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804 lines
30 KiB
Go
804 lines
30 KiB
Go
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// Copyright 2019 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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import (
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"sort"
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"github.com/golang/geo/s1"
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)
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// EdgeQueryOptions holds the options for controlling how EdgeQuery operates.
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//
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// Options can be chained together builder-style:
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//
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// opts = NewClosestEdgeQueryOptions().
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// MaxResults(1).
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// DistanceLimit(s1.ChordAngleFromAngle(3 * s1.Degree)).
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// MaxError(s1.ChordAngleFromAngle(0.001 * s1.Degree))
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// query = NewClosestEdgeQuery(index, opts)
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//
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// or set individually:
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//
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// opts = NewClosestEdgeQueryOptions()
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// opts.IncludeInteriors(true)
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//
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// or just inline:
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//
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// query = NewClosestEdgeQuery(index, NewClosestEdgeQueryOptions().MaxResults(3))
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//
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// If you pass a nil as the options you get the default values for the options.
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type EdgeQueryOptions struct {
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common *queryOptions
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}
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// DistanceLimit specifies that only edges whose distance to the target is
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// within, this distance should be returned. Edges whose distance is equal
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// are not returned. To include values that are equal, specify the limit with
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// the next largest representable distance. i.e. limit.Successor().
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func (e *EdgeQueryOptions) DistanceLimit(limit s1.ChordAngle) *EdgeQueryOptions {
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e.common = e.common.DistanceLimit(limit)
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return e
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}
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// IncludeInteriors specifies whether polygon interiors should be
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// included when measuring distances.
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func (e *EdgeQueryOptions) IncludeInteriors(x bool) *EdgeQueryOptions {
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e.common = e.common.IncludeInteriors(x)
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return e
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}
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// UseBruteForce sets or disables the use of brute force in a query.
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func (e *EdgeQueryOptions) UseBruteForce(x bool) *EdgeQueryOptions {
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e.common = e.common.UseBruteForce(x)
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return e
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}
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// MaxError specifies that edges up to dist away than the true
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// matching edges may be substituted in the result set, as long as such
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// edges satisfy all the remaining search criteria (such as DistanceLimit).
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// This option only has an effect if MaxResults is also specified;
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// otherwise all edges closer than MaxDistance will always be returned.
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func (e *EdgeQueryOptions) MaxError(dist s1.ChordAngle) *EdgeQueryOptions {
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e.common = e.common.MaxError(dist)
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return e
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}
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// MaxResults specifies that at most MaxResults edges should be returned.
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// This must be at least 1.
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func (e *EdgeQueryOptions) MaxResults(n int) *EdgeQueryOptions {
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e.common = e.common.MaxResults(n)
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return e
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}
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// NewClosestEdgeQueryOptions returns a set of edge query options suitable
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// for performing closest edge queries.
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func NewClosestEdgeQueryOptions() *EdgeQueryOptions {
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return &EdgeQueryOptions{
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common: newQueryOptions(minDistance(0)),
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}
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}
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// NewFurthestEdgeQueryOptions returns a set of edge query options suitable
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// for performing furthest edge queries.
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func NewFurthestEdgeQueryOptions() *EdgeQueryOptions {
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return &EdgeQueryOptions{
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common: newQueryOptions(maxDistance(0)),
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}
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}
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// EdgeQueryResult represents an edge that meets the target criteria for the
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// query. Note the following special cases:
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//
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// - ShapeID >= 0 && EdgeID < 0 represents the interior of a shape.
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// Such results may be returned when the option IncludeInteriors is true.
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//
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// - ShapeID < 0 && EdgeID < 0 is returned to indicate that no edge
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// satisfies the requested query options.
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type EdgeQueryResult struct {
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distance distance
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shapeID int32
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edgeID int32
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}
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// Distance reports the distance between the edge in this shape that satisfied
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// the query's parameters.
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func (e EdgeQueryResult) Distance() s1.ChordAngle { return e.distance.chordAngle() }
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// ShapeID reports the ID of the Shape this result is for.
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func (e EdgeQueryResult) ShapeID() int32 { return e.shapeID }
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// EdgeID reports the ID of the edge in the results Shape.
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func (e EdgeQueryResult) EdgeID() int32 { return e.edgeID }
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// newEdgeQueryResult returns a result instance with default values.
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func newEdgeQueryResult(target distanceTarget) EdgeQueryResult {
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return EdgeQueryResult{
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distance: target.distance().infinity(),
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shapeID: -1,
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edgeID: -1,
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}
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}
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// IsInterior reports if this result represents the interior of a Shape.
