pdf.js/src/core/pattern.js

/* Copyright 2012 Mozilla Foundation
 *
 * 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.
 */

import {
  assert,
  FormatError,
  info,
  unreachable,
  Util,
  warn,
} from "../shared/util.js";
import { BaseStream } from "./base_stream.js";
import { ColorSpace } from "./colorspace.js";
import { MissingDataException } from "./core_utils.js";

const ShadingType = {
  FUNCTION_BASED: 1,
  AXIAL: 2,
  RADIAL: 3,
  FREE_FORM_MESH: 4,
  LATTICE_FORM_MESH: 5,
  COONS_PATCH_MESH: 6,
  TENSOR_PATCH_MESH: 7,
};

class Pattern {
  constructor() {
    unreachable("Cannot initialize Pattern.");
  }

  static parseShading(
    shading,
    xref,
    res,
    pdfFunctionFactory,
    localColorSpaceCache
  ) {
    const dict = shading instanceof BaseStream ? shading.dict : shading;
    const type = dict.get("ShadingType");

    try {
      switch (type) {
        case ShadingType.AXIAL:
        case ShadingType.RADIAL:
          return new RadialAxialShading(
            dict,
            xref,
            res,
            pdfFunctionFactory,
            localColorSpaceCache
          );
        case ShadingType.FREE_FORM_MESH:
        case ShadingType.LATTICE_FORM_MESH:
        case ShadingType.COONS_PATCH_MESH:
        case ShadingType.TENSOR_PATCH_MESH:
          return new MeshShading(
            shading,
            xref,
            res,
            pdfFunctionFactory,
            localColorSpaceCache
          );
        default:
          throw new FormatError("Unsupported ShadingType: " + type);
      }
    } catch (ex) {
      if (ex instanceof MissingDataException) {
        throw ex;
      }
      warn(ex);
      return new DummyShading();
    }
  }
}

class BaseShading {
  // A small number to offset the first/last color stops so we can insert ones
  // to support extend. Number.MIN_VALUE is too small and breaks the extend.
  static SMALL_NUMBER = 1e-6;

  constructor() {
    if (this.constructor === BaseShading) {
      unreachable("Cannot initialize BaseShading.");
    }
  }

  getIR() {
    unreachable("Abstract method `getIR` called.");
  }
}

// Radial and axial shading have very similar implementations
// If needed, the implementations can be broken into two classes.
class RadialAxialShading extends BaseShading {
  constructor(dict, xref, resources, pdfFunctionFactory, localColorSpaceCache) {
    super();
    this.coordsArr = dict.getArray("Coords");
    this.shadingType = dict.get("ShadingType");
    const cs = ColorSpace.parse({
      cs: dict.getRaw("CS") || dict.getRaw("ColorSpace"),
      xref,
      resources,
      pdfFunctionFactory,
      localColorSpaceCache,
    });
    const bbox = dict.getArray("BBox");
    this.bbox =
      Array.isArray(bbox) && bbox.length === 4
        ? Util.normalizeRect(bbox)
        : null;

    let t0 = 0.0,
      t1 = 1.0;
    if (dict.has("Domain")) {
      const domainArr = dict.getArray("Domain");
      t0 = domainArr[0];
      t1 = domainArr[1];
    }

    let extendStart = false,
      extendEnd = false;
    if (dict.has("Extend")) {
      const extendArr = dict.getArray("Extend");
      extendStart = extendArr[0];
      extendEnd = extendArr[1];
    }

    if (
      this.shadingType === ShadingType.RADIAL &&
      (!extendStart || !extendEnd)
    ) {
      // Radial gradient only currently works if either circle is fully within
      // the other circle.
      const [x1, y1, r1, x2, y2, r2] = this.coordsArr;
      const distance = Math.hypot(x1 - x2, y1 - y2);
      if (r1 <= r2 + distance && r2 <= r1 + distance) {
        warn("Unsupported radial gradient.");
      }
    }

    this.extendStart = extendStart;
    this.extendEnd = extendEnd;

    const fnObj = dict.getRaw("Function");
    const fn = pdfFunctionFactory.createFromArray(fnObj);

    // Use lcm(1,2,3,4,5,6,7,8,10) = 840 (including 9 increases this to 2520)
    // to catch evenly spaced stops. oeis.org/A003418
    const NUMBER_OF_SAMPLES = 840;
    const step = (t1 - t0) / NUMBER_OF_SAMPLES;

    const colorStops = (this.colorStops = []);

