// This checks if a vertex is reflex (corner > 180 deg) or convex (corner < 180 deg) private static bool IsReflex(EarClipVertex[] t) { // Return true when corner is > 180 deg return(Line2D.GetSideOfLine(t[0].Position, t[2].Position, t[1].Position) < 0.0f); }
// This finds the cut coordinates and splits the other poly with inner vertices private static void SplitOuterWithInner(LinkedListNode <EarClipVertex> start, EarClipPolygon p) { LinkedListNode <EarClipVertex> insertbefore = null; float u, ul, foundu = float.MaxValue; Vector2D foundpos = new Vector2D(); // Create a line from start that goes beyond the right most vertex of p LinkedListNode <EarClipVertex> pr = FindRightMostVertex(p); float startx = start.Value.Position.x; float endx = pr.Value.Position.x + 10.0f; Line2D starttoright = new Line2D(start.Value.Position, new Vector2D(endx, start.Value.Position.y)); // Calculate a small bonus (0.1 mappixel) float bonus = starttoright.GetNearestOnLine(new Vector2D(start.Value.Position.x + 0.1f, start.Value.Position.y)); // Go for all lines in the outer polygon LinkedListNode <EarClipVertex> v1 = p.Last; LinkedListNode <EarClipVertex> v2 = p.First; while (v2 != null) { // Check if the line goes between startx and endx if (((v1.Value.Position.x > startx) || (v2.Value.Position.x > startx)) && ((v1.Value.Position.x < endx) || (v2.Value.Position.x < endx))) { // Find intersection Line2D pl = new Line2D(v1.Value.Position, v2.Value.Position); pl.GetIntersection(starttoright, out u, out ul); if (float.IsNaN(u)) { // We have found a line that is perfectly horizontal // (parallel to the cut scan line) Check if the line // is overlapping the cut scan line. if (v1.Value.Position.y == start.Value.Position.y) { // This is an exceptional situation which causes a bit of a problem, because // this could be a previously made cut, which overlaps another line from the // same cut and we have to determine which of the two we will join with. If we // pick the wrong one, the polygon is no longer valid and triangulation will fail. // Calculate distance of each vertex in units u = starttoright.GetNearestOnLine(v1.Value.Position); ul = starttoright.GetNearestOnLine(v2.Value.Position); // Rule out vertices before the scan line if (u < 0.0f) { u = float.MaxValue; } if (ul < 0.0f) { ul = float.MaxValue; } float insert_u = Math.Min(u, ul); Vector2D inserpos = starttoright.GetCoordinatesAt(insert_u); // Check in which direction the line goes. if (v1.Value.Position.x > v2.Value.Position.x) { // The line goes from right to left (towards our start point) // so we must always insert our cut after this line. // If the next line goes up, we consider this a better candidate than // a horizontal line that goes from left to right (the other cut line) // so we give it a small bonus. LinkedListNode <EarClipVertex> v3 = v2.Next ?? v2.List.First; if (v3.Value.Position.y < v2.Value.Position.y) { insert_u -= bonus; } // Remember this when it is a closer match if (insert_u <= foundu) { insertbefore = v2.Next ?? v2.List.First; foundu = insert_u; foundpos = inserpos; } } else { // The line goes from left to right (away from our start point) // so we must always insert our cut before this line. // If the previous line goes down, we consider this a better candidate than // a horizontal line that goes from right to left (the other cut line) // so we give it a small bonus. LinkedListNode <EarClipVertex> v3 = v1.Previous ?? v1.List.Last; if (v3.Value.Position.y > v1.Value.Position.y) { insert_u -= bonus; } // Remember this when it is a closer match if (insert_u <= foundu) { insertbefore = v2; foundu = insert_u; foundpos = inserpos; } } } } // Found a closer match? else if ((ul >= 0.0f) && (ul <= 1.0f) && (u > 0.0f) && (u <= foundu)) { // Found a closer intersection insertbefore = v2; foundu = u; foundpos = starttoright.GetCoordinatesAt(u); } } // Next v1 = v2; v2 = v2.Next; } // Found anything? if (insertbefore != null) { Sidedef sd = (insertbefore.Previous == null) ? insertbefore.List.Last.Value.Sidedef : insertbefore.Previous.Value.Sidedef; // Find the position where we have to split the outer polygon EarClipVertex split = new EarClipVertex(foundpos, null); // Insert manual split vertices p.AddBefore(insertbefore, new EarClipVertex(split, sd)); // Start inserting from the start (do I make sense this time?) v1 = start; do { // Insert inner polygon vertex p.AddBefore(insertbefore, new EarClipVertex(v1.Value)); v1 = (v1.Next ?? v1.List.First); } while(v1 != start); // Insert manual split vertices p.AddBefore(insertbefore, new EarClipVertex(start.Value, sd)); if (split.Position != insertbefore.Value.Position) { p.AddBefore(insertbefore, new EarClipVertex(split, sd)); } } }
// This clips a polygon and returns the triangles // The polygon may not have any holes or islands // See: http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf private int DoEarClip(EarClipPolygon poly, List <Vector2D> verticeslist, List <Sidedef> sidedefslist) { LinkedList <EarClipVertex> verts = new LinkedList <EarClipVertex>(); List <EarClipVertex> convexes = new List <EarClipVertex>(poly.Count); LinkedList <EarClipVertex> reflexes = new LinkedList <EarClipVertex>(); LinkedList <EarClipVertex> eartips = new LinkedList <EarClipVertex>(); LinkedListNode <EarClipVertex> n1, n2; EarClipVertex v, v1, v2; EarClipVertex[] t, t1, t2; int countvertices = 0; // Go for all vertices to fill list foreach (EarClipVertex vec in poly) { vec.SetVertsLink(verts.AddLast(vec)); } // Remove any zero-length lines, these will give problems n1 = verts.First; do { // Continue until adjacent zero-length lines are removed n2 = n1.Next ?? verts.First; Vector2D d = n1.Value.Position - n2.Value.Position; while ((Math.Abs(d.x) < 0.00001f) && (Math.Abs(d.y) < 0.00001f)) { n2.Value.Remove(); n2 = n1.Next ?? verts.First; if (n2 != null) { d = n1.Value.Position - n2.Value.Position; } else { break; } } // Next! n1 = n2; }while(n1 != verts.First); // Optimization: Vertices which have lines with the // same angle are useless. Remove them! n1 = verts.First; while (n1 != null) { // Get the next vertex n2 = n1.Next; // Get triangle for v t = GetTriangle(n1.Value); // Check if both lines have the same angle Line2D a = new Line2D(t[0].Position, t[1].Position); Line2D b = new Line2D(t[1].Position, t[2].Position); if (Math.Abs(Angle2D.Difference(a.GetAngle(), b.GetAngle())) < 0.00001f) { // Same angles, remove vertex n1.Value.Remove(); } // Next! n1 = n2; } // Go for all vertices to determine reflex or convex foreach (EarClipVertex vv in verts) { // Add to reflex or convex list if (IsReflex(GetTriangle(vv))) { vv.AddReflex(reflexes); } else { convexes.Add(vv); } } // Go for all convex vertices to see if they are ear tips foreach (EarClipVertex cv in convexes) { // Add when this is a valid ear t = GetTriangle(cv); if (CheckValidEar(t, reflexes)) { cv.AddEarTip(eartips); } } #if DEBUG if (OnShowPolygon != null) { OnShowPolygon(verts); } #endif // Process ears until done while ((eartips.Count > 0) && (verts.Count > 2)) { // Get next ear v = eartips.First.Value; t = GetTriangle(v); // Only save this triangle when it has an area if (TriangleHasArea(t)) { // Add