001/*
002 * Copyright 2008 ZXing authors
003 *
004 * Licensed under the Apache License, Version 2.0 (the "License");
005 * you may not use this file except in compliance with the License.
006 * You may obtain a copy of the License at
007 *
008 *      http://www.apache.org/licenses/LICENSE-2.0
009 *
010 * Unless required by applicable law or agreed to in writing, software
011 * distributed under the License is distributed on an "AS IS" BASIS,
012 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
013 * See the License for the specific language governing permissions and
014 * limitations under the License.
015 */
016
017package com.itextpdf.text.pdf.qrcode;
018
019/**
020 * @author satorux@google.com (Satoru Takabayashi) - creator
021 * @author dswitkin@google.com (Daniel Switkin) - ported from C++
022 * @since 5.0.2
023 */
024public final class MatrixUtil {
025
026  private MatrixUtil() {
027    // do nothing
028  }
029
030  private static final int[][] POSITION_DETECTION_PATTERN =  {
031      {1, 1, 1, 1, 1, 1, 1},
032      {1, 0, 0, 0, 0, 0, 1},
033      {1, 0, 1, 1, 1, 0, 1},
034      {1, 0, 1, 1, 1, 0, 1},
035      {1, 0, 1, 1, 1, 0, 1},
036      {1, 0, 0, 0, 0, 0, 1},
037      {1, 1, 1, 1, 1, 1, 1},
038  };
039
040  private static final int[][] HORIZONTAL_SEPARATION_PATTERN = {
041      {0, 0, 0, 0, 0, 0, 0, 0},
042  };
043
044  private static final int[][] VERTICAL_SEPARATION_PATTERN = {
045      {0}, {0}, {0}, {0}, {0}, {0}, {0},
046  };
047
048  private static final int[][] POSITION_ADJUSTMENT_PATTERN = {
049      {1, 1, 1, 1, 1},
050      {1, 0, 0, 0, 1},
051      {1, 0, 1, 0, 1},
052      {1, 0, 0, 0, 1},
053      {1, 1, 1, 1, 1},
054  };
055
056  // From Appendix E. Table 1, JIS0510X:2004 (p 71). The table was double-checked by komatsu.
057  private static final int[][] POSITION_ADJUSTMENT_PATTERN_COORDINATE_TABLE = {
058      {-1, -1, -1, -1,  -1,  -1,  -1},  // Version 1
059      { 6, 18, -1, -1,  -1,  -1,  -1},  // Version 2
060      { 6, 22, -1, -1,  -1,  -1,  -1},  // Version 3
061      { 6, 26, -1, -1,  -1,  -1,  -1},  // Version 4
062      { 6, 30, -1, -1,  -1,  -1,  -1},  // Version 5
063      { 6, 34, -1, -1,  -1,  -1,  -1},  // Version 6
064      { 6, 22, 38, -1,  -1,  -1,  -1},  // Version 7
065      { 6, 24, 42, -1,  -1,  -1,  -1},  // Version 8
066      { 6, 26, 46, -1,  -1,  -1,  -1},  // Version 9
067      { 6, 28, 50, -1,  -1,  -1,  -1},  // Version 10
068      { 6, 30, 54, -1,  -1,  -1,  -1},  // Version 11
069      { 6, 32, 58, -1,  -1,  -1,  -1},  // Version 12
070      { 6, 34, 62, -1,  -1,  -1,  -1},  // Version 13
071      { 6, 26, 46, 66,  -1,  -1,  -1},  // Version 14
072      { 6, 26, 48, 70,  -1,  -1,  -1},  // Version 15
073      { 6, 26, 50, 74,  -1,  -1,  -1},  // Version 16
074      { 6, 30, 54, 78,  -1,  -1,  -1},  // Version 17
075      { 6, 30, 56, 82,  -1,  -1,  -1},  // Version 18
076      { 6, 30, 58, 86,  -1,  -1,  -1},  // Version 19
077      { 6, 34, 62, 90,  -1,  -1,  -1},  // Version 20
078      { 6, 28, 50, 72,  94,  -1,  -1},  // Version 21
079      { 6, 26, 50, 74,  98,  -1,  -1},  // Version 22
080      { 6, 30, 54, 78, 102,  -1,  -1},  // Version 23
081      { 6, 28, 54, 80, 106,  -1,  -1},  // Version 24
