si.InEnd = crossingList[x].FIndices.BeginFIndex;
// NTRAID#WINOS-1132904-2005/04/27-XIAOTU: For a speical case when the first intersection is something like (BF, 0.67).
// As a result the first InSegment should be empty
if (DoubleUtil.AreClose(si.InEnd, StrokeFIndices.BeforeFirst))
{
System.Diagnostics.Debug.Assert(DoubleUtil.AreClose(si.InBegin, StrokeFIndices.BeforeFirst));
si.InBegin = StrokeFIndices.AfterLast;
}
si.HitEnd = crossingList[x].FIndices.EndFIndex;
currentSegmentWithinLasso = SegmentWithinLasso(crossingList[x].StartNode, si.InEnd);
// NTRAID#WINOS-1141831-2005/04/27-XIAOTU: If both the start and end position of the current crossing is
// outside the lasso, the crossing is a hit-only intersection, i.e., the in-segment is empty.
if (!currentSegmentWithinLasso && !SegmentWithinLasso(crossingList[x].EndNode, si.HitEnd))
{
currentSegmentWithinLasso = true;
si.HitBegin = crossingList[x].FIndices.BeginFIndex;
si.InBegin = StrokeFIndices.AfterLast;
si.InEnd = StrokeFIndices.BeforeFirst;
canMerge = false;
}
}
if (currentSegmentWithinLasso)
{
if (x > 0 && previousSegmentInsideLasso && canMerge)
{
// we need to consolidate with the previous segment
StrokeIntersection previousIntersection = strokeIntersections[strokeIntersections.Count - 1];
// For example: previousIntersection = [BF, AL, BF, 0.0027], si = [BF, 0.0027, 0.049, 0.063]
if (previousIntersection.InSegment.IsEmpty)
{
previousIntersection.InBegin = si.InBegin;
}
previousIntersection.InEnd = si.InEnd;
previousIntersection.HitEnd = si.HitEnd;
strokeIntersections[strokeIntersections.Count - 1] = previousIntersection;
}
else
{
strokeIntersections.Add(si);
}
if (DoubleUtil.AreClose(si.HitEnd, StrokeFIndices.AfterLast))
{
// The strokeIntersections already cover the end of the stroke. No need to continue.
return;
}
}
previousSegmentInsideLasso = currentSegmentWithinLasso;
}
}
///
/// This flag is set to true when a lasso point has been modified or removed
/// from the list, which will invalidate incremental lasso hitteting
///
internal bool IsIncrementalLassoDirty
{
get
{
return _incrementalLassoDirty;
}
set
{
_incrementalLassoDirty = value;
}
}
///
/// Get a reference to the lasso points store
///
protected List PointsList
{
get
{
return _points;
}
}
///
/// Filter out duplicate points (and maybe in the futuer colinear points).
/// Return true if the point should be filtered
///
protected virtual bool Filter(Point point)
{
// First point should not be filtered
if (0 == _points.Count)
{
return false;
}
// ISSUE-2004/06/14-vsmirnov - If the new segment is collinear with the last one,
// don't add the point but modify the last point instead.
Point lastPoint = _points[_points.Count - 1];
Vector vector = point - lastPoint;
// The point will be filtered out, i.e. not added to the list, if the distance to the previous point is
// within the tolerance
return (Math.Abs(vector.X) < MinDistance && Math.Abs(vector.Y) < MinDistance);
}
///
/// Implemtnation of add point
///
///
protected virtual void AddPointImpl(Point point)
{
_points.Add(point);
_bounds.Union(point);
}
#endregion
#region Fields
private List _points;
private Rect _bounds = Rect.Empty;
private bool _incrementalLassoDirty = false;
private static readonly double MinDistance = 1.0;
#endregion
///
/// Simple helper struct used to track where the lasso crosses a stroke
/// we should consider making this a class if generics perf is bad for structs
///
private struct LassoCrossing : IComparable
{
internal StrokeFIndices FIndices;
internal StrokeNode StartNode;
internal StrokeNode EndNode;
///
/// Constructor
///
///
///
public LassoCrossing(StrokeFIndices newFIndices, StrokeNode strokeNode)
{
System.Diagnostics.Debug.Assert(!newFIndices.IsEmpty);
System.Diagnostics.Debug.Assert(strokeNode.IsValid);
FIndices = newFIndices;
StartNode = EndNode = strokeNode;
}
///
/// ToString
///
public override string ToString()
{
return FIndices.ToString();
}
///
/// Construct an empty LassoCrossing
///
public static LassoCrossing EmptyCrossing
{
get
{
LassoCrossing crossing = new LassoCrossing();
crossing.FIndices = StrokeFIndices.Empty;
return crossing;
}
}
///
/// Return true if this crossing is an empty one; false otherwise
///
public bool IsEmpty
{
get { return FIndices.IsEmpty;}
}
///
/// Implement the interface used for comparison
///
///
///
/// Merge two crossings into one.
