public void ContainsInsideTest()
{
Assert.IsTrue(m_arrow.ContainsInside(new Vector2(1.5f, 0)));
Assert.IsFalse(m_arrow.ContainsInside(new Vector2(0, 0)));
Assert.IsTrue(m_diamond.ContainsInside(new Vector2(0, 0)));
Assert.IsFalse(m_diamond.ContainsInside(new Vector2(-999, 999)));
Assert.IsTrue(m_containsPoly.ContainsInside(new Vector2(1, 3)));
Assert.IsFalse(m_containsPoly.ContainsInside(new Vector2(3, 1)));
}
/// <inheritdoc />
public bool VisibleToOtherVertex(
Vector2 vertex1,
Vector2 vertex2,
Polygon2D polygon)
{
LineSegment seg1 = new LineSegment(vertex1, vertex2);
foreach (LineSegment lineSegment in polygon.Segments)
{
// Check if any of the line segments intersect with the
// line segments between the two vertices. If they so then
// the two vertices cannot see each other. With the exception
// that an intersection with an endpoint does not count as
// blocking visibility
Vector2?intersection = seg1.IntersectProper(lineSegment);
if (intersection != null)
{
// Check if the two lines are parallel. We allow two vertices
// to see each other if they they are along a straight line
if (!seg1.IsParallel(lineSegment))
{
return(false);
}
}
}
// Non of the line segments of the polygon intersect with the
// visibility line between the two points. Next we need to check if
// the visibility line is inside of the polygon
// We take the midpoint of the line. If this is inside the polygon
// then the two points can see each other
return(polygon.ContainsInside(seg1.Midpoint));
}
/// <summary>
/// Dirty method O(n^2)
/// </summary>
/// <param name="a_poly1"></param>
/// <param name="a_poly2"></param>
/// <returns></returns>
public static Polygon2D IntersectConvex(Polygon2D a_poly1, Polygon2D a_poly2)
{
if (!(a_poly1.IsConvex()))
{
throw new GeomException("Method not defined for nonconvex polygons" + a_poly1);
}
if (!(a_poly2.IsConvex()))
{
throw new GeomException("Method not defined for nonconvex polygons" + a_poly2);
}
// obtain vertices that lie inside both polygons
var resultVertices = a_poly1.Vertices
.Where(v => a_poly2.ContainsInside(v))
.Concat(a_poly2.Vertices.Where(v => a_poly1.ContainsInside(v)))
.ToList();
// add intersections between two polygon segments
resultVertices.AddRange(a_poly1.Segments.SelectMany(seg => seg.Intersect(a_poly2.Segments)));
// remove any duplicates
resultVertices = resultVertices.Distinct().ToList();
// retrieve convex hull of relevant vertices
if (resultVertices.Count() >= 3)
{
var poly = ConvexHull.ComputeConvexHull(resultVertices);
Debug.Assert(poly.IsConvex());
return(poly);
}
return(null);
}
public static int TrianglePoints(List <Vector2> pts, int Anum, int Bnum, int Cnum)
{
int cnt = 0;
var triangleABC = new Polygon2D();
triangleABC.AddVertex(pts[Anum]);
triangleABC.AddVertex(pts[Bnum]);
triangleABC.AddVertex(pts[Cnum]);
for (int i = 0; i < pts.Count; i++)
{
if ((i == Bnum) || (i == Anum) || (i == Cnum))
{
continue;
}
if (triangleABC.ContainsInside(pts[i]))
{
cnt++;
}
}
//Debug.Log(cnt);
triangleABC.Clear();
return(cnt);
}
private int HullRate()
{
m_selected_Hull = ConvexHull.ComputeConvexHull(m_selected_points.Select(v => v.Pos));
if (m_selected_Hull.VertexCount < 3)
{
return(0);
}
int tot = m_selected_Hull.VertexCount;
foreach (var point in m_points)
{
if (m_selected_Hull.ContainsInside(point.Pos))
{
tot++;
}
}
m_selected_Hull.SetPointNumber(tot);
//Draw new convex hull line segments.