    // Protect against bad domains.
    if (t0 >= t1 || step <= 0) {
      // Acrobat doesn't seem to handle these cases so we'll ignore for
      // now.
      info("Bad shading domain.");
      return;
    }

    const color = new Float32Array(cs.numComps),
      ratio = new Float32Array(1);
    let rgbColor;

    let iBase = 0;
    ratio[0] = t0;
    fn(ratio, 0, color, 0);
    let rgbBase = cs.getRgb(color, 0);
    const cssColorBase = Util.makeHexColor(rgbBase[0], rgbBase[1], rgbBase[2]);
    colorStops.push([0, cssColorBase]);

    let iPrev = 1;
    ratio[0] = t0 + step;
    fn(ratio, 0, color, 0);
    let rgbPrev = cs.getRgb(color, 0);

    // Slopes are rise / run.
    // A max slope is from the least value the base component could have been
    // to the greatest value the current component could have been.
    // A min slope is from the greatest value the base component could have been
    // to the least value the current component could have been.
    // Each component could have been rounded up to .5 from its original value
    // so the conservative deltas are +-1 (+-.5 for base and -+.5 for current).

    // The run is iPrev - iBase = 1, so omitted.
    let maxSlopeR = rgbPrev[0] - rgbBase[0] + 1;
    let maxSlopeG = rgbPrev[1] - rgbBase[1] + 1;
    let maxSlopeB = rgbPrev[2] - rgbBase[2] + 1;
    let minSlopeR = rgbPrev[0] - rgbBase[0] - 1;
    let minSlopeG = rgbPrev[1] - rgbBase[1] - 1;
    let minSlopeB = rgbPrev[2] - rgbBase[2] - 1;

    for (let i = 2; i < NUMBER_OF_SAMPLES; i++) {
      ratio[0] = t0 + i * step;
      fn(ratio, 0, color, 0);
      rgbColor = cs.getRgb(color, 0);

      // Keep going if the maximum minimum slope <= the minimum maximum slope.
      // Otherwise add a rgbPrev color stop and make it the new base.

      const run = i - iBase;
      maxSlopeR = Math.min(maxSlopeR, (rgbColor[0] - rgbBase[0] + 1) / run);
      maxSlopeG = Math.min(maxSlopeG, (rgbColor[1] - rgbBase[1] + 1) / run);
      maxSlopeB = Math.min(maxSlopeB, (rgbColor[2] - rgbBase[2] + 1) / run);
      minSlopeR = Math.max(minSlopeR, (rgbColor[0] - rgbBase[0] - 1) / run);
      minSlopeG = Math.max(minSlopeG, (rgbColor[1] - rgbBase[1] - 1) / run);
      minSlopeB = Math.max(minSlopeB, (rgbColor[2] - rgbBase[2] - 1) / run);

      const slopesExist =
        minSlopeR <= maxSlopeR &&
        minSlopeG <= maxSlopeG &&
        minSlopeB <= maxSlopeB;

      if (!slopesExist) {
        const cssColor = Util.makeHexColor(rgbPrev[0], rgbPrev[1], rgbPrev[2]);
        colorStops.push([iPrev / NUMBER_OF_SAMPLES, cssColor]);

        // TODO: When fn frequency is high (iPrev - iBase === 1 twice in a row),
        // send the color space and function to do the sampling display side.

        // The run is i - iPrev = 1, so omitted.
        maxSlopeR = rgbColor[0] - rgbPrev[0] + 1;
        maxSlopeG = rgbColor[1] - rgbPrev[1] + 1;
        maxSlopeB = rgbColor[2] - rgbPrev[2] + 1;
        minSlopeR = rgbColor[0] - rgbPrev[0] - 1;
        minSlopeG = rgbColor[1] - rgbPrev[1] - 1;
        minSlopeB = rgbColor[2] - rgbPrev[2] - 1;

        iBase = iPrev;
        rgbBase = rgbPrev;
      }

      iPrev = i;
      rgbPrev = rgbColor;
    }
    const cssColor = Util.makeHexColor(rgbPrev[0], rgbPrev[1], rgbPrev[2]);
    colorStops.push([1, cssColor]);

    let background = "transparent";
    if (dict.has("Background")) {
      rgbColor = cs.getRgb(dict.get("Background"), 0);
      background = Util.makeHexColor(rgbColor[0], rgbColor[1], rgbColor[2]);
    }

    if (!extendStart) {
      // Insert a color stop at the front and offset the first real color stop
      // so it doesn't conflict with the one we insert.
      colorStops.unshift([0, background]);
      colorStops[1][0] += BaseShading.SMALL_NUMBER;
    }
    if (!extendEnd) {
      // Same idea as above in extendStart but for the end.
      colorStops.at(-1)[0] -= BaseShading.SMALL_NUMBER;
      colorStops.push([1, background]);
    }

