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1242 lines
55 KiB
1242 lines
55 KiB
/* |
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** SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008) |
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** Copyright (C) 2011 Silicon Graphics, Inc. |
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** All Rights Reserved. |
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** |
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** Permission is hereby granted, free of charge, to any person obtaining a copy |
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** of this software and associated documentation files (the "Software"), to deal |
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** in the Software without restriction, including without limitation the rights |
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** to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies |
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** of the Software, and to permit persons to whom the Software is furnished to do so, |
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** subject to the following conditions: |
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** |
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** The above copyright notice including the dates of first publication and either this |
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** permission notice or a reference to http://oss.sgi.com/projects/FreeB/ shall be |
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** included in all copies or substantial portions of the Software. |
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** |
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** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, |
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** INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A |
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** PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL SILICON GRAPHICS, INC. |
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** BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, |
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** TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE |
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** OR OTHER DEALINGS IN THE SOFTWARE. |
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** |
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** Except as contained in this notice, the name of Silicon Graphics, Inc. shall not |
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** be used in advertising or otherwise to promote the sale, use or other dealings in |
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** this Software without prior written authorization from Silicon Graphics, Inc. |
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*/ |
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/* |
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** Original Author: Eric Veach, July 1994. |
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** libtess2: Mikko Mononen, http://code.google.com/p/libtess2/. |
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** LibTessDotNet: Remi Gillig, https://github.com/speps/LibTessDotNet |
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*/ |
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|
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using System; |
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using System.Diagnostics; |
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|
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namespace UnityEngine.Rendering.Universal |
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{ |
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using Real = System.Single; |
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namespace LibTessDotNet |
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{ |
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internal partial class Tess |
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{ |
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internal class ActiveRegion |
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{ |
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internal MeshUtils.Edge _eUp; |
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internal Dict<ActiveRegion>.Node _nodeUp; |
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internal int _windingNumber; |
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internal bool _inside, _sentinel, _dirty, _fixUpperEdge; |
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} |
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|
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private ActiveRegion RegionBelow(ActiveRegion reg) |
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{ |
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return reg._nodeUp._prev._key; |
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} |
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|
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private ActiveRegion RegionAbove(ActiveRegion reg) |
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{ |
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return reg._nodeUp._next._key; |
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} |
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|
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/// <summary> |
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/// Both edges must be directed from right to left (this is the canonical |
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/// direction for the upper edge of each region). |
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/// |
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/// The strategy is to evaluate a "t" value for each edge at the |
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/// current sweep line position, given by tess->event. The calculations |
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/// are designed to be very stable, but of course they are not perfect. |
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/// |
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/// Special case: if both edge destinations are at the sweep event, |
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/// we sort the edges by slope (they would otherwise compare equally). |
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/// </summary> |
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private bool EdgeLeq(ActiveRegion reg1, ActiveRegion reg2) |
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{ |
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var e1 = reg1._eUp; |
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var e2 = reg2._eUp; |
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|
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if (e1._Dst == _event) |
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{ |
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if (e2._Dst == _event) |
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{ |
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// Two edges right of the sweep line which meet at the sweep event. |
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// Sort them by slope. |
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if (Geom.VertLeq(e1._Org, e2._Org)) |
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{ |
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return Geom.EdgeSign(e2._Dst, e1._Org, e2._Org) <= 0.0f; |
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} |
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return Geom.EdgeSign(e1._Dst, e2._Org, e1._Org) >= 0.0f; |
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} |
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return Geom.EdgeSign(e2._Dst, _event, e2._Org) <= 0.0f; |
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} |