082      { 6, 32, 58, 84, 110,  -1,  -1},  // Version 25
083      { 6, 30, 58, 86, 114,  -1,  -1},  // Version 26
084      { 6, 34, 62, 90, 118,  -1,  -1},  // Version 27
085      { 6, 26, 50, 74,  98, 122,  -1},  // Version 28
086      { 6, 30, 54, 78, 102, 126,  -1},  // Version 29
087      { 6, 26, 52, 78, 104, 130,  -1},  // Version 30
088      { 6, 30, 56, 82, 108, 134,  -1},  // Version 31
089      { 6, 34, 60, 86, 112, 138,  -1},  // Version 32
090      { 6, 30, 58, 86, 114, 142,  -1},  // Version 33
091      { 6, 34, 62, 90, 118, 146,  -1},  // Version 34
092      { 6, 30, 54, 78, 102, 126, 150},  // Version 35
093      { 6, 24, 50, 76, 102, 128, 154},  // Version 36
094      { 6, 28, 54, 80, 106, 132, 158},  // Version 37
095      { 6, 32, 58, 84, 110, 136, 162},  // Version 38
096      { 6, 26, 54, 82, 110, 138, 166},  // Version 39
097      { 6, 30, 58, 86, 114, 142, 170},  // Version 40
098  };
099
100  // Type info cells at the left top corner.
101  private static final int[][] TYPE_INFO_COORDINATES = {
102      {8, 0},
103      {8, 1},
104      {8, 2},
105      {8, 3},
106      {8, 4},
107      {8, 5},
108      {8, 7},
109      {8, 8},
110      {7, 8},
111      {5, 8},
112      {4, 8},
113      {3, 8},
114      {2, 8},
115      {1, 8},
116      {0, 8},
117  };
118
119  // From Appendix D in JISX0510:2004 (p. 67)
120  private static final int VERSION_INFO_POLY = 0x1f25;  // 1 1111 0010 0101
121
122  // From Appendix C in JISX0510:2004 (p.65).
123  private static final int TYPE_INFO_POLY = 0x537;
124  private static final int TYPE_INFO_MASK_PATTERN = 0x5412;
125
126  // Set all cells to -1.  -1 means that the cell is empty (not set yet).
127  //
128  // JAVAPORT: We shouldn't need to do this at all. The code should be rewritten to begin encoding
129  // with the ByteMatrix initialized all to zero.
130  public static void clearMatrix(ByteMatrix matrix) {
131    matrix.clear((byte) -1);
132  }
133
134  // Build 2D matrix of QR Code from "dataBits" with "ecLevel", "version" and "getMaskPattern". On
135  // success, store the result in "matrix" and return true.
136  public static void buildMatrix(BitVector dataBits, ErrorCorrectionLevel ecLevel, int version,
137      int maskPattern, ByteMatrix matrix) throws WriterException {
138    clearMatrix(matrix);
139    embedBasicPatterns(version, matrix);
140    // Type information appear with any version.
141    embedTypeInfo(ecLevel, maskPattern, matrix);
142    // Version info appear if version >= 7.
143    maybeEmbedVersionInfo(version, matrix);
144    // Data should be embedded at end.
145    embedDataBits(dataBits, maskPattern, matrix);
146  }
147
148  // Embed basic patterns. On success, modify the matrix and return true.
149  // The basic patterns are:
150  // - Position detection patterns
151  // - Timing patterns
152  // - Dark dot at the left bottom corner
153  // - Position adjustment patterns, if need be
154  public static void embedBasicPatterns(int version, ByteMatrix matrix) throws WriterException {
155    // Let's get started with embedding big squares at corners.
156    embedPositionDetectionPatternsAndSeparators(matrix);
157    // Then, embed the dark dot at the left bottom corner.
