private void CheckEdges(SubdivisionSearch search)
{
foreach (SubdivisionEdge edge in search.Source.Edges.Values)
{
var edgeElement = new SubdivisionElement(edge);
var twinElement = new SubdivisionElement(edge._twin);
// SubdivisionSearch always returns lexicographically increasing half-edges
PointD start = edge._origin, end = edge._twin._origin;
int result = PointDComparerX.CompareEpsilon(start, end, search.Source.Epsilon);
var element = (result < 0 ? edgeElement : twinElement);
PointD q = new PointD((start.X + end.X) / 2, (start.Y + end.Y) / 2);
Assert.AreEqual(element, search.Find(q));
// brute force search may return half-edge or its twin
var found = search.Source.Find(q, 1e-10);
Assert.IsTrue(found == edgeElement || found == twinElement);
// brute force search also supports comparison epsilon
PointD offset = GeoAlgorithms.RandomPoint(-0.1, -0.1, 0.2, 0.2);
found = search.Source.Find(q + offset, 0.25);
Assert.IsTrue(found == edgeElement || found == twinElement);
}
}
private void GeometryTest()
{
Stopwatch timer = new Stopwatch();
var testCases = _geometryTestCases;
Output(String.Format("{0,6}", " "));
foreach (TestCase test in testCases)
{
Output(String.Format("{0,12}", test.Name));
}
Output("\n");
const int outerLoop = 100, innerLoop = 100;
const int iterations = outerLoop * innerLoop;
for (int size = 10; size <= 120; size += 10)
{
PointD[] points = new PointD[size];
for (int i = 0; i < outerLoop; i++)
{
for (int j = 0; j < points.Length; j++)
{
points[j] = GeoAlgorithms.RandomPoint(0, 0, 1000, 1000);
}
foreach (TestCase test in testCases)
{
// trigger JIT compilation and reset ticks
if (i == 0)
{
test.FindPoints(points);
test.Ticks = 0;
}
timer.Restart();
for (int k = 0; k < innerLoop; k++)
{
test.FindPoints(points);
}
timer.Stop();
test.Ticks += timer.ElapsedTicks;
}
}
Output(String.Format("{0,6}", size));
foreach (TestCase test in testCases)
{
Output(String.Format("{0,12:N2}", AverageMicrosecs(test.Ticks, iterations)));
}
Output("\n");
}
Output("\nTimes are µsec averages for point sets of the indicated size.\n");
}
public void VoronoiTest()
{
int count = MersenneTwister.Default.Next(10, 100);
var points = new PointD[count];
for (int i = 0; i < points.Length; i++)
{
points[i] = GeoAlgorithms.RandomPoint(-1000, -1000, 2000, 2000);
}
var results = Voronoi.FindAll(points, new RectD(-1000, -1000, 2000, 2000));
var delaunay = results.ToDelaunySubdivision();
delaunay.Validate();
var voronoi = results.ToVoronoiSubdivision();
voronoi.Source.Validate();
// compare original and subdivision’s Delaunay edges
var delaunayEdges = delaunay.ToLines();
Assert.AreEqual(results.DelaunayEdges.Length, delaunayEdges.Length);
foreach (LineD edge in results.DelaunayEdges)
{
if (PointDComparerY.CompareExact(edge.Start, edge.End) > 0)
{
Assert.Contains(edge.Reverse(), delaunayEdges);
}
else
{
Assert.Contains(edge, delaunayEdges);
}
}
// compare original and subdivision’s Voronoi regions
var voronoiFaces = voronoi.Source.Faces;
Assert.AreEqual(results.VoronoiRegions.Length, voronoiFaces.Count - 1);
foreach (var face in voronoiFaces.Values)
{
if (face.OuterEdge == null)
{
continue;
}
int index = voronoi.FromFace(face);
PointD[] polygon = results.VoronoiRegions[index];
CollectionAssert.AreEquivalent(polygon, face.OuterEdge.CyclePolygon);
PointD site = results.GeneratorSites[index];
Assert.AreNotEqual(PolygonLocation.Outside, face.OuterEdge.Locate(site));
}
}
private void CheckVertices(SubdivisionSearch search)