///
///
/// Return true if these two crossings are actually overlapping and merged; false otherwise
public bool Merge(LassoCrossing crossing)
{
if (crossing.IsEmpty)
{
return false;
}
if (FIndices.IsEmpty && !crossing.IsEmpty)
{
FIndices = crossing.FIndices;
StartNode = crossing.StartNode;
EndNode = crossing.EndNode;
return true;
}
if(DoubleUtil.GreaterThanOrClose(crossing.FIndices.EndFIndex, FIndices.BeginFIndex) &&
DoubleUtil.GreaterThanOrClose(FIndices.EndFIndex, crossing.FIndices.BeginFIndex))
{
if (DoubleUtil.LessThan(crossing.FIndices.BeginFIndex, FIndices.BeginFIndex))
{
FIndices.BeginFIndex = crossing.FIndices.BeginFIndex;
StartNode = crossing.StartNode;
}
if (DoubleUtil.GreaterThan(crossing.FIndices.EndFIndex, FIndices.EndFIndex))
{
FIndices.EndFIndex = crossing.FIndices.EndFIndex;
EndNode = crossing.EndNode;
}
return true;
}
return false;
}
}
}
#endregion
#region Single-Loop Lasso
///
/// Implement a special lasso that considers only the first loop
///
internal class SingleLoopLasso : Lasso
{
///
/// Default constructor
///
internal SingleLoopLasso() : base(){}
///
/// Return true if the point will be filtered out and should NOT be added to the list
///
protected override bool Filter(Point point)
{
List points = PointsList;
// First point should not be filtered
if (0 == points.Count)
{
// Just add the new point to the lasso
return false;
}
// Don't add this point if the lasso already has a loop; or
// if it's filtered by base class's filter.
if (true == _hasLoop || true == base.Filter(point))
{
// Don't add this point to the lasso.
return true;
}
double intersection = 0f;
// Now check whether the line lastPoint->point intersect with the
// existing lasso.
if (true == GetIntersectionWithExistingLasso(point, ref intersection))
{
System.Diagnostics.Debug.Assert(intersection >= 0 && intersection <= points.Count - 2);
if (intersection == points.Count - 2)
{
return true;
}
// Adding the new point will form a loop
int i = (int) intersection;
if (!DoubleUtil.AreClose(i, intersection))
{
// Move points[i] to the intersection position
Point intersectionPoint = new Point(0, 0);
intersectionPoint.X = points[i].X + (intersection - i) * (points[i + 1].X - points[i].X);
intersectionPoint.Y = points[i].Y + (intersection - i) * (points[i + 1].Y - points[i].Y);
points[i] = intersectionPoint;
IsIncrementalLassoDirty = true;
}
// Since the lasso has a self loop and the loop starts at points[i], points[0] to
// points[i-1] should be removed
if (i > 0)
{
points.RemoveRange(0, i /*count*/); // Remove points[0] to points[i-1]
IsIncrementalLassoDirty = true;
}
if (true == IsIncrementalLassoDirty)
{
// Update the bounds
Rect bounds = Rect.Empty;
for (int j = 0; j < points.Count; j++)
{
bounds.Union(points[j]);
}
Bounds = bounds;
}
// The lasso has a self_loop, any more points will be neglected.
_hasLoop = true;
// Don't add this point to the lasso.
return true;
}
// Just add the new point to the lasso
return false;
}
protected override void AddPointImpl(Point point)
{
_prevBounds = Bounds;
base.AddPointImpl(point);
}
///
/// If the line _points[Count -1]->point insersect with the existing lasso, return true
/// and bIndex value is set to a doulbe value representing position of the intersection.
///
private bool GetIntersectionWithExistingLasso(Point point, ref double bIndex)
{
List points = PointsList;
int count = points.Count;
Rect newRect = new Rect(points[count - 1], point);
if (false == _prevBounds.IntersectsWith(newRect))
{
// The point is not contained in the bound of the existing lasso, no intersection.
return false;
}
for (int i = 0; i < count -2; i++)
{
Rect currRect = new Rect(points[i], points[i+1]);
if (!currRect.IntersectsWith(newRect))
{
continue;
}
double s = FindIntersection(points[count-1] - points[i], /*hitBegin*/
point - points[i], /*hitEnd*/
new Vector(0, 0), /*orgBegin*/
points[i+1] - points[i] /*orgEnd*/);
if (s >=0 && s <= 1)
{
// Intersection found, adjust the fIndex
bIndex = i + s;
return true;
}
}
// No intersection
return false;
}
///
/// Finds the intersection between the segment [hitBegin, hitEnd] and the segment [orgBegin, orgEnd].
///
private static double FindIntersection(Vector hitBegin, Vector hitEnd, Vector orgBegin, Vector orgEnd)
{
System.Diagnostics.Debug.Assert(hitEnd != hitBegin && orgBegin != orgEnd);
//---------------------------------------------------------------------
// Source: http://isc.faqs.org/faqs/graphics/algorithms-faq/
// Subject 1.03: How do I find intersections of 2 2D line segments?