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func (e EdgeQueryResult) IsInterior() bool {
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return e.shapeID >= 0 && e.edgeID < 0
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}
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// IsEmpty reports if this has no edge that satisfies the given edge query options.
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// This result is only returned in one special case, namely when FindEdge() does
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// not find any suitable edges.
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func (e EdgeQueryResult) IsEmpty() bool {
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return e.shapeID < 0
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}
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// Less reports if this results is less that the other first by distance,
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// then by (shapeID, edgeID). This is used for sorting.
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func (e EdgeQueryResult) Less(other EdgeQueryResult) bool {
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if e.distance.chordAngle() != other.distance.chordAngle() {
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return e.distance.less(other.distance)
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}
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if e.shapeID != other.shapeID {
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return e.shapeID < other.shapeID
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}
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return e.edgeID < other.edgeID
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}
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// EdgeQuery is used to find the edge(s) between two geometries that match a
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// given set of options. It is flexible enough so that it can be adapted to
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// compute maximum distances and even potentially Hausdorff distances.
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//
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// By using the appropriate options, this type can answer questions such as:
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//
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// - Find the minimum distance between two geometries A and B.
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// - Find all edges of geometry A that are within a distance D of geometry B.
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// - Find the k edges of geometry A that are closest to a given point P.
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//
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// You can also specify whether polygons should include their interiors (i.e.,
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// if a point is contained by a polygon, should the distance be zero or should
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// it be measured to the polygon boundary?)
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//
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// The input geometries may consist of any number of points, polylines, and
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// polygons (collectively referred to as "shapes"). Shapes do not need to be
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// disjoint; they may overlap or intersect arbitrarily. The implementation is
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// designed to be fast for both simple and complex geometries.
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type EdgeQuery struct {
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index *ShapeIndex
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opts *queryOptions
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target distanceTarget
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// True if opts.maxError must be subtracted from ShapeIndex cell distances
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// in order to ensure that such distances are measured conservatively. This
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// is true only if the target takes advantage of maxError in order to
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// return faster results, and 0 < maxError < distanceLimit.
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useConservativeCellDistance bool
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// The decision about whether to use the brute force algorithm is based on
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// counting the total number of edges in the index. However if the index
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// contains a large number of shapes, this in itself might take too long.
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// So instead we only count edges up to (maxBruteForceIndexSize() + 1)
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// for the current target type (stored as indexNumEdgesLimit).
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indexNumEdges int
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indexNumEdgesLimit int
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// The distance beyond which we can safely ignore further candidate edges.
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// (Candidates that are exactly at the limit are ignored; this is more
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// efficient for UpdateMinDistance and should not affect clients since
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// distance measurements have a small amount of error anyway.)
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//
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// Initially this is the same as the maximum distance specified by the user,
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// but it can also be updated by the algorithm (see maybeAddResult).
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distanceLimit distance
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// The current set of results of the query.
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results []EdgeQueryResult
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// This field is true when duplicates must be avoided explicitly. This
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// is achieved by maintaining a separate set keyed by (shapeID, edgeID)
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// only, and checking whether each edge is in that set before computing the
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// distance to it.
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avoidDuplicates bool
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// testedEdges tracks the set of shape and edges that have already been tested.
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testedEdges map[ShapeEdgeID]uint32
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// For the optimized algorihm we precompute the top-level CellIDs that
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// will be added to the priority queue. There can be at most 6 of these
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// cells. Essentially this is just a covering of the indexed edges, except
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// that we also store pointers to the corresponding ShapeIndexCells to
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// reduce the number of index seeks required.
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indexCovering []CellID
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indexCells []*ShapeIndexCell
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// The algorithm maintains a priority queue of unprocessed CellIDs, sorted
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// in increasing order of distance from the target.
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queue *queryQueue
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iter *ShapeIndexIterator
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maxDistanceCovering []CellID
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initialCells []CellID
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}
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// NewClosestEdgeQuery returns an EdgeQuery that is used for finding the
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// closest edge(s) to a given Point, Edge, Cell, or geometry collection.
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//
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// You can find either the k closest edges, or all edges within a given
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// radius, or both (i.e., the k closest edges up to a given maximum radius).
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// E.g. to find all the edges within 5 kilometers, set the DistanceLimit in
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// the options.
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//
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// By default *all* edges are returned, so you should always specify either
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// MaxResults or DistanceLimit options or both.
