gotosocial/vendor/github.com/golang/geo/s2/pointcompression.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

320 lines
10 KiB
Go

// Copyright 2017 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 (
"errors"
"fmt"
"github.com/golang/geo/r3"
)
// maxEncodedVertices is the maximum number of vertices, in a row, to be encoded or decoded.
// On decode, this defends against malicious encodings that try and have us exceed RAM.
const maxEncodedVertices = 50000000
// xyzFaceSiTi represents the The XYZ and face,si,ti coordinates of a Point
// and, if this point is equal to the center of a Cell, the level of this cell
// (-1 otherwise). This is used for Loops and Polygons to store data in a more
// compressed format.
type xyzFaceSiTi struct {
xyz Point
face int
si, ti uint32
level int
}
const derivativeEncodingOrder = 2
func appendFace(faces []faceRun, face int) []faceRun {
if len(faces) == 0 || faces[len(faces)-1].face != face {
return append(faces, faceRun{face, 1})
}
faces[len(faces)-1].count++
return faces
}
// encodePointsCompressed uses an optimized compressed format to encode the given values.
func encodePointsCompressed(e *encoder, vertices []xyzFaceSiTi, level int) {
var faces []faceRun
for _, v := range vertices {
faces = appendFace(faces, v.face)
}
encodeFaces(e, faces)
type piQi struct {
pi, qi uint32
}
verticesPiQi := make([]piQi, len(vertices))
for i, v := range vertices {
verticesPiQi[i] = piQi{siTitoPiQi(v.si, level), siTitoPiQi(v.ti, level)}
}
piCoder, qiCoder := newNthDerivativeCoder(derivativeEncodingOrder), newNthDerivativeCoder(derivativeEncodingOrder)
for i, v := range verticesPiQi {
f := encodePointCompressed
if i == 0 {
// The first point will be just the (pi, qi) coordinates
// of the Point. NthDerivativeCoder will not save anything
// in that case, so we encode in fixed format rather than varint
// to avoid the varint overhead.
f = encodeFirstPointFixedLength
}
f(e, v.pi, v.qi, level, piCoder, qiCoder)
}
var offCenter []int
for i, v := range vertices {
if v.level != level {
offCenter = append(offCenter, i)
}
}
e.writeUvarint(uint64(len(offCenter)))
for _, idx := range offCenter {
e.writeUvarint(uint64(idx))
e.writeFloat64(vertices[idx].xyz.X)
e.writeFloat64(vertices[idx].xyz.Y)
e.writeFloat64(vertices[idx].xyz.Z)
}
}
func encodeFirstPointFixedLength(e *encoder, pi, qi uint32, level int, piCoder, qiCoder *nthDerivativeCoder) {
// Do not ZigZagEncode the first point, since it cannot be negative.
codedPi, codedQi := piCoder.encode(int32(pi)), qiCoder.encode(int32(qi))
// Interleave to reduce overhead from two partial bytes to one.
interleaved := interleaveUint32(uint32(codedPi), uint32(codedQi))
// Write as little endian.
bytesRequired := (level + 7) / 8 * 2
for i := 0; i < bytesRequired; i++ {
e.writeUint8(uint8(interleaved))
interleaved >>= 8
}
}
// encodePointCompressed encodes points into e.
// Given a sequence of Points assumed to be the center of level-k cells,
// compresses it into a stream using the following method:
// - decompose the points into (face, si, ti) tuples.
// - run-length encode the faces, combining face number and count into a
// varint32. See the faceRun struct.
// - right shift the (si, ti) to remove the part that's constant for all cells
// of level-k. The result is called the (pi, qi) space.
// - 2nd derivative encode the pi and qi sequences (linear prediction)
// - zig-zag encode all derivative values but the first, which cannot be
// negative
// - interleave the zig-zag encoded values
// - encode the first interleaved value in a fixed length encoding
// (varint would make this value larger)
// - encode the remaining interleaved values as varint64s, as the
// derivative encoding should make the values small.
// In addition, provides a lossless method to compress a sequence of points even
// if some points are not the center of level-k cells. These points are stored
// exactly, using 3 double precision values, after the above encoded string,
// together with their index in the sequence (this leads to some redundancy - it
// is expected that only a small fraction of the points are not cell centers).
//
// To encode leaf cells, this requires 8 bytes for the first vertex plus
// an average of 3.8 bytes for each additional vertex, when computed on
// Google's geographic repository.
func encodePointCompressed(e *encoder, pi, qi uint32, level int, piCoder, qiCoder *nthDerivativeCoder) {
// ZigZagEncode, as varint requires the maximum number of bytes for
// negative numbers.
zzPi := zigzagEncode(piCoder.encode(int32(pi)))
zzQi := zigzagEncode(qiCoder.encode(int32(qi)))
// Interleave to reduce overhead from two partial bytes to one.
interleaved := interleaveUint32(zzPi, zzQi)
e.writeUvarint(interleaved)
}
type faceRun struct {
face, count int
}
func decodeFaceRun(d *decoder) faceRun {
faceAndCount := d.readUvarint()
ret := faceRun{
face: int(faceAndCount % numFaces),
count: int(faceAndCount / numFaces),
}
if ret.count <= 0 && d.err == nil {
d.err = errors.New("non-positive count for face run")
}
return ret
}
func decodeFaces(numVertices int, d *decoder) []faceRun {
var frs []faceRun
for nparsed := 0; nparsed < numVertices; {
fr := decodeFaceRun(d)
if d.err != nil {
return nil
}
frs = append(frs, fr)
nparsed += fr.count
}
return frs
}
// encodeFaceRun encodes each faceRun as a varint64 with value numFaces * count + face.