//
// Let A,B,C,D be 2-space position vectors. Then the directed line
// segments AB & CD are given by:
//
// AB=A+r(B-A), r in [0,1]
// CD=C+s(D-C), s in [0,1]
//
// If AB & CD intersect, then
//
// A+r(B-A)=C+s(D-C), or Ax+r(Bx-Ax)=Cx+s(Dx-Cx)
// Ay+r(By-Ay)=Cy+s(Dy-Cy) for some r,s in [0,1]
//
// Solving the above for r and s yields
//
// (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
// r = ----------------------------- (eqn 1)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
//
// (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
// s = ----------------------------- (eqn 2)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
//
// Let P be the position vector of the intersection point, then
//
// P=A+r(B-A) or Px=Ax+r(Bx-Ax) and Py=Ay+r(By-Ay)
//
// By examining the values of r & s, you can also determine some
// other limiting conditions:
// If 0 <= r <= 1 && 0 <= s <= 1, intersection exists
// r < 0 or r > 1 or s < 0 or s > 1 line segments do not intersect
// If the denominator in eqn 1 is zero, AB & CD are parallel
// If the numerator in eqn 1 is also zero, AB & CD are collinear.
// If they are collinear, then the segments may be projected to the x-
// or y-axis, and overlap of the projected intervals checked.
//
// If the intersection point of the 2 lines are needed (lines in this
// context mean infinite lines) regardless whether the two line
// segments intersect, then
// If r > 1, P is located on extension of AB
// If r < 0, P is located on extension of BA
// If s > 1, P is located on extension of CD
// If s < 0, P is located on extension of DC
// Also note that the denominators of eqn 1 & 2 are identical.
//
// References:
// [O'Rourke (C)] pp. 249-51
// [Gems III] pp. 199-202 "Faster Line Segment Intersection,"
//---------------------------------------------------------------------
// Calculate the vectors.
Vector AB = orgEnd - orgBegin; // B - A
Vector CA = orgBegin - hitBegin; // A - C
Vector CD = hitEnd - hitBegin; // D - C
double det = Vector.Determinant(AB, CD);
if (DoubleUtil.IsZero(det))
{
// The segments are parallel. no intersection
return NoIntersection;
}
double r = AdjustFIndex(Vector.Determinant(AB, CA) / det);
if (r >= 0 && r <= 1)
{
// The line defined AB does cross the segment CD.
double s = AdjustFIndex(Vector.Determinant(CD, CA) / det);
if (s >= 0 && s <= 1)
{
// The crossing point is on the segment AB as well.
// Intersection found.
return s;
}
}
// No intersection found
return NoIntersection;
}
///
/// Clears double's computation fuzz around 0 and 1
///
internal static double AdjustFIndex(double findex)
{
return DoubleUtil.IsZero(findex) ? 0 : (DoubleUtil.IsOne(findex) ? 1 : findex);
}
private bool _hasLoop = false;
private Rect _prevBounds = Rect.Empty;
private static readonly double NoIntersection = StrokeFIndices.BeforeFirst;
}
#endregion
}
// File provided for Reference Use Only by Microsoft Corporation (c) 2007.
//------------------------------------------------------------------------
//
// Copyright (c) Microsoft Corporation. All rights reserved.
//
//-----------------------------------------------------------------------
//#define TRACE
using System;
using System.Windows;
using System.Windows.Ink;
using System.Windows.Media;
using System.Collections.Generic;
using System.Globalization;
namespace MS.Internal.Ink
{
#region Lasso
///
/// Represents a lasso for selecting/cutting ink strokes with.
/// Lasso is a sequence of points defining a complex region (polygon)
///
internal class Lasso
{
#region Constructors
///
/// Default c-tor. Used in incremental hit-testing.
///
internal Lasso()
{
_points = new List();
}
#endregion
#region API
///
/// Returns the bounds of the lasso
///
internal Rect Bounds
{
get { return _bounds; }
set { _bounds = value;}
}
///
/// Tells whether the lasso captures any area
///
internal bool IsEmpty
{
get
{
System.Diagnostics.Debug.Assert(_points != null);
// The value is based on the assumption that the lasso is normalized
// i.e. it has no duplicate points or collinear sibling segments.
return (_points.Count < 3);
}
}
///
/// Returns the count of points in the lasso
///
internal int PointCount
{
get
{
System.Diagnostics.Debug.Assert(_points != null);
return _points.Count;
}
}
///
/// Index-based read-only accessor to lasso points
///
/// index of the point to return
/// a point in the lasso
internal Point this[int index]
{
get
{
System.Diagnostics.Debug.Assert(_points != null);
System.Diagnostics.Debug.Assert((0 <= index) && (index < _points.Count));
return _points[index];
}
}
///
/// Extends the lasso by appending more points
///
/// new points
internal void AddPoints(IEnumerable points)
{
System.Diagnostics.Debug.Assert(null != points);
foreach (Point point in points)
{
AddPoint(point);
}
}
///
/// Appends a point to the lasso
///
/// new lasso point
internal void AddPoint(Point point)
{
System.Diagnostics.Debug.Assert(_points != null);
if (!Filter(point))
{
// The point is not filtered, add it to the lasso
AddPointImpl(point);
}
}
///
/// This method implement the core algorithm to check whether a point is within a polygon
/// that are formed by the lasso points.
