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Core barcode encoding/decoding library
/*
* Copyright 2008 ZXing authors
*
* 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 com.google.zxing.qrcode.encoder;
import com.google.zxing.WriterException;
import com.google.zxing.common.BitArray;
import com.google.zxing.qrcode.decoder.ErrorCorrectionLevel;
import com.google.zxing.qrcode.decoder.Version;
/**
* @author [email protected] (Satoru Takabayashi) - creator
* @author [email protected] (Daniel Switkin) - ported from C++
*/
final class MatrixUtil {
private MatrixUtil() {
// do nothing
}
private static final int[][] POSITION_DETECTION_PATTERN = {
{1, 1, 1, 1, 1, 1, 1},
{1, 0, 0, 0, 0, 0, 1},
{1, 0, 1, 1, 1, 0, 1},
{1, 0, 1, 1, 1, 0, 1},
{1, 0, 1, 1, 1, 0, 1},
{1, 0, 0, 0, 0, 0, 1},
{1, 1, 1, 1, 1, 1, 1},
};
private static final int[][] POSITION_ADJUSTMENT_PATTERN = {
{1, 1, 1, 1, 1},
{1, 0, 0, 0, 1},
{1, 0, 1, 0, 1},
{1, 0, 0, 0, 1},
{1, 1, 1, 1, 1},
};
// From Appendix E. Table 1, JIS0510X:2004 (p 71). The table was double-checked by komatsu.
private static final int[][] POSITION_ADJUSTMENT_PATTERN_COORDINATE_TABLE = {
{-1, -1, -1, -1, -1, -1, -1}, // Version 1
{ 6, 18, -1, -1, -1, -1, -1}, // Version 2
{ 6, 22, -1, -1, -1, -1, -1}, // Version 3
{ 6, 26, -1, -1, -1, -1, -1}, // Version 4
{ 6, 30, -1, -1, -1, -1, -1}, // Version 5
{ 6, 34, -1, -1, -1, -1, -1}, // Version 6
{ 6, 22, 38, -1, -1, -1, -1}, // Version 7
{ 6, 24, 42, -1, -1, -1, -1}, // Version 8
{ 6, 26, 46, -1, -1, -1, -1}, // Version 9
{ 6, 28, 50, -1, -1, -1, -1}, // Version 10
{ 6, 30, 54, -1, -1, -1, -1}, // Version 11
{ 6, 32, 58, -1, -1, -1, -1}, // Version 12
{ 6, 34, 62, -1, -1, -1, -1}, // Version 13
{ 6, 26, 46, 66, -1, -1, -1}, // Version 14
{ 6, 26, 48, 70, -1, -1, -1}, // Version 15
{ 6, 26, 50, 74, -1, -1, -1}, // Version 16
{ 6, 30, 54, 78, -1, -1, -1}, // Version 17
{ 6, 30, 56, 82, -1, -1, -1}, // Version 18
{ 6, 30, 58, 86, -1, -1, -1}, // Version 19
{ 6, 34, 62, 90, -1, -1, -1}, // Version 20
{ 6, 28, 50, 72, 94, -1, -1}, // Version 21
{ 6, 26, 50, 74, 98, -1, -1}, // Version 22
{ 6, 30, 54, 78, 102, -1, -1}, // Version 23
{ 6, 28, 54, 80, 106, -1, -1}, // Version 24
{ 6, 32, 58, 84, 110, -1, -1}, // Version 25
{ 6, 30, 58, 86, 114, -1, -1}, // Version 26
{ 6, 34, 62, 90, 118, -1, -1}, // Version 27
{ 6, 26, 50, 74, 98, 122, -1}, // Version 28
{ 6, 30, 54, 78, 102, 126, -1}, // Version 29
{ 6, 26, 52, 78, 104, 130, -1}, // Version 30
{ 6, 30, 56, 82, 108, 134, -1}, // Version 31
{ 6, 34, 60, 86, 112, 138, -1}, // Version 32
{ 6, 30, 58, 86, 114, 142, -1}, // Version 33
{ 6, 34, 62, 90, 118, 146, -1}, // Version 34
{ 6, 30, 54, 78, 102, 126, 150}, // Version 35
{ 6, 24, 50, 76, 102, 128, 154}, // Version 36
{ 6, 28, 54, 80, 106, 132, 158}, // Version 37
{ 6, 32, 58, 84, 110, 136, 162}, // Version 38
{ 6, 26, 54, 82, 110, 138, 166}, // Version 39
{ 6, 30, 58, 86, 114, 142, 170}, // Version 40
};
// Type info cells at the left top corner.
