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Diffstat (limited to 'vendor/github.com/golang/geo/s2/edge_crosser.go')
| -rw-r--r-- | vendor/github.com/golang/geo/s2/edge_crosser.go | 227 |
1 files changed, 227 insertions, 0 deletions
diff --git a/vendor/github.com/golang/geo/s2/edge_crosser.go b/vendor/github.com/golang/geo/s2/edge_crosser.go new file mode 100644 index 000000000..69c6da6b9 --- /dev/null +++ b/vendor/github.com/golang/geo/s2/edge_crosser.go @@ -0,0 +1,227 @@ +// Copyright 2017 Google Inc. All rights reserved. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package s2 + +import ( + "math" +) + +// EdgeCrosser allows edges to be efficiently tested for intersection with a +// given fixed edge AB. It is especially efficient when testing for +// intersection with an edge chain connecting vertices v0, v1, v2, ... +// +// Example usage: +// +// func CountIntersections(a, b Point, edges []Edge) int { +// count := 0 +// crosser := NewEdgeCrosser(a, b) +// for _, edge := range edges { +// if crosser.CrossingSign(&edge.First, &edge.Second) != DoNotCross { +// count++ +// } +// } +// return count +// } +// +type EdgeCrosser struct { + a Point + b Point + aXb Point + + // To reduce the number of calls to expensiveSign, we compute an + // outward-facing tangent at A and B if necessary. If the plane + // perpendicular to one of these tangents separates AB from CD (i.e., one + // edge on each side) then there is no intersection. + aTangent Point // Outward-facing tangent at A. + bTangent Point // Outward-facing tangent at B. + + // The fields below are updated for each vertex in the chain. + c Point // Previous vertex in the vertex chain. + acb Direction // The orientation of triangle ACB. +} + +// NewEdgeCrosser returns an EdgeCrosser with the fixed edge AB. +func NewEdgeCrosser(a, b Point) *EdgeCrosser { + norm := a.PointCross(b) + return &EdgeCrosser{ + a: a, + b: b, + aXb: Point{a.Cross(b.Vector)}, + aTangent: Point{a.Cross(norm.Vector)}, + bTangent: Point{norm.Cross(b.Vector)}, + } +} + +// CrossingSign reports whether the edge AB intersects the edge CD. If any two +// vertices from different edges are the same, returns MaybeCross. If either edge +// is degenerate (A == B or C == D), returns either DoNotCross or MaybeCross. +// +// Properties of CrossingSign: +// +// (1) CrossingSign(b,a,c,d) == CrossingSign(a,b,c,d) +// (2) CrossingSign(c,d,a,b) == CrossingSign(a,b,c,d) +// (3) CrossingSign(a,b,c,d) == MaybeCross if a==c, a==d, b==c, b==d +// (3) CrossingSign(a,b,c,d) == DoNotCross or MaybeCross if a==b or c==d +// +// Note that if you want to check an edge against a chain of other edges, +// it is slightly more efficient to use the single-argument version +// ChainCrossingSign below. +func (e *EdgeCrosser) CrossingSign(c, d Point) Crossing { + if c != e.c { + e.RestartAt(c) + } + return e.ChainCrossingSign(d) +} + +// EdgeOrVertexCrossing reports whether if CrossingSign(c, d) > 0, or AB and +// CD share a vertex and VertexCrossing(a, b, c, d) is true. +// +// This method extends the concept of a "crossing" to the case where AB +// and CD have a vertex in common. The two edges may or may not cross, +// according to the rules defined in VertexCrossing above. The rules +// are designed so that point containment tests can be implemented simply +// by counting edge crossings. Similarly, determining whether one edge +// chain crosses another edge chain can be implemented by counting. +func (e *EdgeCrosser) EdgeOrVertexCrossing(c, d Point) bool { + if c != e.c { + e.RestartAt(c) + } + return e.EdgeOrVertexChainCrossing(d) +} + +// NewChainEdgeCrosser is a convenience constructor that uses AB as the fixed edge, +// and C as the first vertex of the vertex chain (equivalent to calling RestartAt(c)). +// +// You don't need to use this or any of the chain functions unless you're trying to +// squeeze out every last drop of performance. Essentially all you are saving is a test +// whether the first vertex of the current edge is the same as the second vertex of the +// previous edge. +func NewChainEdgeCrosser(a, b, c Point) *EdgeCrosser { + e := NewEdgeCrosser(a, b) + e.RestartAt(c) + return e +} + +// RestartAt sets the current point of the edge crosser to be c. +// Call this method when your chain 'jumps' to a new place. +// The argument must point to