///
///
/// true if the point is contained within the lasso; false otherwise
internal bool Contains(Point point)
{
System.Diagnostics.Debug.Assert(_points != null);
if (false == _bounds.Contains(point))
{
return false;
}
bool isHigher = false;
int last = _points.Count;
while (--last >= 0)
{
if (!DoubleUtil.AreClose(_points[last].Y,point.Y))
{
isHigher = (point.Y < _points[last].Y);
break;
}
}
bool isInside = false;
Point prevLassoPoint = _points[_points.Count - 1];
for (int i = 0; i < _points.Count; i++)
{
Point lassoPoint = _points[i];
if (DoubleUtil.AreClose(lassoPoint.Y, point.Y))
{
if (DoubleUtil.AreClose(lassoPoint.X, point.X))
{
isInside = true;
break;
}
if ((0 != i) && DoubleUtil.AreClose(prevLassoPoint.Y, point.Y) &&
DoubleUtil.GreaterThanOrClose(point.X, Math.Min(prevLassoPoint.X, lassoPoint.X)) &&
DoubleUtil.LessThanOrClose(point.X, Math.Max(prevLassoPoint.X, lassoPoint.X)))
{
isInside = true;
break;
}
}
else if (isHigher != (point.Y < lassoPoint.Y))
{
isHigher = !isHigher;
if (DoubleUtil.GreaterThanOrClose(point.X, Math.Max(prevLassoPoint.X, lassoPoint.X)))
{
// there certainly is an intersection on the left
isInside = !isInside;
}
else if (DoubleUtil.GreaterThanOrClose(point.X, Math.Min(prevLassoPoint.X, lassoPoint.X)))
{
// The X of the point lies within the x ranges for the segment.
// Calculate the x value of the point where the segment intersects with the line.
Vector lassoSegment = lassoPoint - prevLassoPoint;
System.Diagnostics.Debug.Assert(lassoSegment.Y != 0);
double x = prevLassoPoint.X + (lassoSegment.X / lassoSegment.Y) * (point.Y - prevLassoPoint.Y);
if (DoubleUtil.GreaterThanOrClose(point.X, x))
{
isInside = !isInside;
}
}
}
prevLassoPoint = lassoPoint;
}
return isInside;
}
internal StrokeIntersection[] HitTest(StrokeNodeIterator iterator)
{
System.Diagnostics.Debug.Assert(_points != null);
System.Diagnostics.Debug.Assert(iterator != null);
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("Lasso: start lasso histtesing a new stroke ..."));
#endif
if (_points.Count < 3)
{
//
// it takes at least 3 points to create a lasso
//
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("Lasso:.............. done. Nothing hit because lasso lasso has only {0} points", _points.Count));
#endif
return new StrokeIntersection[0];
}
//
// We're about to perform hit testing with a lasso.
// To do so we need to iterate through each StrokeNode.
// As we do, we calculate the bounding rect between it
// and the previous StrokeNode and store this in 'currentStrokeSegmentBounds'
//
// Next, we check to see if that StrokeNode pair's bounding box intersects
// with the bounding box of the Lasso points. If not, we continue iterating through
// StrokeNode pairs.
//
// If it does, we do a more granular hit test by pairing points in the Lasso, getting
// their bounding box and seeing if that bounding box intersects our current StrokeNode
// pair
//
Point lastNodePosition = new Point();
Point lassoLastPoint = _points[_points.Count - 1];
Rect currentStrokeSegmentBounds = Rect.Empty;
// Initilize the current crossing to be an empty one
LassoCrossing currentCrossing = LassoCrossing.EmptyCrossing;
// Creat a list to hold all the crossings
List crossingList = new List();
for (int i = 0; i < iterator.Count; i++)
{
StrokeNode strokeNode = iterator[i];
Rect nodeBounds = strokeNode.GetBounds();
currentStrokeSegmentBounds.Union(nodeBounds);
// Skip the node if it's outside of the lasso's bounds
if (currentStrokeSegmentBounds.IntersectsWith(_bounds) == true)
{
// currentStrokeSegmentBounds, made up of the bounding box of
// this StrokeNode unioned with the last StrokeNode,
// intersects the lasso bounding box.
//
// Now we need to iterate through the lasso points and find out where they cross
//
Point lastPoint = lassoLastPoint;
foreach (Point point in _points)
{
//
// calculate a segment of the lasso from the last point
// to the current point
//
Rect lassoSegmentBounds = new Rect(lastPoint, point);
//
// see if this lasso segment intersects with the current stroke segment
//
if (!currentStrokeSegmentBounds.IntersectsWith(lassoSegmentBounds))
{
lastPoint = point;
continue;
}
//
// the lasso segment DOES intersect with the current stroke segment
// find out precisely where
//
StrokeFIndices strokeFIndices = strokeNode.CutTest(lastPoint, point);
#if TRACE
if (!strokeFIndices.IsEmpty)
{
System.Diagnostics.Debug.WriteLine (String.Format("\t\tLasso: found nonempty StrokeFIndices {0} with points [{1}] and [{2}] for strokeNode at {3}", strokeFIndices, lastPoint, point,strokeNode.Position));
}
#endif
lastPoint = point;
if (strokeFIndices.IsEmpty)
{
// current lasso segment does not hit the stroke segment, continue with the next lasso point
continue;
}
// Create a potentially new crossing for the current hit testing result.