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//
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// Note that by default, distances are measured to the boundary and interior
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// of polygons. For example, if a point is inside a polygon then its distance
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// is zero. To change this behavior, set the IncludeInteriors option to false.
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//
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// If you only need to test whether the distance is above or below a given
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// threshold (e.g., 10 km), you can use the IsDistanceLess() method. This is
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// much faster than actually calculating the distance with FindEdge,
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// since the implementation can stop as soon as it can prove that the minimum
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// distance is either above or below the threshold.
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func NewClosestEdgeQuery(index *ShapeIndex, opts *EdgeQueryOptions) *EdgeQuery {
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if opts == nil {
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opts = NewClosestEdgeQueryOptions()
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}
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e := &EdgeQuery{
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testedEdges: make(map[ShapeEdgeID]uint32),
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index: index,
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opts: opts.common,
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queue: newQueryQueue(),
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}
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return e
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}
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// NewFurthestEdgeQuery returns an EdgeQuery that is used for finding the
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// furthest edge(s) to a given Point, Edge, Cell, or geometry collection.
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//
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// The furthest edge is defined as the one which maximizes the
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// distance from any point on that edge to any point on the target geometry.
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//
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// Similar to the example in NewClosestEdgeQuery, to find the 5 furthest edges
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// from a given Point:
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func NewFurthestEdgeQuery(index *ShapeIndex, opts *EdgeQueryOptions) *EdgeQuery {
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if opts == nil {
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opts = NewFurthestEdgeQueryOptions()
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}
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e := &EdgeQuery{
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testedEdges: make(map[ShapeEdgeID]uint32),
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index: index,
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opts: opts.common,
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queue: newQueryQueue(),
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}
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return e
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}
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// Reset resets the state of this EdgeQuery.
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func (e *EdgeQuery) Reset() {
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e.indexNumEdges = 0
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e.indexNumEdgesLimit = 0
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e.indexCovering = nil
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e.indexCells = nil
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}
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// FindEdges returns the edges for the given target that satisfy the current options.
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//
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// Note that if opts.IncludeInteriors is true, the results may include some
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// entries with edge_id == -1. This indicates that the target intersects
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// the indexed polygon with the given ShapeID.
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func (e *EdgeQuery) FindEdges(target distanceTarget) []EdgeQueryResult {
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return e.findEdges(target, e.opts)
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}
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// Distance reports the distance to the target. If the index or target is empty,
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// returns the EdgeQuery's maximal sentinel.
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//
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// Use IsDistanceLess()/IsDistanceGreater() if you only want to compare the
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// distance against a threshold value, since it is often much faster.
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func (e *EdgeQuery) Distance(target distanceTarget) s1.ChordAngle {
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return e.findEdge(target, e.opts).Distance()
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}
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// IsDistanceLess reports if the distance to target is less than the given limit.
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//
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// This method is usually much faster than Distance(), since it is much
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// less work to determine whether the minimum distance is above or below a
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// threshold than it is to calculate the actual minimum distance.
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//
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// If you wish to check if the distance is less than or equal to the limit, use:
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//
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// query.IsDistanceLess(target, limit.Successor())
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//
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func (e *EdgeQuery) IsDistanceLess(target distanceTarget, limit s1.ChordAngle) bool {
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opts := e.opts
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opts = opts.MaxResults(1).
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DistanceLimit(limit).
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MaxError(s1.StraightChordAngle)
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return !e.findEdge(target, opts).IsEmpty()
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}
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// IsDistanceGreater reports if the distance to target is greater than limit.
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//
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// This method is usually much faster than Distance, since it is much
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// less work to determine whether the maximum distance is above or below a
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// threshold than it is to calculate the actual maximum distance.
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// If you wish to check if the distance is less than or equal to the limit, use:
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//
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// query.IsDistanceGreater(target, limit.Predecessor())
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//
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func (e *EdgeQuery) IsDistanceGreater(target distanceTarget, limit s1.ChordAngle) bool {
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return e.IsDistanceLess(target, limit)
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}
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// IsConservativeDistanceLessOrEqual reports if the distance to target is less
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// or equal to the limit, where the limit has been expanded by the maximum error
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// for the distance calculation.
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//
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// For example, suppose that we want to test whether two geometries might
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// intersect each other after they are snapped together using Builder
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// (using the IdentitySnapFunction with a given "snap radius"). Since
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// Builder uses exact distance predicates (s2predicates), we need to
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// measure the distance between the two geometries conservatively. If the
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// distance is definitely greater than "snap radius", then the geometries
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// are guaranteed to not intersect after snapping.