ear as triangle AddTriangleToList(t, verticeslist, sidedefslist, (verts.Count == 3)); countvertices += 3; } // Remove this ear from all lists v.Remove(); v1 = t[0]; v2 = t[2]; #if DEBUG if (TriangleHasArea(t)) { if (OnShowEarClip != null) { OnShowEarClip(t, verts); } } #endif // Test first neighbour t1 = GetTriangle(v1); if (IsReflex(t1)) { // List as reflex if not listed yet if (!v1.IsReflex) { v1.AddReflex(reflexes); } v1.RemoveEarTip(); } else { // Remove from reflexes v1.RemoveReflex(); } // Test second neighbour t2 = GetTriangle(v2); if (IsReflex(t2)) { // List as reflex if not listed yet if (!v2.IsReflex) { v2.AddReflex(reflexes); } v2.RemoveEarTip(); } else { // Remove from reflexes v2.RemoveReflex(); } // Check if any neightbour have become a valid or invalid ear if (!v1.IsReflex && (CheckValidEar(t1, reflexes))) { v1.AddEarTip(eartips); } else { v1.RemoveEarTip(); } if (!v2.IsReflex && (CheckValidEar(t2, reflexes))) { v2.AddEarTip(eartips); } else { v2.RemoveEarTip(); } } #if DEBUG if (OnShowRemaining != null) { OnShowRemaining(verts); } #endif // Dispose remaining vertices foreach (EarClipVertex ecv in verts) { ecv.Dispose(); } // Return the number of vertices in the result return(countvertices); }
// This checks if a line is inside a triangle (touching the triangle is allowed) // NOTE: We already know p1 is on an edge segment of the triangle private static bool LineInsideTriangle(EarClipVertex[] t, Vector2D p1, Vector2D p2) { float s01 = Line2D.GetSideOfLine(t[0].Position, t[1].Position, p2); float s12 = Line2D.GetSideOfLine(t[1].Position, t[2].Position, p2); float s20 = Line2D.GetSideOfLine(t[2].Position, t[0].Position, p2); float p2_on_edge = 2.0f; // somewhere outside the 0 .. 1 range float p1_on_same_edge = 2.0f; // Test if p2 is inside the triangle if ((s01 < 0.0f) && (s12 < 0.0f) && (s20 < 0.0f)) { // Line is inside triangle, because p2 is return(true); } // Test if p2 is on an edge of the triangle and if it is we would // like to know where on the edge segment p2 is if (s01 == 0.0f) { p2_on_edge = Line2D.GetNearestOnLine(t[0].Position, t[1].Position, p2); p1_on_same_edge = Line2D.GetSideOfLine(t[0].Position, t[1].Position, p1); } else if (s12 == 0.0f) { p2_on_edge = Line2D.GetNearestOnLine(t[1].Position, t[2].Position, p2); p1_on_same_edge = Line2D.GetSideOfLine(t[1].Position, t[2].Position, p1); } else if (s20 == 0.0f) { p2_on_edge = Line2D.GetNearestOnLine(t[2].Position, t[0].Position, p2); p1_on_same_edge = Line2D.GetSideOfLine(t[2].Position, t[0].Position, p1); } // Is p2 actually on the edge segment? if ((p2_on_edge >= 0.0f) && (p2_on_edge <= 1.0f)) { // If p1 is on the same edge (or the unlimited line of that edge) // then the line is not inside this triangle. if (p1_on_same_edge == 0.0f) { return(false); } } // Do a complete line-triangle intersection test // We already know p1 is not inside the triangle (possibly on an edge) Line2D p = new Line2D(p1, p2); Line2D t01 = new Line2D(t[0].Position, t[1].Position); Line2D t12 = new Line2D(t[1].Position, t[2].Position); Line2D t20 = new Line2D(t[2].Position, t[0].Position); float pu, pt; // Test intersections t01.GetIntersection(p, out pu, out pt); if (!float.IsNaN(pu) && (pu >= 0.0f) && (pu <= 1.0f) && (pt >= 0.0f) && (pt <= 1.0f)) { return(true); } t12.GetIntersection(p, out pu, out pt); if (!float.IsNaN(pu) && (pu >= 0.0f) && (pu <= 1.0f) && (pt >= 0.0f) && (pt <= 1.0f)) { return(true); } t20.GetIntersection(p, out pu, out pt); if (!float.IsNaN(pu) && (pu >= 0.0f) && (pu <= 1.0f) && (pt >= 0.0f) && (pt <= 1.0f)) { return(true); } return(false); }