    this.colorStops = colorStops;
  }

  getIR() {
    const coordsArr = this.coordsArr;
    const shadingType = this.shadingType;
    let type, p0, p1, r0, r1;
    if (shadingType === ShadingType.AXIAL) {
      p0 = [coordsArr[0], coordsArr[1]];
      p1 = [coordsArr[2], coordsArr[3]];
      r0 = null;
      r1 = null;
      type = "axial";
    } else if (shadingType === ShadingType.RADIAL) {
      p0 = [coordsArr[0], coordsArr[1]];
      p1 = [coordsArr[3], coordsArr[4]];
      r0 = coordsArr[2];
      r1 = coordsArr[5];
      type = "radial";
    } else {
      unreachable(`getPattern type unknown: ${shadingType}`);
    }

    return ["RadialAxial", type, this.bbox, this.colorStops, p0, p1, r0, r1];
  }
}

// All mesh shadings. For now, they will be presented as set of the triangles
// to be drawn on the canvas and rgb color for each vertex.
class MeshStreamReader {
  constructor(stream, context) {
    this.stream = stream;
    this.context = context;
    this.buffer = 0;
    this.bufferLength = 0;

    const numComps = context.numComps;
    this.tmpCompsBuf = new Float32Array(numComps);
    const csNumComps = context.colorSpace.numComps;
    this.tmpCsCompsBuf = context.colorFn
      ? new Float32Array(csNumComps)
      : this.tmpCompsBuf;
  }

  get hasData() {
    if (this.stream.end) {
      return this.stream.pos < this.stream.end;
    }
    if (this.bufferLength > 0) {
      return true;
    }
    const nextByte = this.stream.getByte();
    if (nextByte < 0) {
      return false;
    }
    this.buffer = nextByte;
    this.bufferLength = 8;
    return true;
  }

  readBits(n) {
    let buffer = this.buffer;
    let bufferLength = this.bufferLength;
    if (n === 32) {
      if (bufferLength === 0) {
        return (
          ((this.stream.getByte() << 24) |
            (this.stream.getByte() << 16) |
            (this.stream.getByte() << 8) |
            this.stream.getByte()) >>>
          0
        );
      }
      buffer =
        (buffer << 24) |
        (this.stream.getByte() << 16) |
        (this.stream.getByte() << 8) |
        this.stream.getByte();
      const nextByte = this.stream.getByte();
      this.buffer = nextByte & ((1 << bufferLength) - 1);
      return (
        ((buffer << (8 - bufferLength)) |
          ((nextByte & 0xff) >> bufferLength)) >>>
        0
      );
    }
    if (n === 8 && bufferLength === 0) {
      return this.stream.getByte();
    }
    while (bufferLength < n) {
      buffer = (buffer << 8) | this.stream.getByte();
      bufferLength += 8;
    }
    bufferLength -= n;
    this.bufferLength = bufferLength;
    this.buffer = buffer & ((1 << bufferLength) - 1);
    return buffer >> bufferLength;
  }

  align() {
    this.buffer = 0;
    this.bufferLength = 0;
  }

  readFlag() {
    return this.readBits(this.context.bitsPerFlag);
  }

  readCoordinate() {
    const bitsPerCoordinate = this.context.bitsPerCoordinate;
    const xi = this.readBits(bitsPerCoordinate);
    const yi = this.readBits(bitsPerCoordinate);
    const decode = this.context.decode;
    const scale =
      bitsPerCoordinate < 32
        ? 1 / ((1 << bitsPerCoordinate) - 1)
        : 2.3283064365386963e-10; // 2 ^ -32
    return [
      xi * scale * (decode[1] - decode[0]) + decode[0],
      yi * scale * (decode[3] - decode[2]) + decode[2],
    ];
  }

  readComponents() {
    const numComps = this.context.numComps;
    const bitsPerComponent = this.context.bitsPerComponent;
    const scale =
      bitsPerComponent < 32
        ? 1 / ((1 << bitsPerComponent) - 1)
        : 2.3283064365386963e-10; // 2 ^ -32
    const decode = this.context.decode;
    const components = this.tmpCompsBuf;
    for (let i = 0, j = 4; i < numComps; i++, j += 2) {
      const ci = this.readBits(bitsPerComponent);
      components[i] = ci * scale * (decode[j + 1] - decode[j]) + decode[j];
    }
    const color = this.tmpCsCompsBuf;
    if (this.context.colorFn) {
      this.context.colorFn(components, 0, color, 0);
    }
    return this.context.colorSpace.getRgb(color, 0);
  }
}

let bCache = Object.create(null);

function buildB(count) {
  const lut = [];
  for (let i = 0; i <= count; i++) {
    const t = i / count,
      t_ = 1 - t;
    lut.push(
      new Float32Array([t_ ** 3, 3 * t * t_ ** 2, 3 * t ** 2 * t_, t ** 3])
    );
  }
  return lut;
}
function getB(count) {
  return (bCache[count] ||= buildB(count));
}

function clearPatternCaches() {
  bCache = Object.create(null);
}

class MeshShading extends BaseShading {
  static MIN_SPLIT_PATCH_CHUNKS_AMOUNT = 3;

  static MAX_SPLIT_PATCH_CHUNKS_AMOUNT = 20;