a value that persists until the next call. +func (e *EdgeCrosser) RestartAt(c Point) { + e.c = c + e.acb = -triageSign(e.a, e.b, e.c) +} + +// ChainCrossingSign is like CrossingSign, but uses the last vertex passed to one of +// the crossing methods (or RestartAt) as the first vertex of the current edge. +func (e *EdgeCrosser) ChainCrossingSign(d Point) Crossing { + // For there to be an edge crossing, the triangles ACB, CBD, BDA, DAC must + // all be oriented the same way (CW or CCW). We keep the orientation of ACB + // as part of our state. When each new point D arrives, we compute the + // orientation of BDA and check whether it matches ACB. This checks whether + // the points C and D are on opposite sides of the great circle through AB. + + // Recall that triageSign is invariant with respect to rotating its + // arguments, i.e. ABD has the same orientation as BDA. + bda := triageSign(e.a, e.b, d) + if e.acb == -bda && bda != Indeterminate { + // The most common case -- triangles have opposite orientations. Save the + // current vertex D as the next vertex C, and also save the orientation of + // the new triangle ACB (which is opposite to the current triangle BDA). + e.c = d + e.acb = -bda + return DoNotCross + } + return e.crossingSign(d, bda) +} + +// EdgeOrVertexChainCrossing is like EdgeOrVertexCrossing, but uses the last vertex +// passed to one of the crossing methods (or RestartAt) as the first vertex of the current edge. +func (e *EdgeCrosser) EdgeOrVertexChainCrossing(d Point) bool { + // We need to copy e.c since it is clobbered by ChainCrossingSign. + c := e.c + switch e.ChainCrossingSign(d) { + case DoNotCross: + return false + case Cross: + return true + } + return VertexCrossing(e.a, e.b, c, d) +} + +// crossingSign handle the slow path of CrossingSign. +func (e *EdgeCrosser) crossingSign(d Point, bda Direction) Crossing { + // Compute the actual result, and then save the current vertex D as the next + // vertex C, and save the orientation of the next triangle ACB (which is + // opposite to the current triangle BDA). + defer func() { + e.c = d + e.acb = -bda + }() + + // At this point, a very common situation is that A,B,C,D are four points on + // a line such that AB does not overlap CD. (For example, this happens when + // a line or curve is sampled finely, or when geometry is constructed by + // computing the union of S2CellIds.) Most of the time, we can determine + // that AB and CD do not intersect using the two outward-facing + // tangents at A and B (parallel to AB) and testing whether AB and CD are on + // opposite sides of the plane perpendicular to one of these tangents. This + // is moderately expensive but still much cheaper than expensiveSign. + + // The error in RobustCrossProd is insignificant. The maximum error in + // the call to CrossProd (i.e., the maximum norm of the error vector) is + // (0.5 + 1/sqrt(3)) * dblEpsilon. The maximum error in each call to + // DotProd below is dblEpsilon. (There is also a small relative error + // term that is insignificant because we are comparing the result against a + // constant that is very close to zero.) + maxError := (1.5 + 1/math.Sqrt(3)) * dblEpsilon + if (e.c.Dot(e.aTangent.Vector) > maxError && d.Dot(e.aTangent.Vector) > maxError) || (e.c.Dot(e.bTangent.Vector) > maxError && d.Dot(e.bTangent.Vector) > maxError) { + return DoNotCross + } + + // Otherwise, eliminate the cases where two vertices from different edges are + // equal. (These cases could be handled in the code below, but we would rather + // avoid calling ExpensiveSign if possible.) + if e.a == e.c || e.a == d || e.b == e.c || e.b == d { + return MaybeCross + } + + // Eliminate the cases where an input edge is degenerate. (Note that in + // most cases, if CD is degenerate then this method is not even called + // because acb and bda have different signs.) + if e.a == e.b || e.c == d { + return DoNotCross + } + + // Otherwise it's time to break out the big guns. + if e.acb == Indeterminate { + e.acb = -expensiveSign(e.a, e.b, e.c) + } + if bda == Indeterminate { + bda = expensiveSign(e.a, e.b, d) + } + + if bda != e.acb { + return DoNotCross + } + + cbd := -RobustSign(e.c, d, e.b) + if cbd != e.acb { + return DoNotCross + } + dac := RobustSign(e.c, d, e.a) + if dac != e.acb { + return DoNotCross + } + return Cross +} |