158    embedDarkDotAtLeftBottomCorner(matrix);
159
160    // Position adjustment patterns appear if version >= 2.
161    maybeEmbedPositionAdjustmentPatterns(version, matrix);
162    // Timing patterns should be embedded after position adj. patterns.
163    embedTimingPatterns(matrix);
164  }
165
166  // Embed type information. On success, modify the matrix.
167  public static void embedTypeInfo(ErrorCorrectionLevel ecLevel, int maskPattern, ByteMatrix matrix)
168      throws WriterException {
169    BitVector typeInfoBits = new BitVector();
170    makeTypeInfoBits(ecLevel, maskPattern, typeInfoBits);
171
172    for (int i = 0; i < typeInfoBits.size(); ++i) {
173      // Place bits in LSB to MSB order.  LSB (least significant bit) is the last value in
174      // "typeInfoBits".
175      int bit = typeInfoBits.at(typeInfoBits.size() - 1 - i);
176
177      // Type info bits at the left top corner. See 8.9 of JISX0510:2004 (p.46).
178      int x1 = TYPE_INFO_COORDINATES[i][0];
179      int y1 = TYPE_INFO_COORDINATES[i][1];
180      matrix.set(x1, y1, bit);
181
182      if (i < 8) {
183        // Right top corner.
184        int x2 = matrix.getWidth() - i - 1;
185        int y2 = 8;
186        matrix.set(x2, y2, bit);
187      } else {
188        // Left bottom corner.
189        int x2 = 8;
190        int y2 = matrix.getHeight() - 7 + (i - 8);
191        matrix.set(x2, y2, bit);
192      }
193    }
194  }
195
196  // Embed version information if need be. On success, modify the matrix and return true.
197  // See 8.10 of JISX0510:2004 (p.47) for how to embed version information.
198  public static void maybeEmbedVersionInfo(int version, ByteMatrix matrix) throws WriterException {
199    if (version < 7) {  // Version info is necessary if version >= 7.
200      return;  // Don't need version info.
201    }
202    BitVector versionInfoBits = new BitVector();
203    makeVersionInfoBits(version, versionInfoBits);
204
205    int bitIndex = 6 * 3 - 1;  // It will decrease from 17 to 0.
206    for (int i = 0; i < 6; ++i) {
207      for (int j = 0; j < 3; ++j) {
208        // Place bits in LSB (least significant bit) to MSB order.
209        int bit = versionInfoBits.at(bitIndex);
210        bitIndex--;
211        // Left bottom corner.
212        matrix.set(i, matrix.getHeight() - 11 + j, bit);
213        // Right bottom corner.
214        matrix.set(matrix.getHeight() - 11 + j, i, bit);
215      }
216    }
217  }
218
219  // Embed "dataBits" using "getMaskPattern". On success, modify the matrix and return true.
220  // For debugging purposes, it skips masking process if "getMaskPattern" is -1.
221  // See 8.7 of JISX0510:2004 (p.38) for how to embed data bits.
222  public static void embedDataBits(BitVector dataBits, int maskPattern, ByteMatrix matrix)
223      throws WriterException {
224    int bitIndex = 0;
225    int direction = -1;
226    // Start from the right bottom cell.
227    int x = matrix.getWidth() - 1;
228    int y = matrix.getHeight() - 1;
229    while (x > 0) {
230      // Skip the vertical timing pattern.
231      if (x == 6) {
232        x -= 1;
233      }
234      while (y >= 0 && y < matrix.getHeight()) {
235        for (int i = 0; i < 2; ++i) {
236          int xx = x - i;
237          // Skip the cell if it's not empty.
238          if (!isEmpty(matrix.get(xx, y))) {
239            continue;
240          }
241          int bit;
242          if (bitIndex < dataBits.size()) {
243            bit = dataBits.at(bitIndex);
244            ++bitIndex;
245          } else {
246            // Padding bit. If there is no bit left, we'll fill the left cells with 0, as described
247            // in 8.4.9 of JISX0510:2004 (p. 24).
248            bit = 0;
249          }
250
251          // Skip masking if mask_pattern is -1.
