gotosocial/vendor/github.com/golang/geo/s2/shapeindex.go

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// Copyright 2016 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
import (
"math"
"sort"
"sync"
"sync/atomic"
"github.com/golang/geo/r1"
"github.com/golang/geo/r2"
)
// CellRelation describes the possible relationships between a target cell
// and the cells of the ShapeIndex. If the target is an index cell or is
// contained by an index cell, it is Indexed. If the target is subdivided
// into one or more index cells, it is Subdivided. Otherwise it is Disjoint.
type CellRelation int
// The possible CellRelations for a ShapeIndex.
const (
Indexed CellRelation = iota
Subdivided
Disjoint
)
const (
// cellPadding defines the total error when clipping an edge which comes
// from two sources:
// (1) Clipping the original spherical edge to a cube face (the face edge).
// The maximum error in this step is faceClipErrorUVCoord.
// (2) Clipping the face edge to the u- or v-coordinate of a cell boundary.
// The maximum error in this step is edgeClipErrorUVCoord.
// Finally, since we encounter the same errors when clipping query edges, we
// double the total error so that we only need to pad edges during indexing
// and not at query time.
cellPadding = 2.0 * (faceClipErrorUVCoord + edgeClipErrorUVCoord)
// cellSizeToLongEdgeRatio defines the cell size relative to the length of an
// edge at which it is first considered to be long. Long edges do not
// contribute toward the decision to subdivide a cell further. For example,
// a value of 2.0 means that the cell must be at least twice the size of the
// edge in order for that edge to be counted. There are two reasons for not
// counting long edges: (1) such edges typically need to be propagated to
// several children, which increases time and memory costs without much benefit,
// and (2) in pathological cases, many long edges close together could force
// subdivision to continue all the way to the leaf cell level.
cellSizeToLongEdgeRatio = 1.0
)
// clippedShape represents the part of a shape that intersects a Cell.
// It consists of the set of edge IDs that intersect that cell and a boolean
// indicating whether the center of the cell is inside the shape (for shapes
// that have an interior).
//
// Note that the edges themselves are not clipped; we always use the original
// edges for intersection tests so that the results will be the same as the
// original shape.
type clippedShape struct {
// shapeID is the index of the shape this clipped shape is a part of.
shapeID int32
// containsCenter indicates if the center of the CellID this shape has been
// clipped to falls inside this shape. This is false for shapes that do not
// have an interior.
containsCenter bool
// edges is the ordered set of ShapeIndex original edge IDs. Edges
// are stored in increasing order of edge ID.
edges []int
}
// newClippedShape returns a new clipped shape for the given shapeID and number of expected edges.
func newClippedShape(id int32, numEdges int) *clippedShape {
return &clippedShape{
shapeID: id,
edges: make([]int, numEdges),
}
}
// numEdges returns the number of edges that intersect the CellID of the Cell this was clipped to.
func (c *clippedShape) numEdges() int {
return len(c.edges)
}
// containsEdge reports if this clipped shape contains the given edge ID.
func (c *clippedShape) containsEdge(id int) bool {
// Linear search is fast because the number of edges per shape is typically
// very small (less than 10).
for _, e := range c.edges {
if e == id {
return true
}
}
return false
}
// ShapeIndexCell stores the index contents for a particular CellID.
type ShapeIndexCell struct {
shapes []*clippedShape
}
// NewShapeIndexCell creates a new cell that is sized to hold the given number of shapes.
func NewShapeIndexCell(numShapes int) *ShapeIndexCell {
return &ShapeIndexCell{
shapes: make([]*clippedShape, numShapes),
}
}
// numEdges reports the total number of edges in all clipped shapes in this cell.
func (s *ShapeIndexCell) numEdges() int {
var e int
for _, cs := range s.shapes {
e += cs.numEdges()
}
return e
}
// add adds the given clipped shape to this index cell.
func (s *ShapeIndexCell) add(c *clippedShape) {
// C++ uses a set, so it's ordered and unique. We don't currently catch
// the case when a duplicate value is added.
s.shapes = append(s.shapes, c)
}
// findByShapeID returns the clipped shape that contains the given shapeID,
// or nil if none of the clipped shapes contain it.
func (s *ShapeIndexCell) findByShapeID(shapeID int32) *clippedShape {
// Linear search is fine because the number of shapes per cell is typically
// very small (most often 1), and is large only for pathological inputs
// (e.g. very deeply nested loops).
for _, clipped := range s.shapes {
if clipped.shapeID == shapeID {
return clipped
}
}
return nil
}
// faceEdge and clippedEdge store temporary edge data while the index is being
// updated.
//
// While it would be possible to combine all the edge information into one
// structure, there are two good reasons for separating it:
//
// - Memory usage. Separating the two means that we only need to
// store one copy of the per-face data no matter how many times an edge is
// subdivided, and it also lets us delay computing bounding boxes until
// they are needed for processing each face (when the dataset spans
// multiple faces).
//
// - Performance. UpdateEdges is significantly faster on large polygons when
// the data is separated, because it often only needs to access the data in
// clippedEdge and this data is cached more successfully.
// faceEdge represents an edge that has been projected onto a given face,
type faceEdge struct {
shapeID int32 // The ID of shape that this edge belongs to
edgeID int // Edge ID within that shape
maxLevel int // Not desirable to subdivide this edge beyond this level
hasInterior bool // Belongs to a shape that has a dimension of 2
a, b r2.Point // The edge endpoints, clipped to a given face
edge Edge // The original edge.
}
// clippedEdge represents the portion of that edge that has been clipped to a given Cell.
type clippedEdge struct {
faceEdge *faceEdge // The original unclipped edge
bound r2.Rect // Bounding box for the clipped portion
}
// ShapeIndexIteratorPos defines the set of possible iterator starting positions. By
// default iterators are unpositioned, since this avoids an extra seek in this
// situation where one of the seek methods (such as Locate) is immediately called.
type ShapeIndexIteratorPos int
const (
// IteratorBegin specifies the iterator should be positioned at the beginning of the index.
IteratorBegin ShapeIndexIteratorPos = iota
// IteratorEnd specifies the iterator should be positioned at the end of the index.
IteratorEnd
)
// ShapeIndexIterator is an iterator that provides low-level access to
// the cells of the index. Cells are returned in increasing order of CellID.
