/// <summary>
/// Returns true if the 'other' polygon is fully contained inside this polygon.
/// </summary>
public static bool IsFullyContainedInside(this Polygon2d self, Polygon2d other)
{
// check if all my vertices are inside the other polygon
foreach (var v in self.Points)
{
if (!other.Contains(v))
{
return(false);
}
}
// check if all my edges do NOT intersect with edges of the other polygon
foreach (var e in self.EdgeLines)
{
foreach (var x in other.EdgeLines)
{
if (x.Intersects(e))
{
return(false);
}
}
}
// :-)
return(true);
}
public static bool InPolygon2d(this Vector2d vector2d, Polygon2d polygon2d)
{
//【】判断点是否落在多边形线段上
foreach (Segment2d segment2d in polygon2d.SegmentItr())
{
double distance = segment2d.DistanceSquared(vector2d);
if (distance.EqualZreo())
{
return(false);
}
}
return(polygon2d.Contains(vector2d));
}
public static void test_convex_hull_2()
{
Random r = new Random(31337);
//LocalProfiler p = new LocalProfiler();
//p.Start("Hulls");
QueryNumberType[] modes = new QueryNumberType[] { QueryNumberType.QT_DOUBLE, QueryNumberType.QT_INT64 };
foreach (var queryMode in modes)
{
for (int k = 0; k < 1000; ++k)
{
int N = 2500;
double scale = (r.NextDouble() + 0.1) * 1024.0;
Vector2d[] pts = TestUtil.RandomPoints2(N, r, Vector2d.Zero, scale);
double eps = MathUtil.Epsilonf;
ConvexHull2 hull = new ConvexHull2(pts, eps, queryMode);
Polygon2d hullPoly = hull.GetHullPolygon();
foreach (Vector2d v in pts)
{
if (hullPoly.Contains(v))
{
continue;
}
double d = hullPoly.DistanceSquared(v);
if (d < eps)
{
continue;
}
System.Console.WriteLine("test_convex_hull: Point {0} not contained!", v);
}
}
}
//p.StopAll();
//System.Console.WriteLine(p.AllTimes());
//SVGWriter writer = new SVGWriter();
//foreach (Vector2d v in pts) {
// writer.AddCircle(new Circle2d(v, 3.0), SVGWriter.Style.Outline("black", 1.0f));
//}
//writer.AddPolygon(hullPoly, SVGWriter.Style.Outline("red", 2.0f));
//writer.Write(TestUtil.GetTestOutputPath("test.svg"));
}
public static void test_winding()
{
Random r = new Random(31337);
int NPTS = 1000;
double radius = 1;
Polygon2d poly = Polygon2d.MakeCircle(radius, 777);
Vector2d[] testPts = TestUtil.RandomPoints2(NPTS, r, Vector2d.Zero, radius);
foreach (Vector2d v in testPts)
{
bool really_inside = (v.Length < radius);
bool inside = poly.Contains(v);
double winding0 = poly.WindingIntegral(v);
bool inside_winding = !(Math.Abs(winding0) < MathUtil.Epsilonf);
if (really_inside != inside || really_inside != inside_winding)
{
System.Console.WriteLine("Failed! truth {0} inside {1} winding0 {2}",
really_inside, inside, winding0);
}
}
// test random polygons
int NPOLYS = 100;
for (int k = 0; k < NPOLYS; ++k)
{
poly = new Polygon2d(TestUtil.RandomPoints2(30, r, Vector2d.Zero, radius));
testPts = TestUtil.RandomPoints2(NPTS, r, Vector2d.Zero, radius);
foreach (Vector2d v in testPts)
{
bool inside = poly.Contains(v);
double winding0 = poly.WindingIntegral(v);
bool inside_winding = !(Math.Abs(winding0) < MathUtil.Epsilonf);
if (inside != inside_winding)
{
System.Console.WriteLine("Failed! inside {0} winding0 {1}", inside, winding0);
}
}
}
}
public static bool IsInsidePolygon(Vector2d point, Polygon2d polygon)
{
return(polygon.Contains(point));
}
public bool Insert()
{
Func <int, bool> is_contained_v = (vid) => {
Vector3d v = Mesh.GetVertex(vid);
Vector2f vf2 = ProjectFrame.ToPlaneUV((Vector3f)v, 2);
return(Polygon.Contains(vf2));
};
MeshVertexSelection vertexROI = new MeshVertexSelection(Mesh);
Index3i seedT = Mesh.GetTriangle(SeedTriangle);
// if a seed vert of seed triangle is containd in polygon, we will
// flood-fill out from there, this gives a better ROI.