252          if (maskPattern != -1) {
253            if (MaskUtil.getDataMaskBit(maskPattern, xx, y)) {
254              bit ^= 0x1;
255            }
256          }
257          matrix.set(xx, y, bit);
258        }
259        y += direction;
260      }
261      direction = -direction;  // Reverse the direction.
262      y += direction;
263      x -= 2;  // Move to the left.
264    }
265    // All bits should be consumed.
266    if (bitIndex != dataBits.size()) {
267      throw new WriterException("Not all bits consumed: " + bitIndex + '/' + dataBits.size());
268    }
269  }
270
271  // Return the position of the most significant bit set (to one) in the "value". The most
272  // significant bit is position 32. If there is no bit set, return 0. Examples:
273  // - findMSBSet(0) => 0
274  // - findMSBSet(1) => 1
275  // - findMSBSet(255) => 8
276  public static int findMSBSet(int value) {
277    int numDigits = 0;
278    while (value != 0) {
279      value >>>= 1;
280      ++numDigits;
281    }
282    return numDigits;
283  }
284
285  // Calculate BCH (Bose-Chaudhuri-Hocquenghem) code for "value" using polynomial "poly". The BCH
286  // code is used for encoding type information and version information.
287  // Example: Calculation of version information of 7.
288  // f(x) is created from 7.
289  //   - 7 = 000111 in 6 bits
290  //   - f(x) = x^2 + x^2 + x^1
291  // g(x) is given by the standard (p. 67)
292  //   - g(x) = x^12 + x^11 + x^10 + x^9 + x^8 + x^5 + x^2 + 1
293  // Multiply f(x) by x^(18 - 6)
294  //   - f'(x) = f(x) * x^(18 - 6)
295  //   - f'(x) = x^14 + x^13 + x^12
296  // Calculate the remainder of f'(x) / g(x)
297  //         x^2
298  //         __________________________________________________
299  //   g(x) )x^14 + x^13 + x^12
300  //         x^14 + x^13 + x^12 + x^11 + x^10 + x^7 + x^4 + x^2
301  //         --------------------------------------------------
302  //                              x^11 + x^10 + x^7 + x^4 + x^2
303  //
304  // The remainder is x^11 + x^10 + x^7 + x^4 + x^2
305  // Encode it in binary: 110010010100
306  // The return value is 0xc94 (1100 1001 0100)
307  //
308  // Since all coefficients in the polynomials are 1 or 0, we can do the calculation by bit
309  // operations. We don't care if cofficients are positive or negative.
310  public static int calculateBCHCode(int value, int poly) {
311    // If poly is "1 1111 0010 0101" (version info poly), msbSetInPoly is 13. We'll subtract 1
312    // from 13 to make it 12.
313    int msbSetInPoly = findMSBSet(poly);
314    value <<= msbSetInPoly - 1;
315    // Do the division business using exclusive-or operations.
316    while (findMSBSet(value) >= msbSetInPoly) {
317      value ^= poly << (findMSBSet(value) - msbSetInPoly);
318    }
319    // Now the "value" is the remainder (i.e. the BCH code)
320    return value;
321  }
322
323  // Make bit vector of type information. On success, store the result in "bits" and return true.
324  // Encode error correction level and mask pattern. See 8.9 of
325  // JISX0510:2004 (p.45) for details.
326  public static void makeTypeInfoBits(ErrorCorrectionLevel ecLevel, int maskPattern, BitVector bits)
327      throws WriterException {
328    if (!QRCode.isValidMaskPattern(maskPattern)) {
329      throw new WriterException("Invalid mask pattern");
330    }
331    int typeInfo = (ecLevel.getBits() << 3) | maskPattern;
332    bits.appendBits(typeInfo, 5);
333
334    int bchCode = calculateBCHCode(typeInfo, TYPE_INFO_POLY);
335    bits.appendBits(bchCode, 10);
336
337    BitVector maskBits = new BitVector();
338    maskBits.appendBits(TYPE_INFO_MASK_PATTERN, 15);
339    bits.xor(maskBits);
340
341    if (bits.size() != 15) {  // Just in case.