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func (e *EdgeQuery) IsConservativeDistanceLessOrEqual(target distanceTarget, limit s1.ChordAngle) bool {
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return e.IsDistanceLess(target, limit.Expanded(minUpdateDistanceMaxError(limit)))
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}
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// IsConservativeDistanceGreaterOrEqual reports if the distance to the target is greater
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// than or equal to the given limit with some small tolerance.
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func (e *EdgeQuery) IsConservativeDistanceGreaterOrEqual(target distanceTarget, limit s1.ChordAngle) bool {
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return e.IsDistanceGreater(target, limit.Expanded(-minUpdateDistanceMaxError(limit)))
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}
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// findEdges returns the closest edges to the given target that satisfy the given options.
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//
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// Note that if opts.includeInteriors is true, the results may include some
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// entries with edgeID == -1. This indicates that the target intersects the
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// indexed polygon with the given shapeID.
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func (e *EdgeQuery) findEdges(target distanceTarget, opts *queryOptions) []EdgeQueryResult {
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e.findEdgesInternal(target, opts)
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// TODO(roberts): Revisit this if there is a heap or other sorted and
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// uniquing datastructure we can use instead of just a slice.
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e.results = sortAndUniqueResults(e.results)
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if len(e.results) > e.opts.maxResults {
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e.results = e.results[:e.opts.maxResults]
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}
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return e.results
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}
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func sortAndUniqueResults(results []EdgeQueryResult) []EdgeQueryResult {
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if len(results) <= 1 {
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return results
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}
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sort.Slice(results, func(i, j int) bool { return results[i].Less(results[j]) })
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j := 0
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for i := 1; i < len(results); i++ {
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if results[j] == results[i] {
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continue
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}
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j++
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results[j] = results[i]
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}
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return results[:j+1]
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}
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// findEdge is a convenience method that returns exactly one edge, and if no
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// edges satisfy the given search criteria, then a default Result is returned.
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//
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// This is primarily to ease the usage of a number of the methods in the DistanceTargets
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// and in EdgeQuery.
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func (e *EdgeQuery) findEdge(target distanceTarget, opts *queryOptions) EdgeQueryResult {
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opts.MaxResults(1)
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|
e.findEdges(target, opts)
|
||
|
if len(e.results) > 0 {
|
||
|
return e.results[0]
|
||
|
}
|
||
|
|
||
|
return newEdgeQueryResult(target)
|
||
|
}
|
||
|
|
||
|
// findEdgesInternal does the actual work for find edges that match the given options.
|
||
|
func (e *EdgeQuery) findEdgesInternal(target distanceTarget, opts *queryOptions) {
|
||
|
e.target = target
|
||
|
e.opts = opts
|
||
|
|
||
|
e.testedEdges = make(map[ShapeEdgeID]uint32)
|
||
|
e.distanceLimit = target.distance().fromChordAngle(opts.distanceLimit)
|
||
|
e.results = make([]EdgeQueryResult, 0)
|
||
|
|
||
|
if e.distanceLimit == target.distance().zero() {
|
||
|
return
|
||
|
}
|
||
|
|
||
|
if opts.includeInteriors {
|
||
|
shapeIDs := map[int32]struct{}{}
|
||
|
e.target.visitContainingShapes(e.index, func(containingShape Shape, targetPoint Point) bool {
|
||
|
shapeIDs[e.index.idForShape(containingShape)] = struct{}{}
|
||
|
return len(shapeIDs) < opts.maxResults
|
||
|
})
|
||
|
for shapeID := range shapeIDs {
|
||
|
e.addResult(EdgeQueryResult{target.distance().zero(), shapeID, -1})
|
||
|
}
|
||
|
|
||
|
if e.distanceLimit == target.distance().zero() {
|
||
|
return
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// If maxError > 0 and the target takes advantage of this, then we may
|
||
|
// need to adjust the distance estimates to ShapeIndex cells to ensure
|
||
|
// that they are always a lower bound on the true distance. For example,
|
||
|
// suppose max_distance == 100, maxError == 30, and we compute the distance
|
||
|
// to the target from some cell C0 as d(C0) == 80. Then because the target
|
||
|
// takes advantage of maxError, the true distance could be as low as 50.
|
||
|
// In order not to miss edges contained by such cells, we need to subtract
|
||
|
// maxError from the distance estimates. This behavior is controlled by
|
||
|
// the useConservativeCellDistance flag.
