253 lines
8.4 KiB
Go
253 lines
8.4 KiB
Go
// Copyright 2016 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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"github.com/golang/geo/r1"
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"github.com/golang/geo/r2"
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)
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// PaddedCell represents a Cell whose (u,v)-range has been expanded on
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// all sides by a given amount of "padding". Unlike Cell, its methods and
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// representation are optimized for clipping edges against Cell boundaries
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// to determine which cells are intersected by a given set of edges.
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type PaddedCell struct {
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id CellID
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padding float64
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bound r2.Rect
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middle r2.Rect // A rect in (u, v)-space that belongs to all four children.
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iLo, jLo int // Minimum (i,j)-coordinates of this cell before padding
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orientation int // Hilbert curve orientation of this cell.
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level int
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}
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// PaddedCellFromCellID constructs a padded cell with the given padding.
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func PaddedCellFromCellID(id CellID, padding float64) *PaddedCell {
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p := &PaddedCell{
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id: id,
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padding: padding,
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middle: r2.EmptyRect(),
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}
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// Fast path for constructing a top-level face (the most common case).
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if id.isFace() {
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limit := padding + 1
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p.bound = r2.Rect{r1.Interval{-limit, limit}, r1.Interval{-limit, limit}}
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p.middle = r2.Rect{r1.Interval{-padding, padding}, r1.Interval{-padding, padding}}
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p.orientation = id.Face() & 1
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return p
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}
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_, p.iLo, p.jLo, p.orientation = id.faceIJOrientation()
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p.level = id.Level()
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p.bound = ijLevelToBoundUV(p.iLo, p.jLo, p.level).ExpandedByMargin(padding)
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ijSize := sizeIJ(p.level)
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p.iLo &= -ijSize
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p.jLo &= -ijSize
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return p
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}
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// PaddedCellFromParentIJ constructs the child of parent with the given (i,j) index.
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// The four child cells have indices of (0,0), (0,1), (1,0), (1,1), where the i and j
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// indices correspond to increasing u- and v-values respectively.
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func PaddedCellFromParentIJ(parent *PaddedCell, i, j int) *PaddedCell {
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// Compute the position and orientation of the child incrementally from the
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// orientation of the parent.
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pos := ijToPos[parent.orientation][2*i+j]
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p := &PaddedCell{
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id: parent.id.Children()[pos],
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padding: parent.padding,
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bound: parent.bound,
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orientation: parent.orientation ^ posToOrientation[pos],
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level: parent.level + 1,
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middle: r2.EmptyRect(),
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}
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ijSize := sizeIJ(p.level)
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p.iLo = parent.iLo + i*ijSize
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p.jLo = parent.jLo + j*ijSize
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// For each child, one corner of the bound is taken directly from the parent
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// while the diagonally opposite corner is taken from middle().
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middle := parent.Middle()
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if i == 1 {
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p.bound.X.Lo = middle.X.Lo
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} else {
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p.bound.X.Hi = middle.X.Hi
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}
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if j == 1 {
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p.bound.Y.Lo = middle.Y.Lo
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} else {
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p.bound.Y.Hi = middle.Y.Hi
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}
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return p
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}
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// CellID returns the CellID this padded cell represents.
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func (p PaddedCell) CellID() CellID {
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return p.id
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}
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// Padding returns the amount of padding on this cell.
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func (p PaddedCell) Padding() float64 {
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return p.padding
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}
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// Level returns the level this cell is at.
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func (p PaddedCell) Level() int {
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return p.level
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}
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// Center returns the center of this cell.
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func (p PaddedCell) Center() Point {
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ijSize := sizeIJ(p.level)
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si := uint32(2*p.iLo + ijSize)
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ti := uint32(2*p.jLo + ijSize)
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return Point{faceSiTiToXYZ(p.id.Face(), si, ti).Normalize()}
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}
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// Middle returns the rectangle in the middle of this cell that belongs to
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// all four of its children in (u,v)-space.
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func (p *PaddedCell) Middle() r2.Rect {
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// We compute this field lazily because it is not needed the majority of the
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// time (i.e., for cells where the recursion terminates).
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if p.middle.IsEmpty() {
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ijSize := sizeIJ(p.level)
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u := stToUV(siTiToST(uint32(2*p.iLo + ijSize)))
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v := stToUV(siTiToST(uint32(2*p.jLo + ijSize)))
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p.middle = r2.Rect{
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r1.Interval{u - p.padding, u + p.padding},
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r1.Interval{v - p.padding, v + p.padding},
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}
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}
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return p.middle
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}
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// Bound returns the bounds for this cell in (u,v)-space including padding.
