// -----------------------------------------------------------------------
// <copyright file="TriangleLocator.cs" company="">
// Original Triangle code by Jonathan Richard Shewchuk, http://www.cs.cmu.edu/~quake/triangle.html
// Triangle.NET code by Christian Woltering, http://triangle.codeplex.com/
// </copyright>
// -----------------------------------------------------------------------
namespace TriangleNet
{
using TriangleNet.Geometry;
using TriangleNet.Topology;
/// <summary>
/// Locate triangles in a mesh.
/// </summary>
/// <remarks>
/// WARNING: This routine is designed for convex triangulations, and will
/// not generally work after the holes and concavities have been carved.
///
/// Based on a paper by Ernst P. Mucke, Isaac Saias, and Binhai Zhu, "Fast
/// Randomized Point Location Without Preprocessing in Two- and Three-Dimensional
/// Delaunay Triangulations," Proceedings of the Twelfth Annual Symposium on
/// Computational Geometry, ACM, May 1996.
/// </remarks>
public class TriangleLocator
{
TriangleSampler sampler;
Mesh mesh;
IPredicates predicates;
// Pointer to a recently visited triangle. Improves point location if
// proximate vertices are inserted sequentially.
internal Otri recenttri;
public TriangleLocator(Mesh mesh)
: this(mesh, RobustPredicates.Default)
{
}
public TriangleLocator(Mesh mesh, IPredicates predicates)
{
this.mesh = mesh;
this.predicates = predicates;
sampler = new TriangleSampler(mesh);
}
/// <summary>
/// Suggest the given triangle as a starting triangle for point location.
/// </summary>
/// <param name="otri"></param>
public void Update(ref Otri otri)
{
otri.Copy(ref recenttri);
}
public void Reset()
{
sampler.Reset();
recenttri.tri = null; // No triangle has been visited yet.
}
/// <summary>
/// Find a triangle or edge containing a given point.
/// </summary>
/// <param name="searchpoint">The point to locate.</param>
/// <param name="searchtri">The triangle to start the search at.</param>
/// <param name="stopatsubsegment"> If 'stopatsubsegment' is set, the search
/// will stop if it tries to walk through a subsegment, and will return OUTSIDE.</param>
/// <returns>Location information.</returns>
/// <remarks>
/// Begins its search from 'searchtri'. It is important that 'searchtri'
/// be a handle with the property that 'searchpoint' is strictly to the left
/// of the edge denoted by 'searchtri', or is collinear with that edge and
/// does not intersect that edge. (In particular, 'searchpoint' should not
/// be the origin or destination of that edge.)
///
/// These conditions are imposed because preciselocate() is normally used in
/// one of two situations:
///
/// (1) To try to find the location to insert a new point. Normally, we
/// know an edge that the point is strictly to the left of. In the
/// incremental Delaunay algorithm, that edge is a bounding box edge.
/// In Ruppert's Delaunay refinement algorithm for quality meshing,
/// that edge is the shortest edge of the triangle whose circumcenter
/// is being inserted.
///
/// (2) To try to find an existing point. In this case, any edge on the
/// convex hull is a good starting edge. You must screen out the
/// possibility that the vertex sought is an endpoint of the starting
/// edge before you call preciselocate().
///
/// On completion, 'searchtri' is a triangle that contains 'searchpoint'.
///
/// This implementation differs from that given by Guibas and Stolfi. It
/// walks from triangle to triangle, crossing an edge only if 'searchpoint'
/// is on the other side of the line containing that edge. After entering
/// a triangle, there are two edges by which one can leave that triangle.
/// If both edges are valid ('searchpoint' is on the other side of both
/// edges), one of the two is chosen by drawing a line perpendicular to
/// the entry edge (whose endpoints are 'forg' and 'fdest') passing through
/// 'fapex'. Depending on which side of this perpendicular 'searchpoint'
/// falls on, an exit edge is chosen.
///
/// This implementation is empirically faster than the Guibas and Stolfi
/// point location routine (which I originally used), which tends to spiral
/// in toward its target.