//
// for it := index.Iterator(); !it.Done(); it.Next() {
// fmt.Print(it.CellID())
// }
//
type ShapeIndexIterator struct {
index *ShapeIndex
position int
id CellID
cell *ShapeIndexCell
}
// NewShapeIndexIterator creates a new iterator for the given index. If a starting
// position is specified, the iterator is positioned at the given spot.
func NewShapeIndexIterator(index *ShapeIndex, pos ...ShapeIndexIteratorPos) *ShapeIndexIterator {
s := &ShapeIndexIterator{
index: index,
}
if len(pos) > 0 {
if len(pos) > 1 {
panic("too many ShapeIndexIteratorPos arguments")
}
switch pos[0] {
case IteratorBegin:
s.Begin()
case IteratorEnd:
s.End()
default:
panic("unknown ShapeIndexIteratorPos value")
}
}
return s
}
func (s *ShapeIndexIterator) clone() *ShapeIndexIterator {
return &ShapeIndexIterator{
index: s.index,
position: s.position,
id: s.id,
cell: s.cell,
}
}
// CellID returns the CellID of the current index cell.
// If s.Done() is true, a value larger than any valid CellID is returned.
func (s *ShapeIndexIterator) CellID() CellID {
return s.id
}
// IndexCell returns the current index cell.
func (s *ShapeIndexIterator) IndexCell() *ShapeIndexCell {
// TODO(roberts): C++ has this call a virtual method to allow subclasses
// of ShapeIndexIterator to do other work before returning the cell. Do
// we need such a thing?
return s.cell
}
// Center returns the Point at the center of the current position of the iterator.
func (s *ShapeIndexIterator) Center() Point {
return s.CellID().Point()
}
// Begin positions the iterator at the beginning of the index.
func (s *ShapeIndexIterator) Begin() {
if !s.index.IsFresh() {
s.index.maybeApplyUpdates()
}
s.position = 0
s.refresh()
}
// Next positions the iterator at the next index cell.
func (s *ShapeIndexIterator) Next() {
s.position++
s.refresh()
}
// Prev advances the iterator to the previous cell in the index and returns true to
// indicate it was not yet at the beginning of the index. If the iterator is at the
// first cell the call does nothing and returns false.
func (s *ShapeIndexIterator) Prev() bool {
if s.position <= 0 {
return false
}
s.position--
s.refresh()
return true
}
// End positions the iterator at the end of the index.
func (s *ShapeIndexIterator) End() {
s.position = len(s.index.cells)
s.refresh()
}
// Done reports if the iterator is positioned at or after the last index cell.
func (s *ShapeIndexIterator) Done() bool {
return s.id == SentinelCellID
}
// refresh updates the stored internal iterator values.
func (s *ShapeIndexIterator) refresh() {
if s.position < len(s.index.cells) {
s.id = s.index.cells[s.position]
s.cell = s.index.cellMap[s.CellID()]
} else {
s.id = SentinelCellID
s.cell = nil
}
}
// seek positions the iterator at the first cell whose ID >= target, or at the
// end of the index if no such cell exists.
func (s *ShapeIndexIterator) seek(target CellID) {
s.position = sort.Search(len(s.index.cells), func(i int) bool {
return s.index.cells[i] >= target
})
s.refresh()
}
// LocatePoint positions the iterator at the cell that contains the given Point.
// If no such cell exists, the iterator position is unspecified, and false is returned.
// The cell at the matched position is guaranteed to contain all edges that might
// intersect the line segment between target and the cell's center.
func (s *ShapeIndexIterator) LocatePoint(p Point) bool {
// Let I = cellMap.LowerBound(T), where T is the leaf cell containing
// point P. Then if T is contained by an index cell, then the
// containing cell is either I or I'. We test for containment by comparing
// the ranges of leaf cells spanned by T, I, and I'.
target := cellIDFromPoint(p)
s.seek(target)
if !s.Done() && s.CellID().RangeMin() <= target {
return true
}
if s.Prev() && s.CellID().RangeMax() >= target {
return true
}
return false
}
// LocateCellID attempts to position the iterator at the first matching index cell
// in the index that has some relation to the given CellID. Let T be the target CellID.
// If T is contained by (or equal to) some index cell I, then the iterator is positioned
// at I and returns Indexed. Otherwise if T contains one or more (smaller) index cells,
// then the iterator is positioned at the first such cell I and return Subdivided.
// Otherwise Disjoint is returned and the iterator position is undefined.
func (s *ShapeIndexIterator) LocateCellID(target CellID) CellRelation {
// Let T be the target, let I = cellMap.LowerBound(T.RangeMin()), and
// let I' be the predecessor of I. If T contains any index cells, then T
// contains I. Similarly, if T is contained by an index cell, then the
// containing cell is either I or I'. We test for containment by comparing
// the ranges of leaf cells spanned by T, I, and I'.
s.seek(target.RangeMin())
if !s.Done() {
if s.CellID() >= target && s.CellID().RangeMin() <= target {
return Indexed
}
if s.CellID() <= target.RangeMax() {
return Subdivided
}
}
if s.Prev() && s.CellID().RangeMax() >= target {
return Indexed
}
return Disjoint
}
// tracker keeps track of which shapes in a given set contain a particular point
// (the focus). It provides an efficient way to move the focus from one point
// to another and incrementally update the set of shapes which contain it. We use
// this to compute which shapes contain the center of every CellID in the index,
// by advancing the focus from one cell center to the next.
//
// Initially the focus is at the start of the CellID space-filling curve. We then
// visit all the cells that are being added to the ShapeIndex in increasing order
// of CellID. For each cell, we draw two edges: one from the entry vertex to the
// center, and another from the center to the exit vertex (where entry and exit
// refer to the points where the space-filling curve enters and exits the cell).
// By counting edge crossings we can incrementally compute which shapes contain
// the cell center. Note that the same set of shapes will always contain the exit
// point of one cell and the entry point of the next cell in the index, because
// either (a) these two points are actually the same, or (b) the intervening
// cells in CellID order are all empty, and therefore there are no edge crossings
// if we follow this path from one cell to the other.
//
// In C++, this is S2ShapeIndex::InteriorTracker.
type tracker struct {
isActive bool
a Point
b Point
nextCellID CellID
crosser *EdgeCrosser
shapeIDs []int32
// Shape ids saved by saveAndClearStateBefore. The state is never saved
// recursively so we don't need to worry about maintaining a stack.
savedIDs []int32
}
// newTracker returns a new tracker with the appropriate defaults.
func newTracker() *tracker {
// As shapes are added, we compute which ones contain the start of the
// CellID space-filling curve by drawing an edge from OriginPoint to this
// point and counting how many shape edges cross this edge.
t := &tracker{
isActive: false,
b: trackerOrigin(),
nextCellID: CellIDFromFace(0).ChildBeginAtLevel(maxLevel),
}
t.drawTo(Point{faceUVToXYZ(0, -1, -1).Normalize()}) // CellID curve start
return t
}
// trackerOrigin returns the initial focus point when the tracker is created
// (corresponding to the start of the CellID space-filling curve).
func trackerOrigin() Point {
// The start of the S2CellId space-filling curve.
return Point{faceUVToXYZ(0, -1, -1).Normalize()}
}
// focus returns the current focus point of the tracker.
func (t *tracker) focus() Point { return t.b }
// addShape adds a shape whose interior should be tracked. containsOrigin indicates
// whether the current focus point is inside the shape. Alternatively, if
// the focus point is in the process of being moved (via moveTo/drawTo), you
// can also specify containsOrigin at the old focus point and call testEdge
// for every edge of the shape that might cross the current drawTo line.