// If not, we will try flood-fill from the seed triangles.
List <int> seed_verts = new List <int>();
for (int j = 0; j < 3; ++j)
{
if (is_contained_v(seedT[j]))
{
seed_verts.Add(seedT[j]);
}
}
if (seed_verts.Count == 0)
{
seed_verts.Add(seedT.a);
seed_verts.Add(seedT.b);
seed_verts.Add(seedT.c);
}
// flood-fill out from seed vertices until we have found all vertices
// contained in polygon
vertexROI.FloodFill(seed_verts.ToArray(), is_contained_v);
// convert vertex ROI to face ROI
MeshFaceSelection faceROI = new MeshFaceSelection(Mesh, vertexROI, 1);
faceROI.ExpandToOneRingNeighbours();
faceROI.FillEars(true); // this might be a good idea...
// construct submesh
RegionOperator regionOp = new RegionOperator(Mesh, faceROI);
DSubmesh3 roiSubmesh = regionOp.Region;
DMesh3 roiMesh = roiSubmesh.SubMesh;
// save 3D positions of unmodified mesh
Vector3d[] initialPositions = new Vector3d[roiMesh.MaxVertexID];
// map roi mesh to plane
MeshTransforms.PerVertexTransform(roiMesh, roiMesh.VertexIndices(), (v, vid) => {
Vector2f uv = ProjectFrame.ToPlaneUV((Vector3f)v, 2);
initialPositions[vid] = v;
return(new Vector3d(uv.x, uv.y, 0));
});
// save a copy of 2D mesh and construct bvtree. we will use
// this later to project back to 3d
// [TODO] can we use a better spatial DS here, that takes advantage of 2D?
DMesh3 projectMesh = new DMesh3(roiMesh);
DMeshAABBTree3 projecter = new DMeshAABBTree3(projectMesh, true);
MeshInsertUVPolyCurve insertUV = new MeshInsertUVPolyCurve(roiMesh, Polygon);
//insertUV.Validate()
bool bOK = insertUV.Apply();
if (!bOK)
{
throw new Exception("insertUV.Apply() failed");
}
if (SimplifyInsertion)
{
insertUV.Simplify();
}
int[] insertedPolyVerts = insertUV.CurveVertices;
// grab inserted loop, assuming it worked
EdgeLoop insertedLoop = null;
if (insertUV.Loops.Count == 1)
{
insertedLoop = insertUV.Loops[0];
}
// find interior triangles
List <int> interiorT = new List <int>();
foreach (int tid in roiMesh.TriangleIndices())
{
Vector3d centroid = roiMesh.GetTriCentroid(tid);
if (Polygon.Contains(centroid.xy))
{
interiorT.Add(tid);
}
}
if (RemovePolygonInterior)
{
MeshEditor editor = new MeshEditor(roiMesh);
editor.RemoveTriangles(interiorT, true);
InteriorTriangles = null;
}
else
{
InteriorTriangles = interiorT.ToArray();
}
// map back to 3d
Vector3d a = Vector3d.Zero, b = Vector3d.Zero, c = Vector3d.Zero;
foreach (int vid in roiMesh.VertexIndices())
{
// [TODO] somehow re-use exact positions from regionOp maps?