foreach (var segmesh in lineMeshes)
{
Destroy(segmesh);
}
lineMeshes.Clear();
foreach (var seg in m_selected_Hull.Segments)
{
//Add a line renderer
// instantiate new road mesh
var roadmesh = Instantiate(m_userLineMeshPrefab, Vector3.forward, Quaternion.identity) as GameObject;
roadmesh.transform.parent = this.transform;
instantObjects.Add(roadmesh);
lineMeshes.Add(roadmesh);
//roadmesh.GetComponent<P1HullSegment>().Segment =seg;
var roadmeshScript = roadmesh.GetComponent <ReshapingMesh>();
roadmeshScript.CreateNewMesh(seg.Point1, seg.Point2);
}
//Update current area in information panel
GameObject.Find("PointsNumber").GetComponent <Text>().text = m_selected_Hull.PointNumber.ToString();
// 60%, 80%, 95% pass level
for (int i = 0; i < m_rateList.Count; i++)
{
if (m_selected_Hull.PointNumber < (int)(m_rateList[i] * m_solutionHull.PointNumber))
{
return(i);
}
}
return(m_rateList.Count - 1);
}
public static int PolygonPoints(List <Vector2> pts, Polygon2D plg)
{
int tot = 0;
foreach (var p in pts)
{
if (plg.ContainsInside(p) || plg.OnBoundary(p))
{
tot++;
}
}
return(tot);
}
/// <summary>
/// check if intersect
/// </summary>
/// <param name="a_poly1"></param>
/// <param name="a_poly2"></param>
/// <returns></returns>
public static bool ifIntersect(Polygon2D a_poly1, Polygon2D a_poly2)
{
if (!(a_poly1.IsConvex()))
{
throw new GeomException("Method not defined for nonconvex polygons" + a_poly1);
}
if (!(a_poly2.IsConvex()))
{
throw new GeomException("Method not defined for nonconvex polygons" + a_poly2);
}
// obtain vertices that lie inside both polygons
var resultVertices = a_poly1.Vertices
.Where(v => a_poly2.ContainsInside(v))
.Concat(a_poly2.Vertices.Where(v => a_poly1.ContainsInside(v)))
.ToList();
Debug.Log("result Vertices in Intersector: " + resultVertices.Count);
return(resultVertices.Count > 0);
}
public WeilerAtherton(Polygon2D a_subject, Polygon2D a_clip)
{
// initialize variables
Subject = a_subject;
Clip = a_clip;
SubjectList = new LinkedList <WAPoint>();
ClipList = new LinkedList <WAPoint>();
SubjectNode = new Dictionary <WAPoint, LinkedListNode <WAPoint> >();
ClipNode = new Dictionary <WAPoint, LinkedListNode <WAPoint> >();
EntryIntersections = new HashSet <WAPoint>();
// store intersections for clipping line segment
// saves recomputation of intersections and entry-exit categorization
var intersectSegmentsClip = new Dictionary <LineSegment, List <WAPoint> >();
foreach (var seg in a_clip.Segments)
{
intersectSegmentsClip.Add(seg, new List <WAPoint>());
}
// find all intersections and create subject list
foreach (var seg1 in a_subject.Segments)
{
// retrieve intersection list
var vertices = new List <WAPoint>();
var point = new WAPoint(seg1.Point1, WAList.Vertex);
var node = SubjectList.AddLast(point);
SubjectNode.Add(point, node);
foreach (var seg2 in a_clip.Segments)
{
var intersect = seg1.Intersect(seg2);
if (intersect.HasValue)
{
// store intersection point
point = new WAPoint(intersect.Value, WAList.Ignore);
vertices.Add(point);
intersectSegmentsClip[seg2].Add(point);
}
}
// sort intersections on distance to start vertex
vertices.Sort(new ClosestToPointComparer(seg1.Point1));
foreach (var vertex in vertices)
{
node = SubjectList.AddLast(vertex);
SubjectNode.Add(vertex, node);
}
}
// remove duplicates
for (var node = SubjectList.First; node != null; node = node.Next)