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if (e2._Dst == _event) |
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{ |
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return Geom.EdgeSign(e1._Dst, _event, e1._Org) >= 0.0f; |
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} |
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|
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// General case - compute signed distance *from* e1, e2 to event |
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var t1 = Geom.EdgeEval(e1._Dst, _event, e1._Org); |
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var t2 = Geom.EdgeEval(e2._Dst, _event, e2._Org); |
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return (t1 >= t2); |
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} |
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|
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private void DeleteRegion(ActiveRegion reg) |
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{ |
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if (reg._fixUpperEdge) |
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{ |
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// It was created with zero winding number, so it better be |
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// deleted with zero winding number (ie. it better not get merged |
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// with a real edge). |
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Debug.Assert(reg._eUp._winding == 0); |
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} |
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reg._eUp._activeRegion = null; |
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_dict.Remove(reg._nodeUp); |
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} |
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|
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/// <summary> |
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/// Replace an upper edge which needs fixing (see ConnectRightVertex). |
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/// </summary> |
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private void FixUpperEdge(ActiveRegion reg, MeshUtils.Edge newEdge) |
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{ |
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Debug.Assert(reg._fixUpperEdge); |
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_mesh.Delete(reg._eUp); |
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reg._fixUpperEdge = false; |
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reg._eUp = newEdge; |
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newEdge._activeRegion = reg; |
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} |
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|
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private ActiveRegion TopLeftRegion(ActiveRegion reg) |
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{ |
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var org = reg._eUp._Org; |
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|
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// Find the region above the uppermost edge with the same origin |
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do |
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{ |
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reg = RegionAbove(reg); |
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} |
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while (reg._eUp._Org == org); |
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|
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// If the edge above was a temporary edge introduced by ConnectRightVertex, |
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// now is the time to fix it. |
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if (reg._fixUpperEdge) |
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{ |
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var e = _mesh.Connect(RegionBelow(reg)._eUp._Sym, reg._eUp._Lnext); |
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FixUpperEdge(reg, e); |
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reg = RegionAbove(reg); |
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} |
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return reg; |
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} |
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private ActiveRegion TopRightRegion(ActiveRegion reg) |
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{ |
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var dst = reg._eUp._Dst; |
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|
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// Find the region above the uppermost edge with the same destination |
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do |
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{ |
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reg = RegionAbove(reg); |
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} |
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while (reg._eUp._Dst == dst); |
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|
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return reg; |
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} |
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/// <summary> |
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/// Add a new active region to the sweep line, *somewhere* below "regAbove" |
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/// (according to where the new edge belongs in the sweep-line dictionary). |
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/// The upper edge of the new region will be "eNewUp". |
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/// Winding number and "inside" flag are not updated. |
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/// </summary> |
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private ActiveRegion AddRegionBelow(ActiveRegion regAbove, MeshUtils.Edge eNewUp) |
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{ |
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var regNew = new ActiveRegion(); |
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|
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regNew._eUp = eNewUp; |
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regNew._nodeUp = _dict.InsertBefore(regAbove._nodeUp, regNew); |
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regNew._fixUpperEdge = false; |
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regNew._sentinel = false; |
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regNew._dirty = false; |
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eNewUp._activeRegion = regNew; |
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return regNew; |
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} |
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private void ComputeWinding(ActiveRegion reg) |
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{ |
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reg._windingNumber = RegionAbove(reg)._windingNumber + reg._eUp._winding; |
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reg._inside = Geom.IsWindingInside(_windingRule, reg._windingNumber); |
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} |
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|
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/// <summary> |
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/// Delete a region from the sweep line. This happens when the upper |
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/// and lower chains of a region meet (at a vertex on the sweep line). |
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/// The "inside" flag is copied to the appropriate mesh face (we could |
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/// not do this before -- since the structure of the mesh is always |