// construct new 3D pos w/ barycentric interpolation
Vector3d v = roiMesh.GetVertex(vid);
int tid = projecter.FindNearestTriangle(v);
Index3i tri = projectMesh.GetTriangle(tid);
projectMesh.GetTriVertices(tid, ref a, ref b, ref c);
Vector3d bary = MathUtil.BarycentricCoords(ref v, ref a, ref b, ref c);
Vector3d pos = bary.x * initialPositions[tri.a] + bary.y * initialPositions[tri.b] + bary.z * initialPositions[tri.c];
roiMesh.SetVertex(vid, pos);
}
bOK = BackPropagate(regionOp, insertedPolyVerts, insertedLoop);
return(bOK);
}
public static bool OnPolygon2d(this Vector2d vector2d, Polygon2d polygon2d)
{
return(polygon2d.Contains(vector2d));
}
/// <summary>
/// Returns the unified Polygon of the two given ones.
/// Works only with convex-Polygons
/// Returns an empty Polygon if the two do not intersect
/// </summary>
public static IEnumerable <Polygon2d> Union(this Polygon2d p0, Polygon2d p1)
{
Polygon2d[] arr = new Polygon2d[2];
arr[0] = p0;
arr[1] = p1;
int current = 0;
int other = 1;
List <V2d> points = new List <V2d>();
bool enter = false;
int index = -1;
V2d point = V2d.NaN;
bool firstIntersectionFound = false;
V2d firstIntersectionPoint = V2d.NaN;
for (int i = 0; i >= 0; i = (i + 1) % arr[current].PointCount)
{
V2d start = arr[current][(i + arr[current].PointCount - 1) % arr[current].PointCount];
V2d end = arr[current][i];
if (arr[other].ClosestIntersection(start, end, out enter, out index, out point))
{
if (!firstIntersectionFound)
{
firstIntersectionFound = true;
firstIntersectionPoint = point;
}
else
{
if ((point - firstIntersectionPoint).Length < 0.001)
{
break;
}
}
if (enter)
{
points.Add(point);
while ((arr[other][(index + 1) % arr[other].PointCount] - point).Length < 0.001)
{
index = (index + 1) % arr[other].PointCount;
}
if (!arr[current].Contains(arr[other][(index + 1) % arr[other].PointCount]))
{
points.Add(arr[other][(index + 1) % arr[other].PointCount]);
index = (index + 1) % arr[other].PointCount;
}
i = index;
current = (current == 1 ? 0 : 1);
other = (current == 1 ? 0 : 1);
}
else
{
points.Add(point);
if (!arr[other].Contains(arr[current][i]))
{
points.Add(arr[current][i]);
}
}
}
else
{
if (i == arr[current].PointCount - 1 && !firstIntersectionFound)
{
break;
}
if (!arr[other].Contains(end) && firstIntersectionFound)
{
points.Add(end);
}
}
}
if (!firstIntersectionFound)
{
if (p0.Contains(p1[0]))
{
yield return(p0);
}
else if (p1.Contains(p0[0]))
{
yield return(p1);
}
else
{
yield return(p0);
yield return(p1);
}
}
else
{
yield return(new Polygon2d(points));
}
}
/// <summary>
/// Returns the Line-Segments of line inside the Polygon (CCW ordered).
/// Works only with Convex-Polygons
/// </summary>
public static Line2d ClipWithConvex(this Line2d line, Polygon2d poly)
{
V2d p = V2d.NaN;
bool i0, i1;
i0 = poly.Contains(line.P0);
i1 = poly.Contains(line.P1);
if (i0 && i1)
{
return(line);
}
else if ((!i0 && i1) || (i0 && !i1))
{
foreach (var l in poly.EdgeLines)
{
if (line.Intersects(l, out p))
{
break;
}
}
if (i0)
{
return(new Line2d(line.P0, p));
}
else
{
return(new Line2d(p, line.P1));
}
}
else
{
V2d p0 = V2d.NaN;
V2d p1 = V2d.NaN;
int c = 0;
foreach (var l in poly.EdgeLines)
{
if (line.Intersects(l, out p))
{
if (c == 0)
{
p0 = p;
}
else
{
p1 = p;
}
c++;
}
}
if (c == 2)
{
V2d u = p1 - p0;
if (u.Dot(line.Direction) > 0)
{
return(new Line2d(p0, p1));
}
else
{
return(new Line2d(p1, p0));
}
}
else
{
return(new Line2d(V2d.NaN, V2d.NaN));
}
}
}
/// <summary>
/// Returns the Line-Segments of line inside the Polygon (CCW ordered).