private static final int[][] TYPE_INFO_COORDINATES = {
{8, 0},
{8, 1},
{8, 2},
{8, 3},
{8, 4},
{8, 5},
{8, 7},
{8, 8},
{7, 8},
{5, 8},
{4, 8},
{3, 8},
{2, 8},
{1, 8},
{0, 8},
};
// From Appendix D in JISX0510:2004 (p. 67)
private static final int VERSION_INFO_POLY = 0x1f25; // 1 1111 0010 0101
// From Appendix C in JISX0510:2004 (p.65).
private static final int TYPE_INFO_POLY = 0x537;
private static final int TYPE_INFO_MASK_PATTERN = 0x5412;
// Set all cells to -1. -1 means that the cell is empty (not set yet).
//
// JAVAPORT: We shouldn't need to do this at all. The code should be rewritten to begin encoding
// with the ByteMatrix initialized all to zero.
static void clearMatrix(ByteMatrix matrix) {
matrix.clear((byte) -1);
}
// Build 2D matrix of QR Code from "dataBits" with "ecLevel", "version" and "getMaskPattern". On
// success, store the result in "matrix" and return true.
static void buildMatrix(BitArray dataBits,
ErrorCorrectionLevel ecLevel,
Version version,
int maskPattern,
ByteMatrix matrix) throws WriterException {
clearMatrix(matrix);
embedBasicPatterns(version, matrix);
// Type information appear with any version.
embedTypeInfo(ecLevel, maskPattern, matrix);
// Version info appear if version >= 7.
maybeEmbedVersionInfo(version, matrix);
// Data should be embedded at end.
embedDataBits(dataBits, maskPattern, matrix);
}
// Embed basic patterns. On success, modify the matrix and return true.
// The basic patterns are:
// - Position detection patterns
// - Timing patterns
// - Dark dot at the left bottom corner
// - Position adjustment patterns, if need be
static void embedBasicPatterns(Version version, ByteMatrix matrix) throws WriterException {
// Let's get started with embedding big squares at corners.
embedPositionDetectionPatternsAndSeparators(matrix);
// Then, embed the dark dot at the left bottom corner.
embedDarkDotAtLeftBottomCorner(matrix);
// Position adjustment patterns appear if version >= 2.
maybeEmbedPositionAdjustmentPatterns(version, matrix);
// Timing patterns should be embedded after position adj. patterns.
embedTimingPatterns(matrix);
}
// Embed type information. On success, modify the matrix.
static void embedTypeInfo(ErrorCorrectionLevel ecLevel, int maskPattern, ByteMatrix matrix)
throws WriterException {
BitArray typeInfoBits = new BitArray();
makeTypeInfoBits(ecLevel, maskPattern, typeInfoBits);
for (int i = 0; i < typeInfoBits.getSize(); ++i) {
// Place bits in LSB to MSB order. LSB (least significant bit) is the last value in
// "typeInfoBits".
boolean bit = typeInfoBits.get(typeInfoBits.getSize() - 1 - i);
// Type info bits at the left top corner. See 8.9 of JISX0510:2004 (p.46).
int x1 = TYPE_INFO_COORDINATES[i][0];
int y1 = TYPE_INFO_COORDINATES[i][1];
matrix.set(x1, y1, bit);
if (i < 8) {
// Right top corner.
int x2 = matrix.getWidth() - i - 1;
int y2 = 8;
matrix.set(x2, y2, bit);
} else {
// Left bottom corner.
int x2 = 8;
int y2 = matrix.getHeight() - 7 + (i - 8);
matrix.set(x2, y2, bit);
}
}
}
// Embed version information if need be. On success, modify the matrix and return true.