{
var next = node.Next ?? SubjectList.First;
while (node != next && MathUtil.EqualsEps(node.Value.Pos, next.Value.Pos))
{
if (node.Value.Type == WAList.Vertex)
{
node.Value.Type = WAList.Ignore;
SubjectList.Remove(node);
EntryIntersections.Remove(node.Value);
node = next;
}
else
{
next.Value.Type = WAList.Ignore;
SubjectList.Remove(next);
EntryIntersections.Remove(next.Value);
}
next = node.Next ?? SubjectList.First;
}
}
// set entry/exit types correctly
for (var node = SubjectList.First; node != null; node = node.Next)
{
var prev = node.Previous ?? SubjectList.Last;
var vertex = node.Value;
var inside1 = Clip.ContainsInside(prev.Value.Pos);
var inside2 = Clip.ContainsInside(vertex.Pos);
if (!inside1 && inside2)
{
vertex.Type = WAList.Entry;
}
else if (inside1 && !inside2)
{
prev.Value.Type = WAList.Exit;
EntryIntersections.Remove(vertex);
}
if (vertex.Type == WAList.Entry)
{
EntryIntersections.Add(vertex);
}
}
// create clip list and intersections
foreach (var seg in a_clip.Segments)
{
var vertices = intersectSegmentsClip[seg];
// sort intersections on distance to start vertex
intersectSegmentsClip[seg].Sort(new ClosestToPointComparer(seg.Point1));
vertices.Insert(0, new WAPoint(seg.Point1, WAList.Vertex));
// loop over intersections
foreach (var vertex in vertices)
{
if (vertex.Type == WAList.Ignore)
{
continue;
}
// add intersection to clipping list
var node = ClipList.AddLast(vertex);
ClipNode.Add(vertex, node);
}
}
}
/// <summary>
/// Computes the visibility polygon from the given point
/// inside of a simple polygon (given as n vertices in CCW order) in O(n) time.
/// Based on: https://cs.uwaterloo.ca/research/tr/1985/CS-85-38.pdf
/// </summary>
/// <param name="polygon"></param>
/// <param name="z"></param>
/// <returns></returns>
public static Polygon2D Vision(Polygon2D polygon, Vector2 z)
{
// check for invalid polygon
if (polygon.VertexCount < 3)
{
return(null);
}
if (!(polygon.ContainsInside(z) || polygon.OnBoundary(z)))
{
throw new ArgumentException("Visibility point must be inside polygon");
}
// list v, satisfies assumptions made in paper (section 2, paragraph 1
// and 2).
double initAngle;
var vs = Preprocess(polygon, z, out initAngle);
var s = new Stack <VertDispl>();
var i = 0;
VertDispl w = null;
var ccw = true;
var v0 = vs.Get(0);
s.Push(v0);
Debug.Assert(vs.n > 1);
NextCall m_nextCall;
if (MathUtil.GEQEps(vs.Get(1).alpha, v0.alpha))
{
m_nextCall = Advance(ref vs, ref s, ref i, ref w, ref ccw);
}
else
{
m_nextCall = Scan(ref vs, ref s, ref i, ref w, ref ccw); // CounterClockWise
}
while (m_nextCall != NextCall.STOP)
{
switch (m_nextCall)
{
case NextCall.ADVANCE:
m_nextCall = Advance(ref vs, ref s, ref i, ref w, ref ccw);
break;
case NextCall.RETARD:
m_nextCall = Retard(ref vs, ref s, ref i, ref w, ref ccw);
break;
case NextCall.SCAN:
m_nextCall = Scan(ref vs, ref s, ref i, ref w, ref ccw);
break;
}
}
var sList = s.ToList();
// error occurred due to robustness
if (sList.Count == 0)
{
return(new Polygon2D());
}
Debug.Assert(MathUtil.EqualsEps(sList[s.Count - 1].p.Cartesian, v0.p.Cartesian));
var poly = Postprocess(sList, vs, z, initAngle);
return(poly);
}
public WeilerAtherton(Polygon2D a_subject, Polygon2D a_clip)
{
// initialize variables
Subject = a_subject;
Clip = a_clip;