/// Works with all (convex and non-convex) Polygons
/// </summary>
public static IEnumerable <Line2d> ClipWith(this Line2d line, Polygon2d poly)
{
bool i0, i1;
i0 = poly.Contains(line.P0);
i1 = poly.Contains(line.P1);
List <V2d> resulting = new List <V2d>();
List <bool> enter = new List <bool>();
if (i0)
{
resulting.Add(line.P0);
enter.Add(true);
}
if (i1)
{
resulting.Add(line.P1);
enter.Add(false);
}
V2d p = V2d.NaN;
V2d direction = line.Direction;
foreach (var l in poly.EdgeLines)
{
if (line.Intersects(l, out p))
{
V2d d = l.Direction;
V2d n = new V2d(-d.Y, d.X);
if (!p.IsNaN)
{
bool addflag = true;
bool flag = direction.Dot(n) > 0;
for (int i = 0; i < resulting.Count; i++)
{
if (Fun.IsTiny((resulting[i] - p).Length))
{
if (flag != enter[i])
{
resulting.RemoveAt(i);
enter.RemoveAt(i);
}
addflag = false;
break;
}
}
if (addflag)
{
resulting.Add(p);
enter.Add(flag);
}
}
}
}
V2d dir = line.P1 - line.P0;
resulting = (from r in resulting select r).OrderBy(x => x.Dot(dir)).ToList();
int counter = resulting.Count;
List <Line2d> lines = new List <Line2d>();
for (int i = 0; i < counter - 1; i += 2)
{
lines.Add(new Line2d(resulting[i], resulting[i + 1]));
}
return(lines);
}
/// <summary>
/// Trim / split a segment by a polygon.
/// </summary>
/// <param name="_type">0 = inside; 1 = outside ; 2 = both sides</param>
public static List <Segment2d> Trim(this Polygon2d _polygon, Segment2d _seg, int _type)
{
var list = new List <Segment2d>();
//find intersections
List <KeyValuePair <double, Vector2d> > intPs = new List <KeyValuePair <double, Vector2d> >();
foreach (var edge in _polygon.SegmentItr())
{
var segIntr = new IntrSegment2Segment2(_seg, edge);
bool b = segIntr.Find();
if (b)
{
intPs.Add(new KeyValuePair <double, Vector2d>(segIntr.Parameter0, segIntr.Point0));
}
}
//if no intersection
if (intPs.Count == 0)
{
if (_type == 1)
{
//return empty list
}
else
{
//check if segment is contained inside polygon
if (_polygon.Contains(_seg))
{
list.Add(_seg);
}
}
return(list);
}
//sort intersection points by position
var sortedIntPs = intPs.OrderBy(x => x.Key).Select(x => x.Value).ToList();
//get two list of segments from intersections
var list0 = new List <Segment2d>();
var list1 = new List <Segment2d>()
{
new Segment2d(_seg.P0, sortedIntPs[0])
};
for (int i = 1; i < sortedIntPs.Count; i += 2)
{
Vector2d p0, p1, p2;
p0 = sortedIntPs[i - 1];
p1 = sortedIntPs[i];
list0.Add(new Segment2d(p0, p1));
if (i + 1 < sortedIntPs.Count)
{
p2 = sortedIntPs[i + 1];
list1.Add(new Segment2d(p1, p2));
}
}
//use even/odd of intr num to decide the last segment
var last = new Segment2d(sortedIntPs.Last(), _seg.P1);
if (sortedIntPs.Count % 2 == 0)
{
list1.Add(last);
}
else
{
list0.Add(last);
}
//check starting point inside or outside
bool startInside = _polygon.Contains(_seg.P0);
//return coresponding list of segments
if (_type == 0)
{
return(startInside ? list1 : list0);
}
else if (_type == 1)
{
return(startInside ? list0 : list1);
}
else
{
list.AddRange(list0);
list.AddRange(list1);