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/// changing, this face may not have even existed until now). |
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/// </summary> |
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private void FinishRegion(ActiveRegion reg) |
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{ |
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var e = reg._eUp; |
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var f = e._Lface; |
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|
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f._inside = reg._inside; |
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f._anEdge = e; |
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DeleteRegion(reg); |
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} |
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|
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/// <summary> |
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/// We are given a vertex with one or more left-going edges. All affected |
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/// edges should be in the edge dictionary. Starting at regFirst->eUp, |
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/// we walk down deleting all regions where both edges have the same |
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/// origin vOrg. At the same time we copy the "inside" flag from the |
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/// active region to the face, since at this point each face will belong |
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/// to at most one region (this was not necessarily true until this point |
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/// in the sweep). The walk stops at the region above regLast; if regLast |
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/// is null we walk as far as possible. At the same time we relink the |
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/// mesh if necessary, so that the ordering of edges around vOrg is the |
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/// same as in the dictionary. |
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/// </summary> |
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private MeshUtils.Edge FinishLeftRegions(ActiveRegion regFirst, ActiveRegion regLast) |
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{ |
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var regPrev = regFirst; |
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var ePrev = regFirst._eUp; |
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|
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while (regPrev != regLast) |
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{ |
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regPrev._fixUpperEdge = false; // placement was OK |
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var reg = RegionBelow(regPrev); |
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var e = reg._eUp; |
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if (e._Org != ePrev._Org) |
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{ |
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if (!reg._fixUpperEdge) |
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{ |
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// Remove the last left-going edge. Even though there are no further |
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// edges in the dictionary with this origin, there may be further |
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// such edges in the mesh (if we are adding left edges to a vertex |
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// that has already been processed). Thus it is important to call |
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// FinishRegion rather than just DeleteRegion. |
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FinishRegion(regPrev); |
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break; |
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} |
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// If the edge below was a temporary edge introduced by |
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// ConnectRightVertex, now is the time to fix it. |
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e = _mesh.Connect(ePrev._Lprev, e._Sym); |
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FixUpperEdge(reg, e); |
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} |
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|
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// Relink edges so that ePrev.Onext == e |
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if (ePrev._Onext != e) |
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{ |
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_mesh.Splice(e._Oprev, e); |
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_mesh.Splice(ePrev, e); |
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} |
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FinishRegion(regPrev); // may change reg.eUp |
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ePrev = reg._eUp; |
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regPrev = reg; |
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} |
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|
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return ePrev; |
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} |
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/// <summary> |
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/// Purpose: insert right-going edges into the edge dictionary, and update |
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/// winding numbers and mesh connectivity appropriately. All right-going |
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/// edges share a common origin vOrg. Edges are inserted CCW starting at |
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/// eFirst; the last edge inserted is eLast.Oprev. If vOrg has any |
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/// left-going edges already processed, then eTopLeft must be the edge |
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/// such that an imaginary upward vertical segment from vOrg would be |
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/// contained between eTopLeft.Oprev and eTopLeft; otherwise eTopLeft |
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/// should be null. |
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/// </summary> |
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private void AddRightEdges(ActiveRegion regUp, MeshUtils.Edge eFirst, MeshUtils.Edge eLast, MeshUtils.Edge eTopLeft, bool cleanUp) |
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{ |
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bool firstTime = true; |
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|
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var e = eFirst; do |
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{ |
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Debug.Assert(Geom.VertLeq(e._Org, e._Dst)); |
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AddRegionBelow(regUp, e._Sym); |
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e = e._Onext; |
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} |
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while (e != eLast); |
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|
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// Walk *all* right-going edges from e.Org, in the dictionary order, |
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// updating the winding numbers of each region, and re-linking the mesh |
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// edges to match the dictionary ordering (if necessary). |
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if (eTopLeft == null) |
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{ |
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eTopLeft = RegionBelow(regUp)._eUp._Rprev; |