|
||
|
//
|
||
|
// However there is one important case where this adjustment is not
|
||
|
// necessary, namely when distanceLimit < maxError, This is because
|
||
|
// maxError only affects the algorithm once at least maxEdges edges
|
||
|
// have been found that satisfy the given distance limit. At that point,
|
||
|
// maxError is subtracted from distanceLimit in order to ensure that
|
||
|
// any further matches are closer by at least that amount. But when
|
||
|
// distanceLimit < maxError, this reduces the distance limit to 0,
|
||
|
// i.e. all remaining candidate cells and edges can safely be discarded.
|
||
|
// (This is how IsDistanceLess() and friends are implemented.)
|
||
|
targetUsesMaxError := opts.maxError != target.distance().zero().chordAngle() &&
|
||
|
e.target.setMaxError(opts.maxError)
|
||
|
|
||
|
// Note that we can't compare maxError and distanceLimit directly
|
||
|
// because one is a Delta and one is a Distance. Instead we subtract them.
|
||
|
e.useConservativeCellDistance = targetUsesMaxError &&
|
||
|
(e.distanceLimit == target.distance().infinity() ||
|
||
|
target.distance().zero().less(e.distanceLimit.sub(target.distance().fromChordAngle(opts.maxError))))
|
||
|
|
||
|
// Use the brute force algorithm if the index is small enough. To avoid
|
||
|
// spending too much time counting edges when there are many shapes, we stop
|
||
|
// counting once there are too many edges. We may need to recount the edges
|
||
|
// if we later see a target with a larger brute force edge threshold.
|
||
|
minOptimizedEdges := e.target.maxBruteForceIndexSize() + 1
|
||
|
if minOptimizedEdges > e.indexNumEdgesLimit && e.indexNumEdges >= e.indexNumEdgesLimit {
|
||
|
e.indexNumEdges = e.index.NumEdgesUpTo(minOptimizedEdges)
|
||
|
e.indexNumEdgesLimit = minOptimizedEdges
|
||
|
}
|
||
|
|
||
|
if opts.useBruteForce || e.indexNumEdges < minOptimizedEdges {
|
||
|
// The brute force algorithm already considers each edge exactly once.
|
||
|
e.avoidDuplicates = false
|
||
|
e.findEdgesBruteForce()
|
||
|
} else {
|
||
|
// If the target takes advantage of maxError then we need to avoid
|
||
|
// duplicate edges explicitly. (Otherwise it happens automatically.)
|
||
|
e.avoidDuplicates = targetUsesMaxError && opts.maxResults > 1
|
||
|
e.findEdgesOptimized()
|
||
|
}
|
||
|
}
|
||
|
|
||
|
func (e *EdgeQuery) addResult(r EdgeQueryResult) {
|
||
|
e.results = append(e.results, r)
|
||
|
if e.opts.maxResults == 1 {
|
||
|
// Optimization for the common case where only the closest edge is wanted.
|
||
|
e.distanceLimit = r.distance.sub(e.target.distance().fromChordAngle(e.opts.maxError))
|
||
|
}
|
||
|
// TODO(roberts): Add the other if/else cases when a different data structure
|
||
|
// is used for the results.
|
||
|
}
|
||
|
|
||
|
func (e *EdgeQuery) maybeAddResult(shape Shape, edgeID int32) {
|
||
|
if _, ok := e.testedEdges[ShapeEdgeID{e.index.idForShape(shape), edgeID}]; e.avoidDuplicates && !ok {
|
||
|
return
|
||
|
}
|
||
|
edge := shape.Edge(int(edgeID))
|
||
|
dist := e.distanceLimit
|
||
|
|
||
|
if dist, ok := e.target.updateDistanceToEdge(edge, dist); ok {
|
||
|
e.addResult(EdgeQueryResult{dist, e.index.idForShape(shape), edgeID})
|
||
|
}
|
||
|
}
|
||
|
|
||
|
func (e *EdgeQuery) findEdgesBruteForce() {
|
||
|
// Range over all shapes in the index. Does order matter here? if so
|
||
|
// switch to for i = 0 .. n?
|
||
|
for _, shape := range e.index.shapes {
|
||
|
// TODO(roberts): can this happen if we are only ranging over current entries?
