307 lines
12 KiB
Go
307 lines
12 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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"math"
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"github.com/golang/geo/s1"
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)
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// maxDistance implements distance as the supplementary distance (Pi - x) to find
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// results that are the furthest using the distance related algorithms.
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type maxDistance s1.ChordAngle
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func (m maxDistance) chordAngle() s1.ChordAngle { return s1.ChordAngle(m) }
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func (m maxDistance) zero() distance { return maxDistance(s1.StraightChordAngle) }
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func (m maxDistance) negative() distance { return maxDistance(s1.InfChordAngle()) }
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func (m maxDistance) infinity() distance { return maxDistance(s1.NegativeChordAngle) }
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func (m maxDistance) less(other distance) bool { return m.chordAngle() > other.chordAngle() }
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func (m maxDistance) sub(other distance) distance {
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return maxDistance(m.chordAngle() + other.chordAngle())
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}
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func (m maxDistance) chordAngleBound() s1.ChordAngle {
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return s1.StraightChordAngle - m.chordAngle()
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}
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func (m maxDistance) updateDistance(dist distance) (distance, bool) {
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if dist.less(m) {
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m = maxDistance(dist.chordAngle())
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return m, true
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}
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return m, false
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}
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func (m maxDistance) fromChordAngle(o s1.ChordAngle) distance {
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return maxDistance(o)
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}
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// MaxDistanceToPointTarget is used for computing the maximum distance to a Point.
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type MaxDistanceToPointTarget struct {
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point Point
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dist distance
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}
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// NewMaxDistanceToPointTarget returns a new target for the given Point.
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func NewMaxDistanceToPointTarget(point Point) *MaxDistanceToPointTarget {
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m := maxDistance(0)
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return &MaxDistanceToPointTarget{point: point, dist: &m}
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}
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func (m *MaxDistanceToPointTarget) capBound() Cap {
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return CapFromCenterChordAngle(Point{m.point.Mul(-1)}, (s1.ChordAngle(0)))
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}
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func (m *MaxDistanceToPointTarget) updateDistanceToPoint(p Point, dist distance) (distance, bool) {
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return dist.updateDistance(maxDistance(ChordAngleBetweenPoints(p, m.point)))
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}
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func (m *MaxDistanceToPointTarget) updateDistanceToEdge(edge Edge, dist distance) (distance, bool) {
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if d, ok := UpdateMaxDistance(m.point, edge.V0, edge.V1, dist.chordAngle()); ok {
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dist, _ = dist.updateDistance(maxDistance(d))
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return dist, true
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}
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return dist, false
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}
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func (m *MaxDistanceToPointTarget) updateDistanceToCell(cell Cell, dist distance) (distance, bool) {
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return dist.updateDistance(maxDistance(cell.MaxDistance(m.point)))
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}
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func (m *MaxDistanceToPointTarget) visitContainingShapes(index *ShapeIndex, v shapePointVisitorFunc) bool {
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// For furthest points, we visit the polygons whose interior contains
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// the antipode of the target point. These are the polygons whose
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// distance to the target is maxDistance.zero()
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q := NewContainsPointQuery(index, VertexModelSemiOpen)
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return q.visitContainingShapes(Point{m.point.Mul(-1)}, func(shape Shape) bool {
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return v(shape, m.point)
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})
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}
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func (m *MaxDistanceToPointTarget) setMaxError(maxErr s1.ChordAngle) bool { return false }
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func (m *MaxDistanceToPointTarget) maxBruteForceIndexSize() int { return 30 }
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func (m *MaxDistanceToPointTarget) distance() distance { return m.dist }
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// MaxDistanceToEdgeTarget is used for computing the maximum distance to an Edge.
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type MaxDistanceToEdgeTarget struct {
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e Edge
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dist distance
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}
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// NewMaxDistanceToEdgeTarget returns a new target for the given Edge.
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func NewMaxDistanceToEdgeTarget(e Edge) *MaxDistanceToEdgeTarget {
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m := maxDistance(0)
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return &MaxDistanceToEdgeTarget{e: e, dist: m}
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}
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// capBound returns a Cap that bounds the antipode of the target. (This
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// is the set of points whose maxDistance to the target is maxDistance.zero)
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func (m *MaxDistanceToEdgeTarget) capBound() Cap {
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// The following computes a radius equal to half the edge length in an
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// efficient and numerically stable way.