{
foreach (PointD vertex in search.Source.Vertices.Keys)
{
var element = new SubdivisionElement(vertex);
Assert.AreEqual(element, search.Find(vertex));
Assert.AreEqual(element, search.Source.Find(vertex));
// brute force search also supports comparison epsilon
PointD offset = GeoAlgorithms.RandomPoint(-0.1, -0.1, 0.2, 0.2);
Assert.AreEqual(element, search.Source.Find(vertex + offset, 0.25));
}
}
public void Empty()
{
var search = new SubdivisionSearch(new Subdivision());
search.Validate();
for (int i = 0; i < 10; i++)
{
PointD q = GeoAlgorithms.RandomPoint(-100, -100, 200, 200);
Assert.IsTrue(search.Find(q).IsUnboundedFace);
Assert.IsTrue(search.Source.Find(q).IsUnboundedFace);
}
}
private static void CheckGridDivision(PolygonGrid.SubdivisionMap map)
{
map.Source.Validate();
// test finding vertices with FindNearestVertex
for (int i = 0; i < map.Source.Vertices.Count; i++)
{
PointD q = map.Source.Vertices.GetKey(i) + GeoAlgorithms.RandomPoint(-2, -2, 4, 4);
Assert.AreEqual(i, map.Source.FindNearestVertex(q));
}
// test GetElementVertices and face mapping
for (int x = 0; x < map.Target.Size.Width; x++)
{
for (int y = 0; y < map.Target.Size.Height; y++)
{
var polygon = map.Target.GetElementVertices(x, y);
var face = map.Source.FindFace(polygon, true);
Assert.AreSame(face, map.ToFace(new PointI(x, y)));
Assert.AreEqual(new PointI(x, y), map.FromFace(face));
}
}
}
private void RangeTreeTest()
{
Stopwatch timer = new Stopwatch();
var testCases = _rangeTreeTestCases;
Output(String.Format("{0,8}", " "));
foreach (TestCase test in testCases)
{
Output(String.Format("{0,14}", test.Name));
}
Output("\n");
// count units of size x operation in milliseconds,
// rather than individual operations in microseconds
const int outerLoop = 10, innerLoop = 10;
const int iterations = outerLoop * innerLoop * 1000;
// bounds of search space, size of point set,
// range & iterations for range search
const int bounds = 10000, size = 60000;
const int range = size / 80, rangeIterations = size / 120;
long[] addTicks = new long[testCases.Length],
iterateTicks = new long[testCases.Length],
searchTicks = new long[testCases.Length],
rangeTicks = new long[testCases.Length],
removeTicks = new long[testCases.Length];
var array = new KeyValuePair <PointD, String> [size];
for (int i = 0; i < outerLoop; i++)
{
// generate random spatial keys
for (int j = 0; j < array.Length; j++)
{
var key = GeoAlgorithms.RandomPoint(0, 0, bounds, bounds);
array[j] = new KeyValuePair <PointD, String>(key, null);
}
// trigger JIT compilation
if (i == 0)
{
foreach (TestCase test in testCases)
{
test.RangeTree.Clear();
foreach (var pair in array)
{
test.RangeTree.Add(pair.Key, pair.Value);
}
}
}
for (int j = 0; j < innerLoop; j++)
{
for (int k = 0; k < testCases.Length; k++)
{
TestCase test = testCases[k];
test.RangeTree.Clear();
timer.Restart();
foreach (var pair in array)
{
test.RangeTree.Add(pair.Key, pair.Value);
}
timer.Stop();
addTicks[k] += timer.ElapsedTicks;
double sum = 0;
timer.Restart();
foreach (var pair in test.RangeTree)
{
sum += pair.Key.X;
}
timer.Stop();
iterateTicks[k] += timer.ElapsedTicks;
timer.Restart();
foreach (var pair in array)
{
test.RangeTree.ContainsKey(pair.Key);
}
timer.Stop();
searchTicks[k] += timer.ElapsedTicks;
/*
* BraidedTree performs one-dimensional range searches within a point set
* sorted by y-coordinates, using PointDComparerY. Therefore, we supply a
* condition that limits x-coordinates.