// See 8.10 of JISX0510:2004 (p.47) for how to embed version information.
static void maybeEmbedVersionInfo(Version version, ByteMatrix matrix) throws WriterException {
if (version.getVersionNumber() < 7) { // Version info is necessary if version >= 7.
return; // Don't need version info.
}
BitArray versionInfoBits = new BitArray();
makeVersionInfoBits(version, versionInfoBits);
int bitIndex = 6 * 3 - 1; // It will decrease from 17 to 0.
for (int i = 0; i < 6; ++i) {
for (int j = 0; j < 3; ++j) {
// Place bits in LSB (least significant bit) to MSB order.
boolean bit = versionInfoBits.get(bitIndex);
bitIndex--;
// Left bottom corner.
matrix.set(i, matrix.getHeight() - 11 + j, bit);
// Right bottom corner.
matrix.set(matrix.getHeight() - 11 + j, i, bit);
}
}
}
// Embed "dataBits" using "getMaskPattern". On success, modify the matrix and return true.
// For debugging purposes, it skips masking process if "getMaskPattern" is -1.
// See 8.7 of JISX0510:2004 (p.38) for how to embed data bits.
static void embedDataBits(BitArray dataBits, int maskPattern, ByteMatrix matrix)
throws WriterException {
int bitIndex = 0;
int direction = -1;
// Start from the right bottom cell.
int x = matrix.getWidth() - 1;
int y = matrix.getHeight() - 1;
while (x > 0) {
// Skip the vertical timing pattern.
if (x == 6) {
x -= 1;
}
while (y >= 0 && y < matrix.getHeight()) {
for (int i = 0; i < 2; ++i) {
int xx = x - i;
// Skip the cell if it's not empty.
if (!isEmpty(matrix.get(xx, y))) {
continue;
}
boolean bit;
if (bitIndex < dataBits.getSize()) {
bit = dataBits.get(bitIndex);
++bitIndex;
} else {
// Padding bit. If there is no bit left, we'll fill the left cells with 0, as described
// in 8.4.9 of JISX0510:2004 (p. 24).
bit = false;
}
// Skip masking if mask_pattern is -1.
if (maskPattern != -1 && MaskUtil.getDataMaskBit(maskPattern, xx, y)) {
bit = !bit;
}
matrix.set(xx, y, bit);
}
y += direction;
}
direction = -direction; // Reverse the direction.
y += direction;
x -= 2; // Move to the left.
}
// All bits should be consumed.
if (bitIndex != dataBits.getSize()) {
throw new WriterException("Not all bits consumed: " + bitIndex + '/' + dataBits.getSize());
}
}
// Return the position of the most significant bit set (to one) in the "value". The most
// significant bit is position 32. If there is no bit set, return 0. Examples:
// - findMSBSet(0) => 0
// - findMSBSet(1) => 1
// - findMSBSet(255) => 8
static int findMSBSet(int value) {
int numDigits = 0;
while (value != 0) {
value >>>= 1;
++numDigits;
}
return numDigits;
}
// Calculate BCH (Bose-Chaudhuri-Hocquenghem) code for "value" using polynomial "poly". The BCH
// code is used for encoding type information and version information.
// Example: Calculation of version information of 7.
// f(x) is created from 7.