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} |
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|
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ActiveRegion regPrev = regUp, reg; |
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var ePrev = eTopLeft; |
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while (true) |
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{ |
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reg = RegionBelow(regPrev); |
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e = reg._eUp._Sym; |
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if (e._Org != ePrev._Org) break; |
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|
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if (e._Onext != ePrev) |
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{ |
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// Unlink e from its current position, and relink below ePrev |
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_mesh.Splice(e._Oprev, e); |
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_mesh.Splice(ePrev._Oprev, e); |
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} |
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// Compute the winding number and "inside" flag for the new regions |
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reg._windingNumber = regPrev._windingNumber - e._winding; |
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reg._inside = Geom.IsWindingInside(_windingRule, reg._windingNumber); |
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|
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// Check for two outgoing edges with same slope -- process these |
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// before any intersection tests (see example in tessComputeInterior). |
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regPrev._dirty = true; |
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if (!firstTime && CheckForRightSplice(regPrev)) |
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{ |
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Geom.AddWinding(e, ePrev); |
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DeleteRegion(regPrev); |
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_mesh.Delete(ePrev); |
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} |
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firstTime = false; |
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regPrev = reg; |
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ePrev = e; |
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} |
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regPrev._dirty = true; |
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Debug.Assert(regPrev._windingNumber - e._winding == reg._windingNumber); |
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|
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if (cleanUp) |
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{ |
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// Check for intersections between newly adjacent edges. |
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WalkDirtyRegions(regPrev); |
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} |
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} |
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|
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/// <summary> |
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/// Two vertices with idential coordinates are combined into one. |
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/// e1.Org is kept, while e2.Org is discarded. |
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/// </summary> |
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private void SpliceMergeVertices(MeshUtils.Edge e1, MeshUtils.Edge e2) |
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{ |
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_mesh.Splice(e1, e2); |
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} |
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|
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/// <summary> |
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/// Find some weights which describe how the intersection vertex is |
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/// a linear combination of "org" and "dest". Each of the two edges |
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/// which generated "isect" is allocated 50% of the weight; each edge |
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/// splits the weight between its org and dst according to the |
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/// relative distance to "isect". |
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/// </summary> |
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private void VertexWeights(MeshUtils.Vertex isect, MeshUtils.Vertex org, MeshUtils.Vertex dst, out Real w0, out Real w1) |
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{ |
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var t1 = Geom.VertL1dist(org, isect); |
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var t2 = Geom.VertL1dist(dst, isect); |
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|
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w0 = (t2 / (t1 + t2)) / 2.0f; |
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w1 = (t1 / (t1 + t2)) / 2.0f; |
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|
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isect._coords.X += w0 * org._coords.X + w1 * dst._coords.X; |
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isect._coords.Y += w0 * org._coords.Y + w1 * dst._coords.Y; |
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isect._coords.Z += w0 * org._coords.Z + w1 * dst._coords.Z; |
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} |
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|
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/// <summary> |
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/// We've computed a new intersection point, now we need a "data" pointer |
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/// from the user so that we can refer to this new vertex in the |
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/// rendering callbacks. |
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/// </summary> |
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private void GetIntersectData(MeshUtils.Vertex isect, MeshUtils.Vertex orgUp, MeshUtils.Vertex dstUp, MeshUtils.Vertex orgLo, MeshUtils.Vertex dstLo) |
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{ |
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isect._coords = Vec3.Zero; |
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Real w0, w1, w2, w3; |
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VertexWeights(isect, orgUp, dstUp, out w0, out w1); |
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VertexWeights(isect, orgLo, dstLo, out w2, out w3); |
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|
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if (_combineCallback != null) |
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{ |
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isect._data = _combineCallback( |
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isect._coords, |
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new object[] { orgUp._data, dstUp._data, orgLo._data, dstLo._data }, |
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new Real[] { w0, w1, w2, w3 } |
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); |
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} |
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} |
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|
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/// <summary> |
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/// Check the upper and lower edge of "regUp", to make sure that the |