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d2 := float64(ChordAngleBetweenPoints(m.e.V0, m.e.V1))
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r2 := (0.5 * d2) / (1 + math.Sqrt(1-0.25*d2))
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return CapFromCenterChordAngle(Point{m.e.V0.Add(m.e.V1.Vector).Mul(-1).Normalize()}, s1.ChordAngleFromSquaredLength(r2))
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}
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func (m *MaxDistanceToEdgeTarget) updateDistanceToPoint(p Point, dist distance) (distance, bool) {
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if d, ok := UpdateMaxDistance(p, m.e.V0, m.e.V1, dist.chordAngle()); ok {
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dist, _ = dist.updateDistance(maxDistance(d))
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return dist, true
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}
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return dist, false
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}
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func (m *MaxDistanceToEdgeTarget) updateDistanceToEdge(edge Edge, dist distance) (distance, bool) {
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if d, ok := updateEdgePairMaxDistance(m.e.V0, m.e.V1, edge.V0, edge.V1, dist.chordAngle()); ok {
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dist, _ = dist.updateDistance(maxDistance(d))
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return dist, true
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}
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return dist, false
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}
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func (m *MaxDistanceToEdgeTarget) updateDistanceToCell(cell Cell, dist distance) (distance, bool) {
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return dist.updateDistance(maxDistance(cell.MaxDistanceToEdge(m.e.V0, m.e.V1)))
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}
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func (m *MaxDistanceToEdgeTarget) visitContainingShapes(index *ShapeIndex, v shapePointVisitorFunc) bool {
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// We only need to test one edge point. That is because the method *must*
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// visit a polygon if it fully contains the target, and *is allowed* to
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// visit a polygon if it intersects the target. If the tested vertex is not
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// contained, we know the full edge is not contained; if the tested vertex is
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// contained, then the edge either is fully contained (must be visited) or it
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// intersects (is allowed to be visited). We visit the center of the edge so
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// that edge AB gives identical results to BA.
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target := NewMaxDistanceToPointTarget(Point{m.e.V0.Add(m.e.V1.Vector).Normalize()})
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return target.visitContainingShapes(index, v)
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}
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func (m *MaxDistanceToEdgeTarget) setMaxError(maxErr s1.ChordAngle) bool { return false }
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func (m *MaxDistanceToEdgeTarget) maxBruteForceIndexSize() int { return 30 }
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func (m *MaxDistanceToEdgeTarget) distance() distance { return m.dist }
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// MaxDistanceToCellTarget is used for computing the maximum distance to a Cell.
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type MaxDistanceToCellTarget struct {
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cell Cell
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dist distance
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}
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// NewMaxDistanceToCellTarget returns a new target for the given Cell.
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func NewMaxDistanceToCellTarget(cell Cell) *MaxDistanceToCellTarget {
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m := maxDistance(0)
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return &MaxDistanceToCellTarget{cell: cell, dist: m}
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}
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func (m *MaxDistanceToCellTarget) capBound() Cap {
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c := m.cell.CapBound()
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return CapFromCenterAngle(Point{c.Center().Mul(-1)}, c.Radius())
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}
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func (m *MaxDistanceToCellTarget) updateDistanceToPoint(p Point, dist distance) (distance, bool) {
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return dist.updateDistance(maxDistance(m.cell.MaxDistance(p)))
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}
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func (m *MaxDistanceToCellTarget) updateDistanceToEdge(edge Edge, dist distance) (distance, bool) {
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return dist.updateDistance(maxDistance(m.cell.MaxDistanceToEdge(edge.V0, edge.V1)))
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}
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func (m *MaxDistanceToCellTarget) updateDistanceToCell(cell Cell, dist distance) (distance, bool) {
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return dist.updateDistance(maxDistance(m.cell.MaxDistanceToCell(cell)))
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}
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func (m *MaxDistanceToCellTarget) visitContainingShapes(index *ShapeIndex, v shapePointVisitorFunc) bool {
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// We only need to check one point here - cell center is simplest.
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// See comment at MaxDistanceToEdgeTarget's visitContainingShapes.
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target := NewMaxDistanceToPointTarget(m.cell.Center())
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return target.visitContainingShapes(index, v)
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}
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func (m *MaxDistanceToCellTarget) setMaxError(maxErr s1.ChordAngle) bool { return false }
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func (m *MaxDistanceToCellTarget) maxBruteForceIndexSize() int { return 30 }
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func (m *MaxDistanceToCellTarget) distance() distance { return m.dist }
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// MaxDistanceToShapeIndexTarget is used for computing the maximum distance to a ShapeIndex.