  // Count of triangles per entire mesh bounds.
  static TRIANGLE_DENSITY = 20;

  constructor(
    stream,
    xref,
    resources,
    pdfFunctionFactory,
    localColorSpaceCache
  ) {
    super();
    if (!(stream instanceof BaseStream)) {
      throw new FormatError("Mesh data is not a stream");
    }
    const dict = stream.dict;
    this.shadingType = dict.get("ShadingType");
    const bbox = dict.getArray("BBox");
    this.bbox =
      Array.isArray(bbox) && bbox.length === 4
        ? Util.normalizeRect(bbox)
        : null;
    const cs = ColorSpace.parse({
      cs: dict.getRaw("CS") || dict.getRaw("ColorSpace"),
      xref,
      resources,
      pdfFunctionFactory,
      localColorSpaceCache,
    });
    this.background = dict.has("Background")
      ? cs.getRgb(dict.get("Background"), 0)
      : null;

    const fnObj = dict.getRaw("Function");
    const fn = fnObj ? pdfFunctionFactory.createFromArray(fnObj) : null;

    this.coords = [];
    this.colors = [];
    this.figures = [];

    const decodeContext = {
      bitsPerCoordinate: dict.get("BitsPerCoordinate"),
      bitsPerComponent: dict.get("BitsPerComponent"),
      bitsPerFlag: dict.get("BitsPerFlag"),
      decode: dict.getArray("Decode"),
      colorFn: fn,
      colorSpace: cs,
      numComps: fn ? 1 : cs.numComps,
    };
    const reader = new MeshStreamReader(stream, decodeContext);

    let patchMesh = false;
    switch (this.shadingType) {
      case ShadingType.FREE_FORM_MESH:
        this._decodeType4Shading(reader);
        break;
      case ShadingType.LATTICE_FORM_MESH:
        const verticesPerRow = dict.get("VerticesPerRow") | 0;
        if (verticesPerRow < 2) {
          throw new FormatError("Invalid VerticesPerRow");
        }
        this._decodeType5Shading(reader, verticesPerRow);
        break;
      case ShadingType.COONS_PATCH_MESH:
        this._decodeType6Shading(reader);
        patchMesh = true;
        break;
      case ShadingType.TENSOR_PATCH_MESH:
        this._decodeType7Shading(reader);
        patchMesh = true;
        break;
      default:
        unreachable("Unsupported mesh type.");
        break;
    }

    if (patchMesh) {
      // Dirty bounds calculation, to determine how dense the triangles will be.
      this._updateBounds();
      for (let i = 0, ii = this.figures.length; i < ii; i++) {
        this._buildFigureFromPatch(i);
      }
    }
    // Calculate bounds.
    this._updateBounds();

    this._packData();
  }

  _decodeType4Shading(reader) {
    const coords = this.coords;
    const colors = this.colors;
    const operators = [];
    const ps = []; // not maintaining cs since that will match ps
    let verticesLeft = 0; // assuming we have all data to start a new triangle
    while (reader.hasData) {
      const f = reader.readFlag();
      const coord = reader.readCoordinate();
      const color = reader.readComponents();
      if (verticesLeft === 0) {
        // ignoring flags if we started a triangle
        if (!(0 <= f && f <= 2)) {
          throw new FormatError("Unknown type4 flag");
        }
        switch (f) {
          case 0:
            verticesLeft = 3;
            break;
          case 1:
            ps.push(ps.at(-2), ps.at(-1));
            verticesLeft = 1;
            break;
          case 2:
            ps.push(ps.at(-3), ps.at(-1));
            verticesLeft = 1;
            break;
        }
        operators.push(f);
      }
      ps.push(coords.length);
      coords.push(coord);
      colors.push(color);
      verticesLeft--;

      reader.align();
    }
    this.figures.push({
      type: "triangles",
      coords: new Int32Array(ps),
      colors: new Int32Array(ps),
    });
  }

  _decodeType5Shading(reader, verticesPerRow) {
    const coords = this.coords;
    const colors = this.colors;
    const ps = []; // not maintaining cs since that will match ps
    while (reader.hasData) {
      const coord = reader.readCoordinate();
      const color = reader.readComponents();
      ps.push(coords.length);
      coords.push(coord);
      colors.push(color);
    }
    this.figures.push({
      type: "lattice",
      coords: new Int32Array(ps),
      colors: new Int32Array(ps),
      verticesPerRow,
    });
  }