*/
var braidedTree = test.RangeTree as BraidedTree <PointD, String>;
var quadTree = test.RangeTree as QuadTree <String>;
timer.Restart();
for (int l = 0; l < array.Length; l += size / rangeIterations)
{
PointD p = array[l].Key;
RectD rect = new RectD(p.X, p.Y, range, range);
if (braidedTree != null)
{
braidedTree.FindRange(rect.TopLeft, rect.BottomRight,
n => (n.Key.X >= rect.Left && n.Key.X <= rect.Right));
}
else if (quadTree != null)
{
quadTree.FindRange(rect);
}
}
timer.Stop();
rangeTicks[k] += timer.ElapsedTicks;
timer.Restart();
foreach (var pair in array)
{
test.RangeTree.Remove(pair.Key);
}
timer.Stop();
removeTicks[k] += timer.ElapsedTicks;
}
}
}
Output(String.Format("{0,8}", "Add"));
for (int i = 0; i < testCases.Length; i++)
{
Output(String.Format("{0,14:N2}", AverageMicrosecs(addTicks[i], iterations)));
}
Output(String.Format("\n{0,8}", "Iterate"));
for (int i = 0; i < testCases.Length; i++)
{
Output(String.Format("{0,14:N2}", AverageMicrosecs(iterateTicks[i], iterations)));
}
Output(String.Format("\n{0,8}", "Search"));
for (int i = 0; i < testCases.Length; i++)
{
Output(String.Format("{0,14:N2}", AverageMicrosecs(searchTicks[i], iterations)));
}
Output(String.Format("\n{0,8}", "Range"));
for (int i = 0; i < testCases.Length; i++)
{
Output(String.Format("{0,14:N2}", AverageMicrosecs(rangeTicks[i], iterations)));
}
Output(String.Format("\n{0,8}", "Remove"));
for (int i = 0; i < testCases.Length; i++)
{
Output(String.Format("{0,14:N2}", AverageMicrosecs(removeTicks[i], iterations)));
}
const double share = range / (double)bounds;
Output(String.Format("\n\nTimes are msec averages for {0:N0} random points.\n", size));
Output(String.Format("Range search performs {0} iterations on {1:0.00%} of search space.\n",
rangeIterations, share * share));
}
private void NearestPointTest()
{
Stopwatch timer = new Stopwatch();
var testCases = _nearestPointTestCases;
Output(String.Format("{0,6}", " "));
foreach (TestCase test in testCases)
{
Output(String.Format("{0,12}", test.Name));
}
Output("\n");
const int outerLoop = 100, innerLoop = 100;
const int iterations = outerLoop * innerLoop;
var comparer = new PointDComparerY();
PointD[] query = new PointD[innerLoop];
for (int size = 1000; size <= 12000; size += 1000)
{
PointD[] points = new PointD[size];
for (int i = 0; i < points.Length; i++)
{
points[i] = GeoAlgorithms.RandomPoint(0, 0, 1000, 1000);
}
Array.Sort <PointD>(points, comparer);
// trigger JIT compilation and reset ticks
foreach (TestCase test in testCases)
{
test.FindPointIndex(comparer, points, PointD.Empty);
test.Ticks = 0;
}
for (int j = 0; j < outerLoop; j++)
{
for (int k = 0; k < query.Length; k++)
{
query[k] = GeoAlgorithms.RandomPoint(0, 0, 1000, 1000);
}
foreach (TestCase test in testCases)
{
timer.Restart();
for (int k = 0; k < query.Length; k++)
{
test.FindPointIndex(comparer, points, query[k]);
}
timer.Stop();
test.Ticks += timer.ElapsedTicks;
}
}
Output(String.Format("{0,6:N0}", size));
foreach (TestCase test in testCases)
{
Output(String.Format("{0,12:N2}", AverageMicrosecs(test.Ticks, iterations)));
}
Output("\n");
}
Output("\nTimes are µsec averages for point arrays of the indicated size.\n");
}
private void GeometryBasicTest()
{
Stopwatch timer = new Stopwatch();
long polyTicks = 0, polyEpsilonTicks = 0, lineTicks = 0, lineEpsilonTicks = 0;
const double epsilon = 1e-10;
const int outerLoop = 10000, innerLoop = 1000;
const int iterations = outerLoop * innerLoop;
for (int i = 0; i < outerLoop; i++)
{
PointD[] polygon = GeoAlgorithms.RandomPolygon(0, 0, 1000, 1000);
LineD line = GeoAlgorithms.RandomLine(0, 0, 1000, 1000);
LineD line2 = GeoAlgorithms.RandomLine(0, 0, 1000, 1000);
PointD q = GeoAlgorithms.RandomPoint(0, 0, 1000, 1000);
// trigger JIT compilation
if (i == 0)
