Merge pull request #19736 from Snuffleupagus/compileType3Glyph-worker

[api-minor] Move Type3-glyph compilation to the worker-thread

src/core/evaluator.js

@@ -32,6 +32,7 @@ import {
 } from "../shared/util.js";
 import { CMapFactory, IdentityCMap } from "./cmap.js";
 import { Cmd, Dict, EOF, isName, Name, Ref, RefSet } from "./primitives.js";
+import { compileType3Glyph, FontFlags } from "./fonts_utils.js";
 import { ErrorFont, Font } from "./fonts.js";
 import {
   fetchBinaryData,
@@ -72,7 +73,6 @@ import { bidi } from "./bidi.js";
 import { ColorSpace } from "./colorspace.js";
 import { ColorSpaceUtils } from "./colorspace_utils.js";
 import { DecodeStream } from "./decode_stream.js";
-import { FontFlags } from "./fonts_utils.js";
 import { getFontSubstitution } from "./font_substitutions.js";
 import { getGlyphsUnicode } from "./glyphlist.js";
 import { getMetrics } from "./metrics.js";
@@ -180,14 +180,17 @@ function normalizeBlendMode(value, parsingArray = false) {
   return "source-over";
 }
 
-function addLocallyCachedImageOps(opList, data) {
+function addCachedImageOps(
-  if (data.objId) {
+  opList,
-    opList.addDependency(data.objId);
+  { objId, fn, args, optionalContent, hasMask }
+) {
+  if (objId) {
+    opList.addDependency(objId);
   }
-  opList.addImageOps(data.fn, data.args, data.optionalContent, data.hasMask);
+  opList.addImageOps(fn, args, optionalContent, hasMask);
 
-  if (data.fn === OPS.paintImageMaskXObject && data.args[0]?.count > 0) {
+  if (fn === OPS.paintImageMaskXObject && args[0]?.count > 0) {
-    data.args[0].count++;
+    args[0].count++;
   }
 }
 
@@ -608,6 +611,12 @@ class PartialEvaluator {
       const decode = dict.getArray("D", "Decode");
 
       if (this.parsingType3Font) {
+        // NOTE: Compared to other image resources we don't bother caching
+        // Type3-glyph image masks, since we've not come across any cases
+        // where that actually helps.
+        // In Type3-glyphs image masks are "always" inline resources,
+        // they're usually fairly small and aren't being re-used either.
+
         imgData = PDFImage.createRawMask({
           imgArray,
           width: w,
@@ -616,25 +625,21 @@ class PartialEvaluator {
           inverseDecode: decode?.[0] > 0,
           interpolate,
         });
+        args = compileType3Glyph(imgData);
 
-        imgData.cached = !!cacheKey;
+        if (args) {
-
+          operatorList.addImageOps(OPS.constructPath, args, optionalContent);
-        fn = OPS.paintImageMaskXObject;
+          return;
-        args = [imgData];
-        operatorList.addImageOps(fn, args, optionalContent);
-
-        if (cacheKey) {
-          const cacheData = { fn, args, optionalContent };
-          localImageCache.set(cacheKey, imageRef, cacheData);
-
-          if (imageRef) {
-            this._regionalImageCache.set(
-              /* name = */ null,
-              imageRef,
-              cacheData
-            );
-          }
         }
+        warn("Cannot compile Type3 glyph.");
+
+        // If compilation failed, or was disabled, fallback to using an inline
+        // image mask; this case should be extremely rare.
+        operatorList.addImageOps(
+          OPS.paintImageMaskXObject,
+          [imgData],
+          optionalContent
+        );
         return;
       }
 
@@ -742,7 +747,8 @@ class PartialEvaluator {
     // If there is no imageMask, create the PDFImage and a lot
     // of image processing can be done here.
     let objId = `img_${this.idFactory.createObjId()}`,
-      cacheGlobally = false;
+      cacheGlobally = false,
+      globalCacheData = null;
 
     if (this.parsingType3Font) {
       objId = `${this.idFactory.getDocId()}_type3_${objId}`;
@@ -767,15 +773,17 @@ class PartialEvaluator {
     operatorList.addImageOps(fn, args, optionalContent, hasMask);
 
     if (cacheGlobally) {
+      globalCacheData = {
+        objId,
+        fn,
+        args,
+        optionalContent,
+        hasMask,
+        byteSize: 0, // Temporary entry, to avoid `setData` returning early.
+      };
+
       if (this.globalImageCache.hasDecodeFailed(imageRef)) {
-        this.globalImageCache.setData(imageRef, {
+        this.globalImageCache.setData(imageRef, globalCacheData);
-          objId,
-          fn,
-          args,
-          optionalContent,
-          hasMask,
-          byteSize: 0, // Data is `null`, since decoding failed previously.
-        });
 
         this._sendImgData(objId, /* imgData = */ null, cacheGlobally);
         return;
@@ -792,14 +800,7 @@ class PartialEvaluator {
         ]);
 