SubjectList = new LinkedList <WAPoint>(Subject.Vertices.Select(v => new WAPoint(v, WAList.Vertex)));
ClipList = new LinkedList <WAPoint>(Clip.Vertices.Select(v => new WAPoint(v, WAList.Vertex)));
SubjectNode = new Dictionary <WAPoint, LinkedListNode <WAPoint> >();
ClipNode = new Dictionary <WAPoint, LinkedListNode <WAPoint> >();
Entry = new HashSet <WAPoint>();
Exit = new HashSet <WAPoint>();
// find all intersections and create subject and clip list
for (var node1 = SubjectList.First; node1 != null; node1 = node1.Next)
{
// calculate subject segment
var next1 = node1.Next ?? SubjectList.First;
var seg1 = new LineSegment(node1.Value.Pos, next1.Value.Pos);
// obtain intersection lists
var intersections = new List <Vector2>();
var intersectNodes = new Dictionary <Vector2, LinkedListNode <WAPoint> >();
for (var node2 = ClipList.Last; node2 != null; node2 = node2.Previous)
{
var prev2 = node2.Previous ?? ClipList.Last;
var seg2 = new LineSegment(node2.Value.Pos, prev2.Value.Pos);
var intersect = seg1.Intersect(seg2);
if (intersect.HasValue && !intersectNodes.ContainsKey(intersect.Value))
{
// store intersection point
intersectNodes.Add(intersect.Value, node2);
intersections.Add(intersect.Value);
}
}
// sort intersections on distance to start vertex
intersections.Sort(new ClosestToPointComparer(seg1.Point1));
// insert intersections into subject/clip lists
foreach (var vertex in intersections)
{
var point = new WAPoint(vertex, WAList.Ignore);
var newNode1 = SubjectList.AddAfter(node1, point);
SubjectNode.Add(point, newNode1);
var newNode2 = ClipList.AddBefore(intersectNodes[vertex], point);
ClipNode.Add(point, newNode2);
// increment node1 since we added a vertex
node1 = newNode1;
}
}
// remove duplicates of subject
for (var node = SubjectList.First; node != null;)
{
var next = node.Next ?? SubjectList.First;
while (MathUtil.EqualsEps(node.Value.Pos, next.Value.Pos, MathUtil.EPS * 10))
{
if (next.Value.Type != WAList.Vertex)
{
if (ClipNode.ContainsKey(node.Value))
{
ClipList.Remove(ClipNode[node.Value]);
}
SubjectList.Remove(node);
node = next;
}
else
{
SubjectList.Remove(next);
}
if (node == null)
{
break;
}
next = node.Next ?? SubjectList.First;
}
if (node != null)
{
node = node.Next;
}
}
// remove duplicates of clip
for (var node = ClipList.Last; node != null;)
{
var prev = node.Previous ?? ClipList.Last;
while (MathUtil.EqualsEps(node.Value.Pos, prev.Value.Pos, MathUtil.EPS * 10))
{
if (prev.Value.Type != WAList.Vertex)
{
if (SubjectNode.ContainsKey(node.Value))
{
SubjectList.Remove(SubjectNode[node.Value]);
}
ClipList.Remove(node);
node = prev;
}
else
{
ClipList.Remove(prev);
}
if (node == null)
{
break;
}
prev = node.Previous ?? ClipList.Last;
}
if (node != null)
{
node = node.Previous;
}
}
// set entry/exit types correctly
for (var node = SubjectList.First; node != null; node = node.Next)
{
if (node.Value.Type == WAList.Vertex)
{
continue;
}
var prev = node.Previous ?? SubjectList.Last;
var next = node.Next ?? SubjectList.First;
var inside1 = Clip.ContainsInside(prev.Value.Pos) || Clip.OnBoundary(prev.Value.Pos);
var inside2 = Clip.ContainsInside(next.Value.Pos) || Clip.OnBoundary(next.Value.Pos);
if (!inside1 && inside2)
{
node.Value.Type = WAList.Entry;
Entry.Add(node.Value);
}
else if (inside1 && !inside2)
{
node.Value.Type = WAList.Exit;
Exit.Add(node.Value);
}
}
}