// This updates the state to correspond to the new focus point.
//
// This requires shape.HasInterior
func (t *tracker) addShape(shapeID int32, containsFocus bool) {
t.isActive = true
if containsFocus {
t.toggleShape(shapeID)
}
}
// moveTo moves the focus of the tracker to the given point. This method should
// only be used when it is known that there are no edge crossings between the old
// and new focus locations; otherwise use drawTo.
func (t *tracker) moveTo(b Point) { t.b = b }
// drawTo moves the focus of the tracker to the given point. After this method is
// called, testEdge should be called with all edges that may cross the line
// segment between the old and new focus locations.
func (t *tracker) drawTo(b Point) {
t.a = t.b
t.b = b
// TODO: the edge crosser may need an in-place Init method if this gets expensive
t.crosser = NewEdgeCrosser(t.a, t.b)
}
// testEdge checks if the given edge crosses the current edge, and if so, then
// toggle the state of the given shapeID.
// This requires shape to have an interior.
func (t *tracker) testEdge(shapeID int32, edge Edge) {
if t.crosser.EdgeOrVertexCrossing(edge.V0, edge.V1) {
t.toggleShape(shapeID)
}
}
// setNextCellID is used to indicate that the last argument to moveTo or drawTo
// was the entry vertex of the given CellID, i.e. the tracker is positioned at the
// start of this cell. By using this method together with atCellID, the caller
// can avoid calling moveTo in cases where the exit vertex of the previous cell
// is the same as the entry vertex of the current cell.
func (t *tracker) setNextCellID(nextCellID CellID) {
t.nextCellID = nextCellID.RangeMin()
}
// atCellID reports if the focus is already at the entry vertex of the given
// CellID (provided that the caller calls setNextCellID as each cell is processed).
func (t *tracker) atCellID(cellid CellID) bool {
return cellid.RangeMin() == t.nextCellID
}
// toggleShape adds or removes the given shapeID from the set of IDs it is tracking.
func (t *tracker) toggleShape(shapeID int32) {
// Most shapeIDs slices are small, so special case the common steps.
// If there is nothing here, add it.
if len(t.shapeIDs) == 0 {
t.shapeIDs = append(t.shapeIDs, shapeID)
return
}
// If it's the first element, drop it from the slice.
if t.shapeIDs[0] == shapeID {
t.shapeIDs = t.shapeIDs[1:]
return
}
for i, s := range t.shapeIDs {
if s < shapeID {
continue
}
// If it's in the set, cut it out.
if s == shapeID {
copy(t.shapeIDs[i:], t.shapeIDs[i+1:]) // overwrite the ith element
t.shapeIDs = t.shapeIDs[:len(t.shapeIDs)-1]
return
}
// We've got to a point in the slice where we should be inserted.
// (the given shapeID is now less than the current positions id.)
t.shapeIDs = append(t.shapeIDs[0:i],
append([]int32{shapeID}, t.shapeIDs[i:len(t.shapeIDs)]...)...)
return
}
// We got to the end and didn't find it, so add it to the list.
t.shapeIDs = append(t.shapeIDs, shapeID)
}
// saveAndClearStateBefore makes an internal copy of the state for shape ids below
// the given limit, and then clear the state for those shapes. This is used during
// incremental updates to track the state of added and removed shapes separately.
func (t *tracker) saveAndClearStateBefore(limitShapeID int32) {
limit := t.lowerBound(limitShapeID)
t.savedIDs = append([]int32(nil), t.shapeIDs[:limit]...)
t.shapeIDs = t.shapeIDs[limit:]
}
// restoreStateBefore restores the state previously saved by saveAndClearStateBefore.
// This only affects the state for shapeIDs below "limitShapeID".
func (t *tracker) restoreStateBefore(limitShapeID int32) {
limit := t.lowerBound(limitShapeID)
t.shapeIDs = append(append([]int32(nil), t.savedIDs...), t.shapeIDs[limit:]...)
t.savedIDs = nil
}
// lowerBound returns the shapeID of the first entry x where x >= shapeID.
func (t *tracker) lowerBound(shapeID int32) int32 {
panic("not implemented")
}
// removedShape represents a set of edges from the given shape that is queued for removal.
type removedShape struct {
shapeID int32
hasInterior bool
containsTrackerOrigin bool
edges []Edge
}
// There are three basic states the index can be in.
const (
stale int32 = iota // There are pending updates.
updating // Updates are currently being applied.
fresh // There are no pending updates.
)
// ShapeIndex indexes a set of Shapes, where a Shape is some collection of edges
// that optionally defines an interior. It can be used to represent a set of
// points, a set of polylines, or a set of polygons. For Shapes that have
// interiors, the index makes it very fast to determine which Shape(s) contain
// a given point or region.
//
// The index can be updated incrementally by adding or removing shapes. It is
// designed to handle up to hundreds of millions of edges. All data structures
// are designed to be small, so the index is compact; generally it is smaller
// than the underlying data being indexed. The index is also fast to construct.
//
// Polygon, Loop, and Polyline implement Shape which allows these objects to
// be indexed easily. You can find useful query methods in CrossingEdgeQuery
// and ClosestEdgeQuery (Not yet implemented in Go).
//
// Example showing how to build an index of Polylines:
//
// index := NewShapeIndex()
// for _, polyline := range polylines {
// index.Add(polyline);
// }
// // Now you can use a CrossingEdgeQuery or ClosestEdgeQuery here.
//
type ShapeIndex struct {
// shapes is a map of shape ID to shape.
shapes map[int32]Shape
// The maximum number of edges per cell.
// TODO(roberts): Update the comments when the usage of this is implemented.
maxEdgesPerCell int
// nextID tracks the next ID to hand out. IDs are not reused when shapes
// are removed from the index.
nextID int32
// cellMap is a map from CellID to the set of clipped shapes that intersect that
// cell. The cell IDs cover a set of non-overlapping regions on the sphere.
// In C++, this is a BTree, so the cells are ordered naturally by the data structure.
cellMap map[CellID]*ShapeIndexCell
// Track the ordered list of cell IDs.
cells []CellID
// The current status of the index; accessed atomically.
status int32
// Additions and removals are queued and processed on the first subsequent
// query. There are several reasons to do this:
//
// - It is significantly more efficient to process updates in batches if
// the amount of entities added grows.
// - Often the index will never be queried, in which case we can save both
// the time and memory required to build it. Examples:
// + Loops that are created simply to pass to an Polygon. (We don't
// need the Loop index, because Polygon builds its own index.)