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/// eUp->Org is above eLo, or eLo->Org is below eUp (depending on which |
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/// origin is leftmost). |
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/// |
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/// The main purpose is to splice right-going edges with the same |
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/// dest vertex and nearly identical slopes (ie. we can't distinguish |
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/// the slopes numerically). However the splicing can also help us |
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/// to recover from numerical errors. For example, suppose at one |
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/// point we checked eUp and eLo, and decided that eUp->Org is barely |
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/// above eLo. Then later, we split eLo into two edges (eg. from |
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/// a splice operation like this one). This can change the result of |
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/// our test so that now eUp->Org is incident to eLo, or barely below it. |
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/// We must correct this condition to maintain the dictionary invariants. |
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/// |
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/// One possibility is to check these edges for intersection again |
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/// (ie. CheckForIntersect). This is what we do if possible. However |
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/// CheckForIntersect requires that tess->event lies between eUp and eLo, |
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/// so that it has something to fall back on when the intersection |
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/// calculation gives us an unusable answer. So, for those cases where |
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/// we can't check for intersection, this routine fixes the problem |
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/// by just splicing the offending vertex into the other edge. |
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/// This is a guaranteed solution, no matter how degenerate things get. |
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/// Basically this is a combinatorial solution to a numerical problem. |
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/// </summary> |
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private bool CheckForRightSplice(ActiveRegion regUp) |
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{ |
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var regLo = RegionBelow(regUp); |
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var eUp = regUp._eUp; |
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var eLo = regLo._eUp; |
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|
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if (Geom.VertLeq(eUp._Org, eLo._Org)) |
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{ |
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if (Geom.EdgeSign(eLo._Dst, eUp._Org, eLo._Org) > 0.0f) |
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{ |
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return false; |
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} |
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|
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// eUp.Org appears to be below eLo |
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if (!Geom.VertEq(eUp._Org, eLo._Org)) |
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{ |
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// Splice eUp._Org into eLo |
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_mesh.SplitEdge(eLo._Sym); |
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_mesh.Splice(eUp, eLo._Oprev); |
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regUp._dirty = regLo._dirty = true; |
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} |
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else if (eUp._Org != eLo._Org) |
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{ |
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// merge the two vertices, discarding eUp.Org |
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_pq.Remove(eUp._Org._pqHandle); |
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SpliceMergeVertices(eLo._Oprev, eUp); |
|
} |
|
} |
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else |
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{ |
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if (Geom.EdgeSign(eUp._Dst, eLo._Org, eUp._Org) < 0.0f) |
|
{ |
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return false; |
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} |
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|
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// eLo.Org appears to be above eUp, so splice eLo.Org into eUp |
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RegionAbove(regUp)._dirty = regUp._dirty = true; |
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_mesh.SplitEdge(eUp._Sym); |
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_mesh.Splice(eLo._Oprev, eUp); |
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} |
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return true; |
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} |
|
|
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/// <summary> |
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/// Check the upper and lower edge of "regUp", to make sure that the |
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/// eUp->Dst is above eLo, or eLo->Dst is below eUp (depending on which |
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/// destination is rightmost). |
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/// |
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/// Theoretically, this should always be true. However, splitting an edge |
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/// into two pieces can change the results of previous tests. For example, |
|
/// suppose at one point we checked eUp and eLo, and decided that eUp->Dst |
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/// is barely above eLo. Then later, we split eLo into two edges (eg. from |
|
/// a splice operation like this one). This can change the result of |
|
/// the test so that now eUp->Dst is incident to eLo, or barely below it. |
|
/// We must correct this condition to maintain the dictionary invariants |
|
/// (otherwise new edges might get inserted in the wrong place in the |
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/// dictionary, and bad stuff will happen). |
|
/// |
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/// We fix the problem by just splicing the offending vertex into the |
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/// other edge. |
|
/// </summary> |
|
private bool CheckForLeftSplice(ActiveRegion regUp) |
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{ |
|
var regLo = RegionBelow(regUp); |
|
var eUp = regUp._eUp; |
|
var eLo = regLo._eUp; |
|
|
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Debug.Assert(!Geom.VertEq(eUp._Dst, eLo._Dst)); |
|
|
|
if (Geom.VertLeq(eUp._Dst, eLo._Dst)) |
|
{ |
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if (Geom.EdgeSign(eUp._Dst, eLo._Dst, eUp._Org) < 0.0f) |
|
{ |
|
return false; |
|
} |
|
|
|
// eLo.Dst is above eUp, so splice eLo.Dst into eUp |
|
RegionAbove(regUp)._dirty = regUp._dirty = true; |
|
var e = _mesh.SplitEdge(eUp); |
|
_mesh.Splice(eLo._Sym, e); |
|
e._Lface._inside = regUp._inside; |
|
} |
|
else |
|
{ |
|
if (Geom.EdgeSign(eLo._Dst, eUp._Dst, eLo._Org) > 0.0f) |
|
{ |
|
return false; |
|
} |
|
|
|
// eUp.Dst is below eLo, so splice eUp.Dst into eLo |
|
regUp._dirty = regLo._dirty = true; |
|
