mtsatellite/common/coords.go

// Copyright 2014 by Sascha L. Teichmann
// Use of this source code is governed by the MIT license
// that can be found in the LICENSE file.

package common

import (
	"encoding/binary"
	"fmt"
	"strconv"
)

const (
	numBitsPerComponent = 12
	modulo              = 1 << numBitsPerComponent
	maxPositive         = modulo / 2
	minValue            = -1 << (numBitsPerComponent - 1)
	maxValue            = 1<<(numBitsPerComponent-1) - 1
)

type (
	Coord struct {
		X, Y, Z int16
	}

	Cuboid struct {
		P1, P2 Coord
	}

	KeyTransformer func(int64) int64
	KeyEncoder     func(int64) ([]byte, error)
	KeyDecoder     func([]byte) (int64, error)
	KeyTranscoder  func([]byte) ([]byte, error)
	KeySplitter    func(int64) Coord
	KeyJoiner      func(Coord) int64
)

func (cub Cuboid) Contains(c Coord) bool {
	return c.X >= cub.P1.X && c.X <= cub.P2.X &&
		c.Y >= cub.P1.Y && c.Y <= cub.P2.Y &&
		c.Z >= cub.P1.Z && c.Z <= cub.P2.Z
}

func (c Coord) String() string {
	return fmt.Sprintf("(%d, %d, %d)", c.X, c.Y, c.Z)
}

func minComponent(a, b int16) int16 {
	if a < b {
		return a
	}
	return b
}

func maxComponent(a, b int16) int16 {
	if a > b {
		return a
	}
	return b
}

func clipComponent(x int16) int16 {
	if x < minValue {
		return minValue
	}
	if x > maxValue {
		return maxValue
	}
	return x
}

func ClipCoord(c Coord) Coord {
	return Coord{
		X: clipComponent(c.X),
		Y: clipComponent(c.Y),
		Z: clipComponent(c.Z)}
}

func MinCoord(a, b Coord) Coord {
	return Coord{
		X: minComponent(a.X, b.X),
		Y: minComponent(a.Y, b.Y),
		Z: minComponent(a.Z, b.Z)}
}

func MaxCoord(a, b Coord) Coord {
	return Coord{
		X: maxComponent(a.X, b.X),
		Y: maxComponent(a.Y, b.Y),
		Z: maxComponent(a.Z, b.Z)}
}

// DecodeStringFromBytes constructs a database key out of byte slice.
func DecodeStringFromBytes(key []byte) (pos int64, err error) {
	return strconv.ParseInt(string(key), 10, 64)
}

func StringToBytes(key int64) []byte {
	return []byte(strconv.FormatInt(key, 10))
}

// EncodeStringToBytes encodes a block pos to byte slice.
func EncodeStringToBytes(key int64) ([]byte, error) {
	return StringToBytes(key), nil
}

func ToBigEndian(key int64) []byte {
	enc := make([]byte, 8)
	binary.BigEndian.PutUint64(enc, uint64(key))
	return enc
}

func EncodeToBigEndian(key int64) ([]byte, error) {
	return ToBigEndian(key), nil
}

func FromBigEndian(key []byte) int64 {
	return int64(binary.BigEndian.Uint64(key))
}

func DecodeFromBigEndian(key []byte) (int64, error) {
	return FromBigEndian(key), nil
}

func CoordToInterleaved(c Coord) (result int64) {
	const end = 1 << (numBitsPerComponent + 1)
	x := c.X - minValue
	y := c.Y - minValue
	z := c.Z - minValue
	setmask := int64(1)
	for mask := int16(1); mask != end; mask <<= 1 {
		if x&mask != 0 {
			result |= setmask
		}
		setmask <<= 1
		if y&mask != 0 {
			result |= setmask
		}
		setmask <<= 1
		if z&mask != 0 {
			result |= setmask
		}
		setmask <<= 1
	}
	return
}

func InterleavedToCoord(pos int64) Coord {
	const end = 1 << (numBitsPerComponent + 1)
	var x, y, z int16
	for mask := int16(1); mask != end; mask <<= 1 {
		if pos&1 == 1 {
			x |= mask
		}
		pos >>= 1
		if pos&1 == 1 {
			y |= mask
		}
		pos >>= 1
		if pos&1 == 1 {
			z |= mask
		}
		pos >>= 1
	}
	return Coord{X: x + minValue, Y: y + minValue, Z: z + minValue}
}

func CoordToPlain(c Coord) int64 {
	return int64(c.Z)<<(2*numBitsPerComponent) +
		int64(c.Y)<<numBitsPerComponent +
		int64(c.X)
}

func unsignedToSigned(i int16) int16 {
	if i < maxPositive {
		return i
	}
	return i - maxPositive*2
}

