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// 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
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// See the License for the specific language governing permissions and
// limitations under the License.
package s2
// WedgeRel enumerates the possible relation between two wedges A and B.
type WedgeRel int
// Define the different possible relationships between two wedges.
// Given an edge chain (x0, x1, x2), the wedge at x1 is the region to the
// left of the edges. More precisely, it is the set of all rays from x1x0
// (inclusive) to x1x2 (exclusive) in the *clockwise* direction.
const (
WedgeEquals WedgeRel = iota // A and B are equal.
WedgeProperlyContains // A is a strict superset of B.
WedgeIsProperlyContained // A is a strict subset of B.
WedgeProperlyOverlaps // A-B, B-A, and A intersect B are non-empty.
WedgeIsDisjoint // A and B are disjoint.
// WedgeRelation reports the relation between two non-empty wedges
// A=(a0, ab1, a2) and B=(b0, ab1, b2).
func WedgeRelation(a0, ab1, a2, b0, b2 Point) WedgeRel {
// There are 6 possible edge orderings at a shared vertex (all
// of these orderings are circular, i.e. abcd == bcda):
// (1) a2 b2 b0 a0: A contains B
// (2) a2 a0 b0 b2: B contains A
// (3) a2 a0 b2 b0: A and B are disjoint
// (4) a2 b0 a0 b2: A and B intersect in one wedge
// (5) a2 b2 a0 b0: A and B intersect in one wedge
// (6) a2 b0 b2 a0: A and B intersect in two wedges
// We do not distinguish between 4, 5, and 6.
// We pay extra attention when some of the edges overlap. When edges
// overlap, several of these orderings can be satisfied, and we take
// the most specific.
if a0 == b0 && a2 == b2 {
return WedgeEquals
// Cases 1, 2, 5, and 6
if OrderedCCW(a0, a2, b2, ab1) {
// The cases with this vertex ordering are 1, 5, and 6,
if OrderedCCW(b2, b0, a0, ab1) {
return WedgeProperlyContains
// We are in case 5 or 6, or case 2 if a2 == b2.
if a2 == b2 {
return WedgeIsProperlyContained
return WedgeProperlyOverlaps
// We are in case 2, 3, or 4.
if OrderedCCW(a0, b0, b2, ab1) {
return WedgeIsProperlyContained
if OrderedCCW(a0, b0, a2, ab1) {
return WedgeIsDisjoint
return WedgeProperlyOverlaps
// WedgeContains reports whether non-empty wedge A=(a0, ab1, a2) contains B=(b0, ab1, b2).
// Equivalent to WedgeRelation == WedgeProperlyContains || WedgeEquals.
func WedgeContains(a0, ab1, a2, b0, b2 Point) bool {
// For A to contain B (where each loop interior is defined to be its left
// side), the CCW edge order around ab1 must be a2 b2 b0 a0. We split
// this test into two parts that test three vertices each.
return OrderedCCW(a2, b2, b0, ab1) && OrderedCCW(b0, a0, a2, ab1)
// WedgeIntersects reports whether non-empty wedge A=(a0, ab1, a2) intersects B=(b0, ab1, b2).
// Equivalent but faster than WedgeRelation != WedgeIsDisjoint
func WedgeIntersects(a0, ab1, a2, b0, b2 Point) bool {
// For A not to intersect B (where each loop interior is defined to be
// its left side), the CCW edge order around ab1 must be a0 b2 b0 a2.
// Note that it's important to write these conditions as negatives
// (!OrderedCCW(a,b,c,o) rather than Ordered(c,b,a,o)) to get correct
// results when two vertices are the same.
return !(OrderedCCW(a0, b2, b0, ab1) && OrderedCCW(b0, a2, a0, ab1))
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