gtsocial-umbx

paddedcell.go (8581B)

---

 // 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)
 }