|
||
|
if shape == nil {
|
||
|
continue
|
||
|
}
|
||
|
for edgeID := int32(0); edgeID < int32(shape.NumEdges()); edgeID++ {
|
||
|
e.maybeAddResult(shape, edgeID)
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
func (e *EdgeQuery) findEdgesOptimized() {
|
||
|
e.initQueue()
|
||
|
// Repeatedly find the closest Cell to "target" and either split it into
|
||
|
// its four children or process all of its edges.
|
||
|
for e.queue.size() > 0 {
|
||
|
// We need to copy the top entry before removing it, and we need to
|
||
|
// remove it before adding any new entries to the queue.
|
||
|
entry := e.queue.pop()
|
||
|
|
||
|
if !entry.distance.less(e.distanceLimit) {
|
||
|
e.queue.reset() // Clear any remaining entries.
|
||
|
break
|
||
|
}
|
||
|
// If this is already known to be an index cell, just process it.
|
||
|
if entry.indexCell != nil {
|
||
|
e.processEdges(entry)
|
||
|
continue
|
||
|
}
|
||
|
// Otherwise split the cell into its four children. Before adding a
|
||
|
// child back to the queue, we first check whether it is empty. We do
|
||
|
// this in two seek operations rather than four by seeking to the key
|
||
|
// between children 0 and 1 and to the key between children 2 and 3.
|
||
|
id := entry.id
|
||
|
ch := id.Children()
|
||
|
e.iter.seek(ch[1].RangeMin())
|
||
|
|
||
|
if !e.iter.Done() && e.iter.CellID() <= ch[1].RangeMax() {
|
||
|
e.processOrEnqueueCell(ch[1])
|
||
|
}
|
||
|
if e.iter.Prev() && e.iter.CellID() >= id.RangeMin() {
|
||
|
e.processOrEnqueueCell(ch[0])
|
||
|
}
|
||
|
|
||
|
e.iter.seek(ch[3].RangeMin())
|
||
|
if !e.iter.Done() && e.iter.CellID() <= id.RangeMax() {
|
||
|
e.processOrEnqueueCell(ch[3])
|
||
|
}
|
||
|
if e.iter.Prev() && e.iter.CellID() >= ch[2].RangeMin() {
|
||
|
e.processOrEnqueueCell(ch[2])
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
func (e *EdgeQuery) processOrEnqueueCell(id CellID) {
|
||
|
if e.iter.CellID() == id {
|
||
|
e.processOrEnqueue(id, e.iter.IndexCell())
|
||
|
} else {
|
||
|
e.processOrEnqueue(id, nil)
|
||
|
}
|
||
|
}
|
||
|
|
||
|
func (e *EdgeQuery) initQueue() {
|
||
|
if len(e.indexCovering) == 0 {
|
||
|
// We delay iterator initialization until now to make queries on very
|
||
|
// small indexes a bit faster (i.e., where brute force is used).
|
||
|
e.iter = NewShapeIndexIterator(e.index)
|
||
|
}
|
||
|
|
||
|
// Optimization: if the user is searching for just the closest edge, and the
|
||
|
// center of the target's bounding cap happens to intersect an index cell,
|
||
|
// then we try to limit the search region to a small disc by first
|
||
|
// processing the edges in that cell. This sets distance_limit_ based on
|
||
|
// the closest edge in that cell, which we can then use to limit the search
|
||
|
// area. This means that the cell containing "target" will be processed
|
||
|
// twice, but in general this is still faster.
|
||
|
//
|
||
|
// TODO(roberts): Even if the cap center is not contained, we could still
|
||
|
// process one or both of the adjacent index cells in CellID order,
|
||
|
// provided that those cells are closer than distanceLimit.
|
||
|
cb := e.target.capBound()
|
||
|
if cb.IsEmpty() {
|
||
|
return // Empty target.
|
||
|
}
|
||
|
|
||
|
if e.opts.maxResults == 1 && e.iter.LocatePoint(cb.Center()) {
|
||
|
e.processEdges(&queryQueueEntry{
|
||
|
distance: e.target.distance().zero(),
|
||
|
id: e.iter.CellID(),
|
||
|
indexCell: e.iter.IndexCell(),
|
||
|
})
|
||
|
// Skip the rest of the algorithm if we found an intersecting edge.
|
||
|
if e.distanceLimit == e.target.distance().zero() {
|
||
|
return
|
||
|
}
|
||
|
}
|
||
|
if len(e.indexCovering) == 0 {
|
||
|
e.initCovering()
|
||
|
}
|
||
|
if e.distanceLimit == e.target.distance().infinity() {
|
||
|
// Start with the precomputed index covering.