var e = _mesh.SplitEdge(eLo); |
|
_mesh.Splice(eUp._Lnext, eLo._Sym); |
|
e._Rface._inside = regUp._inside; |
|
} |
|
return true; |
|
} |
|
|
|
/// <summary> |
|
/// Check the upper and lower edges of the given region to see if |
|
/// they intersect. If so, create the intersection and add it |
|
/// to the data structures. |
|
/// |
|
/// Returns TRUE if adding the new intersection resulted in a recursive |
|
/// call to AddRightEdges(); in this case all "dirty" regions have been |
|
/// checked for intersections, and possibly regUp has been deleted. |
|
/// </summary> |
|
private bool CheckForIntersect(ActiveRegion regUp) |
|
{ |
|
var regLo = RegionBelow(regUp); |
|
var eUp = regUp._eUp; |
|
var eLo = regLo._eUp; |
|
var orgUp = eUp._Org; |
|
var orgLo = eLo._Org; |
|
var dstUp = eUp._Dst; |
|
var dstLo = eLo._Dst; |
|
|
|
Debug.Assert(!Geom.VertEq(dstLo, dstUp)); |
|
Debug.Assert(Geom.EdgeSign(dstUp, _event, orgUp) <= 0.0f); |
|
Debug.Assert(Geom.EdgeSign(dstLo, _event, orgLo) >= 0.0f); |
|
Debug.Assert(orgUp != _event && orgLo != _event); |
|
Debug.Assert(!regUp._fixUpperEdge && !regLo._fixUpperEdge); |
|
|
|
if (orgUp == orgLo) |
|
{ |
|
// right endpoints are the same |
|
return false; |
|
} |
|
|
|
var tMinUp = Math.Min(orgUp._t, dstUp._t); |
|
var tMaxLo = Math.Max(orgLo._t, dstLo._t); |
|
if (tMinUp > tMaxLo) |
|
{ |
|
// t ranges do not overlap |
|
return false; |
|
} |
|
|
|
if (Geom.VertLeq(orgUp, orgLo)) |
|
{ |
|
if (Geom.EdgeSign(dstLo, orgUp, orgLo) > 0.0f) |
|
{ |
|
return false; |
|
} |
|
} |
|
else |
|
{ |
|
if (Geom.EdgeSign(dstUp, orgLo, orgUp) < 0.0f) |
|
{ |
|
return false; |
|
} |
|
} |
|
|
|
// At this point the edges intersect, at least marginally |
|
|
|
var isect = MeshUtils.Vertex.Create(); |
|
Geom.EdgeIntersect(dstUp, orgUp, dstLo, orgLo, isect); |
|
// The following properties are guaranteed: |
|
Debug.Assert(Math.Min(orgUp._t, dstUp._t) <= isect._t); |
|
Debug.Assert(isect._t <= Math.Max(orgLo._t, dstLo._t)); |
|
Debug.Assert(Math.Min(dstLo._s, dstUp._s) <= isect._s); |
|
Debug.Assert(isect._s <= Math.Max(orgLo._s, orgUp._s)); |
|
|
|
if (Geom.VertLeq(isect, _event)) |
|
{ |
|
// The intersection point lies slightly to the left of the sweep line, |
|
// so move it until it''s slightly to the right of the sweep line. |
|
// (If we had perfect numerical precision, this would never happen |
|
// in the first place). The easiest and safest thing to do is |
|
// replace the intersection by tess._event. |
|
isect._s = _event._s; |
|
isect._t = _event._t; |
|
} |
|
// Similarly, if the computed intersection lies to the right of the |
|
// rightmost origin (which should rarely happen), it can cause |
|
// unbelievable inefficiency on sufficiently degenerate inputs. |
|
// (If you have the test program, try running test54.d with the |
|
// "X zoom" option turned on). |
|
var orgMin = Geom.VertLeq(orgUp, orgLo) ? orgUp : orgLo; |
|
if (Geom.VertLeq(orgMin, isect)) |
|
{ |
|
isect._s = orgMin._s; |
|
isect._t = orgMin._t; |
|
} |
|
|
|
if (Geom.VertEq(isect, orgUp) || Geom.VertEq(isect, orgLo)) |
|
{ |
|
// Easy case -- intersection at one of the right endpoints |
|
CheckForRightSplice(regUp); |
|
return false; |
|
} |
|
|
|
if ((!Geom.VertEq(dstUp, _event) |
|
&& Geom.EdgeSign(dstUp, _event, isect) >= 0.0f) |
|
|| (!Geom.VertEq(dstLo, _event) |
|
&& Geom.EdgeSign(dstLo, _event, isect) <= 0.0f)) |
|
{ |
|
// Very unusual -- the new upper or lower edge would pass on the |
|
// wrong side of the sweep event, or through it. This can happen |
|
// due to very small numerical errors in the intersection calculation. |
|
if (dstLo == _event) |
|
{ |
|
// Splice dstLo into eUp, and process the new region(s) |
|
_mesh.SplitEdge(eUp._Sym); |
|
_mesh.Splice(eLo._Sym, eUp); |
|
regUp = TopLeftRegion(regUp); |
|
eUp = RegionBelow(regUp)._eUp; |
|
FinishLeftRegions(RegionBelow(regUp), regLo); |
|
AddRightEdges(regUp, eUp._Oprev, eUp, eUp, true); |
|
return true; |
|
} |
|
if (dstUp == _event) |
|
{ |
|
/* Splice dstUp into eLo, and process the new region(s) */ |
|
_mesh.SplitEdge(eLo._Sym); |
|
_mesh.Splice(eUp._Lnext, eLo._Oprev); |
|
regLo = regUp; |
|
regUp = TopRightRegion(regUp); |
|
var e = RegionBelow(regUp)._eUp._Rprev; |
|
regLo._eUp = eLo._Oprev; |
|
eLo = FinishLeftRegions(regLo, null); |
|
AddRightEdges(regUp, eLo._Onext, eUp._Rprev, e, true); |
|
return true; |
|
} |
|
// Special case: called from ConnectRightVertex. If either |
|
// edge passes on the wrong side of tess._event, split it |
|
// (and wait for ConnectRightVertex to splice it appropriately). |
|
if (Geom.EdgeSign(dstUp, _event, isect) >= 0.0f) |
|
{ |
|
RegionAbove(regUp)._dirty = regUp._dirty = true; |
|
_mesh.SplitEdge(eUp._Sym); |
|
eUp._Org._s = _event._s; |
|
eUp._Org._t = _event._t; |
|
} |
|
if (Geom.EdgeSign(dstLo, _event, isect) <= 0.0f) |
|
{ |
|
regUp._dirty = regLo._dirty = true; |
|
_mesh.SplitEdge(eLo._Sym); |
|
eLo._Org._s = _event._s; |
|
eLo._Org._t = _event._t; |
|
} |
|
// leave the rest for ConnectRightVertex |
|
return false; |
|
} |
|
|
|
// General case -- split both edges, splice into new vertex. |
|
// When we do the splice operation, the order of the arguments is |
|
// arbitrary as far as correctness goes. However, when the operation |
|
// creates a new face, the work done is proportional to the size of |
|
// the new face. We expect the faces in the processed part of |
|
// the mesh (ie. eUp._Lface) to be smaller than the faces in the |
|
// unprocessed original contours (which will be eLo._Oprev._Lface). |
|
_mesh.SplitEdge(eUp._Sym); |
|
_mesh.SplitEdge(eLo._Sym); |
|
_mesh.Splice(eLo._Oprev, eUp); |
|
eUp._Org._s = isect._s; |
|
eUp._Org._t = isect._t; |
|
eUp._Org._pqHandle = _pq.Insert(eUp._Org); |
|
if (eUp._Org._pqHandle._handle == PQHandle.Invalid) |
|
{ |
|
throw new InvalidOperationException("PQHandle should not be invalid"); |
|
} |
|
GetIntersectData(eUp._Org, orgUp, dstUp, orgLo, dstLo); |
|
RegionAbove(regUp)._dirty = regUp._dirty = regLo._dirty = true; |
|
return false; |
|
} |
|
|
|
/// <summary> |
|
/// When the upper or lower edge of any region changes, the region is |
|
/// marked "dirty". This routine walks through all the dirty regions |
|
/// and makes sure that the dictionary invariants are satisfied |
|
/// (see the comments at the beginning of this file). Of course |
|
/// new dirty regions can be created as we make changes to restore |
|
/// the invariants. |
|
/// </summary> |
|
private void WalkDirtyRegions(ActiveRegion regUp) |
|
{ |
|
var regLo = RegionBelow(regUp); |
|
MeshUtils.Edge eUp, eLo; |
|
|
|
while (true) |
|
{ |
|
// Find the lowest dirty region (we walk from the bottom up). |
|
while (regLo._dirty) |
|
{ |
|
regUp = regLo; |
|
regLo = RegionBelow(regLo); |
|
} |
|
if (!regUp._dirty) |
|
{ |
|
regLo = regUp; |
|
regUp = RegionAbove(regUp); |
|
if (regUp == null || !regUp._dirty) |
|
{ |
|
// We've walked all the dirty regions |
|
return; |
|
} |
|
} |
|
regUp._dirty = false; |
|
eUp = regUp._eUp; |
|
eLo = regLo._eUp; |
|
|
|
if (eUp._Dst != eLo._Dst) |
|
{ |
|
// Check that the edge ordering is obeyed at the Dst vertices. |
|
if (CheckForLeftSplice(regUp)) |
|
{ |
|
// If the upper or lower edge was marked fixUpperEdge, then |
|
// we no longer need it (since these edges are needed only for |
|
// vertices which otherwise have no right-going edges). |
|
if (regLo._fixUpperEdge) |
|
{ |
|
DeleteRegion(regLo); |
|
_mesh.Delete(eLo); |
|
regLo = RegionBelow(regUp); |
|
eLo = regLo._eUp; |
|
} |
|
else if (regUp._fixUpperEdge) |
|
{ |
|
DeleteRegion(regUp); |
|
_mesh.Delete(eUp); |
|
regUp = RegionAbove(regLo); |
|
eUp = regUp._eUp; |
|
} |
|
} |
|
} |
|
if (eUp._Org != eLo._Org) |
|
{ |
|
if (eUp._Dst != eLo._Dst |
|
&& !regUp._fixUpperEdge && !regLo._fixUpperEdge |
|
&& (eUp._Dst == _event || eLo._Dst == _event)) |
|
{ |
|
// When all else fails in CheckForIntersect(), it uses tess._event |
|
// as the intersection location. To make this possible, it requires |
|
// that tess._event lie between the upper and lower edges, and also |
|
// that neither of these is marked fixUpperEdge (since in the worst |
|
// case it might splice one of these edges into tess.event, and |