LassoCrossing potentialNewCrossing = new LassoCrossing(strokeFIndices, strokeNode);
// Try to merge with the current crossing. If the merge is succussful (return true), the new crossing is actually
// continueing the current crossing, so do not start a new crossing. Otherwise, start a new one and add the existing
// one to the list.
if (!currentCrossing.Merge(potentialNewCrossing))
{
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("\tLasso: adding {0} to crossingList and starting a new crossing {1}", currentCrossing, potentialNewCrossing));
#endif
// start a new crossing and add the existing on to the list
crossingList.Add(currentCrossing);
currentCrossing = potentialNewCrossing;
}
}
}
// Continue with the next node
currentStrokeSegmentBounds = nodeBounds;
lastNodePosition = strokeNode.Position;
}
// Adding the last crossing to the list, if valid
if (!currentCrossing.IsEmpty)
{
crossingList.Add(currentCrossing);
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("\tLasso: adding the last crossing {0} to crossingList", currentCrossing));
#endif
}
// Handle the special case of no intersection at all
if (crossingList.Count == 0)
{
// the stroke was either completely inside the lasso
// or outside the lasso
if (this.Contains(lastNodePosition))
{
StrokeIntersection[] strokeIntersections = new StrokeIntersection[1];
strokeIntersections[0] = StrokeIntersection.Full;
return strokeIntersections;
}
else
{
return new StrokeIntersection[0];
}
}
// It is still possible that the current crossing list is not sorted or overlapping.
// Sort the list and merge the overlapping ones.
SortAndMerge(ref crossingList);
// Produce the hit test results and store them in a list
List strokeIntersectionList = new List();
ProduceHitTestResults(crossingList, strokeIntersectionList);
#if TRACE
System.Diagnostics.Debug.WriteLine(String.Format("Lasso:.............. done. Lasso hit {0} segments", strokeIntersectionList.Count));
#endif
return strokeIntersectionList.ToArray();
}
///
/// Sort and merge the crossing list
///
/// The crossing list to sort/merge
private static void SortAndMerge(ref List crossingList)
{
// Sort the crossings based on the BeginFIndex values
crossingList.Sort();
List mergedList = new List();
LassoCrossing mcrossing = LassoCrossing.EmptyCrossing;
foreach (LassoCrossing crossing in crossingList)
{
System.Diagnostics.Debug.Assert(!crossing.IsEmpty && crossing.StartNode.IsValid && crossing.EndNode.IsValid);
if (!mcrossing.Merge(crossing))
{
System.Diagnostics.Debug.Assert(!mcrossing.IsEmpty && mcrossing.StartNode.IsValid && mcrossing.EndNode.IsValid);
mergedList.Add(mcrossing);
mcrossing = crossing;
}
}
if (!mcrossing.IsEmpty)
{
System.Diagnostics.Debug.Assert(!mcrossing.IsEmpty && mcrossing.StartNode.IsValid && mcrossing.EndNode.IsValid);
mergedList.Add(mcrossing);
}
crossingList = mergedList;
}
///
/// Helper function to find out whether a point is inside the lasso
///
private bool SegmentWithinLasso(StrokeNode strokeNode, double fIndex)
{
bool currentSegmentWithinLasso;
if (DoubleUtil.AreClose(fIndex, StrokeFIndices.BeforeFirst))
{
// This should check against the very first stroke node
currentSegmentWithinLasso = this.Contains(strokeNode.GetPointAt(0f));
}
else if (DoubleUtil.AreClose(fIndex, StrokeFIndices.AfterLast))
{
// This should check against the last stroke node
currentSegmentWithinLasso = this.Contains(strokeNode.Position);
}
else
{
currentSegmentWithinLasso = this.Contains(strokeNode.GetPointAt(fIndex));
}
return currentSegmentWithinLasso;
}
///
/// Helper function to find out the hit test result
///
private void ProduceHitTestResults(
List crossingList, List strokeIntersections)
{
bool previousSegmentInsideLasso = false;
for (int x = 0; x <= crossingList.Count; x++)
{
bool currentSegmentWithinLasso = false;
bool canMerge = true;
StrokeIntersection si = new StrokeIntersection();
if (x == 0)
{
si.HitBegin = StrokeFIndices.BeforeFirst;
si.InBegin = StrokeFIndices.BeforeFirst;
}
else
{
si.InBegin = crossingList[x - 1].FIndices.EndFIndex;
si.HitBegin = crossingList[x - 1].FIndices.BeginFIndex;
currentSegmentWithinLasso = SegmentWithinLasso(crossingList[x - 1].EndNode, si.InBegin);
}
if (x == crossingList.Count)
{
// NTRAID#WINOS-1132904-2005/04/27-XIAOTU: For a special case when the last intersection is something like (1.2, AL).
// As a result the last InSegment should be empty.
if (DoubleUtil.AreClose(si.InBegin, StrokeFIndices.AfterLast))
{
si.InEnd = StrokeFIndices.BeforeFirst;
}
else
{
si.InEnd = StrokeFIndices.AfterLast;
}
si.HitEnd = StrokeFIndices.AfterLast;
}
else
{
si.InEnd = crossingList[x].FIndices.BeginFIndex;
// NTRAID#WINOS-1132904-2005/04/27-XIAOTU: For a speical case when the first intersection is something like (BF, 0.67).