|
||
|
for i := range e.indexCovering {
|
||
|
e.processOrEnqueue(e.indexCovering[i], e.indexCells[i])
|
||
|
}
|
||
|
} else {
|
||
|
// Compute a covering of the search disc and intersect it with the
|
||
|
// precomputed index covering.
|
||
|
coverer := &RegionCoverer{MaxCells: 4, LevelMod: 1, MaxLevel: maxLevel}
|
||
|
|
||
|
radius := cb.Radius() + e.distanceLimit.chordAngleBound().Angle()
|
||
|
searchCB := CapFromCenterAngle(cb.Center(), radius)
|
||
|
maxDistCover := coverer.FastCovering(searchCB)
|
||
|
e.initialCells = CellUnionFromIntersection(e.indexCovering, maxDistCover)
|
||
|
|
||
|
// Now we need to clean up the initial cells to ensure that they all
|
||
|
// contain at least one cell of the ShapeIndex. (Some may not intersect
|
||
|
// the index at all, while other may be descendants of an index cell.)
|
||
|
i, j := 0, 0
|
||
|
for i < len(e.initialCells) {
|
||
|
idI := e.initialCells[i]
|
||
|
// Find the top-level cell that contains this initial cell.
|
||
|
for e.indexCovering[j].RangeMax() < idI {
|
||
|
j++
|
||
|
}
|
||
|
|
||
|
idJ := e.indexCovering[j]
|
||
|
if idI == idJ {
|
||
|
// This initial cell is one of the top-level cells. Use the
|
||
|
// precomputed ShapeIndexCell pointer to avoid an index seek.
|
||
|
e.processOrEnqueue(idJ, e.indexCells[j])
|
||
|
i++
|
||
|
j++
|
||
|
} else {
|
||
|
// This initial cell is a proper descendant of a top-level cell.
|
||
|
// Check how it is related to the cells of the ShapeIndex.
|
||
|
r := e.iter.LocateCellID(idI)
|
||
|
if r == Indexed {
|
||
|
// This cell is a descendant of an index cell.
|
||
|
// Enqueue it and skip any other initial cells
|
||
|
// that are also descendants of this cell.
|
||
|
e.processOrEnqueue(e.iter.CellID(), e.iter.IndexCell())
|
||
|
lastID := e.iter.CellID().RangeMax()
|
||
|
for i < len(e.initialCells) && e.initialCells[i] <= lastID {
|
||
|
i++
|
||
|
}
|
||
|
} else {
|
||
|
// Enqueue the cell only if it contains at least one index cell.
|
||
|
if r == Subdivided {
|
||
|
e.processOrEnqueue(idI, nil)
|
||
|
}
|
||
|
i++
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
func (e *EdgeQuery) initCovering() {
|
||
|
// Find the range of Cells spanned by the index and choose a level such
|
||
|
// that the entire index can be covered with just a few cells. These are
|
||
|
// the "top-level" cells. There are two cases:
|
||
|
//
|
||
|
// - If the index spans more than one face, then there is one top-level cell
|
||
|
// per spanned face, just big enough to cover the index cells on that face.
|
||
|
//
|
||
|
// - If the index spans only one face, then we find the smallest cell "C"
|
||
|
// that covers the index cells on that face (just like the case above).
|
||
|
// Then for each of the 4 children of "C", if the child contains any index
|
||
|
// cells then we create a top-level cell that is big enough to just fit
|
||
|
// those index cells (i.e., shrinking the child as much as possible to fit
|
||
|
// its contents). This essentially replicates what would happen if we
|
||
|
// started with "C" as the top-level cell, since "C" would immediately be
|
||
|
// split, except that we take the time to prune the children further since
|
||
|
// this will save work on every subsequent query.
|
||
|
e.indexCovering = make([]CellID, 0, 6)
|
||
|
|
||
|
// TODO(roberts): Use a single iterator below and save position
|
||
|
// information using pair {CellID, ShapeIndexCell}.
|
||
|
next := NewShapeIndexIterator(e.index, IteratorBegin)
|
||
|
last := NewShapeIndexIterator(e.index, IteratorEnd)
|
||
|
last.Prev()
|
||
|
if next.CellID() != last.CellID() {
|
||
|
// The index has at least two cells. Choose a level such that the entire
|
||
|
// index can be spanned with at most 6 cells (if the index spans multiple
|
||
|
// faces) or 4 cells (it the index spans a single face).