|
// violate the invariant that fixable edges are the only right-going |
|
// edge from their associated vertex). |
|
if (CheckForIntersect(regUp)) |
|
{ |
|
// WalkDirtyRegions() was called recursively; we're done |
|
return; |
|
} |
|
} |
|
else |
|
{ |
|
// Even though we can't use CheckForIntersect(), the Org vertices |
|
// may violate the dictionary edge ordering. Check and correct this. |
|
CheckForRightSplice(regUp); |
|
} |
|
} |
|
if (eUp._Org == eLo._Org && eUp._Dst == eLo._Dst) |
|
{ |
|
// A degenerate loop consisting of only two edges -- delete it. |
|
Geom.AddWinding(eLo, eUp); |
|
DeleteRegion(regUp); |
|
_mesh.Delete(eUp); |
|
regUp = RegionAbove(regLo); |
|
} |
|
} |
|
} |
|
|
|
/// <summary> |
|
/// Purpose: connect a "right" vertex vEvent (one where all edges go left) |
|
/// to the unprocessed portion of the mesh. Since there are no right-going |
|
/// edges, two regions (one above vEvent and one below) are being merged |
|
/// into one. "regUp" is the upper of these two regions. |
|
/// |
|
/// There are two reasons for doing this (adding a right-going edge): |
|
/// - if the two regions being merged are "inside", we must add an edge |
|
/// to keep them separated (the combined region would not be monotone). |
|
/// - in any case, we must leave some record of vEvent in the dictionary, |
|
/// so that we can merge vEvent with features that we have not seen yet. |
|
/// For example, maybe there is a vertical edge which passes just to |
|
/// the right of vEvent; we would like to splice vEvent into this edge. |
|
/// |
|
/// However, we don't want to connect vEvent to just any vertex. We don''t |
|
/// want the new edge to cross any other edges; otherwise we will create |
|
/// intersection vertices even when the input data had no self-intersections. |
|
/// (This is a bad thing; if the user's input data has no intersections, |
|
/// we don't want to generate any false intersections ourselves.) |
|
/// |
|
/// Our eventual goal is to connect vEvent to the leftmost unprocessed |
|
/// vertex of the combined region (the union of regUp and regLo). |
|
/// But because of unseen vertices with all right-going edges, and also |
|
/// new vertices which may be created by edge intersections, we don''t |
|
/// know where that leftmost unprocessed vertex is. In the meantime, we |
|
/// connect vEvent to the closest vertex of either chain, and mark the region |
|
/// as "fixUpperEdge". This flag says to delete and reconnect this edge |
|
/// to the next processed vertex on the boundary of the combined region. |
|
/// Quite possibly the vertex we connected to will turn out to be the |
|
/// closest one, in which case we won''t need to make any changes. |
|
/// </summary> |
|
private void ConnectRightVertex(ActiveRegion regUp, MeshUtils.Edge eBottomLeft) |
|
{ |
|
var eTopLeft = eBottomLeft._Onext; |
|
var regLo = RegionBelow(regUp); |
|
var eUp = regUp._eUp; |
|
var eLo = regLo._eUp; |
|
bool degenerate = false; |
|
|
|
if (eUp._Dst != eLo._Dst) |
|
{ |
|
CheckForIntersect(regUp); |
|
} |
|
|
|
// Possible new degeneracies: upper or lower edge of regUp may pass |
|
// through vEvent, or may coincide with new intersection vertex |
|
if (Geom.VertEq(eUp._Org, _event)) |
|
{ |
|
_mesh.Splice(eTopLeft._Oprev, eUp); |
|
regUp = TopLeftRegion(regUp); |
|
eTopLeft = RegionBelow(regUp)._eUp; |
|
FinishLeftRegions(RegionBelow(regUp), regLo); |
|
degenerate = true; |
|
} |
|
if (Geom.VertEq(eLo._Org, _event)) |
|
{ |
|
_mesh.Splice(eBottomLeft, eLo._Oprev); |
|
eBottomLeft = FinishLeftRegions(regLo, null); |
|
degenerate = true; |
|
} |
|
if (degenerate) |
|
{ |
|
AddRightEdges(regUp, eBottomLeft._Onext, eTopLeft, eTopLeft, true); |
|
return; |
|
} |
|
|
|
// Non-degenerate situation -- need to add a temporary, fixable edge. |
|
// Connect to the closer of eLo.Org, eUp.Org. |
|
MeshUtils.Edge eNew; |
|
if (Geom.VertLeq(eLo._Org, eUp._Org)) |
|
{ |
|
eNew = eLo._Oprev; |
|
} |
|
else |
|
{ |
|
eNew = eUp; |
|
} |
|
eNew = _mesh.Connect(eBottomLeft._Lprev, eNew); |
|
|
|
// Prevent cleanup, otherwise eNew might disappear before we've even |
|
// had a chance to mark it as a temporary edge. |
|
AddRightEdges(regUp, eNew, eNew._Onext, eNew._Onext, false); |
|
eNew._Sym._activeRegion._fixUpperEdge = true; |
|
WalkDirtyRegions(regUp); |
|
} |
|
|
|
/// <summary> |
|
/// The event vertex lies exacty on an already-processed edge or vertex. |
|
/// Adding the new vertex involves splicing it into the already-processed |
|
/// part of the mesh. |
|
/// </summary> |
|
private void ConnectLeftDegenerate(ActiveRegion regUp, MeshUtils.Vertex vEvent) |
|
{ |
|
var e = regUp._eUp; |
|
if (Geom.VertEq(e._Org, vEvent)) |
|
{ |
|
// e.Org is an unprocessed vertex - just combine them, and wait |
|
// for e.Org to be pulled from the queue |
|
// C# : in the C version, there is a flag but it was never implemented |
|
// the vertices are before beginning the tessellation |
|
throw new InvalidOperationException("Vertices should have been merged before"); |
|
} |
|
|
|
if (!Geom.VertEq(e._Dst, vEvent)) |
|
{ |
|
// General case -- splice vEvent into edge e which passes through it |
|
_mesh.SplitEdge(e._Sym); |
|
if (regUp._fixUpperEdge) |
|
{ |
|
// This edge was fixable -- delete unused portion of original edge |
|
_mesh.Delete(e._Onext); |
|
regUp._fixUpperEdge = false; |
|
} |
|
_mesh.Splice(vEvent._anEdge, e); |
|
SweepEvent(vEvent); // recurse |
|
return; |
|
} |
|
|
|
// See above |
|
throw new InvalidOperationException("Vertices should have been merged before"); |
|
} |
|
|
|
/// <summary> |
|
/// Purpose: connect a "left" vertex (one where both edges go right) |
|
/// to the processed portion of the mesh. Let R be the active region |
|
/// containing vEvent, and let U and L be the upper and lower edge |
|
/// chains of R. There are two possibilities: |
|
/// |
|
/// - the normal case: split R into two regions, by connecting vEvent to |
|
/// the rightmost vertex of U or L lying to the left of the sweep line |
|
/// |
|
/// - the degenerate case: if vEvent is close enough to U or L, we |
|
/// merge vEvent into that edge chain. The subcases are: |
|
/// - merging with the rightmost vertex of U or L |
|
/// - merging with the active edge of U or L |
|
/// - merging with an already-processed portion of U or L |
|
/// </summary> |
|
private void ConnectLeftVertex(MeshUtils.Vertex vEvent) |
|
{ |
|
var tmp = new ActiveRegion(); |
|
|
|
// Get a pointer to the active region containing vEvent |
|
tmp._eUp = vEvent._anEdge._Sym; |
|
var regUp = _dict.Find(tmp).Key; |
|
var regLo = RegionBelow(regUp); |
|
if (regLo == null) |
|
{ |
|
// This may happen if the input polygon is coplanar. |
|
return; |
|
} |
|
var eUp = regUp._eUp; |
|
var eLo = regLo._eUp; |
|
|
|
// Try merging with U or L first |
|
if (Geom.EdgeSign(eUp._Dst, vEvent, eUp._Org) == 0.0f) |
|
{ |
|
ConnectLeftDegenerate(regUp, vEvent); |
|
return; |
|
} |
|
|
|
// Connect vEvent to rightmost processed vertex of either chain. |
|
// e._Dst is the vertex that we will connect to vEvent. |
|
var reg = Geom.VertLeq(eLo._Dst, eUp._Dst) ? regUp : regLo; |
|
|
|
if (regUp._inside || reg._fixUpperEdge) |
|
{ |
|
MeshUtils.Edge eNew; |
|
if (reg == regUp) |
|
{ |
|
eNew = _mesh.Connect(vEvent._anEdge._Sym, eUp._Lnext); |
|
} |
|
else |
|
{ |
|
eNew = _mesh.Connect(eLo._Dnext, vEvent._anEdge)._Sym; |
|
} |
|
if (reg._fixUpperEdge) |
|
{ |
|
FixUpperEdge(reg, eNew); |
|
} |
|
else |
|
{ |
|
ComputeWinding(AddRegionBelow(regUp, eNew)); |
|
} |
|
SweepEvent(vEvent); |
|
} |
|
else |
|
{ |
|
// The new vertex is in a region which does not belong to the polygon. |
|
// We don't need to connect this vertex to the rest of the mesh. |
|
AddRightEdges(regUp, vEvent._anEdge, vEvent._anEdge, null, true); |
|
} |
|
} |
|
|
|
/// <summary> |
|
/// Does everything necessary when the sweep line crosses a vertex. |
|
/// Updates the mesh and the edge dictionary. |
|
/// </summary> |
|
private void SweepEvent(MeshUtils.Vertex vEvent) |
|
{ |
|
_event = vEvent; |
|
|
|
// Check if this vertex is the right endpoint of an edge that is |
|