342      throw new WriterException("should not happen but we got: " + bits.size());
343    }
344  }
345
346  // Make bit vector of version information. On success, store the result in "bits" and return true.
347  // See 8.10 of JISX0510:2004 (p.45) for details.
348  public static void makeVersionInfoBits(int version, BitVector bits) throws WriterException {
349    bits.appendBits(version, 6);
350    int bchCode = calculateBCHCode(version, VERSION_INFO_POLY);
351    bits.appendBits(bchCode, 12);
352
353    if (bits.size() != 18) {  // Just in case.
354      throw new WriterException("should not happen but we got: " + bits.size());
355    }
356  }
357
358  // Check if "value" is empty.
359  private static boolean isEmpty(int value) {
360    return value == -1;
361  }
362
363  // Check if "value" is valid.
364  private static boolean isValidValue(int value) {
365    return (value == -1 ||  // Empty.
366        value == 0 ||  // Light (white).
367        value == 1);  // Dark (black).
368  }
369
370  private static void embedTimingPatterns(ByteMatrix matrix) throws WriterException {
371    // -8 is for skipping position detection patterns (size 7), and two horizontal/vertical
372    // separation patterns (size 1). Thus, 8 = 7 + 1.
373    for (int i = 8; i < matrix.getWidth() - 8; ++i) {
374      int bit = (i + 1) % 2;
375      // Horizontal line.
376      if (!isValidValue(matrix.get(i, 6))) {
377        throw new WriterException();
378      }
379      if (isEmpty(matrix.get(i, 6))) {
380        matrix.set(i, 6, bit);
381      }
382      // Vertical line.
383      if (!isValidValue(matrix.get(6, i))) {
384        throw new WriterException();
385      }
386      if (isEmpty(matrix.get(6, i))) {
387        matrix.set(6, i, bit);
388      }
389    }
390  }
391
392  // Embed the lonely dark dot at left bottom corner. JISX0510:2004 (p.46)
393  private static void embedDarkDotAtLeftBottomCorner(ByteMatrix matrix) throws WriterException {
394    if (matrix.get(8, matrix.getHeight() - 8) == 0) {
395      throw new WriterException();
396    }
397    matrix.set(8, matrix.getHeight() - 8, 1);
398  }
399
400  private static void embedHorizontalSeparationPattern(int xStart, int yStart,
401      ByteMatrix matrix) throws WriterException {
402    // We know the width and height.
403    if (HORIZONTAL_SEPARATION_PATTERN[0].length != 8 || HORIZONTAL_SEPARATION_PATTERN.length != 1) {
404      throw new WriterException("Bad horizontal separation pattern");
405    }
406    for (int x = 0; x < 8; ++x) {
407      if (!isEmpty(matrix.get(xStart + x, yStart))) {
408        throw new WriterException();
409      }
410      matrix.set(xStart + x, yStart, HORIZONTAL_SEPARATION_PATTERN[0][x]);
411    }
412  }
413
414  private static void embedVerticalSeparationPattern(int xStart, int yStart,
415      ByteMatrix matrix) throws WriterException {
416    // We know the width and height.
417    if (VERTICAL_SEPARATION_PATTERN[0].length != 1 || VERTICAL_SEPARATION_PATTERN.length != 7) {
418      throw new WriterException("Bad vertical separation pattern");
419    }
420    for (int y = 0; y < 7; ++y) {
421      if (!isEmpty(matrix.get(xStart, yStart + y))) {
422        throw new WriterException();
423      }
424      matrix.set(xStart, yStart + y, VERTICAL_SEPARATION_PATTERN[y][0]);
425    }
426  }
427
428  // Note that we cannot unify the function with embedPositionDetectionPattern() despite they are
429  // almost identical, since we cannot write a function that takes 2D arrays in different sizes in
430  // C/C++. We should live with the fact.
431  private static void embedPositionAdjustmentPattern(int xStart, int yStart,
432      ByteMatrix matrix) throws WriterException {
433    // We know the width and height.