// As a result the first InSegment should be empty
if (DoubleUtil.AreClose(si.InEnd, StrokeFIndices.BeforeFirst))
{
System.Diagnostics.Debug.Assert(DoubleUtil.AreClose(si.InBegin, StrokeFIndices.BeforeFirst));
si.InBegin = StrokeFIndices.AfterLast;
}
si.HitEnd = crossingList[x].FIndices.EndFIndex;
currentSegmentWithinLasso = SegmentWithinLasso(crossingList[x].StartNode, si.InEnd);
// NTRAID#WINOS-1141831-2005/04/27-XIAOTU: If both the start and end position of the current crossing is
// outside the lasso, the crossing is a hit-only intersection, i.e., the in-segment is empty.
if (!currentSegmentWithinLasso && !SegmentWithinLasso(crossingList[x].EndNode, si.HitEnd))
{
currentSegmentWithinLasso = true;
si.HitBegin = crossingList[x].FIndices.BeginFIndex;
si.InBegin = StrokeFIndices.AfterLast;
si.InEnd = StrokeFIndices.BeforeFirst;
canMerge = false;
}
}
if (currentSegmentWithinLasso)
{
if (x > 0 && previousSegmentInsideLasso && canMerge)
{
// we need to consolidate with the previous segment
StrokeIntersection previousIntersection = strokeIntersections[strokeIntersections.Count - 1];
// For example: previousIntersection = [BF, AL, BF, 0.0027], si = [BF, 0.0027, 0.049, 0.063]
if (previousIntersection.InSegment.IsEmpty)
{
previousIntersection.InBegin = si.InBegin;
}
previousIntersection.InEnd = si.InEnd;
previousIntersection.HitEnd = si.HitEnd;
strokeIntersections[strokeIntersections.Count - 1] = previousIntersection;
}
else
{
strokeIntersections.Add(si);
}
if (DoubleUtil.AreClose(si.HitEnd, StrokeFIndices.AfterLast))
{
// The strokeIntersections already cover the end of the stroke. No need to continue.
return;
}
}
previousSegmentInsideLasso = currentSegmentWithinLasso;
}
}
///
/// This flag is set to true when a lasso point has been modified or removed
/// from the list, which will invalidate incremental lasso hitteting
///
internal bool IsIncrementalLassoDirty
{
get
{
return _incrementalLassoDirty;
}
set
{
_incrementalLassoDirty = value;
}
}
///
/// Get a reference to the lasso points store
///
protected List PointsList
{
get
{
return _points;
}
}
///
/// Filter out duplicate points (and maybe in the futuer colinear points).
/// Return true if the point should be filtered
///
protected virtual bool Filter(Point point)
{
// First point should not be filtered
if (0 == _points.Count)
{
return false;
}
// ISSUE-2004/06/14-vsmirnov - If the new segment is collinear with the last one,
// don't add the point but modify the last point instead.
Point lastPoint = _points[_points.Count - 1];
Vector vector = point - lastPoint;
// The point will be filtered out, i.e. not added to the list, if the distance to the previous point is
// within the tolerance
return (Math.Abs(vector.X) < MinDistance && Math.Abs(vector.Y) < MinDistance);
}
///
/// Implemtnation of add point
///
///
protected virtual void AddPointImpl(Point point)
{
_points.Add(point);
_bounds.Union(point);
}
#endregion
#region Fields
private List _points;
private Rect _bounds = Rect.Empty;
private bool _incrementalLassoDirty = false;
private static readonly double MinDistance = 1.0;
#endregion
///
/// Simple helper struct used to track where the lasso crosses a stroke
/// we should consider making this a class if generics perf is bad for structs
///
private struct LassoCrossing : IComparable
{
internal StrokeFIndices FIndices;
internal StrokeNode StartNode;
internal StrokeNode EndNode;
///
/// Constructor
///
///
///
public LassoCrossing(StrokeFIndices newFIndices, StrokeNode strokeNode)
{
System.Diagnostics.Debug.Assert(!newFIndices.IsEmpty);
System.Diagnostics.Debug.Assert(strokeNode.IsValid);
FIndices = newFIndices;
StartNode = EndNode = strokeNode;
}
///
/// ToString
///
public override string ToString()
{
return FIndices.ToString();
}
///
/// Construct an empty LassoCrossing
///
public static LassoCrossing EmptyCrossing
{
get
{
LassoCrossing crossing = new LassoCrossing();
crossing.FIndices = StrokeFIndices.Empty;
return crossing;
}
}
///
/// Return true if this crossing is an empty one; false otherwise
///
public bool IsEmpty
{
get { return FIndices.IsEmpty;}
}
///
/// Implement the interface used for comparison
///
///
///
/// Merge two crossings into one.
