mirror of
https://github.com/superseriousbusiness/gotosocial.git
synced 2024-12-05 01:52:46 +00:00
229 lines
8.1 KiB
Go
229 lines
8.1 KiB
Go
|
// 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
|
||
|
|
||
|
// CrossingType defines different ways of reporting edge intersections.
|
||
|
type CrossingType int
|
||
|
|
||
|
const (
|
||
|
// CrossingTypeInterior reports intersections that occur at a point
|
||
|
// interior to both edges (i.e., not at a vertex).
|
||
|
CrossingTypeInterior CrossingType = iota
|
||
|
|
||
|
// CrossingTypeAll reports all intersections, even those where two edges
|
||
|
// intersect only because they share a common vertex.
|
||
|
CrossingTypeAll
|
||
|
|
||
|
// CrossingTypeNonAdjacent reports all intersections except for pairs of
|
||
|
// the form (AB, BC) where both edges are from the same ShapeIndex.
|
||
|
CrossingTypeNonAdjacent
|
||
|
)
|
||
|
|
||
|
// rangeIterator is a wrapper over ShapeIndexIterator with extra methods
|
||
|
// that are useful for merging the contents of two or more ShapeIndexes.
|
||
|
type rangeIterator struct {
|
||
|
it *ShapeIndexIterator
|
||
|
// The min and max leaf cell ids covered by the current cell. If done() is
|
||
|
// true, these methods return a value larger than any valid cell id.
|
||
|
rangeMin CellID
|
||
|
rangeMax CellID
|
||
|
}
|
||
|
|
||
|
// newRangeIterator creates a new rangeIterator positioned at the first cell of the given index.
|
||
|
func newRangeIterator(index *ShapeIndex) *rangeIterator {
|
||
|
r := &rangeIterator{
|
||
|
it: index.Iterator(),
|
||
|
}
|
||
|
r.refresh()
|
||
|
return r
|
||
|
}
|
||
|
|
||
|
func (r *rangeIterator) cellID() CellID { return r.it.CellID() }
|
||
|
func (r *rangeIterator) indexCell() *ShapeIndexCell { return r.it.IndexCell() }
|
||
|
func (r *rangeIterator) next() { r.it.Next(); r.refresh() }
|
||
|
func (r *rangeIterator) done() bool { return r.it.Done() }
|
||
|
|
||
|
// seekTo positions the iterator at the first cell that overlaps or follows
|
||
|
// the current range minimum of the target iterator, i.e. such that its
|
||
|
// rangeMax >= target.rangeMin.
|
||
|
func (r *rangeIterator) seekTo(target *rangeIterator) {
|
||
|
r.it.seek(target.rangeMin)
|
||
|
// If the current cell does not overlap target, it is possible that the
|
||
|
// previous cell is the one we are looking for. This can only happen when
|
||
|
// the previous cell contains target but has a smaller CellID.
|
||
|
if r.it.Done() || r.it.CellID().RangeMin() > target.rangeMax {
|
||
|
if r.it.Prev() && r.it.CellID().RangeMax() < target.cellID() {
|
||
|
r.it.Next()
|
||
|
}
|
||
|
}
|
||
|
r.refresh()
|
||
|
}
|
||
|
|
||
|
// seekBeyond positions the iterator at the first cell that follows the current
|
||
|
// range minimum of the target iterator. i.e. the first cell such that its
|
||
|
// rangeMin > target.rangeMax.
|
||
|
func (r *rangeIterator) seekBeyond(target *rangeIterator) {
|
||
|
r.it.seek(target.rangeMax.Next())
|
||
|
if !r.it.Done() && r.it.CellID().RangeMin() <= target.rangeMax {
|
||
|
r.it.Next()
|
||
|
}
|
||
|
r.refresh()
|
||
|
}
|
||
|
|
||
|
// refresh updates the iterators min and max values.
|
||
|
func (r *rangeIterator) refresh() {
|
||
|
r.rangeMin = r.cellID().RangeMin()
|
||
|
r.rangeMax = r.cellID().RangeMax()
|
||
|
}
|
||
|
|
||
|
// referencePointForShape is a helper function for implementing various Shapes
|
||
|
// ReferencePoint functions.
|
||
|
//
|
||
|
// 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 Loop and Polygon, 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
|
||
|
// laxPolygon 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.
|
||
|
//
|
||
|
// This function requires that the given Shape have an interior.
|
||
|
func referencePointForShape(shape Shape) ReferencePoint {
|
||
|
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 OriginReferencePoint(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.