///
/// Returns ONVERTEX if the point lies on an existing vertex. 'searchtri'
/// is a handle whose origin is the existing vertex.
///
/// Returns ONEDGE if the point lies on a mesh edge. 'searchtri' is a
/// handle whose primary edge is the edge on which the point lies.
///
/// Returns INTRIANGLE if the point lies strictly within a triangle.
/// 'searchtri' is a handle on the triangle that contains the point.
///
/// Returns OUTSIDE if the point lies outside the mesh. 'searchtri' is a
/// handle whose primary edge the point is to the right of. This might
/// occur when the circumcenter of a triangle falls just slightly outside
/// the mesh due to floating-point roundoff error. It also occurs when
/// seeking a hole or region point that a foolish user has placed outside
/// the mesh.
///
/// WARNING: This routine is designed for convex triangulations, and will
/// not generally work after the holes and concavities have been carved.
/// However, it can still be used to find the circumcenter of a triangle, as
/// long as the search is begun from the triangle in question.</remarks>
public LocateResult PreciseLocate(Point searchpoint, ref Otri searchtri,
bool stopatsubsegment)
{
Otri backtracktri = default(Otri);
Osub checkedge = default(Osub);
Vertex forg, fdest, fapex;
double orgorient, destorient;
bool moveleft;
// Where are we?
forg = searchtri.Org();
fdest = searchtri.Dest();
fapex = searchtri.Apex();
while (true)
{
// Check whether the apex is the point we seek.
if ((fapex.x == searchpoint.x) && (fapex.y == searchpoint.y))
{
searchtri.Lprev();
return LocateResult.OnVertex;
}
// Does the point lie on the other side of the line defined by the
// triangle edge opposite the triangle's destination?
destorient = predicates.CounterClockwise(forg, fapex, searchpoint);
// Does the point lie on the other side of the line defined by the
// triangle edge opposite the triangle's origin?
orgorient = predicates.CounterClockwise(fapex, fdest, searchpoint);
if (destorient > 0.0)
{
if (orgorient > 0.0)
{
// Move left if the inner product of (fapex - searchpoint) and
// (fdest - forg) is positive. This is equivalent to drawing
// a line perpendicular to the line (forg, fdest) and passing
// through 'fapex', and determining which side of this line
// 'searchpoint' falls on.
moveleft = (fapex.x - searchpoint.x) * (fdest.x - forg.x) +
(fapex.y - searchpoint.y) * (fdest.y - forg.y) > 0.0;
}
else
{
moveleft = true;
}
}
else
{
if (orgorient > 0.0)
{
moveleft = false;
}
else
{
// The point we seek must be on the boundary of or inside this
// triangle.
if (destorient == 0.0)
{
searchtri.Lprev();
return LocateResult.OnEdge;
}
if (orgorient == 0.0)
{
searchtri.Lnext();
return LocateResult.OnEdge;
}
return LocateResult.InTriangle;
}
}
// Move to another triangle. Leave a trace 'backtracktri' in case
// floating-point roundoff or some such bogey causes us to walk
// off a boundary of the triangulation.
if (moveleft)
{
searchtri.Lprev(ref backtracktri);
fdest = fapex;
}
else
{
searchtri.Lnext(ref backtracktri);
forg = fapex;
}
backtracktri.Sym(ref searchtri);
if (mesh.checksegments && stopatsubsegment)
{
// Check for walking through a subsegment.
backtracktri.Pivot(ref checkedge);
if (checkedge.seg.hash != Mesh.DUMMY)
{
// Go back to the last triangle.
backtracktri.Copy(ref searchtri);
return LocateResult.Outside;
}
}
// Check for walking right out of the triangulation.
if (searchtri.tri.id == Mesh.DUMMY)
{
// Go back to the last triangle.
backtracktri.Copy(ref searchtri);
return LocateResult.Outside;
}
fapex = searchtri.Apex();
}
}
/// <summary>
/// Find a triangle or edge containing a given point.