// + Applications that load a database of geometry and then query only
// a small fraction of it.
//
// The main drawback is that we need to go to some extra work to ensure that
// some methods are still thread-safe. Note that the goal is *not* to
// make this thread-safe in general, but simply to hide the fact that
// we defer some of the indexing work until query time.
//
// This mutex protects all of following fields in the index.
mu sync.RWMutex
// pendingAdditionsPos is the index of the first entry that has not been processed
// via applyUpdatesInternal.
pendingAdditionsPos int32
// The set of shapes that have been queued for removal but not processed yet by
// applyUpdatesInternal.
pendingRemovals []*removedShape
}
// NewShapeIndex creates a new ShapeIndex.
func NewShapeIndex() *ShapeIndex {
return &ShapeIndex{
maxEdgesPerCell: 10,
shapes: make(map[int32]Shape),
cellMap: make(map[CellID]*ShapeIndexCell),
cells: nil,
status: fresh,
}
}
// Iterator returns an iterator for this index.
func (s *ShapeIndex) Iterator() *ShapeIndexIterator {
s.maybeApplyUpdates()
return NewShapeIndexIterator(s, IteratorBegin)
}
// Begin positions the iterator at the first cell in the index.
func (s *ShapeIndex) Begin() *ShapeIndexIterator {
s.maybeApplyUpdates()
return NewShapeIndexIterator(s, IteratorBegin)
}
// End positions the iterator at the last cell in the index.
func (s *ShapeIndex) End() *ShapeIndexIterator {
// TODO(roberts): It's possible that updates could happen to the index between
// the time this is called and the time the iterators position is used and this
// will be invalid or not the end. For now, things will be undefined if this
// happens. See about referencing the IsFresh to guard for this in the future.
s.maybeApplyUpdates()
return NewShapeIndexIterator(s, IteratorEnd)
}
// Len reports the number of Shapes in this index.
func (s *ShapeIndex) Len() int {
return len(s.shapes)
}
// Reset resets the index to its original state.
func (s *ShapeIndex) Reset() {
s.shapes = make(map[int32]Shape)
s.nextID = 0
s.cellMap = make(map[CellID]*ShapeIndexCell)
s.cells = nil
atomic.StoreInt32(&s.status, fresh)
}
// NumEdges returns the number of edges in this index.
func (s *ShapeIndex) NumEdges() int {
numEdges := 0
for _, shape := range s.shapes {
numEdges += shape.NumEdges()
}
return numEdges
}
// NumEdgesUpTo returns the number of edges in the given index, up to the given
// limit. If the limit is encountered, the current running total is returned,
// which may be more than the limit.
func (s *ShapeIndex) NumEdgesUpTo(limit int) int {
var numEdges int
// We choose to iterate over the shapes in order to match the counting
// up behavior in C++ and for test compatibility instead of using a
// more idiomatic range over the shape map.
for i := int32(0); i <= s.nextID; i++ {
s := s.Shape(i)
if s == nil {
continue
}
numEdges += s.NumEdges()
if numEdges >= limit {
break
}
}
return numEdges
}
// Shape returns the shape with the given ID, or nil if the shape has been removed from the index.
func (s *ShapeIndex) Shape(id int32) Shape { return s.shapes[id] }
// idForShape returns the id of the given shape in this index, or -1 if it is
// not in the index.
//
// TODO(roberts): Need to figure out an appropriate way to expose this on a Shape.
// C++ allows a given S2 type (Loop, Polygon, etc) to be part of multiple indexes.
// By having each type extend S2Shape which has an id element, they all inherit their
// own id field rather than having to track it themselves.
func (s *ShapeIndex) idForShape(shape Shape) int32 {
for k, v := range s.shapes {
if v == shape {
return k
}
}
return -1
}
// Add adds the given shape to the index and returns the assigned ID..
func (s *ShapeIndex) Add(shape Shape) int32 {
s.shapes[s.nextID] = shape
s.nextID++
atomic.StoreInt32(&s.status, stale)
return s.nextID - 1
}
// Remove removes the given shape from the index.
func (s *ShapeIndex) Remove(shape Shape) {
// The index updates itself lazily because it is much more efficient to
// process additions and removals in batches.
id := s.idForShape(shape)
// If the shape wasn't found, it's already been removed or was not in the index.
if s.shapes[id] == nil {
return
}
// Remove the shape from the shapes map.
delete(s.shapes, id)
// We are removing a shape that has not yet been added to the index,
// so there is nothing else to do.
if id >= s.pendingAdditionsPos {
return
}
numEdges := shape.NumEdges()
removed := &removedShape{
shapeID: id,
hasInterior: shape.Dimension() == 2,
containsTrackerOrigin: shape.ReferencePoint().Contained,
edges: make([]Edge, numEdges),
}
for e := 0; e < numEdges; e++ {
removed.edges[e] = shape.Edge(e)
}
s.pendingRemovals = append(s.pendingRemovals, removed)
atomic.StoreInt32(&s.status, stale)
}
// Build triggers the update of the index. Calls to Add and Release are normally
// queued and processed on the first subsequent query. This has many advantages,
// the most important of which is that sometimes there *is* no subsequent
// query, which lets us avoid building the index completely.
//
// This method forces any pending updates to be applied immediately.
func (s *ShapeIndex) Build() {
s.maybeApplyUpdates()
}
// IsFresh reports if there are no pending updates that need to be applied.
// This can be useful to avoid building the index unnecessarily, or for
// choosing between two different algorithms depending on whether the index
// is available.
//
// The returned index status may be slightly out of date if the index was
// built in a different thread. This is fine for the intended use (as an
// efficiency hint), but it should not be used by internal methods.
func (s *ShapeIndex) IsFresh() bool {
return atomic.LoadInt32(&s.status) == fresh
}
// isFirstUpdate reports if this is the first update to the index.
func (s *ShapeIndex) isFirstUpdate() bool {
// Note that it is not sufficient to check whether cellMap is empty, since
// entries are added to it during the update process.
return s.pendingAdditionsPos == 0
}
// isShapeBeingRemoved reports if the shape with the given ID is currently slated for removal.
func (s *ShapeIndex) isShapeBeingRemoved(shapeID int32) bool {
// All shape ids being removed fall below the index position of shapes being added.
return shapeID < s.pendingAdditionsPos
}
// maybeApplyUpdates checks if the index pieces have changed, and if so, applies pending updates.
func (s *ShapeIndex) maybeApplyUpdates() {
// TODO(roberts): To avoid acquiring and releasing the mutex on every
// query, we should use atomic operations when testing whether the status
// is fresh and when updating the status to be fresh. This guarantees
// that any thread that sees a status of fresh will also see the
// corresponding index updates.