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func (p PaddedCell) Bound() r2.Rect {
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return p.bound
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}
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// ChildIJ returns the (i,j) coordinates for the child cell at the given traversal
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// position. The traversal position corresponds to the order in which child
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// cells are visited by the Hilbert curve.
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func (p PaddedCell) ChildIJ(pos int) (i, j int) {
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ij := posToIJ[p.orientation][pos]
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return ij >> 1, ij & 1
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}
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// EntryVertex return the vertex where the space-filling curve enters this cell.
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func (p PaddedCell) EntryVertex() Point {
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// The curve enters at the (0,0) vertex unless the axis directions are
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// reversed, in which case it enters at the (1,1) vertex.
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i := p.iLo
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j := p.jLo
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if p.orientation&invertMask != 0 {
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ijSize := sizeIJ(p.level)
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i += ijSize
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j += ijSize
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}
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return Point{faceSiTiToXYZ(p.id.Face(), uint32(2*i), uint32(2*j)).Normalize()}
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}
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// ExitVertex returns the vertex where the space-filling curve exits this cell.
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func (p PaddedCell) ExitVertex() Point {
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// The curve exits at the (1,0) vertex unless the axes are swapped or
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// inverted but not both, in which case it exits at the (0,1) vertex.
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i := p.iLo
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j := p.jLo
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ijSize := sizeIJ(p.level)
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if p.orientation == 0 || p.orientation == swapMask+invertMask {
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i += ijSize
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} else {
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j += ijSize
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}
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return Point{faceSiTiToXYZ(p.id.Face(), uint32(2*i), uint32(2*j)).Normalize()}
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}
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// ShrinkToFit returns the smallest CellID that contains all descendants of this
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// padded cell whose bounds intersect the given rect. For algorithms that use
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// recursive subdivision to find the cells that intersect a particular object, this
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// method can be used to skip all of the initial subdivision steps where only
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// one child needs to be expanded.
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//
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// Note that this method is not the same as returning the smallest cell that contains
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// the intersection of this cell with rect. Because of the padding, even if one child
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// completely contains rect it is still possible that a neighboring child may also
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// intersect the given rect.
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//
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// The provided Rect must intersect the bounds of this cell.
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func (p *PaddedCell) ShrinkToFit(rect r2.Rect) CellID {
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// Quick rejection test: if rect contains the center of this cell along
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// either axis, then no further shrinking is possible.
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if p.level == 0 {
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// Fast path (most calls to this function start with a face cell).
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if rect.X.Contains(0) || rect.Y.Contains(0) {
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return p.id
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}
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}
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ijSize := sizeIJ(p.level)
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if rect.X.Contains(stToUV(siTiToST(uint32(2*p.iLo+ijSize)))) ||
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rect.Y.Contains(stToUV(siTiToST(uint32(2*p.jLo+ijSize)))) {
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return p.id
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}
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// Otherwise we expand rect by the given padding on all sides and find
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// the range of coordinates that it spans along the i- and j-axes. We then
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// compute the highest bit position at which the min and max coordinates
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// differ. This corresponds to the first cell level at which at least two
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// children intersect rect.
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// Increase the padding to compensate for the error in uvToST.
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// (The constant below is a provable upper bound on the additional error.)
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padded := rect.ExpandedByMargin(p.padding + 1.5*dblEpsilon)
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iMin, jMin := p.iLo, p.jLo // Min i- or j- coordinate spanned by padded
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var iXor, jXor int // XOR of the min and max i- or j-coordinates
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if iMin < stToIJ(uvToST(padded.X.Lo)) {
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iMin = stToIJ(uvToST(padded.X.Lo))
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}
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if a, b := p.iLo+ijSize-1, stToIJ(uvToST(padded.X.Hi)); a <= b {
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iXor = iMin ^ a
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} else {
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iXor = iMin ^ b
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}
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if jMin < stToIJ(uvToST(padded.Y.Lo)) {
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jMin = stToIJ(uvToST(padded.Y.Lo))
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}
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if a, b := p.jLo+ijSize-1, stToIJ(uvToST(padded.Y.Hi)); a <= b {
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jXor = jMin ^ a
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} else {
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jXor = jMin ^ b
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}
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// Compute the highest bit position where the two i- or j-endpoints differ,
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// and then choose the cell level that includes both of these endpoints. So
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// if both pairs of endpoints are equal we choose maxLevel; if they differ
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// only at bit 0, we choose (maxLevel - 1), and so on.
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levelMSB := uint64(((iXor | jXor) << 1) + 1)
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level := maxLevel - findMSBSetNonZero64(levelMSB)
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if level <= p.level {
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return p.id
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}
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return cellIDFromFaceIJ(p.id.Face(), iMin, jMin).Parent(level)
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}
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