///
///
/// Return true if these two crossings are actually overlapping and merged; false otherwise
public bool Merge(LassoCrossing crossing)
{
if (crossing.IsEmpty)
{
return false;
}
if (FIndices.IsEmpty && !crossing.IsEmpty)
{
FIndices = crossing.FIndices;
StartNode = crossing.StartNode;
EndNode = crossing.EndNode;
return true;
}
if(DoubleUtil.GreaterThanOrClose(crossing.FIndices.EndFIndex, FIndices.BeginFIndex) &&
DoubleUtil.GreaterThanOrClose(FIndices.EndFIndex, crossing.FIndices.BeginFIndex))
{
if (DoubleUtil.LessThan(crossing.FIndices.BeginFIndex, FIndices.BeginFIndex))
{
FIndices.BeginFIndex = crossing.FIndices.BeginFIndex;
StartNode = crossing.StartNode;
}
if (DoubleUtil.GreaterThan(crossing.FIndices.EndFIndex, FIndices.EndFIndex))
{
FIndices.EndFIndex = crossing.FIndices.EndFIndex;
EndNode = crossing.EndNode;
}
return true;
}
return false;
}
}
}
#endregion
#region Single-Loop Lasso
///
/// Implement a special lasso that considers only the first loop
///
internal class SingleLoopLasso : Lasso
{
///
/// Default constructor
///
internal SingleLoopLasso() : base(){}
///
/// Return true if the point will be filtered out and should NOT be added to the list
///
protected override bool Filter(Point point)
{
List points = PointsList;
// First point should not be filtered
if (0 == points.Count)
{
// Just add the new point to the lasso
return false;
}
// Don't add this point if the lasso already has a loop; or
// if it's filtered by base class's filter.
if (true == _hasLoop || true == base.Filter(point))
{
// Don't add this point to the lasso.
return true;
}
double intersection = 0f;
// Now check whether the line lastPoint->point intersect with the
// existing lasso.
if (true == GetIntersectionWithExistingLasso(point, ref intersection))
{
System.Diagnostics.Debug.Assert(intersection >= 0 && intersection <= points.Count - 2);
if (intersection == points.Count - 2)
{
return true;
}
// Adding the new point will form a loop
int i = (int) intersection;
if (!DoubleUtil.AreClose(i, intersection))
{
// Move points[i] to the intersection position
Point intersectionPoint = new Point(0, 0);
intersectionPoint.X = points[i].X + (intersection - i) * (points[i + 1].X - points[i].X);
intersectionPoint.Y = points[i].Y + (intersection - i) * (points[i + 1].Y - points[i].Y);
points[i] = intersectionPoint;
IsIncrementalLassoDirty = true;
}
// Since the lasso has a self loop and the loop starts at points[i], points[0] to
// points[i-1] should be removed
if (i > 0)
{
points.RemoveRange(0, i /*count*/); // Remove points[0] to points[i-1]
IsIncrementalLassoDirty = true;
}
if (true == IsIncrementalLassoDirty)
{
// Update the bounds
Rect bounds = Rect.Empty;
for (int j = 0; j < points.Count; j++)
{
bounds.Union(points[j]);
}
Bounds = bounds;
}
// The lasso has a self_loop, any more points will be neglected.
_hasLoop = true;
// Don't add this point to the lasso.
return true;
}
// Just add the new point to the lasso
return false;
}
protected override void AddPointImpl(Point point)
{
_prevBounds = Bounds;
base.AddPointImpl(point);
}
///
/// If the line _points[Count -1]->point insersect with the existing lasso, return true
/// and bIndex value is set to a doulbe value representing position of the intersection.
///
private bool GetIntersectionWithExistingLasso(Point point, ref double bIndex)
{
List points = PointsList;
int count = points.Count;
Rect newRect = new Rect(points[count - 1], point);
if (false == _prevBounds.IntersectsWith(newRect))
{
// The point is not contained in the bound of the existing lasso, no intersection.
return false;
}
for (int i = 0; i < count -2; i++)
{
Rect currRect = new Rect(points[i], points[i+1]);
if (!currRect.IntersectsWith(newRect))
{
continue;
}
double s = FindIntersection(points[count-1] - points[i], /*hitBegin*/
point - points[i], /*hitEnd*/
new Vector(0, 0), /*orgBegin*/
points[i+1] - points[i] /*orgEnd*/);
if (s >=0 && s <= 1)
{
// Intersection found, adjust the fIndex
bIndex = i + s;
return true;
}
}
// No intersection
return false;
}
///
/// Finds the intersection between the segment [hitBegin, hitEnd] and the segment [orgBegin, orgEnd].
///
private static double FindIntersection(Vector hitBegin, Vector hitEnd, Vector orgBegin, Vector orgEnd)
{
System.Diagnostics.Debug.Assert(hitEnd != hitBegin && orgBegin != orgEnd);
//---------------------------------------------------------------------
// Source: http://isc.faqs.org/faqs/graphics/algorithms-faq/
// Subject 1.03: How do I find intersections of 2 2D line segments?
