/// <summary>
/// Verifies that all methods of the two S2Shapes return identical results,
/// except for id() and type_tag().
/// </summary>
public static void ExpectEqual(S2Shape a, S2Shape b)
{
Assert.True(a.NumEdges() == b.NumEdges());
for (int i = 0; i < a.NumEdges(); ++i)
{
Assert.Equal(a.GetEdge(i), b.GetEdge(i));
Assert.True(a.GetChainPosition(i) == b.GetChainPosition(i));
}
Assert.True(a.Dimension() == b.Dimension());
Assert.True(a.GetReferencePoint() == b.GetReferencePoint());
Assert.True(a.NumChains() == b.NumChains());
for (int i = 0; i < a.NumChains(); ++i)
{
Assert.True(a.GetChain(i) == b.GetChain(i));
int chain_length = a.GetChain(i).Length;
for (int j = 0; j < chain_length; ++j)
{
Assert.True(a.ChainEdge(i, j) == b.ChainEdge(i, j));
}
}
}
// Overwrites "vertices" with the vertices of the given edge chain of "shape".
// If dimension == 1, the chain will have (chain.length + 1) vertices, and
// otherwise it will have (chain.length) vertices.
//
// This is a low-level helper method used in the implementations of some of
// the methods above.
public static void GetChainVertices(S2Shape shape, int chain_id, out S2Point[] vertices)
{
S2Shape.Chain chain = shape.GetChain(chain_id);
int num_vertices = chain.Length + (shape.Dimension() == 1 ? 1 : 0);
int e = 0;
var verts = new List <S2Point>();
if ((num_vertices & 1) != 0)
{
verts.Add(shape.ChainEdge(chain_id, e++).V0);
}
for (; e < num_vertices; e += 2)
{
var edge = shape.ChainEdge(chain_id, e);
verts.Add(edge.V0);
verts.Add(edge.V1);
}
vertices = verts.ToArray();
}
// This is a helper function for implementing S2Shape.GetReferencePoint().
//
// Given a shape consisting of closed polygonal loops, the interior of the
// shape is defined as the region to the left of all edges (which must be
// oriented consistently). This function then chooses an arbitrary point and
// returns true if that point is contained by the shape.
//
// Unlike S2Loop and S2Polygon, this method allows duplicate vertices and
// edges, which requires some extra care with definitions. The rule that we
// apply is that an edge and its reverse edge "cancel" each other: the result
// is the same as if that edge pair were not present. Therefore shapes that
// consist only of degenerate loop(s) are either empty or full; by convention,
// the shape is considered full if and only if it contains an empty loop (see
// S2LaxPolygonShape for details).
//
// Determining whether a loop on the sphere contains a point is harder than
// the corresponding problem in 2D plane geometry. It cannot be implemented
// just by counting edge crossings because there is no such thing as a "point
// at infinity" that is guaranteed to be outside the loop.
public static S2Shape.ReferencePoint GetReferencePoint(this S2Shape shape)
{
System.Diagnostics.Debug.Assert(shape.Dimension() == 2);
if (shape.NumEdges() == 0)
{
// A shape with no edges is defined to be full if and only if it
// contains at least one chain.
return(S2Shape.ReferencePoint.FromContained(shape.NumChains() > 0));
}
// Define a "matched" edge as one that can be paired with a corresponding
// reversed edge. Define a vertex as "balanced" if all of its edges are
// matched. In order to determine containment, we must find an unbalanced
// vertex. Often every vertex is unbalanced, so we start by trying an
// arbitrary vertex.
var edge = shape.GetEdge(0);
if (GetReferencePointAtVertex(shape, edge.V0, out var result))
{
return(result);
}
// That didn't work, so now we do some extra work to find an unbalanced
// vertex (if any). Essentially we gather a list of edges and a list of
// reversed edges, and then sort them. The first edge that appears in one
// list but not the other is guaranteed to be unmatched.
int n = shape.NumEdges();
var edges = new S2Shape.Edge[n];
var rev_edges = new S2Shape.Edge[n];
for (int i = 0; i < n; ++i)
{
var edge2 = shape.GetEdge(i);
edges[i] = edge2;
rev_edges[i] = new S2Shape.Edge(edge2.V1, edge2.V0);
}
Array.Sort(edges);
Array.Sort(rev_edges);
for (int i = 0; i < n; ++i)
{
if (edges[i] < rev_edges[i])
{ // edges[i] is unmatched
System.Diagnostics.Debug.Assert(GetReferencePointAtVertex(shape, edges[i].V0, out result));
return(result);
}
if (rev_edges[i] < edges[i])
{ // rev_edges[i] is unmatched
System.Diagnostics.Debug.Assert(GetReferencePointAtVertex(shape, rev_edges[i].V0, out result));
return(result);
}
}
// All vertices are balanced, so this polygon is either empty or full except
// for degeneracies. By convention it is defined to be full if it contains
// any chain with no edges.
for (int i = 0; i < shape.NumChains(); ++i)
{
if (shape.GetChain(i).Length == 0)
{
return(S2Shape.ReferencePoint.FromContained(true));
}
}
return(S2Shape.ReferencePoint.FromContained(false));
}