// To match C++ code.
func pythonModulo(i int16) int16 {
	const mask = modulo - 1
	if i >= 0 {
		return i & mask
	}
	return modulo - -i&mask
}

func PlainToCoord(i int64) (c Coord) {
	c.X = unsignedToSigned(pythonModulo(int16(i)))
	i = (i - int64(c.X)) >> numBitsPerComponent
	c.Y = unsignedToSigned(pythonModulo(int16(i)))
	i = (i - int64(c.Y)) >> numBitsPerComponent
	c.Z = unsignedToSigned(pythonModulo(int16(i)))
	return
}

func TransformPlainToInterleaved(pos int64) int64 {
	return CoordToInterleaved(PlainToCoord(pos))
}

func TransformInterleavedToPlain(pos int64) int64 {
	return CoordToPlain(InterleavedToCoord(pos))
}

func DecodeStringFromBytesToInterleaved(key []byte) (v int64, err error) {
	if v, err = DecodeStringFromBytes(key); err != nil {
		return
	}
	v = TransformPlainToInterleaved(v)
	return
}

func DecodeStringBytesToCoord(key []byte) (coord Coord, err error) {
	var k int64
	if k, err = DecodeStringFromBytes(key); err != nil {
		return
	}
	coord = PlainToCoord(k)
	return
}

func EncodeStringToBytesFromInterleaved(key int64) ([]byte, error) {
	return EncodeStringToBytes(TransformInterleavedToPlain(key))
}

func IdentityTranscoder(key []byte) ([]byte, error) {
	return key, nil
}

func TranscodePlainToInterleaved(key []byte) ([]byte, error) {
	pos, err := DecodeStringFromBytesToInterleaved(key)
	if err != nil {
		return nil, err
	}
	return EncodeToBigEndian(pos)
}

func TranscodeInterleavedToPlain(key []byte) ([]byte, error) {
	pos, err := DecodeFromBigEndian(key)
	if err != nil {
		return nil, err
	}
	return EncodeStringToBytes(TransformInterleavedToPlain(pos))
}

// NaiveBigMin is for correctness checks of BigMin only.
func NaiveBigMin(minz, maxz, zcode int64) int64 {
	var (
		c1   = InterleavedToCoord(minz)
		c2   = InterleavedToCoord(maxz)
		cand = maxz
		c    Coord
	)

	for c.X = c1.X; c.X <= c2.X; c.X++ {
		for c.Y = c1.Y; c.Y <= c2.Y; c.Y++ {
			for c.Z = c1.Z; c.Z <= c2.Z; c.Z++ {
				if z := CoordToInterleaved(c); z > zcode && z < cand {
					cand = z
				}
			}
		}
	}

	return cand
}

const (
	msb  = uint8(3*numBitsPerComponent - 1)
	mask = int64(0x924924924)
	full = int64(0xfffffffff)
)

func setbits(p uint8, v int64) int64 {
	m := (mask >> (msb - p)) & (^(full << p) & full)
	return (v | m) & ^(1 << p) & full
}

func unsetbits(p uint8, v int64) int64 {
	m := ^(mask >> (msb - p)) & full
	return (v & m) | (int64(1) << p)
}

func BigMin(minz, maxz, zcode int64) int64 {
	const (
		_001_ = 1
		_010_ = 2
		_011_ = 2 | 1
		_100_ = 4
		_101_ = 4 | 1
	)
	bigmin := maxz
	pos := msb
	for m := int64(1) << msb; m != 0; m >>= 1 {
		var v uint8
		if zcode&m == m {
			v = _100_
		}
		if minz&m == m {
			v |= _010_
		}
		if maxz&m == m {
			v |= _001_
		}
		switch v {
		case _001_:
			bigmin = unsetbits(pos, minz)
			maxz = setbits(pos, maxz)
		case _011_:
			return minz
		case _100_:
			return bigmin
		case _101_:
			minz = unsetbits(pos, minz)
		}
		pos--
	}
	return bigmin
}