434    if (POSITION_ADJUSTMENT_PATTERN[0].length != 5 || POSITION_ADJUSTMENT_PATTERN.length != 5) {
435      throw new WriterException("Bad position adjustment");
436    }
437    for (int y = 0; y < 5; ++y) {
438      for (int x = 0; x < 5; ++x) {
439        if (!isEmpty(matrix.get(xStart + x, yStart + y))) {
440          throw new WriterException();
441        }
442        matrix.set(xStart + x, yStart + y, POSITION_ADJUSTMENT_PATTERN[y][x]);
443      }
444    }
445  }
446
447  private static void embedPositionDetectionPattern(int xStart, int yStart,
448      ByteMatrix matrix) throws WriterException {
449    // We know the width and height.
450    if (POSITION_DETECTION_PATTERN[0].length != 7 || POSITION_DETECTION_PATTERN.length != 7) {
451      throw new WriterException("Bad position detection pattern");
452    }
453    for (int y = 0; y < 7; ++y) {
454      for (int x = 0; x < 7; ++x) {
455        if (!isEmpty(matrix.get(xStart + x, yStart + y))) {
456          throw new WriterException();
457        }
458        matrix.set(xStart + x, yStart + y, POSITION_DETECTION_PATTERN[y][x]);
459      }
460    }
461  }
462
463  // Embed position detection patterns and surrounding vertical/horizontal separators.
464  private static void embedPositionDetectionPatternsAndSeparators(ByteMatrix matrix) throws WriterException {
465    // Embed three big squares at corners.
466    int pdpWidth = POSITION_DETECTION_PATTERN[0].length;
467    // Left top corner.
468    embedPositionDetectionPattern(0, 0, matrix);
469    // Right top corner.
470    embedPositionDetectionPattern(matrix.getWidth() - pdpWidth, 0, matrix);
471    // Left bottom corner.
472    embedPositionDetectionPattern(0, matrix.getWidth() - pdpWidth, matrix);
473
474    // Embed horizontal separation patterns around the squares.
475    int hspWidth = HORIZONTAL_SEPARATION_PATTERN[0].length;
476    // Left top corner.
477    embedHorizontalSeparationPattern(0, hspWidth - 1, matrix);
478    // Right top corner.
479    embedHorizontalSeparationPattern(matrix.getWidth() - hspWidth,
480        hspWidth - 1, matrix);
481    // Left bottom corner.
482    embedHorizontalSeparationPattern(0, matrix.getWidth() - hspWidth, matrix);
483
484    // Embed vertical separation patterns around the squares.
485    int vspSize = VERTICAL_SEPARATION_PATTERN.length;
486    // Left top corner.
487    embedVerticalSeparationPattern(vspSize, 0, matrix);
488    // Right top corner.
489    embedVerticalSeparationPattern(matrix.getHeight() - vspSize - 1, 0, matrix);
490    // Left bottom corner.
491    embedVerticalSeparationPattern(vspSize, matrix.getHeight() - vspSize,
492        matrix);
493  }
494
495  // Embed position adjustment patterns if need be.
496  private static void maybeEmbedPositionAdjustmentPatterns(int version, ByteMatrix matrix)
497      throws WriterException {
498    if (version < 2) {  // The patterns appear if version >= 2
499      return;
500    }
501    int index = version - 1;
502    int[] coordinates = POSITION_ADJUSTMENT_PATTERN_COORDINATE_TABLE[index];
503    int numCoordinates = POSITION_ADJUSTMENT_PATTERN_COORDINATE_TABLE[index].length;
504    for (int i = 0; i < numCoordinates; ++i) {
505      for (int j = 0; j < numCoordinates; ++j) {
506        int y = coordinates[i];
507        int x = coordinates[j];
508        if (x == -1 || y == -1) {
509          continue;
510        }
511        // If the cell is unset, we embed the position adjustment pattern here.
512        if (isEmpty(matrix.get(x, y))) {
513          // -2 is necessary since the x/y coordinates point to the center of the pattern, not the
514          // left top corner.
515          embedPositionAdjustmentPattern(x - 2, y - 2, matrix);
516        }
517      }
518    }
519  }
520
521}