if atomic.LoadInt32(&s.status) != fresh {
s.mu.Lock()
s.applyUpdatesInternal()
atomic.StoreInt32(&s.status, fresh)
s.mu.Unlock()
}
}
// applyUpdatesInternal does the actual work of updating the index by applying all
// pending additions and removals. It does *not* update the indexes status.
func (s *ShapeIndex) applyUpdatesInternal() {
// TODO(roberts): Building the index can use up to 20x as much memory per
// edge as the final index memory size. If this causes issues, add in
// batched updating to limit the amount of items per batch to a
// configurable memory footprint overhead.
t := newTracker()
// allEdges maps a Face to a collection of faceEdges.
allEdges := make([][]faceEdge, 6)
for _, p := range s.pendingRemovals {
s.removeShapeInternal(p, allEdges, t)
}
for id := s.pendingAdditionsPos; id < int32(len(s.shapes)); id++ {
s.addShapeInternal(id, allEdges, t)
}
for face := 0; face < 6; face++ {
s.updateFaceEdges(face, allEdges[face], t)
}
s.pendingRemovals = s.pendingRemovals[:0]
s.pendingAdditionsPos = int32(len(s.shapes))
// It is the caller's responsibility to update the index status.
}
// addShapeInternal clips all edges of the given shape to the six cube faces,
// adds the clipped edges to the set of allEdges, and starts tracking its
// interior if necessary.
func (s *ShapeIndex) addShapeInternal(shapeID int32, allEdges [][]faceEdge, t *tracker) {
shape, ok := s.shapes[shapeID]
if !ok {
// This shape has already been removed.
return
}
faceEdge := faceEdge{
shapeID: shapeID,
hasInterior: shape.Dimension() == 2,
}
if faceEdge.hasInterior {
t.addShape(shapeID, containsBruteForce(shape, t.focus()))
}
numEdges := shape.NumEdges()
for e := 0; e < numEdges; e++ {
edge := shape.Edge(e)
faceEdge.edgeID = e
faceEdge.edge = edge
faceEdge.maxLevel = maxLevelForEdge(edge)
s.addFaceEdge(faceEdge, allEdges)
}
}
// addFaceEdge adds the given faceEdge into the collection of all edges.
func (s *ShapeIndex) addFaceEdge(fe faceEdge, allEdges [][]faceEdge) {
aFace := face(fe.edge.V0.Vector)
// See if both endpoints are on the same face, and are far enough from
// the edge of the face that they don't intersect any (padded) adjacent face.
if aFace == face(fe.edge.V1.Vector) {
x, y := validFaceXYZToUV(aFace, fe.edge.V0.Vector)
fe.a = r2.Point{x, y}
x, y = validFaceXYZToUV(aFace, fe.edge.V1.Vector)
fe.b = r2.Point{x, y}
maxUV := 1 - cellPadding
if math.Abs(fe.a.X) <= maxUV && math.Abs(fe.a.Y) <= maxUV &&
math.Abs(fe.b.X) <= maxUV && math.Abs(fe.b.Y) <= maxUV {
allEdges[aFace] = append(allEdges[aFace], fe)
return
}
}
// Otherwise, we simply clip the edge to all six faces.
for face := 0; face < 6; face++ {
if aClip, bClip, intersects := ClipToPaddedFace(fe.edge.V0, fe.edge.V1, face, cellPadding); intersects {
fe.a = aClip
fe.b = bClip
allEdges[face] = append(allEdges[face], fe)
}
}
}
// updateFaceEdges adds or removes the various edges from the index.
// An edge is added if shapes[id] is not nil, and removed otherwise.
func (s *ShapeIndex) updateFaceEdges(face int, faceEdges []faceEdge, t *tracker) {
numEdges := len(faceEdges)
if numEdges == 0 && len(t.shapeIDs) == 0 {
return
}
// Create the initial clippedEdge for each faceEdge. Additional clipped
// edges are created when edges are split between child cells. We create
// two arrays, one containing the edge data and another containing pointers
// to those edges, so that during the recursion we only need to copy
// pointers in order to propagate an edge to the correct child.
clippedEdges := make([]*clippedEdge, numEdges)
bound := r2.EmptyRect()
for e := 0; e < numEdges; e++ {
clipped := &clippedEdge{
faceEdge: &faceEdges[e],
}
clipped.bound = r2.RectFromPoints(faceEdges[e].a, faceEdges[e].b)
clippedEdges[e] = clipped
bound = bound.AddRect(clipped.bound)
}
// Construct the initial face cell containing all the edges, and then update
// all the edges in the index recursively.
faceID := CellIDFromFace(face)
pcell := PaddedCellFromCellID(faceID, cellPadding)
disjointFromIndex := s.isFirstUpdate()
if numEdges > 0 {
shrunkID := s.shrinkToFit(pcell, bound)
if shrunkID != pcell.id {
// All the edges are contained by some descendant of the face cell. We
// can save a lot of work by starting directly with that cell, but if we
// are in the interior of at least one shape then we need to create
// index entries for the cells we are skipping over.
s.skipCellRange(faceID.RangeMin(), shrunkID.RangeMin(), t, disjointFromIndex)
pcell = PaddedCellFromCellID(shrunkID, cellPadding)
s.updateEdges(pcell, clippedEdges, t, disjointFromIndex)
s.skipCellRange(shrunkID.RangeMax().Next(), faceID.RangeMax().Next(), t, disjointFromIndex)
return
}
}
// Otherwise (no edges, or no shrinking is possible), subdivide normally.
s.updateEdges(pcell, clippedEdges, t, disjointFromIndex)
}
// shrinkToFit shrinks the PaddedCell to fit within the given bounds.
func (s *ShapeIndex) shrinkToFit(pcell *PaddedCell, bound r2.Rect) CellID {
shrunkID := pcell.ShrinkToFit(bound)
if !s.isFirstUpdate() && shrunkID != pcell.CellID() {
// Don't shrink any smaller than the existing index cells, since we need
// to combine the new edges with those cells.
iter := s.Iterator()
if iter.LocateCellID(shrunkID) == Indexed {
shrunkID = iter.CellID()
}
}
return shrunkID
}
// skipCellRange skips over the cells in the given range, creating index cells if we are
// currently in the interior of at least one shape.
func (s *ShapeIndex) skipCellRange(begin, end CellID, t *tracker, disjointFromIndex bool) {
// If we aren't in the interior of a shape, then skipping over cells is easy.
if len(t.shapeIDs) == 0 {
return
}
// Otherwise generate the list of cell ids that we need to visit, and create
// an index entry for each one.
skipped := CellUnionFromRange(begin, end)
for _, cell := range skipped {
var clippedEdges []*clippedEdge
s.updateEdges(PaddedCellFromCellID(cell, cellPadding), clippedEdges, t, disjointFromIndex)
}
}
// updateEdges adds or removes the given edges whose bounding boxes intersect a
// given cell. disjointFromIndex is an optimization hint indicating that cellMap
// does not contain any entries that overlap the given cell.
func (s *ShapeIndex) updateEdges(pcell *PaddedCell, edges []*clippedEdge, t *tracker, disjointFromIndex bool) {
// This function is recursive with a maximum recursion depth of 30 (maxLevel).