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type MaxDistanceToShapeIndexTarget struct {
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index *ShapeIndex
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query *EdgeQuery
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dist distance
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}
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// NewMaxDistanceToShapeIndexTarget returns a new target for the given ShapeIndex.
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func NewMaxDistanceToShapeIndexTarget(index *ShapeIndex) *MaxDistanceToShapeIndexTarget {
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m := maxDistance(0)
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return &MaxDistanceToShapeIndexTarget{
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index: index,
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dist: m,
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query: NewFurthestEdgeQuery(index, NewFurthestEdgeQueryOptions()),
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}
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}
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// capBound returns a Cap that bounds the antipode of the target. This
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// is the set of points whose maxDistance to the target is maxDistance.zero()
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func (m *MaxDistanceToShapeIndexTarget) capBound() Cap {
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// TODO(roberts): Depends on ShapeIndexRegion
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// c := makeShapeIndexRegion(m.index).CapBound()
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// return CapFromCenterRadius(Point{c.Center.Mul(-1)}, c.Radius())
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panic("not implemented yet")
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}
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func (m *MaxDistanceToShapeIndexTarget) updateDistanceToPoint(p Point, dist distance) (distance, bool) {
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m.query.opts.distanceLimit = dist.chordAngle()
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target := NewMaxDistanceToPointTarget(p)
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r := m.query.findEdge(target, m.query.opts)
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if r.shapeID < 0 {
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return dist, false
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}
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return r.distance, true
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}
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func (m *MaxDistanceToShapeIndexTarget) updateDistanceToEdge(edge Edge, dist distance) (distance, bool) {
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m.query.opts.distanceLimit = dist.chordAngle()
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target := NewMaxDistanceToEdgeTarget(edge)
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r := m.query.findEdge(target, m.query.opts)
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if r.shapeID < 0 {
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return dist, false
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}
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return r.distance, true
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}
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func (m *MaxDistanceToShapeIndexTarget) updateDistanceToCell(cell Cell, dist distance) (distance, bool) {
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m.query.opts.distanceLimit = dist.chordAngle()
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target := NewMaxDistanceToCellTarget(cell)
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r := m.query.findEdge(target, m.query.opts)
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if r.shapeID < 0 {
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return dist, false
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}
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return r.distance, true
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}
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// visitContainingShapes returns the polygons containing the antipodal
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// reflection of *any* connected component for target types consisting of
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// multiple connected components. It is sufficient to test containment of
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// one vertex per connected component, since this allows us to also return
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// any polygon whose boundary has distance.zero() to the target.
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func (m *MaxDistanceToShapeIndexTarget) visitContainingShapes(index *ShapeIndex, v shapePointVisitorFunc) bool {
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// It is sufficient to find the set of chain starts in the target index
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// (i.e., one vertex per connected component of edges) that are contained by
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// the query index, except for one special case to handle full polygons.
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//
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// TODO(roberts): Do this by merge-joining the two ShapeIndexes and share
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// the code with BooleanOperation.
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for _, shape := range m.index.shapes {
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numChains := shape.NumChains()
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// Shapes that don't have any edges require a special case (below).
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testedPoint := false
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for c := 0; c < numChains; c++ {
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chain := shape.Chain(c)
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if chain.Length == 0 {
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continue
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}
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testedPoint = true
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target := NewMaxDistanceToPointTarget(shape.ChainEdge(c, 0).V0)
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if !target.visitContainingShapes(index, v) {
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return false
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}
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}
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if !testedPoint {
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// Special case to handle full polygons.
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ref := shape.ReferencePoint()
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if !ref.Contained {
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continue
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}
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target := NewMaxDistanceToPointTarget(ref.Point)
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if !target.visitContainingShapes(index, v) {
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return false
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}
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}
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}
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return true
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}
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func (m *MaxDistanceToShapeIndexTarget) setMaxError(maxErr s1.ChordAngle) bool {
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m.query.opts.maxError = maxErr
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return true
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}
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func (m *MaxDistanceToShapeIndexTarget) maxBruteForceIndexSize() int { return 30 }
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func (m *MaxDistanceToShapeIndexTarget) distance() distance { return m.dist }
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func (m *MaxDistanceToShapeIndexTarget) setIncludeInteriors(b bool) {
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m.query.opts.includeInteriors = b
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}
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func (m *MaxDistanceToShapeIndexTarget) setUseBruteForce(b bool) { m.query.opts.useBruteForce = b }
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// TODO(roberts): Remaining methods
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//
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// func (m *MaxDistanceToShapeIndexTarget) capBound() Cap {
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// CellUnionTarget
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