|
||
|
edge := shape.Edge(0)
|
||
|
|
||
|
if ref, ok := referencePointAtVertex(shape, edge.V0); ok {
|
||
|
return ref
|
||
|
}
|
||
|
|
||
|
// 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.
|
||
|
n := shape.NumEdges()
|
||
|
var edges = make([]Edge, n)
|
||
|
var revEdges = make([]Edge, n)
|
||
|
for i := 0; i < n; i++ {
|
||
|
edge := shape.Edge(i)
|
||
|
edges[i] = edge
|
||
|
revEdges[i] = Edge{V0: edge.V1, V1: edge.V0}
|
||
|
}
|
||
|
|
||
|
sortEdges(edges)
|
||
|
sortEdges(revEdges)
|
||
|
|
||
|
for i := 0; i < n; i++ {
|
||
|
if edges[i].Cmp(revEdges[i]) == -1 { // edges[i] is unmatched
|
||
|
if ref, ok := referencePointAtVertex(shape, edges[i].V0); ok {
|
||
|
return ref
|
||
|
}
|
||
|
}
|
||
|
if revEdges[i].Cmp(edges[i]) == -1 { // revEdges[i] is unmatched
|
||
|
if ref, ok := referencePointAtVertex(shape, revEdges[i].V0); ok {
|
||
|
return ref
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// 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 i := 0; i < shape.NumChains(); i++ {
|
||
|
if shape.Chain(i).Length == 0 {
|
||
|
return OriginReferencePoint(true)
|
||
|
}
|
||
|
}
|
||
|
|
||
|
return OriginReferencePoint(false)
|
||
|
}
|
||
|
|
||
|
// referencePointAtVertex reports whether the given vertex is unbalanced, and
|
||
|
// returns a ReferencePoint indicating if the point is contained.
|
||
|
// Otherwise returns false.
|
||
|
func referencePointAtVertex(shape Shape, vTest Point) (ReferencePoint, bool) {
|
||
|
var ref ReferencePoint
|
||
|
|
||
|
// Let P be an unbalanced vertex. Vertex P is defined to be inside the
|
||
|
// region if the region contains a particular direction vector starting from
|
||
|
// P, namely the direction p.Ortho(). This can be calculated using
|
||
|
// ContainsVertexQuery.
|
||
|
|
||
|
containsQuery := NewContainsVertexQuery(vTest)
|
||
|
n := shape.NumEdges()
|
||
|
for e := 0; e < n; e++ {
|
||
|
edge := shape.Edge(e)
|
||
|
if edge.V0 == vTest {
|
||
|
containsQuery.AddEdge(edge.V1, 1)
|
||
|
}
|
||
|
if edge.V1 == vTest {
|
||
|
containsQuery.AddEdge(edge.V0, -1)
|
||
|
}
|
||
|
}
|
||
|
containsSign := containsQuery.ContainsVertex()
|
||
|
if containsSign == 0 {
|
||
|
return ref, false // There are no unmatched edges incident to this vertex.
|
||
|
}
|
||
|
ref.Point = vTest
|
||
|
ref.Contained = containsSign > 0
|
||
|
|
||
|
return ref, true
|
||
|
}
|
||
|
|
||
|
// containsBruteForce reports whether the given shape contains the given point.
|
||
|
// Most clients should not use this method, since its running time is linear in
|
||
|
// the number of shape edges. Instead clients should create a ShapeIndex and use
|
||
|
// ContainsPointQuery, since this strategy is much more efficient when many
|
||
|
// points need to be tested.
|
||
|
//
|
||
|
// Polygon boundaries are treated as being semi-open (see ContainsPointQuery
|
||
|
// and VertexModel for other options).
|
||
|
func containsBruteForce(shape Shape, point Point) bool {
|
||
|
if shape.Dimension() != 2 {
|
||
|
return false
|
||
|
}
|
||
|
|
||
|
refPoint := shape.ReferencePoint()
|
||
|
if refPoint.Point == point {
|
||
|
return refPoint.Contained
|
||
|
}
|
||
|
|
||
|
crosser := NewEdgeCrosser(refPoint.Point, point)
|
||
|
inside := refPoint.Contained
|
||
|
for e := 0; e < shape.NumEdges(); e++ {
|
||
|
edge := shape.Edge(e)
|
||
|
inside = inside != crosser.EdgeOrVertexCrossing(edge.V0, edge.V1)
|
||
|
}
|
||
|
return inside
|
||
|
}
|