  _decodeType6Shading(reader) {
    // A special case of Type 7. The p11, p12, p21, p22 automatically filled
    const coords = this.coords;
    const colors = this.colors;
    const ps = new Int32Array(16); // p00, p10, ..., p30, p01, ..., p33
    const cs = new Int32Array(4); // c00, c30, c03, c33
    while (reader.hasData) {
      const f = reader.readFlag();
      if (!(0 <= f && f <= 3)) {
        throw new FormatError("Unknown type6 flag");
      }
      const pi = coords.length;
      for (let i = 0, ii = f !== 0 ? 8 : 12; i < ii; i++) {
        coords.push(reader.readCoordinate());
      }
      const ci = colors.length;
      for (let i = 0, ii = f !== 0 ? 2 : 4; i < ii; i++) {
        colors.push(reader.readComponents());
      }
      let tmp1, tmp2, tmp3, tmp4;
      switch (f) {
        // prettier-ignore
        case 0:
          ps[12] = pi + 3; ps[13] = pi + 4;  ps[14] = pi + 5;  ps[15] = pi + 6;
          ps[ 8] = pi + 2; /* values for 5, 6, 9, 10 are    */ ps[11] = pi + 7;
          ps[ 4] = pi + 1; /* calculated below              */ ps[ 7] = pi + 8;
          ps[ 0] = pi;     ps[ 1] = pi + 11; ps[ 2] = pi + 10; ps[ 3] = pi + 9;
          cs[2] = ci + 1; cs[3] = ci + 2;
          cs[0] = ci;     cs[1] = ci + 3;
          break;
        // prettier-ignore
        case 1:
          tmp1 = ps[12]; tmp2 = ps[13]; tmp3 = ps[14]; tmp4 = ps[15];
          ps[12] = tmp4; ps[13] = pi + 0;  ps[14] = pi + 1;  ps[15] = pi + 2;
          ps[ 8] = tmp3; /* values for 5, 6, 9, 10 are    */ ps[11] = pi + 3;
          ps[ 4] = tmp2; /* calculated below              */ ps[ 7] = pi + 4;
          ps[ 0] = tmp1; ps[ 1] = pi + 7;   ps[ 2] = pi + 6; ps[ 3] = pi + 5;
          tmp1 = cs[2]; tmp2 = cs[3];
          cs[2] = tmp2;   cs[3] = ci;
          cs[0] = tmp1;   cs[1] = ci + 1;
          break;
        // prettier-ignore
        case 2:
          tmp1 = ps[15];
          tmp2 = ps[11];
          ps[12] = ps[3];  ps[13] = pi + 0; ps[14] = pi + 1;   ps[15] = pi + 2;
          ps[ 8] = ps[7];  /* values for 5, 6, 9, 10 are    */ ps[11] = pi + 3;
          ps[ 4] = tmp2;   /* calculated below              */ ps[ 7] = pi + 4;
          ps[ 0] = tmp1;  ps[ 1] = pi + 7;   ps[ 2] = pi + 6;  ps[ 3] = pi + 5;
          tmp1 = cs[3];
          cs[2] = cs[1]; cs[3] = ci;
          cs[0] = tmp1;  cs[1] = ci + 1;
          break;
        // prettier-ignore
        case 3:
          ps[12] = ps[0];  ps[13] = pi + 0;   ps[14] = pi + 1; ps[15] = pi + 2;
          ps[ 8] = ps[1];  /* values for 5, 6, 9, 10 are    */ ps[11] = pi + 3;
          ps[ 4] = ps[2];  /* calculated below              */ ps[ 7] = pi + 4;
          ps[ 0] = ps[3];  ps[ 1] = pi + 7;   ps[ 2] = pi + 6; ps[ 3] = pi + 5;
          cs[2] = cs[0]; cs[3] = ci;
          cs[0] = cs[1]; cs[1] = ci + 1;
          break;
      }
      // set p11, p12, p21, p22
      ps[5] = coords.length;
      coords.push([
        (-4 * coords[ps[0]][0] -
          coords[ps[15]][0] +
          6 * (coords[ps[4]][0] + coords[ps[1]][0]) -
          2 * (coords[ps[12]][0] + coords[ps[3]][0]) +
          3 * (coords[ps[13]][0] + coords[ps[7]][0])) /
          9,
        (-4 * coords[ps[0]][1] -
          coords[ps[15]][1] +
          6 * (coords[ps[4]][1] + coords[ps[1]][1]) -
          2 * (coords[ps[12]][1] + coords[ps[3]][1]) +
          3 * (coords[ps[13]][1] + coords[ps[7]][1])) /
          9,
      ]);
      ps[6] = coords.length;
      coords.push([
        (-4 * coords[ps[3]][0] -
          coords[ps[12]][0] +
          6 * (coords[ps[2]][0] + coords[ps[7]][0]) -
          2 * (coords[ps[0]][0] + coords[ps[15]][0]) +
          3 * (coords[ps[4]][0] + coords[ps[14]][0])) /
          9,
        (-4 * coords[ps[3]][1] -
          coords[ps[12]][1] +
          6 * (coords[ps[2]][1] + coords[ps[7]][1]) -
          2 * (coords[ps[0]][1] + coords[ps[15]][1]) +
          3 * (coords[ps[4]][1] + coords[ps[14]][1])) /
          9,
      ]);
      ps[9] = coords.length;
      coords.push([
        (-4 * coords[ps[12]][0] -
          coords[ps[3]][0] +
          6 * (coords[ps[8]][0] + coords[ps[13]][0]) -
          2 * (coords[ps[0]][0] + coords[ps[15]][0]) +
          3 * (coords[ps[11]][0] + coords[ps[1]][0])) /
          9,
        (-4 * coords[ps[12]][1] -
          coords[ps[3]][1] +
          6 * (coords[ps[8]][1] + coords[ps[13]][1]) -
          2 * (coords[ps[0]][1] + coords[ps[15]][1]) +
          3 * (coords[ps[11]][1] + coords[ps[1]][1])) /
          9,
      ]);
      ps[10] = coords.length;
      coords.push([
        (-4 * coords[ps[15]][0] -
          coords[ps[0]][0] +
          6 * (coords[ps[11]][0] + coords[ps[14]][0]) -
          2 * (coords[ps[12]][0] + coords[ps[3]][0]) +
          3 * (coords[ps[2]][0] + coords[ps[8]][0])) /
          9,
        (-4 * coords[ps[15]][1] -
          coords[ps[0]][1] +
          6 * (coords[ps[11]][1] + coords[ps[14]][1]) -
          2 * (coords[ps[12]][1] + coords[ps[3]][1]) +
          3 * (coords[ps[2]][1] + coords[ps[8]][1])) /
          9,
      ]);
      this.figures.push({
        type: "patch",
        coords: new Int32Array(ps), // making copies of ps and cs
        colors: new Int32Array(cs),
      });
    }
  }