{
GeoAlgorithms.PointInPolygon(q, polygon);
GeoAlgorithms.PointInPolygon(q, polygon, epsilon);
line.Intersect(line2);
line.Intersect(line2, epsilon);
}
timer.Restart();
for (int j = 0; j < innerLoop; j++)
{
line.Intersect(line2);
}
timer.Stop();
lineTicks += timer.ElapsedTicks;
timer.Restart();
for (int j = 0; j < innerLoop; j++)
{
line.Intersect(line2, epsilon);
}
timer.Stop();
lineEpsilonTicks += timer.ElapsedTicks;
timer.Restart();
for (int j = 0; j < innerLoop; j++)
{
GeoAlgorithms.PointInPolygon(q, polygon);
}
timer.Stop();
polyTicks += timer.ElapsedTicks;
timer.Restart();
for (int j = 0; j < innerLoop; j++)
{
GeoAlgorithms.PointInPolygon(q, polygon, epsilon);
}
timer.Stop();
polyEpsilonTicks += timer.ElapsedTicks;
}
Output(" ");
Output(String.Format("{0,12}", "Exact"));
Output(String.Format("{0,12}", "Epsilon"));
Output("\nLine Intersection ");
Output(String.Format("{0,12:N2}", 1000 * AverageMicrosecs(lineTicks, iterations)));
Output(String.Format("{0,12:N2}", 1000 * AverageMicrosecs(lineEpsilonTicks, iterations)));
Output("\nPoint in Polygon ");
Output(String.Format("{0,12:N2}", 1000 * AverageMicrosecs(polyTicks, iterations)));
Output(String.Format("{0,12:N2}", 1000 * AverageMicrosecs(polyEpsilonTicks, iterations)));
Output("\nTimes are nsec averages for exact and epsilon comparisons.\n");
Output("Point in Polygon uses random polygons with 3-60 vertices.\n");
}
private void SubdivisionSearchTest(bool random)
{
Stopwatch timer = new Stopwatch();
var testCases = _subdivSearchTestCases;
Output(String.Format("{0,6}", " "));
foreach (TestCase test in testCases)
{
Output(String.Format("{0,12}", test.Name));
}
Output("\n");
const int outerLoop = 100, innerLoop = 200;
const int iterations = outerLoop * innerLoop;
PointD[] query = new PointD[innerLoop];
PolygonGrid grid = null;
int sizeMin, sizeMax, sizeStep;
if (random)
{
sizeMin = 100; sizeMax = 1200; sizeStep = 100;
}
else
{
sizeMin = 6; sizeMax = 30; sizeStep = 2;
RegularPolygon polygon = new RegularPolygon(10, 4, PolygonOrientation.OnEdge);
grid = new PolygonGrid(polygon);
}
for (int size = sizeMin; size <= sizeMax; size += sizeStep)
{
Subdivision division;
if (random)
{
// create subdivision from random lines (few faces)
division = CreateSubdivision(size, 1e-10);
}
else
{
// create subdivision from grid of diamonds (many faces)
grid.Element = new RegularPolygon(900 / size, 4, PolygonOrientation.OnEdge);
grid.Size = new SizeI(size, size);
division = grid.ToSubdivision(PointD.Empty).Source;
}
var ordered = new SubdivisionSearch(division, true);
var randomized = new SubdivisionSearch(division, false);
// test cases: BruteForce, Ordered, Randomized
testCases[0].FindSubdivision = (q) => division.Find(q, division.Epsilon);
testCases[1].FindSubdivision = (q) => ordered.Find(q);
testCases[2].FindSubdivision = (q) => randomized.Find(q);
// trigger JIT compilation and reset ticks
foreach (TestCase test in testCases)
{
test.FindSubdivision(PointD.Empty);
test.Ticks = 0;
}
for (int j = 0; j < outerLoop; j++)
{
for (int k = 0; k < query.Length; k++)
{
query[k] = GeoAlgorithms.RandomPoint(0, 0, 1000, 1000);
}
foreach (TestCase test in testCases)
{
timer.Restart();
for (int k = 0; k < query.Length; k++)
{
test.FindSubdivision(query[k]);
}
timer.Stop();
test.Ticks += timer.ElapsedTicks;
}
}
Output(String.Format("{0,6:N0}", division.Edges.Count / 2));
foreach (TestCase test in testCases)
{
Output(String.Format("{0,12:N2}", AverageMicrosecs(test.Ticks, iterations)));
}
Output("\n");
}
Output("\nTimes are µsec averages for subdivisions of the indicated edge count,\n");
if (random)
{
Output("based on random line sets (few faces, completely random edges).\n");
}
else
{
Output("based on grids of squares (many faces, strictly ordered edges).\n");
}
}