// already in the dictionary. In this case we don't need to waste |
|
// time searching for the location to insert new edges. |
|
var e = vEvent._anEdge; |
|
while (e._activeRegion == null) |
|
{ |
|
e = e._Onext; |
|
if (e == vEvent._anEdge) |
|
{ |
|
// All edges go right -- not incident to any processed edges |
|
ConnectLeftVertex(vEvent); |
|
return; |
|
} |
|
} |
|
|
|
// Processing consists of two phases: first we "finish" all the |
|
// active regions where both the upper and lower edges terminate |
|
// at vEvent (ie. vEvent is closing off these regions). |
|
// We mark these faces "inside" or "outside" the polygon according |
|
// to their winding number, and delete the edges from the dictionary. |
|
// This takes care of all the left-going edges from vEvent. |
|
var regUp = TopLeftRegion(e._activeRegion); |
|
var reg = RegionBelow(regUp); |
|
var eTopLeft = reg._eUp; |
|
var eBottomLeft = FinishLeftRegions(reg, null); |
|
|
|
// Next we process all the right-going edges from vEvent. This |
|
// involves adding the edges to the dictionary, and creating the |
|
// associated "active regions" which record information about the |
|
// regions between adjacent dictionary edges. |
|
if (eBottomLeft._Onext == eTopLeft) |
|
{ |
|
// No right-going edges -- add a temporary "fixable" edge |
|
ConnectRightVertex(regUp, eBottomLeft); |
|
} |
|
else |
|
{ |
|
AddRightEdges(regUp, eBottomLeft._Onext, eTopLeft, eTopLeft, true); |
|
} |
|
} |
|
|
|
/// <summary> |
|
/// Make the sentinel coordinates big enough that they will never be |
|
/// merged with real input features. |
|
/// |
|
/// We add two sentinel edges above and below all other edges, |
|
/// to avoid special cases at the top and bottom. |
|
/// </summary> |
|
private void AddSentinel(Real smin, Real smax, Real t) |
|
{ |
|
var e = _mesh.MakeEdge(); |
|
e._Org._s = smax; |
|
e._Org._t = t; |
|
e._Dst._s = smin; |
|
e._Dst._t = t; |
|
_event = e._Dst; // initialize it |
|
|
|
var reg = new ActiveRegion(); |
|
reg._eUp = e; |
|
reg._windingNumber = 0; |
|
reg._inside = false; |
|
reg._fixUpperEdge = false; |
|
reg._sentinel = true; |
|
reg._dirty = false; |
|
reg._nodeUp = _dict.Insert(reg); |
|
} |
|
|
|
/// <summary> |
|
/// We maintain an ordering of edge intersections with the sweep line. |
|
/// This order is maintained in a dynamic dictionary. |
|
/// </summary> |
|
private void InitEdgeDict() |
|
{ |
|
_dict = new Dict<ActiveRegion>(EdgeLeq); |
|
|
|
AddSentinel(-SentinelCoord, SentinelCoord, -SentinelCoord); |
|
AddSentinel(-SentinelCoord, SentinelCoord, +SentinelCoord); |
|
} |
|
|
|
private void DoneEdgeDict() |
|
{ |
|
int fixedEdges = 0; |
|
|
|
ActiveRegion reg; |
|
while ((reg = _dict.Min().Key) != null) |
|
{ |
|
// At the end of all processing, the dictionary should contain |
|
// only the two sentinel edges, plus at most one "fixable" edge |
|
// created by ConnectRightVertex(). |
|
if (!reg._sentinel) |
|
{ |
|
Debug.Assert(reg._fixUpperEdge); |
|
Debug.Assert(++fixedEdges == 1); |
|
} |
|
Debug.Assert(reg._windingNumber == 0); |
|
DeleteRegion(reg); |
|
} |
|
|
|
_dict = null; |
|
} |
|
|
|
/// <summary> |
|
/// Remove zero-length edges, and contours with fewer than 3 vertices. |
|
/// </summary> |
|
private void RemoveDegenerateEdges() |
|
{ |
|
MeshUtils.Edge eHead = _mesh._eHead, e, eNext, eLnext; |
|
|
|
for (e = eHead._next; e != eHead; e = eNext) |
|
{ |
|
eNext = e._next; |
|
eLnext = e._Lnext; |
|
|
|
if (Geom.VertEq(e._Org, e._Dst) && e._Lnext._Lnext != e) |
|
{ |
|
// Zero-length edge, contour has at least 3 edges |
|
|
|
SpliceMergeVertices(eLnext, e); // deletes e.Org |
|
_mesh.Delete(e); // e is a self-loop |
|
e = eLnext; |
|
eLnext = e._Lnext; |
|
} |
|
if (eLnext._Lnext == e) |
|
{ |
|
// Degenerate contour (one or two edges) |
|
|
|
if (eLnext != e) |
|
{ |
|
if (eLnext == eNext || eLnext == eNext._Sym) |
|
{ |
|
eNext = eNext._next; |
|
} |
|
_mesh.Delete(eLnext); |
|
} |
|
if (e == eNext || e == eNext._Sym) |
|
{ |
|
eNext = eNext._next; |
|
} |
|
_mesh.Delete(e); |
|
} |
|
} |
|
} |
|
|
|
/// <summary> |
|
/// Insert all vertices into the priority queue which determines the |
|
/// order in which vertices cross the sweep line. |
|
/// </summary> |
|
private void InitPriorityQ() |
|
{ |
|
MeshUtils.Vertex vHead = _mesh._vHead, v; |
|
int vertexCount = 0; |
|
|
|
for (v = vHead._next; v != vHead; v = v._next) |
|
{ |
|
vertexCount++; |
|
} |
|
// Make sure there is enough space for sentinels. |
|
vertexCount += 8; |
|
|
|
_pq = new PriorityQueue<MeshUtils.Vertex>(vertexCount, Geom.VertLeq); |
|
|
|
vHead = _mesh._vHead; |
|
for (v = vHead._next; v != vHead; v = v._next) |
|
{ |
|
v._pqHandle = _pq.Insert(v); |
|
if (v._pqHandle._handle == PQHandle.Invalid) |
|
{ |
|
throw new InvalidOperationException("PQHandle should not be invalid"); |
|
} |
|
} |
|
_pq.Init(); |
|
} |
|
|
|
private void DonePriorityQ() |
|
{ |
|
_pq = null; |
|
} |
|
|
|
/// <summary> |
|
/// Delete any degenerate faces with only two edges. WalkDirtyRegions() |
|
/// will catch almost all of these, but it won't catch degenerate faces |
|
/// produced by splice operations on already-processed edges. |
|
/// The two places this can happen are in FinishLeftRegions(), when |
|
/// we splice in a "temporary" edge produced by ConnectRightVertex(), |
|
/// and in CheckForLeftSplice(), where we splice already-processed |
|
/// edges to ensure that our dictionary invariants are not violated |
|
/// by numerical errors. |
|
/// |
|
/// In both these cases it is *very* dangerous to delete the offending |
|
/// edge at the time, since one of the routines further up the stack |
|
/// will sometimes be keeping a pointer to that edge. |
|
/// </summary> |
|
private void RemoveDegenerateFaces() |
|
{ |
|
MeshUtils.Face f, fNext; |
|
MeshUtils.Edge e; |
|
|
|
for (f = _mesh._fHead._next; f != _mesh._fHead; f = fNext) |
|
{ |
|
fNext = f._next; |
|
e = f._anEdge; |
|
Debug.Assert(e._Lnext != e); |
|
|
|
if (e._Lnext._Lnext == e) |
|
{ |
|
// A face with only two edges |
|
Geom.AddWinding(e._Onext, e); |
|
_mesh.Delete(e); |
|
} |
|
} |
|
} |
|
|
|
/// <summary> |
|
/// ComputeInterior computes the planar arrangement specified |
|
/// by the given contours, and further subdivides this arrangement |
|
/// into regions. Each region is marked "inside" if it belongs |
|
/// to the polygon, according to the rule given by windingRule. |
|
/// Each interior region is guaranteed to be monotone. |
|
/// </summary> |
|
protected void ComputeInterior() |
|
{ |
|
// Each vertex defines an event for our sweep line. Start by inserting |
|
// all the vertices in a priority queue. Events are processed in |
|
// lexicographic order, ie. |
|
// |
|
// e1 < e2 iff e1.x < e2.x || (e1.x == e2.x && e1.y < e2.y) |
|
RemoveDegenerateEdges(); |
|
InitPriorityQ(); |
|
RemoveDegenerateFaces(); |
|
InitEdgeDict(); |
|
|
|
MeshUtils.Vertex v, vNext; |
|
while ((v = _pq.ExtractMin()) != null) |
|
{ |
|
while (true) |
|
{ |
|
vNext = _pq.Minimum(); |
|
if (vNext == null || !Geom.VertEq(vNext, v)) |
|
{ |
|
break; |
|
} |
|
|
|
// Merge together all vertices at exactly the same location. |
|
// This is more efficient than processing them one at a time, |
|
// simplifies the code (see ConnectLeftDegenerate), and is also |
|
// important for correct handling of certain degenerate cases. |
|
// For example, suppose there are two identical edges A and B |
|
// that belong to different contours (so without this code they would |
|
// be processed by separate sweep events). Suppose another edge C |
|
// crosses A and B from above. When A is processed, we split it |
|
// at its intersection point with C. However this also splits C, |
|
// so when we insert B we may compute a slightly different |
|
// intersection point. This might leave two edges with a small |
|
// gap between them. This kind of error is especially obvious |
|
// when using boundary extraction (BoundaryOnly). |
|
vNext = _pq.ExtractMin(); |
|
SpliceMergeVertices(v._anEdge, vNext._anEdge); |
|
} |
|
SweepEvent(v); |
|
} |
|
|
|
DoneEdgeDict(); |
|
DonePriorityQ(); |
|
|
|
RemoveDegenerateFaces(); |
|
_mesh.Check(); |
|
} |
|
} |
|
} |
|
}
|
|
|