  _decodeType7Shading(reader) {
    const coords = this.coords;
    const colors = this.colors;
    const ps = new Int32Array(16); // p00, p10, ..., p30, p01, ..., p33
    const cs = new Int32Array(4); // c00, c30, c03, c33
    while (reader.hasData) {
      const f = reader.readFlag();
      if (!(0 <= f && f <= 3)) {
        throw new FormatError("Unknown type7 flag");
      }
      const pi = coords.length;
      for (let i = 0, ii = f !== 0 ? 12 : 16; i < ii; i++) {
        coords.push(reader.readCoordinate());
      }
      const ci = colors.length;
      for (let i = 0, ii = f !== 0 ? 2 : 4; i < ii; i++) {
        colors.push(reader.readComponents());
      }
      let tmp1, tmp2, tmp3, tmp4;
      switch (f) {
        // prettier-ignore
        case 0:
          ps[12] = pi + 3; ps[13] = pi + 4;  ps[14] = pi + 5;  ps[15] = pi + 6;
          ps[ 8] = pi + 2; ps[ 9] = pi + 13; ps[10] = pi + 14; ps[11] = pi + 7;
          ps[ 4] = pi + 1; ps[ 5] = pi + 12; ps[ 6] = pi + 15; ps[ 7] = pi + 8;
          ps[ 0] = pi;     ps[ 1] = pi + 11; ps[ 2] = pi + 10; ps[ 3] = pi + 9;
          cs[2] = ci + 1; cs[3] = ci + 2;
          cs[0] = ci;     cs[1] = ci + 3;
          break;
        // prettier-ignore
        case 1:
          tmp1 = ps[12]; tmp2 = ps[13]; tmp3 = ps[14]; tmp4 = ps[15];
          ps[12] = tmp4;   ps[13] = pi + 0;  ps[14] = pi + 1;  ps[15] = pi + 2;
          ps[ 8] = tmp3;   ps[ 9] = pi + 9;  ps[10] = pi + 10; ps[11] = pi + 3;
          ps[ 4] = tmp2;   ps[ 5] = pi + 8;  ps[ 6] = pi + 11; ps[ 7] = pi + 4;
          ps[ 0] = tmp1;   ps[ 1] = pi + 7;  ps[ 2] = pi + 6;  ps[ 3] = pi + 5;
          tmp1 = cs[2]; tmp2 = cs[3];
          cs[2] = tmp2;   cs[3] = ci;
          cs[0] = tmp1;   cs[1] = ci + 1;
          break;
        // prettier-ignore
        case 2:
          tmp1 = ps[15];
          tmp2 = ps[11];
          ps[12] = ps[3]; ps[13] = pi + 0; ps[14] = pi + 1;  ps[15] = pi + 2;
          ps[ 8] = ps[7]; ps[ 9] = pi + 9; ps[10] = pi + 10; ps[11] = pi + 3;
          ps[ 4] = tmp2;  ps[ 5] = pi + 8; ps[ 6] = pi + 11; ps[ 7] = pi + 4;
          ps[ 0] = tmp1;  ps[ 1] = pi + 7; ps[ 2] = pi + 6;  ps[ 3] = pi + 5;
          tmp1 = cs[3];
          cs[2] = cs[1]; cs[3] = ci;
          cs[0] = tmp1;  cs[1] = ci + 1;
          break;
        // prettier-ignore
        case 3:
          ps[12] = ps[0];  ps[13] = pi + 0;  ps[14] = pi + 1;  ps[15] = pi + 2;
          ps[ 8] = ps[1];  ps[ 9] = pi + 9;  ps[10] = pi + 10; ps[11] = pi + 3;
          ps[ 4] = ps[2];  ps[ 5] = pi + 8;  ps[ 6] = pi + 11; ps[ 7] = pi + 4;
          ps[ 0] = ps[3];  ps[ 1] = pi + 7;  ps[ 2] = pi + 6;  ps[ 3] = pi + 5;
          cs[2] = cs[0]; cs[3] = ci;
          cs[0] = cs[1]; cs[1] = ci + 1;
          break;
      }
      this.figures.push({
        type: "patch",
        coords: new Int32Array(ps), // making copies of ps and cs
        colors: new Int32Array(cs),
      });
    }
  }