// - 7 = 000111 in 6 bits
// - f(x) = x^2 + x^1 + x^0
// g(x) is given by the standard (p. 67)
// - g(x) = x^12 + x^11 + x^10 + x^9 + x^8 + x^5 + x^2 + 1
// Multiply f(x) by x^(18 - 6)
// - f'(x) = f(x) * x^(18 - 6)
// - f'(x) = x^14 + x^13 + x^12
// Calculate the remainder of f'(x) / g(x)
// x^2
// __________________________________________________
// g(x) )x^14 + x^13 + x^12
// x^14 + x^13 + x^12 + x^11 + x^10 + x^7 + x^4 + x^2
// --------------------------------------------------
// x^11 + x^10 + x^7 + x^4 + x^2
//
// The remainder is x^11 + x^10 + x^7 + x^4 + x^2
// Encode it in binary: 110010010100
// The return value is 0xc94 (1100 1001 0100)
//
// Since all coefficients in the polynomials are 1 or 0, we can do the calculation by bit
// operations. We don't care if cofficients are positive or negative.
static int calculateBCHCode(int value, int poly) {
if (poly == 0) {
throw new IllegalArgumentException("0 polynomial");
}
// If poly is "1 1111 0010 0101" (version info poly), msbSetInPoly is 13. We'll subtract 1
// from 13 to make it 12.
int msbSetInPoly = findMSBSet(poly);
value <<= msbSetInPoly - 1;
// Do the division business using exclusive-or operations.
while (findMSBSet(value) >= msbSetInPoly) {
value ^= poly << (findMSBSet(value) - msbSetInPoly);
}
// Now the "value" is the remainder (i.e. the BCH code)
return value;
}
// Make bit vector of type information. On success, store the result in "bits" and return true.
// Encode error correction level and mask pattern. See 8.9 of
// JISX0510:2004 (p.45) for details.
static void makeTypeInfoBits(ErrorCorrectionLevel ecLevel, int maskPattern, BitArray bits)
throws WriterException {
if (!QRCode.isValidMaskPattern(maskPattern)) {
throw new WriterException("Invalid mask pattern");
}
int typeInfo = (ecLevel.getBits() << 3) | maskPattern;
bits.appendBits(typeInfo, 5);
int bchCode = calculateBCHCode(typeInfo, TYPE_INFO_POLY);
bits.appendBits(bchCode, 10);
BitArray maskBits = new BitArray();
maskBits.appendBits(TYPE_INFO_MASK_PATTERN, 15);
bits.xor(maskBits);
if (bits.getSize() != 15) { // Just in case.
throw new WriterException("should not happen but we got: " + bits.getSize());
}
}
// Make bit vector of version information. On success, store the result in "bits" and return true.
// See 8.10 of JISX0510:2004 (p.45) for details.
static void makeVersionInfoBits(Version version, BitArray bits) throws WriterException {
bits.appendBits(version.getVersionNumber(), 6);
int bchCode = calculateBCHCode(version.getVersionNumber(), VERSION_INFO_POLY);
bits.appendBits(bchCode, 12);
if (bits.getSize() != 18) { // Just in case.
throw new WriterException("should not happen but we got: " + bits.getSize());
}
}
// Check if "value" is empty.
private static boolean isEmpty(int value) {
return value == -1;
}
private static void embedTimingPatterns(ByteMatrix matrix) {
// -8 is for skipping position detection patterns (size 7), and two horizontal/vertical
// separation patterns (size 1). Thus, 8 = 7 + 1.
for (int i = 8; i < matrix.getWidth() - 8; ++i) {
int bit = (i + 1) % 2;
// Horizontal line.
if (isEmpty(matrix.get(i, 6))) {
matrix.set(i, 6, bit);
}
// Vertical line.