//
// Let A,B,C,D be 2-space position vectors. Then the directed line
// segments AB & CD are given by:
//
// AB=A+r(B-A), r in [0,1]
// CD=C+s(D-C), s in [0,1]
//
// If AB & CD intersect, then
//
// A+r(B-A)=C+s(D-C), or Ax+r(Bx-Ax)=Cx+s(Dx-Cx)
// Ay+r(By-Ay)=Cy+s(Dy-Cy) for some r,s in [0,1]
//
// Solving the above for r and s yields
//
// (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
// r = ----------------------------- (eqn 1)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
//
// (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
// s = ----------------------------- (eqn 2)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
//
// Let P be the position vector of the intersection point, then
//
// P=A+r(B-A) or Px=Ax+r(Bx-Ax) and Py=Ay+r(By-Ay)
//
// By examining the values of r & s, you can also determine some
// other limiting conditions:
// If 0 <= r <= 1 && 0 <= s <= 1, intersection exists
// r < 0 or r > 1 or s < 0 or s > 1 line segments do not intersect
// If the denominator in eqn 1 is zero, AB & CD are parallel
// If the numerator in eqn 1 is also zero, AB & CD are collinear.
// If they are collinear, then the segments may be projected to the x-
// or y-axis, and overlap of the projected intervals checked.
//
// If the intersection point of the 2 lines are needed (lines in this
// context mean infinite lines) regardless whether the two line
// segments intersect, then
// If r > 1, P is located on extension of AB
// If r < 0, P is located on extension of BA
// If s > 1, P is located on extension of CD
// If s < 0, P is located on extension of DC
// Also note that the denominators of eqn 1 & 2 are identical.
//
// References:
// [O'Rourke (C)] pp. 249-51
// [Gems III] pp. 199-202 "Faster Line Segment Intersection,"
//---------------------------------------------------------------------
// Calculate the vectors.
Vector AB = orgEnd - orgBegin; // B - A
Vector CA = orgBegin - hitBegin; // A - C
Vector CD = hitEnd - hitBegin; // D - C
double det = Vector.Determinant(AB, CD);
if (DoubleUtil.IsZero(det))
{
// The segments are parallel. no intersection
return NoIntersection;
}
double r = AdjustFIndex(Vector.Determinant(AB, CA) / det);
if (r >= 0 && r <= 1)
{
// The line defined AB does cross the segment CD.
double s = AdjustFIndex(Vector.Determinant(CD, CA) / det);
if (s >= 0 && s <= 1)
{
// The crossing point is on the segment AB as well.
// Intersection found.
return s;
}
}
// No intersection found
return NoIntersection;
}
///
/// Clears double's computation fuzz around 0 and 1
///
internal static double AdjustFIndex(double findex)
{
return DoubleUtil.IsZero(findex) ? 0 : (DoubleUtil.IsOne(findex) ? 1 : findex);
}
private bool _hasLoop = false;
private Rect _prevBounds = Rect.Empty;
private static readonly double NoIntersection = StrokeFIndices.BeforeFirst;
}
#endregion
}
// File provided for Reference Use Only by Microsoft Corporation (c) 2007.
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- XPathNode.cs
- XmlEnumAttribute.cs
- DateTimeOffset.cs
- BrowserDefinition.cs
- ZipFileInfoCollection.cs
- BaseParser.cs
- HttpHandlersSection.cs
- CreateSequence.cs
- Reference.cs
- RelatedPropertyManager.cs
- KerberosSecurityTokenAuthenticator.cs
- ExportException.cs
- TextRenderingModeValidation.cs
- ToggleButton.cs
- ActivityLocationReferenceEnvironment.cs
- ProgressChangedEventArgs.cs
- GAC.cs
- DisplayToken.cs
- ScriptingWebServicesSectionGroup.cs
- ADMembershipProvider.cs
- ErrorTableItemStyle.cs
- SelectionPatternIdentifiers.cs
- MetadataItem_Static.cs
- Vector3DAnimation.cs
- ThemeConfigurationDialog.cs
- ManualResetEventSlim.cs
- BitmapImage.cs
- PreviousTrackingServiceAttribute.cs
- CFGGrammar.cs
- Authorization.cs
- CacheEntry.cs
- WorkflowInstanceContextProvider.cs
- SoapReflectionImporter.cs
- RbTree.cs
- CollectionChangeEventArgs.cs
- FirstMatchCodeGroup.cs
- SystemDropShadowChrome.cs
- EditorPartDesigner.cs
- DataGridViewLinkCell.cs
- PropertyConverter.cs
- ExpandCollapseIsCheckedConverter.cs
- TextBox.cs
- StringFreezingAttribute.cs
- SmtpReplyReader.cs
- MissingFieldException.cs
- CssClassPropertyAttribute.cs
- IgnoreFileBuildProvider.cs
- StreamUpdate.cs
- FileLogRecordStream.cs
- OdbcInfoMessageEvent.cs
- XmlQualifiedName.cs
- RestClientProxyHandler.cs
- AspNetSynchronizationContext.cs
- CompareValidator.cs
- PropertyChangedEventArgs.cs
- TouchDevice.cs
- QueryAsyncResult.cs
- ReferentialConstraint.cs
- KnownAssembliesSet.cs
- StrokeCollectionDefaultValueFactory.cs
- TemplateParser.cs
- ConfigXmlReader.cs
- InputBinder.cs
- AvtEvent.cs
- WebEventTraceProvider.cs
- DataControlCommands.cs
- HttpRawResponse.cs
- MenuBase.cs
- EventHandlerService.cs
- SymbolTable.cs