func encodeFaceRun(e *encoder, fr faceRun) {
// It isn't necessary to encode the number of faces left for the last run,
// but since this would only help if there were more than 21 faces, it will
// be a small overall savings, much smaller than the bound encoding.
coded := numFaces*uint64(fr.count) + uint64(fr.face)
e.writeUvarint(coded)
}
func encodeFaces(e *encoder, frs []faceRun) {
for _, fr := range frs {
encodeFaceRun(e, fr)
}
}
type facesIterator struct {
faces []faceRun
// How often have we yet shown the current face?
numCurrentFaceShown int
curFace int
}
func (fi *facesIterator) next() (ok bool) {
if len(fi.faces) == 0 {
return false
}
fi.curFace = fi.faces[0].face
fi.numCurrentFaceShown++
// Advance fs if needed.
if fi.faces[0].count <= fi.numCurrentFaceShown {
fi.faces = fi.faces[1:]
fi.numCurrentFaceShown = 0
}
return true
}
func decodePointsCompressed(d *decoder, level int, target []Point) {
faces := decodeFaces(len(target), d)
piCoder := newNthDerivativeCoder(derivativeEncodingOrder)
qiCoder := newNthDerivativeCoder(derivativeEncodingOrder)
iter := facesIterator{faces: faces}
for i := range target {
decodeFn := decodePointCompressed
if i == 0 {
decodeFn = decodeFirstPointFixedLength
}
pi, qi := decodeFn(d, level, piCoder, qiCoder)
if ok := iter.next(); !ok && d.err == nil {
d.err = fmt.Errorf("ran out of faces at target %d", i)
return
}
target[i] = Point{facePiQitoXYZ(iter.curFace, pi, qi, level)}
}
numOffCenter := int(d.readUvarint())
if d.err != nil {
return
}
if numOffCenter > len(target) {
d.err = fmt.Errorf("numOffCenter = %d, should be at most len(target) = %d", numOffCenter, len(target))
return
}
for i := 0; i < numOffCenter; i++ {
idx := int(d.readUvarint())
if d.err != nil {
return
}
if idx >= len(target) {
d.err = fmt.Errorf("off center index = %d, should be < len(target) = %d", idx, len(target))
return
}
target[idx].X = d.readFloat64()
target[idx].Y = d.readFloat64()
target[idx].Z = d.readFloat64()
}
}
func decodeFirstPointFixedLength(d *decoder, level int, piCoder, qiCoder *nthDerivativeCoder) (pi, qi uint32) {
bytesToRead := (level + 7) / 8 * 2
var interleaved uint64
for i := 0; i < bytesToRead; i++ {
rr := d.readUint8()
interleaved |= (uint64(rr) << uint(i*8))
}
piCoded, qiCoded := deinterleaveUint32(interleaved)
return uint32(piCoder.decode(int32(piCoded))), uint32(qiCoder.decode(int32(qiCoded)))
}
func zigzagEncode(x int32) uint32 {
return (uint32(x) << 1) ^ uint32(x>>31)
}
func zigzagDecode(x uint32) int32 {
return int32((x >> 1) ^ uint32((int32(x&1)<<31)>>31))
}
func decodePointCompressed(d *decoder, level int, piCoder, qiCoder *nthDerivativeCoder) (pi, qi uint32) {
interleavedZigZagEncodedDerivPiQi := d.readUvarint()
piZigzag, qiZigzag := deinterleaveUint32(interleavedZigZagEncodedDerivPiQi)
return uint32(piCoder.decode(zigzagDecode(piZigzag))), uint32(qiCoder.decode(zigzagDecode(qiZigzag)))
}
// We introduce a new coordinate system (pi, qi), which is (si, ti)
// with the bits that are constant for cells of that level shifted
// off to the right.
// si = round(s * 2^31)
// pi = si >> (31 - level)
// = floor(s * 2^level)
// If the point has been snapped to the level, the bits that are
// shifted off will be a 1 in the msb, then 0s after that, so the
// fractional part discarded by the cast is (close to) 0.5.
// stToPiQi returns the value transformed to the PiQi coordinate space.
func stToPiQi(s float64, level uint) uint32 {
return uint32(s * float64(int(1)<<level))
}
// siTiToPiQi returns the value transformed into the PiQi coordinate spade.
// encodeFirstPointFixedLength encodes the return value using level bits,
// so we clamp si to the range [0, 2**level - 1] before trying to encode
// it. This is okay because if si == maxSiTi, then it is not a cell center
// anyway and will be encoded separately as an off-center point.
func siTitoPiQi(siTi uint32, level int) uint32 {
s := uint(siTi)
const max = maxSiTi - 1
if s > max {
s = max
}
return uint32(s >> (maxLevel + 1 - uint(level)))
}
// piQiToST returns the value transformed to ST space.
func piQiToST(pi uint32, level int) float64 {
// We want to recover the position at the center of the cell. If the point
// was snapped to the center of the cell, then math.Modf(s * 2^level) == 0.5.
// Inverting STtoPiQi gives:
// s = (pi + 0.5) / 2^level.
return (float64(pi) + 0.5) / float64(int(1)<<uint(level))
}
func facePiQitoXYZ(face int, pi, qi uint32, level int) r3.Vector {
return faceUVToXYZ(face, stToUV(piQiToST(pi, level)), stToUV(piQiToST(qi, level))).Normalize()
}