if (isEmpty(matrix.get(6, i))) {
matrix.set(6, i, bit);
}
}
}
// Embed the lonely dark dot at left bottom corner. JISX0510:2004 (p.46)
private static void embedDarkDotAtLeftBottomCorner(ByteMatrix matrix) throws WriterException {
if (matrix.get(8, matrix.getHeight() - 8) == 0) {
throw new WriterException();
}
matrix.set(8, matrix.getHeight() - 8, 1);
}
private static void embedHorizontalSeparationPattern(int xStart,
int yStart,
ByteMatrix matrix) throws WriterException {
for (int x = 0; x < 8; ++x) {
if (!isEmpty(matrix.get(xStart + x, yStart))) {
throw new WriterException();
}
matrix.set(xStart + x, yStart, 0);
}
}
private static void embedVerticalSeparationPattern(int xStart,
int yStart,
ByteMatrix matrix) throws WriterException {
for (int y = 0; y < 7; ++y) {
if (!isEmpty(matrix.get(xStart, yStart + y))) {
throw new WriterException();
}
matrix.set(xStart, yStart + y, 0);
}
}
// Note that we cannot unify the function with embedPositionDetectionPattern() despite they are
// almost identical, since we cannot write a function that takes 2D arrays in different sizes in
// C/C++. We should live with the fact.
private static void embedPositionAdjustmentPattern(int xStart, int yStart, ByteMatrix matrix) {
for (int y = 0; y < 5; ++y) {
for (int x = 0; x < 5; ++x) {
matrix.set(xStart + x, yStart + y, POSITION_ADJUSTMENT_PATTERN[y][x]);
}
}
}
private static void embedPositionDetectionPattern(int xStart, int yStart, ByteMatrix matrix) {
for (int y = 0; y < 7; ++y) {
for (int x = 0; x < 7; ++x) {
matrix.set(xStart + x, yStart + y, POSITION_DETECTION_PATTERN[y][x]);
}
}
}
// Embed position detection patterns and surrounding vertical/horizontal separators.
private static void embedPositionDetectionPatternsAndSeparators(ByteMatrix matrix) throws WriterException {
// Embed three big squares at corners.
int pdpWidth = POSITION_DETECTION_PATTERN[0].length;
// Left top corner.
embedPositionDetectionPattern(0, 0, matrix);
// Right top corner.
embedPositionDetectionPattern(matrix.getWidth() - pdpWidth, 0, matrix);
// Left bottom corner.
embedPositionDetectionPattern(0, matrix.getWidth() - pdpWidth, matrix);
// Embed horizontal separation patterns around the squares.
int hspWidth = 8;
// Left top corner.
embedHorizontalSeparationPattern(0, hspWidth - 1, matrix);
// Right top corner.
embedHorizontalSeparationPattern(matrix.getWidth() - hspWidth,
hspWidth - 1, matrix);
// Left bottom corner.
embedHorizontalSeparationPattern(0, matrix.getWidth() - hspWidth, matrix);
// Embed vertical separation patterns around the squares.
int vspSize = 7;
// Left top corner.
embedVerticalSeparationPattern(vspSize, 0, matrix);
// Right top corner.
embedVerticalSeparationPattern(matrix.getHeight() - vspSize - 1, 0, matrix);
// Left bottom corner.
embedVerticalSeparationPattern(vspSize, matrix.getHeight() - vspSize,
matrix);
}
// Embed position adjustment patterns if need be.
private static void maybeEmbedPositionAdjustmentPatterns(Version version, ByteMatrix matrix) {
if (version.getVersionNumber() < 2) { // The patterns appear if version >= 2
return;
}
int index = version.getVersionNumber() - 1;
int[] coordinates = POSITION_ADJUSTMENT_PATTERN_COORDINATE_TABLE[index];
int numCoordinates = POSITION_ADJUSTMENT_PATTERN_COORDINATE_TABLE[index].length;
for (int i = 0; i < numCoordinates; ++i) {
for (int j = 0; j < numCoordinates; ++j) {
int y = coordinates[i];
int x = coordinates[j];
if (x == -1 || y == -1) {
continue;
}
// If the cell is unset, we embed the position adjustment pattern here.
if (isEmpty(matrix.get(x, y))) {
// -2 is necessary since the x/y coordinates point to the center of the pattern, not the
// left top corner.
embedPositionAdjustmentPattern(x - 2, y - 2, matrix);
}
}
}
}
}
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