  _buildFigureFromPatch(index) {
    const figure = this.figures[index];
    assert(figure.type === "patch", "Unexpected patch mesh figure");

    const coords = this.coords,
      colors = this.colors;
    const pi = figure.coords;
    const ci = figure.colors;

    const figureMinX = Math.min(
      coords[pi[0]][0],
      coords[pi[3]][0],
      coords[pi[12]][0],
      coords[pi[15]][0]
    );
    const figureMinY = Math.min(
      coords[pi[0]][1],
      coords[pi[3]][1],
      coords[pi[12]][1],
      coords[pi[15]][1]
    );
    const figureMaxX = Math.max(
      coords[pi[0]][0],
      coords[pi[3]][0],
      coords[pi[12]][0],
      coords[pi[15]][0]
    );
    const figureMaxY = Math.max(
      coords[pi[0]][1],
      coords[pi[3]][1],
      coords[pi[12]][1],
      coords[pi[15]][1]
    );
    let splitXBy = Math.ceil(
      ((figureMaxX - figureMinX) * MeshShading.TRIANGLE_DENSITY) /
        (this.bounds[2] - this.bounds[0])
    );
    splitXBy = Math.max(
      MeshShading.MIN_SPLIT_PATCH_CHUNKS_AMOUNT,
      Math.min(MeshShading.MAX_SPLIT_PATCH_CHUNKS_AMOUNT, splitXBy)
    );
    let splitYBy = Math.ceil(
      ((figureMaxY - figureMinY) * MeshShading.TRIANGLE_DENSITY) /
        (this.bounds[3] - this.bounds[1])
    );
    splitYBy = Math.max(
      MeshShading.MIN_SPLIT_PATCH_CHUNKS_AMOUNT,
      Math.min(MeshShading.MAX_SPLIT_PATCH_CHUNKS_AMOUNT, splitYBy)
    );

    const verticesPerRow = splitXBy + 1;
    const figureCoords = new Int32Array((splitYBy + 1) * verticesPerRow);
    const figureColors = new Int32Array((splitYBy + 1) * verticesPerRow);
    let k = 0;
    const cl = new Uint8Array(3),
      cr = new Uint8Array(3);
    const c0 = colors[ci[0]],
      c1 = colors[ci[1]],
      c2 = colors[ci[2]],
      c3 = colors[ci[3]];
    const bRow = getB(splitYBy),
      bCol = getB(splitXBy);
    for (let row = 0; row <= splitYBy; row++) {
      cl[0] = ((c0[0] * (splitYBy - row) + c2[0] * row) / splitYBy) | 0;
      cl[1] = ((c0[1] * (splitYBy - row) + c2[1] * row) / splitYBy) | 0;
      cl[2] = ((c0[2] * (splitYBy - row) + c2[2] * row) / splitYBy) | 0;

