gotosocial/vendor/github.com/golang/geo/s2/paddedcell.go
Tobi Smethurst 98263a7de6
Grand test fixup (#138)
* start fixing up tests

* fix up tests + automate with drone

* fiddle with linting

* messing about with drone.yml

* some more fiddling

* hmmm

* add cache

* add vendor directory

* verbose

* ci updates

* update some little things

* update sig
2021-08-12 21:03:24 +02:00

252 lines
8.4 KiB
Go

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