// Incremental updates are handled as follows. All edges being added or
// removed are combined together in edges, and all shapes with interiors
// are tracked using tracker. We subdivide recursively as usual until we
// encounter an existing index cell. At this point we absorb the index
// cell as follows:
//
// - Edges and shapes that are being removed are deleted from edges and
// tracker.
// - All remaining edges and shapes from the index cell are added to
// edges and tracker.
// - Continue subdividing recursively, creating new index cells as needed.
// - When the recursion gets back to the cell that was absorbed, we
// restore edges and tracker to their previous state.
//
// Note that the only reason that we include removed shapes in the recursive
// subdivision process is so that we can find all of the index cells that
// contain those shapes efficiently, without maintaining an explicit list of
// index cells for each shape (which would be expensive in terms of memory).
indexCellAbsorbed := false
if !disjointFromIndex {
// There may be existing index cells contained inside pcell. If we
// encounter such a cell, we need to combine the edges being updated with
// the existing cell contents by absorbing the cell.
iter := s.Iterator()
r := iter.LocateCellID(pcell.id)
if r == Disjoint {
disjointFromIndex = true
} else if r == Indexed {
// Absorb the index cell by transferring its contents to edges and
// deleting it. We also start tracking the interior of any new shapes.
s.absorbIndexCell(pcell, iter, edges, t)
indexCellAbsorbed = true
disjointFromIndex = true
} else {
// DCHECK_EQ(SUBDIVIDED, r)
}
}
// If there are existing index cells below us, then we need to keep
// subdividing so that we can merge with those cells. Otherwise,
// makeIndexCell checks if the number of edges is small enough, and creates
// an index cell if possible (returning true when it does so).
if !disjointFromIndex || !s.makeIndexCell(pcell, edges, t) {
// TODO(roberts): If it turns out to have memory problems when there
// are 10M+ edges in the index, look into pre-allocating space so we
// are not always appending.
childEdges := [2][2][]*clippedEdge{} // [i][j]
// Compute the middle of the padded cell, defined as the rectangle in
// (u,v)-space that belongs to all four (padded) children. By comparing
// against the four boundaries of middle we can determine which children
// each edge needs to be propagated to.
middle := pcell.Middle()
// Build up a vector edges to be passed to each child cell. The (i,j)
// directions are left (i=0), right (i=1), lower (j=0), and upper (j=1).
// Note that the vast majority of edges are propagated to a single child.
for _, edge := range edges {
if edge.bound.X.Hi <= middle.X.Lo {
// Edge is entirely contained in the two left children.
a, b := s.clipVAxis(edge, middle.Y)
if a != nil {
childEdges[0][0] = append(childEdges[0][0], a)
}
if b != nil {
childEdges[0][1] = append(childEdges[0][1], b)
}
} else if edge.bound.X.Lo >= middle.X.Hi {
// Edge is entirely contained in the two right children.
a, b := s.clipVAxis(edge, middle.Y)
if a != nil {
childEdges[1][0] = append(childEdges[1][0], a)
}
if b != nil {
childEdges[1][1] = append(childEdges[1][1], b)
}
} else if edge.bound.Y.Hi <= middle.Y.Lo {
// Edge is entirely contained in the two lower children.
if a := s.clipUBound(edge, 1, middle.X.Hi); a != nil {
childEdges[0][0] = append(childEdges[0][0], a)
}
if b := s.clipUBound(edge, 0, middle.X.Lo); b != nil {
childEdges[1][0] = append(childEdges[1][0], b)
}
} else if edge.bound.Y.Lo >= middle.Y.Hi {
// Edge is entirely contained in the two upper children.
if a := s.clipUBound(edge, 1, middle.X.Hi); a != nil {
childEdges[0][1] = append(childEdges[0][1], a)
}
if b := s.clipUBound(edge, 0, middle.X.Lo); b != nil {
childEdges[1][1] = append(childEdges[1][1], b)
}
} else {
// The edge bound spans all four children. The edge
// itself intersects either three or four padded children.
left := s.clipUBound(edge, 1, middle.X.Hi)
a, b := s.clipVAxis(left, middle.Y)
if a != nil {
childEdges[0][0] = append(childEdges[0][0], a)
}
if b != nil {
childEdges[0][1] = append(childEdges[0][1], b)
}
right := s.clipUBound(edge, 0, middle.X.Lo)
a, b = s.clipVAxis(right, middle.Y)
if a != nil {
childEdges[1][0] = append(childEdges[1][0], a)
}
if b != nil {
childEdges[1][1] = append(childEdges[1][1], b)
}
}
}
// Now recursively update the edges in each child. We call the children in
// increasing order of CellID so that when the index is first constructed,
// all insertions into cellMap are at the end (which is much faster).
for pos := 0; pos < 4; pos++ {
i, j := pcell.ChildIJ(pos)
if len(childEdges[i][j]) > 0 || len(t.shapeIDs) > 0 {
s.updateEdges(PaddedCellFromParentIJ(pcell, i, j), childEdges[i][j],
t, disjointFromIndex)
}
}
}
if indexCellAbsorbed {
// Restore the state for any edges being removed that we are tracking.
t.restoreStateBefore(s.pendingAdditionsPos)
}
}
// makeIndexCell builds an indexCell from the given padded cell and set of edges and adds
// it to the index. If the cell or edges are empty, no cell is added.
func (s *ShapeIndex) makeIndexCell(p *PaddedCell, edges []*clippedEdge, t *tracker) bool {
// If the cell is empty, no index cell is needed. (In most cases this
// situation is detected before we get to this point, but this can happen
// when all shapes in a cell are removed.)
if len(edges) == 0 && len(t.shapeIDs) == 0 {
return true
}
// Count the number of edges that have not reached their maximum level yet.
// Return false if there are too many such edges.
count := 0
for _, ce := range edges {
if p.Level() < ce.faceEdge.maxLevel {
count++
}
if count > s.maxEdgesPerCell {
return false
}
}
// Possible optimization: Continue subdividing as long as exactly one child
// of the padded cell intersects the given edges. This can be done by finding
// the bounding box of all the edges and calling ShrinkToFit:
//
// cellID = p.ShrinkToFit(RectBound(edges));
//
// Currently this is not beneficial; it slows down construction by 4-25%
// (mainly computing the union of the bounding rectangles) and also slows
// down queries (since more recursive clipping is required to get down to
// the level of a spatial index cell). But it may be worth trying again
// once containsCenter is computed and all algorithms are modified to
// take advantage of it.