return(list);
}
}
public static void test_uv_insert_segment()
{
DMesh3 mesh = TestUtil.LoadTestInputMesh("plane_250v.obj");
mesh.EnableVertexUVs(Vector2f.Zero);
MeshTransforms.ConvertYUpToZUp(mesh);
DMeshAABBTree3 spatial = new DMeshAABBTree3(mesh);
spatial.Build();
int tid = spatial.FindNearestTriangle(Vector3d.Zero);
//Polygon2d poly = Polygon2d.MakeRectangle(Vector2d.Zero, 5, 5);
Polygon2d poly = Polygon2d.MakeCircle(5, 13);
//PolyLine2d poly = new PolyLine2d( new Vector2d[] { -5 * Vector2d.One, 5 * Vector2d.One });
//int tri_edge0 = mesh.GetTriEdge(tid, 0);
//Index2i edge0_tris = mesh.GetEdgeT(tri_edge0);
//Index2i edge0_verts = mesh.GetEdgeV(tri_edge0);
//Vector3d v0 = mesh.GetVertex(edge0_verts.a), v1 = mesh.GetVertex(edge0_verts.b);
//Vector3d c = mesh.GetTriCentroid(tid);
//Polygon2d poly = new Polygon2d(new Vector2d[] {
// Vector2d.Lerp(v0.xy, v1.xy, -0.25),
// Vector2d.Lerp(v0.xy, v1.xy, 1.5),
// c.xy
//});
MeshInsertUVPolyCurve insert = new MeshInsertUVPolyCurve(mesh, poly);
insert.Apply();
Polygon2d test_poly = new Polygon2d();
List <double> distances = new List <double>();
List <int> nearests = new List <int>();
for (int i = 0; i < insert.Loops[0].VertexCount; ++i)
{
Vector2d v = mesh.GetVertex(insert.Loops[0].Vertices[i]).xy;
test_poly.AppendVertex(v);
int iNear; double fNear;
distances.Add(poly.DistanceSquared(v, out iNear, out fNear));
nearests.Add(iNear);
}
System.Console.WriteLine("inserted loop poly has {0} edges", insert.Loops[0].EdgeCount);
// find a triangle connected to loop that is inside the polygon
// [TODO] maybe we could be a bit more robust about this? at least
// check if triangle is too degenerate...
int seed_tri = -1;
for (int i = 0; i < insert.Loops[0].EdgeCount; ++i)
{
Index2i et = mesh.GetEdgeT(insert.Loops[0].Edges[i]);
Vector3d ca = mesh.GetTriCentroid(et.a);
bool in_a = poly.Contains(ca.xy);
Vector3d cb = mesh.GetTriCentroid(et.b);
bool in_b = poly.Contains(cb.xy);
if (in_a && in_b == false)
{
seed_tri = et.a;
break;
}
else if (in_b && in_a == false)
{
seed_tri = et.b;
break;
}
}
Util.gDevAssert(seed_tri != -1);
// flood-fill inside loop
HashSet <int> loopEdges = new HashSet <int>(insert.Loops[0].Edges);
MeshFaceSelection sel = new MeshFaceSelection(mesh);
sel.FloodFill(seed_tri, null, (eid) => { return(loopEdges.Contains(eid) == false); });
// delete inside loop
MeshEditor editor = new MeshEditor(mesh);
editor.RemoveTriangles(sel, true);
MeshTransforms.ConvertZUpToYUp(mesh);
TestUtil.WriteTestOutputMesh(mesh, "insert_uv_segment.obj");
//OBJWriter writer = new OBJWriter();
//var s = new System.IO.StreamWriter(Program.TEST_OUTPUT_PATH + "mesh_local_param.obj", false);
//List<WriteMesh> wm = new List<WriteMesh>() { new WriteMesh(mesh) };
//WriteOptions opt = new WriteOptions() {
// bCombineMeshes = false, bWriteGroups = false, bPerVertexColors = true, bPerVertexUVs = true,
// AsciiHeaderFunc = () => { return "mttllib checkerboard.mtl\r\nusemtl checkerboard\r\n"; }
//};
//writer.Write(s, wm, opt);
//s.Close();
}