      cr[0] = ((c1[0] * (splitYBy - row) + c3[0] * row) / splitYBy) | 0;
      cr[1] = ((c1[1] * (splitYBy - row) + c3[1] * row) / splitYBy) | 0;
      cr[2] = ((c1[2] * (splitYBy - row) + c3[2] * row) / splitYBy) | 0;

      for (let col = 0; col <= splitXBy; col++, k++) {
        if (
          (row === 0 || row === splitYBy) &&
          (col === 0 || col === splitXBy)
        ) {
          continue;
        }
        let x = 0,
          y = 0;
        let q = 0;
        for (let i = 0; i <= 3; i++) {
          for (let j = 0; j <= 3; j++, q++) {
            const m = bRow[row][i] * bCol[col][j];
            x += coords[pi[q]][0] * m;
            y += coords[pi[q]][1] * m;
          }
        }
        figureCoords[k] = coords.length;
        coords.push([x, y]);
        figureColors[k] = colors.length;
        const newColor = new Uint8Array(3);
        newColor[0] = ((cl[0] * (splitXBy - col) + cr[0] * col) / splitXBy) | 0;
        newColor[1] = ((cl[1] * (splitXBy - col) + cr[1] * col) / splitXBy) | 0;
        newColor[2] = ((cl[2] * (splitXBy - col) + cr[2] * col) / splitXBy) | 0;
        colors.push(newColor);
      }
    }
    figureCoords[0] = pi[0];
    figureColors[0] = ci[0];
    figureCoords[splitXBy] = pi[3];
    figureColors[splitXBy] = ci[1];
    figureCoords[verticesPerRow * splitYBy] = pi[12];
    figureColors[verticesPerRow * splitYBy] = ci[2];
    figureCoords[verticesPerRow * splitYBy + splitXBy] = pi[15];
    figureColors[verticesPerRow * splitYBy + splitXBy] = ci[3];

    this.figures[index] = {
      type: "lattice",
      coords: figureCoords,
      colors: figureColors,
      verticesPerRow,
    };
  }

  _updateBounds() {
    let minX = this.coords[0][0],
      minY = this.coords[0][1],
      maxX = minX,
      maxY = minY;
    for (let i = 1, ii = this.coords.length; i < ii; i++) {
      const x = this.coords[i][0],
        y = this.coords[i][1];
      minX = minX > x ? x : minX;
      minY = minY > y ? y : minY;
      maxX = maxX < x ? x : maxX;
      maxY = maxY < y ? y : maxY;
    }
    this.bounds = [minX, minY, maxX, maxY];
  }

  _packData() {
    let i, ii, j, jj;

    const coords = this.coords;
    const coordsPacked = new Float32Array(coords.length * 2);
    for (i = 0, j = 0, ii = coords.length; i < ii; i++) {
      const xy = coords[i];
      coordsPacked[j++] = xy[0];
      coordsPacked[j++] = xy[1];
    }
    this.coords = coordsPacked;

    const colors = this.colors;
    const colorsPacked = new Uint8Array(colors.length * 3);
    for (i = 0, j = 0, ii = colors.length; i < ii; i++) {
      const c = colors[i];
      colorsPacked[j++] = c[0];
      colorsPacked[j++] = c[1];
      colorsPacked[j++] = c[2];
    }
    this.colors = colorsPacked;

    const figures = this.figures;
    for (i = 0, ii = figures.length; i < ii; i++) {
      const figure = figures[i],
        ps = figure.coords,
        cs = figure.colors;
      for (j = 0, jj = ps.length; j < jj; j++) {
        ps[j] *= 2;
        cs[j] *= 3;
      }
    }
  }

  getIR() {
    return [
      "Mesh",
      this.shadingType,
      this.coords,
      this.colors,
      this.figures,
      this.bounds,
      this.bbox,
      this.background,
    ];
  }
}

class DummyShading extends BaseShading {
  getIR() {
    return ["Dummy"];
  }
}

function getTilingPatternIR(operatorList, dict, color) {
  const matrix = dict.getArray("Matrix");
  const bbox = Util.normalizeRect(dict.getArray("BBox"));
  const xstep = dict.get("XStep");
  const ystep = dict.get("YStep");
  const paintType = dict.get("PaintType");
  const tilingType = dict.get("TilingType");

  // Ensure that the pattern has a non-zero width and height, to prevent errors
  // in `pattern_helper.js` (fixes issue8330.pdf).
  if (bbox[2] - bbox[0] === 0 || bbox[3] - bbox[1] === 0) {
    throw new FormatError(`Invalid getTilingPatternIR /BBox array: [${bbox}].`);
  }

  return [
    "TilingPattern",
    color,
    operatorList,
    matrix,
    bbox,
    xstep,
    ystep,
    paintType,
    tilingType,
  ];
}

export { clearPatternCaches, getTilingPatternIR, Pattern };