/// </summary>
/// <param name="searchpoint">The point to locate.</param>
/// <param name="searchtri">The triangle to start the search at.</param>
/// <returns>Location information.</returns>
/// <remarks>
/// Searching begins from one of: the input 'searchtri', a recently
/// encountered triangle 'recenttri', or from a triangle chosen from a
/// random sample. The choice is made by determining which triangle's
/// origin is closest to the point we are searching for. Normally,
/// 'searchtri' should be a handle on the convex hull of the triangulation.
///
/// Details on the random sampling method can be found in the Mucke, Saias,
/// and Zhu paper cited in the header of this code.
///
/// On completion, 'searchtri' is a triangle that contains 'searchpoint'.
///
/// Returns ONVERTEX if the point lies on an existing vertex. 'searchtri'
/// is a handle whose origin is the existing vertex.
///
/// Returns ONEDGE if the point lies on a mesh edge. 'searchtri' is a
/// handle whose primary edge is the edge on which the point lies.
///
/// Returns INTRIANGLE if the point lies strictly within a triangle.
/// 'searchtri' is a handle on the triangle that contains the point.
///
/// Returns OUTSIDE if the point lies outside the mesh. 'searchtri' is a
/// handle whose primary edge the point is to the right of. This might
/// occur when the circumcenter of a triangle falls just slightly outside
/// the mesh due to floating-point roundoff error. It also occurs when
/// seeking a hole or region point that a foolish user has placed outside
/// the mesh.
///
/// WARNING: This routine is designed for convex triangulations, and will
/// not generally work after the holes and concavities have been carved.
/// </remarks>
public LocateResult Locate(Point searchpoint, ref Otri searchtri)
{
Otri sampletri = default(Otri);
Vertex torg, tdest;
double searchdist, dist;
double ahead;
// Record the distance from the suggested starting triangle to the
// point we seek.
torg = searchtri.Org();
searchdist = (searchpoint.x - torg.x) * (searchpoint.x - torg.x) +
(searchpoint.y - torg.y) * (searchpoint.y - torg.y);
// If a recently encountered triangle has been recorded and has not been
// deallocated, test it as a good starting point.
if (recenttri.tri != null)
{
if (!Otri.IsDead(recenttri.tri))
{
torg = recenttri.Org();
if ((torg.x == searchpoint.x) && (torg.y == searchpoint.y))
{
recenttri.Copy(ref searchtri);
return LocateResult.OnVertex;
}
dist = (searchpoint.x - torg.x) * (searchpoint.x - torg.x) +
(searchpoint.y - torg.y) * (searchpoint.y - torg.y);
if (dist < searchdist)
{
recenttri.Copy(ref searchtri);
searchdist = dist;
}
}
}
// TODO: Improve sampling.
sampler.Update();
foreach (var t in sampler)
{
sampletri.tri = t;
if (!Otri.IsDead(sampletri.tri))
{
torg = sampletri.Org();
dist = (searchpoint.x - torg.x) * (searchpoint.x - torg.x) +
(searchpoint.y - torg.y) * (searchpoint.y - torg.y);
if (dist < searchdist)
{
sampletri.Copy(ref searchtri);
searchdist = dist;
}
}
}
// Where are we?
torg = searchtri.Org();
tdest = searchtri.Dest();
// Check the starting triangle's vertices.
if ((torg.x == searchpoint.x) && (torg.y == searchpoint.y))
{
return LocateResult.OnVertex;
}
if ((tdest.x == searchpoint.x) && (tdest.y == searchpoint.y))
{
searchtri.Lnext();
return LocateResult.OnVertex;
}
// Orient 'searchtri' to fit the preconditions of calling preciselocate().
ahead = predicates.CounterClockwise(torg, tdest, searchpoint);
if (ahead < 0.0)
{
// Turn around so that 'searchpoint' is to the left of the
// edge specified by 'searchtri'.
searchtri.Sym();
}
else if (ahead == 0.0)
{
// Check if 'searchpoint' is between 'torg' and 'tdest'.
if (((torg.x < searchpoint.x) == (searchpoint.x < tdest.x)) &&
((torg.y < searchpoint.y) == (searchpoint.y < tdest.y)))
{
return LocateResult.OnEdge;
}
}
return PreciseLocate(searchpoint, ref searchtri, false);
}
}
}