// We update the InteriorTracker as follows. For every Cell in the index
// we construct two edges: one edge from entry vertex of the cell to its
// center, and one from the cell center to its exit vertex. Here entry
// and exit refer the CellID ordering, i.e. the order in which points
// are encountered along the 2 space-filling curve. The exit vertex then
// becomes the entry vertex for the next cell in the index, unless there are
// one or more empty intervening cells, in which case the InteriorTracker
// state is unchanged because the intervening cells have no edges.
// Shift the InteriorTracker focus point to the center of the current cell.
if t.isActive && len(edges) != 0 {
if !t.atCellID(p.id) {
t.moveTo(p.EntryVertex())
}
t.drawTo(p.Center())
s.testAllEdges(edges, t)
}
// Allocate and fill a new index cell. To get the total number of shapes we
// need to merge the shapes associated with the intersecting edges together
// with the shapes that happen to contain the cell center.
cshapeIDs := t.shapeIDs
numShapes := s.countShapes(edges, cshapeIDs)
cell := NewShapeIndexCell(numShapes)
// To fill the index cell we merge the two sources of shapes: edge shapes
// (those that have at least one edge that intersects this cell), and
// containing shapes (those that contain the cell center). We keep track
// of the index of the next intersecting edge and the next containing shape
// as we go along. Both sets of shape ids are already sorted.
eNext := 0
cNextIdx := 0
for i := 0; i < numShapes; i++ {
var clipped *clippedShape
// advance to next value base + i
eshapeID := int32(s.Len())
cshapeID := eshapeID // Sentinels
if eNext != len(edges) {
eshapeID = edges[eNext].faceEdge.shapeID
}
if cNextIdx < len(cshapeIDs) {
cshapeID = cshapeIDs[cNextIdx]
}
eBegin := eNext
if cshapeID < eshapeID {
// The entire cell is in the shape interior.
clipped = newClippedShape(cshapeID, 0)
clipped.containsCenter = true
cNextIdx++
} else {
// Count the number of edges for this shape and allocate space for them.
for eNext < len(edges) && edges[eNext].faceEdge.shapeID == eshapeID {
eNext++
}
clipped = newClippedShape(eshapeID, eNext-eBegin)
for e := eBegin; e < eNext; e++ {
clipped.edges[e-eBegin] = edges[e].faceEdge.edgeID
}
if cshapeID == eshapeID {
clipped.containsCenter = true
cNextIdx++
}
}
cell.shapes[i] = clipped
}
// Add this cell to the map.
s.cellMap[p.id] = cell
s.cells = append(s.cells, p.id)
// Shift the tracker focus point to the exit vertex of this cell.
if t.isActive && len(edges) != 0 {
t.drawTo(p.ExitVertex())
s.testAllEdges(edges, t)
t.setNextCellID(p.id.Next())
}
return true
}
// updateBound updates the specified endpoint of the given clipped edge and returns the
// resulting clipped edge.
func (s *ShapeIndex) updateBound(edge *clippedEdge, uEnd int, u float64, vEnd int, v float64) *clippedEdge {
c := &clippedEdge{faceEdge: edge.faceEdge}
if uEnd == 0 {
c.bound.X.Lo = u
c.bound.X.Hi = edge.bound.X.Hi
} else {
c.bound.X.Lo = edge.bound.X.Lo
c.bound.X.Hi = u
}
if vEnd == 0 {
c.bound.Y.Lo = v
c.bound.Y.Hi = edge.bound.Y.Hi
} else {
c.bound.Y.Lo = edge.bound.Y.Lo
c.bound.Y.Hi = v
}
return c
}
// clipUBound clips the given endpoint (lo=0, hi=1) of the u-axis so that
// it does not extend past the given value of the given edge.
func (s *ShapeIndex) clipUBound(edge *clippedEdge, uEnd int, u float64) *clippedEdge {
// First check whether the edge actually requires any clipping. (Sometimes
// this method is called when clipping is not necessary, e.g. when one edge
// endpoint is in the overlap area between two padded child cells.)
if uEnd == 0 {
if edge.bound.X.Lo >= u {
return edge
}
} else {
if edge.bound.X.Hi <= u {
return edge
}
}
// We interpolate the new v-value from the endpoints of the original edge.
// This has two advantages: (1) we don't need to store the clipped endpoints
// at all, just their bounding box; and (2) it avoids the accumulation of
// roundoff errors due to repeated interpolations. The result needs to be
// clamped to ensure that it is in the appropriate range.
e := edge.faceEdge
v := edge.bound.Y.ClampPoint(interpolateFloat64(u, e.a.X, e.b.X, e.a.Y, e.b.Y))
// Determine which endpoint of the v-axis bound to update. If the edge
// slope is positive we update the same endpoint, otherwise we update the
// opposite endpoint.
var vEnd int
positiveSlope := (e.a.X > e.b.X) == (e.a.Y > e.b.Y)
if (uEnd == 1) == positiveSlope {
vEnd = 1
}
return s.updateBound(edge, uEnd, u, vEnd, v)
}
// clipVBound clips the given endpoint (lo=0, hi=1) of the v-axis so that
// it does not extend past the given value of the given edge.
func (s *ShapeIndex) clipVBound(edge *clippedEdge, vEnd int, v float64) *clippedEdge {
if vEnd == 0 {
if edge.bound.Y.Lo >= v {
return edge
}
} else {
if edge.bound.Y.Hi <= v {
return edge
}
}
// We interpolate the new v-value from the endpoints of the original edge.
// This has two advantages: (1) we don't need to store the clipped endpoints
// at all, just their bounding box; and (2) it avoids the accumulation of
// roundoff errors due to repeated interpolations. The result needs to be
// clamped to ensure that it is in the appropriate range.
e := edge.faceEdge
u := edge.bound.X.ClampPoint(interpolateFloat64(v, e.a.Y, e.b.Y, e.a.X, e.b.X))
// Determine which endpoint of the v-axis bound to update. If the edge
// slope is positive we update the same endpoint, otherwise we update the
// opposite endpoint.
var uEnd int
positiveSlope := (e.a.X > e.b.X) == (e.a.Y > e.b.Y)
if (vEnd == 1) == positiveSlope {
uEnd = 1
}
return s.updateBound(edge, uEnd, u, vEnd, v)
}
// cliupVAxis returns the given edge clipped to within the boundaries of the middle
// interval along the v-axis, and adds the result to its children.
func (s *ShapeIndex) clipVAxis(edge *clippedEdge, middle r1.Interval) (a, b *clippedEdge) {
if edge.bound.Y.Hi <= middle.Lo {
// Edge is entirely contained in the lower child.
return edge, nil
} else if edge.bound.Y.Lo >= middle.Hi {
// Edge is entirely contained in the upper child.
return nil, edge
}
// The edge bound spans both children.
return s.clipVBound(edge, 1, middle.Hi), s.clipVBound(edge, 0, middle.Lo)
}
// absorbIndexCell absorbs an index cell by transferring its contents to edges
// and/or "tracker", and then delete this cell from the index. If edges includes
// any edges that are being removed, this method also updates their
// InteriorTracker state to correspond to the exit vertex of this cell.
func (s *ShapeIndex) absorbIndexCell(p *PaddedCell, iter *ShapeIndexIterator, edges []*clippedEdge, t *tracker) {
// When we absorb a cell, we erase all the edges that are being removed.
