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97 lines
3.7 KiB
Go
97 lines
3.7 KiB
Go
// Copyright 2017 Google Inc. All rights reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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package s2
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// WedgeRel enumerates the possible relation between two wedges A and B.
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type WedgeRel int
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// Define the different possible relationships between two wedges.
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//
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// Given an edge chain (x0, x1, x2), the wedge at x1 is the region to the
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// left of the edges. More precisely, it is the set of all rays from x1x0
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// (inclusive) to x1x2 (exclusive) in the *clockwise* direction.
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const (
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WedgeEquals WedgeRel = iota // A and B are equal.
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WedgeProperlyContains // A is a strict superset of B.
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WedgeIsProperlyContained // A is a strict subset of B.
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WedgeProperlyOverlaps // A-B, B-A, and A intersect B are non-empty.
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WedgeIsDisjoint // A and B are disjoint.
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)
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// WedgeRelation reports the relation between two non-empty wedges
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// A=(a0, ab1, a2) and B=(b0, ab1, b2).
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func WedgeRelation(a0, ab1, a2, b0, b2 Point) WedgeRel {
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// There are 6 possible edge orderings at a shared vertex (all
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// of these orderings are circular, i.e. abcd == bcda):
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//
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// (1) a2 b2 b0 a0: A contains B
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// (2) a2 a0 b0 b2: B contains A
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// (3) a2 a0 b2 b0: A and B are disjoint
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// (4) a2 b0 a0 b2: A and B intersect in one wedge
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// (5) a2 b2 a0 b0: A and B intersect in one wedge
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// (6) a2 b0 b2 a0: A and B intersect in two wedges
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//
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// We do not distinguish between 4, 5, and 6.
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// We pay extra attention when some of the edges overlap. When edges
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// overlap, several of these orderings can be satisfied, and we take
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// the most specific.
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if a0 == b0 && a2 == b2 {
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return WedgeEquals
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}
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// Cases 1, 2, 5, and 6
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if OrderedCCW(a0, a2, b2, ab1) {
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// The cases with this vertex ordering are 1, 5, and 6,
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if OrderedCCW(b2, b0, a0, ab1) {
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return WedgeProperlyContains
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}
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// We are in case 5 or 6, or case 2 if a2 == b2.
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if a2 == b2 {
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return WedgeIsProperlyContained
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}
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return WedgeProperlyOverlaps
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}
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// We are in case 2, 3, or 4.
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if OrderedCCW(a0, b0, b2, ab1) {
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return WedgeIsProperlyContained
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}
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if OrderedCCW(a0, b0, a2, ab1) {
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return WedgeIsDisjoint
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}
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return WedgeProperlyOverlaps
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}
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// WedgeContains reports whether non-empty wedge A=(a0, ab1, a2) contains B=(b0, ab1, b2).
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// Equivalent to WedgeRelation == WedgeProperlyContains || WedgeEquals.
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func WedgeContains(a0, ab1, a2, b0, b2 Point) bool {
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// For A to contain B (where each loop interior is defined to be its left
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// side), the CCW edge order around ab1 must be a2 b2 b0 a0. We split
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// this test into two parts that test three vertices each.
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return OrderedCCW(a2, b2, b0, ab1) && OrderedCCW(b0, a0, a2, ab1)
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}
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// WedgeIntersects reports whether non-empty wedge A=(a0, ab1, a2) intersects B=(b0, ab1, b2).
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// Equivalent but faster than WedgeRelation != WedgeIsDisjoint
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func WedgeIntersects(a0, ab1, a2, b0, b2 Point) bool {
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// For A not to intersect B (where each loop interior is defined to be
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// its left side), the CCW edge order around ab1 must be a0 b2 b0 a2.
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// Note that it's important to write these conditions as negatives
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// (!OrderedCCW(a,b,c,o) rather than Ordered(c,b,a,o)) to get correct
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// results when two vertices are the same.
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return !(OrderedCCW(a0, b2, b0, ab1) && OrderedCCW(b0, a2, a0, ab1))
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}
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