|
||
|
level, ok := next.CellID().CommonAncestorLevel(last.CellID())
|
||
|
if !ok {
|
||
|
level = 0
|
||
|
} else {
|
||
|
level++
|
||
|
}
|
||
|
|
||
|
// Visit each potential top-level cell except the last (handled below).
|
||
|
lastID := last.CellID().Parent(level)
|
||
|
for id := next.CellID().Parent(level); id != lastID; id = id.Next() {
|
||
|
// Skip any top-level cells that don't contain any index cells.
|
||
|
if id.RangeMax() < next.CellID() {
|
||
|
continue
|
||
|
}
|
||
|
|
||
|
// Find the range of index cells contained by this top-level cell and
|
||
|
// then shrink the cell if necessary so that it just covers them.
|
||
|
cellFirst := next.clone()
|
||
|
next.seek(id.RangeMax().Next())
|
||
|
cellLast := next.clone()
|
||
|
cellLast.Prev()
|
||
|
e.addInitialRange(cellFirst, cellLast)
|
||
|
break
|
||
|
}
|
||
|
|
||
|
}
|
||
|
e.addInitialRange(next, last)
|
||
|
}
|
||
|
|
||
|
// addInitialRange adds an entry to the indexCovering and indexCells that covers the given
|
||
|
// inclusive range of cells.
|
||
|
//
|
||
|
// This requires that first and last cells have a common ancestor.
|
||
|
func (e *EdgeQuery) addInitialRange(first, last *ShapeIndexIterator) {
|
||
|
if first.CellID() == last.CellID() {
|
||
|
// The range consists of a single index cell.
|
||
|
e.indexCovering = append(e.indexCovering, first.CellID())
|
||
|
e.indexCells = append(e.indexCells, first.IndexCell())
|
||
|
} else {
|
||
|
// Add the lowest common ancestor of the given range.
|
||
|
level, _ := first.CellID().CommonAncestorLevel(last.CellID())
|
||
|
e.indexCovering = append(e.indexCovering, first.CellID().Parent(level))
|
||
|
e.indexCells = append(e.indexCells, nil)
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// processEdges processes all the edges of the given index cell.
|
||
|
func (e *EdgeQuery) processEdges(entry *queryQueueEntry) {
|
||
|
for _, clipped := range entry.indexCell.shapes {
|
||
|
shape := e.index.Shape(clipped.shapeID)
|
||
|
for j := 0; j < clipped.numEdges(); j++ {
|
||
|
e.maybeAddResult(shape, int32(clipped.edges[j]))
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// processOrEnqueue the given cell id and indexCell.
|
||
|
func (e *EdgeQuery) processOrEnqueue(id CellID, indexCell *ShapeIndexCell) {
|
||
|
if indexCell != nil {
|
||
|
// If this index cell has only a few edges, then it is faster to check
|
||
|
// them directly rather than computing the minimum distance to the Cell
|
||
|
// and inserting it into the queue.
|
||
|
const minEdgesToEnqueue = 10
|
||
|
numEdges := indexCell.numEdges()
|
||
|
if numEdges == 0 {
|
||
|
return
|
||
|
}
|
||
|
if numEdges < minEdgesToEnqueue {
|
||
|
// Set "distance" to zero to avoid the expense of computing it.
|
||
|
e.processEdges(&queryQueueEntry{
|
||
|
distance: e.target.distance().zero(),
|
||
|
id: id,
|
||
|
indexCell: indexCell,
|
||
|
})
|
||
|
return
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// Otherwise compute the minimum distance to any point in the cell and add
|
||
|
// it to the priority queue.
|
||
|
cell := CellFromCellID(id)
|
||
|
dist := e.distanceLimit
|
||
|
var ok bool
|
||
|
if dist, ok = e.target.updateDistanceToCell(cell, dist); !ok {
|
||
|
return
|
||
|
}
|
||
|
if e.useConservativeCellDistance {
|
||
|
// Ensure that "distance" is a lower bound on the true distance to the cell.
|
||
|
dist = dist.sub(e.target.distance().fromChordAngle(e.opts.maxError))
|
||
|
}
|
||
|
|
||
|
e.queue.push(&queryQueueEntry{
|
||
|
distance: dist,
|
||
|
id: id,
|
||
|
indexCell: indexCell,
|
||
|
})
|
||
|
}
|
||
|
|
||
|
// TODO(roberts): Remaining pieces
|
||
|
// GetEdge
|
||
|
// Project
|