// However when we are finished with this cell, we want to restore the state
// of those edges (since that is how we find all the index cells that need
// to be updated). The edges themselves are restored automatically when
// UpdateEdges returns from its recursive call, but the InteriorTracker
// state needs to be restored explicitly.
//
// Here we first update the InteriorTracker state for removed edges to
// correspond to the exit vertex of this cell, and then save the
// InteriorTracker state. This state will be restored by UpdateEdges when
// it is finished processing the contents of this cell.
if t.isActive && len(edges) != 0 && s.isShapeBeingRemoved(edges[0].faceEdge.shapeID) {
// We probably need to update the tracker. ("Probably" because
// it's possible that all shapes being removed do not have interiors.)
if !t.atCellID(p.id) {
t.moveTo(p.EntryVertex())
}
t.drawTo(p.ExitVertex())
t.setNextCellID(p.id.Next())
for _, edge := range edges {
fe := edge.faceEdge
if !s.isShapeBeingRemoved(fe.shapeID) {
break // All shapes being removed come first.
}
if fe.hasInterior {
t.testEdge(fe.shapeID, fe.edge)
}
}
}
// Save the state of the edges being removed, so that it can be restored
// when we are finished processing this cell and its children. We don't
// need to save the state of the edges being added because they aren't being
// removed from "edges" and will therefore be updated normally as we visit
// this cell and its children.
t.saveAndClearStateBefore(s.pendingAdditionsPos)
// Create a faceEdge for each edge in this cell that isn't being removed.
var faceEdges []*faceEdge
trackerMoved := false
cell := iter.IndexCell()
for _, clipped := range cell.shapes {
shapeID := clipped.shapeID
shape := s.Shape(shapeID)
if shape == nil {
continue // This shape is being removed.
}
numClipped := clipped.numEdges()
// If this shape has an interior, start tracking whether we are inside the
// shape. updateEdges wants to know whether the entry vertex of this
// cell is inside the shape, but we only know whether the center of the
// cell is inside the shape, so we need to test all the edges against the
// line segment from the cell center to the entry vertex.
edge := &faceEdge{
shapeID: shapeID,
hasInterior: shape.Dimension() == 2,
}
if edge.hasInterior {
t.addShape(shapeID, clipped.containsCenter)
// There might not be any edges in this entire cell (i.e., it might be
// in the interior of all shapes), so we delay updating the tracker
// until we see the first edge.
if !trackerMoved && numClipped > 0 {
t.moveTo(p.Center())
t.drawTo(p.EntryVertex())
t.setNextCellID(p.id)
trackerMoved = true
}
}
for i := 0; i < numClipped; i++ {
edgeID := clipped.edges[i]
edge.edgeID = edgeID
edge.edge = shape.Edge(edgeID)
edge.maxLevel = maxLevelForEdge(edge.edge)
if edge.hasInterior {
t.testEdge(shapeID, edge.edge)
}
var ok bool
edge.a, edge.b, ok = ClipToPaddedFace(edge.edge.V0, edge.edge.V1, p.id.Face(), cellPadding)
if !ok {
panic("invariant failure in ShapeIndex")
}
faceEdges = append(faceEdges, edge)
}
}
// Now create a clippedEdge for each faceEdge, and put them in "new_edges".
var newEdges []*clippedEdge
for _, faceEdge := range faceEdges {
clipped := &clippedEdge{
faceEdge: faceEdge,
bound: clippedEdgeBound(faceEdge.a, faceEdge.b, p.bound),
}
newEdges = append(newEdges, clipped)
}
// Discard any edges from "edges" that are being removed, and append the
// remainder to "newEdges" (This keeps the edges sorted by shape id.)
for i, clipped := range edges {
if !s.isShapeBeingRemoved(clipped.faceEdge.shapeID) {
newEdges = append(newEdges, edges[i:]...)
break
}
}
// Update the edge list and delete this cell from the index.
edges, newEdges = newEdges, edges
delete(s.cellMap, p.id)
// TODO(roberts): delete from s.Cells
}
// testAllEdges calls the trackers testEdge on all edges from shapes that have interiors.
func (s *ShapeIndex) testAllEdges(edges []*clippedEdge, t *tracker) {
for _, edge := range edges {
if edge.faceEdge.hasInterior {
t.testEdge(edge.faceEdge.shapeID, edge.faceEdge.edge)
}
}
}
// countShapes reports the number of distinct shapes that are either associated with the
// given edges, or that are currently stored in the InteriorTracker.
func (s *ShapeIndex) countShapes(edges []*clippedEdge, shapeIDs []int32) int {
count := 0
lastShapeID := int32(-1)
// next clipped shape id in the shapeIDs list.
clippedNext := int32(0)
// index of the current element in the shapeIDs list.
shapeIDidx := 0
for _, edge := range edges {
if edge.faceEdge.shapeID == lastShapeID {
continue
}
count++
lastShapeID = edge.faceEdge.shapeID
// Skip over any containing shapes up to and including this one,
// updating count as appropriate.
for ; shapeIDidx < len(shapeIDs); shapeIDidx++ {
clippedNext = shapeIDs[shapeIDidx]
if clippedNext > lastShapeID {
break
}
if clippedNext < lastShapeID {
count++
}
}
}
// Count any remaining containing shapes.
count += len(shapeIDs) - shapeIDidx
return count
}
// maxLevelForEdge reports the maximum level for a given edge.
func maxLevelForEdge(edge Edge) int {
// Compute the maximum cell size for which this edge is considered long.
// The calculation does not need to be perfectly accurate, so we use Norm
// rather than Angle for speed.
cellSize := edge.V0.Sub(edge.V1.Vector).Norm() * cellSizeToLongEdgeRatio
// Now return the first level encountered during subdivision where the
// average cell size is at most cellSize.
return AvgEdgeMetric.MinLevel(cellSize)
}
// removeShapeInternal does the actual work for removing a given shape from the index.
func (s *ShapeIndex) removeShapeInternal(removed *removedShape, allEdges [][]faceEdge, t *tracker) {
// TODO(roberts): finish the implementation of this.
}