         if (localLength) {
-          this.globalImageCache.setData(imageRef, {
+          this.globalImageCache.setData(imageRef, globalCacheData);
-            objId,
-            fn,
-            args,
-            optionalContent,
-            hasMask,
-            byteSize: 0, // Temporary entry, to avoid `setData` returning early.
-          });
           this.globalImageCache.addByteSize(imageRef, localLength);
           return;
         }
@@ -848,14 +849,8 @@ class PartialEvaluator {
         this._regionalImageCache.set(/* name = */ null, imageRef, cacheData);
 
         if (cacheGlobally) {
-          this.globalImageCache.setData(imageRef, {
+          assert(globalCacheData, "The global cache-data must be available.");
-            objId,
+          this.globalImageCache.setData(imageRef, globalCacheData);
-            fn,
-            args,
-            optionalContent,
-            hasMask,
-            byteSize: 0, // Temporary entry, note `addByteSize` above.
-          });
         }
       }
     }
@@ -1779,7 +1774,7 @@ class PartialEvaluator {
             if (isValidName) {
               const localImage = localImageCache.getByName(name);
               if (localImage) {
-                addLocallyCachedImageOps(operatorList, localImage);
+                addCachedImageOps(operatorList, localImage);
                 args = null;
                 continue;
               }
@@ -1793,28 +1788,12 @@ class PartialEvaluator {
 
                 let xobj = xobjs.getRaw(name);
                 if (xobj instanceof Ref) {
-                  const localImage =
+                  const cachedImage =
                     localImageCache.getByRef(xobj) ||
-                    self._regionalImageCache.getByRef(xobj);
+                    self._regionalImageCache.getByRef(xobj) ||
-                  if (localImage) {
+                    self.globalImageCache.getData(xobj, self.pageIndex);
-                    addLocallyCachedImageOps(operatorList, localImage);
+                  if (cachedImage) {
-                    resolveXObject();
+                    addCachedImageOps(operatorList, cachedImage);
-                    return;
-                  }
-
-                  const globalImage = self.globalImageCache.getData(
-                    xobj,
-                    self.pageIndex
-                  );
-                  if (globalImage) {
-                    operatorList.addDependency(globalImage.objId);
-                    operatorList.addImageOps(
-                      globalImage.fn,
-                      globalImage.args,
-                      globalImage.optionalContent,
-                      globalImage.hasMask
-                    );
-
                     resolveXObject();
                     return;
                   }
@@ -1907,7 +1886,7 @@ class PartialEvaluator {
             if (cacheKey) {
               const localImage = localImageCache.getByName(cacheKey);
               if (localImage) {
-                addLocallyCachedImageOps(operatorList, localImage);
+                addCachedImageOps(operatorList, localImage);
                 args = null;
                 continue;
               }

src/core/fonts_utils.js

@@ -13,11 +13,11 @@
  * limitations under the License.
  */
 
+import { DrawOPS, info, OPS } from "../shared/util.js";
 import { getEncoding, StandardEncoding } from "./encodings.js";
 import { getGlyphsUnicode } from "./glyphlist.js";
 import { getLookupTableFactory } from "./core_utils.js";
 import { getUnicodeForGlyph } from "./unicode.js";
-import { info } from "../shared/util.js";
 
 // Accented characters have issues on Windows and Linux. When this flag is
 // enabled glyphs that use seac and seac style endchar operators are truncated
@@ -207,7 +207,177 @@ const getVerticalPresentationForm = getLookupTableFactory(t => {
   t[0xff5d] = 0xfe38; // FULLWIDTH RIGHT CURLY BRACKET
 });
 
+// To disable Type3 compilation, set the value to `-1`.
+const MAX_SIZE_TO_COMPILE = 1000;
+
+function compileType3Glyph({ data: img, width, height }) {
+  if (width > MAX_SIZE_TO_COMPILE || height > MAX_SIZE_TO_COMPILE) {
+    return null;
+  }
+
+  const POINT_TO_PROCESS_LIMIT = 1000;
+  const POINT_TYPES = new Uint8Array([
+    0, 2, 4, 0, 1, 0, 5, 4, 8, 10, 0, 8, 0, 2, 1, 0,
+  ]);
+
+  const width1 = width + 1;
+  const points = new Uint8Array(width1 * (height + 1));
+  let i, j, j0;
+
+  // decodes bit-packed mask data
+  const lineSize = (width + 7) & ~7;
+  const data = new Uint8Array(lineSize * height);
+  let pos = 0;
+  for (const elem of img) {
+    let mask = 128;
+    while (mask > 0) {
+      data[pos++] = elem & mask ? 0 : 255;
+      mask >>= 1;
+    }
+  }
+
+  // finding interesting points: every point is located between mask pixels,
+  // so there will be points of the (width + 1)x(height + 1) grid. Every point
+  // will have flags assigned based on neighboring mask pixels:
+  //   4 | 8
+  //   --P--
+  //   2 | 1
+  // We are interested only in points with the flags:
+  //   - outside corners: 1, 2, 4, 8;
+  //   - inside corners: 7, 11, 13, 14;
+  //   - and, intersections: 5, 10.
+  let count = 0;
+  pos = 0;
+  if (data[pos] !== 0) {
+    points[0] = 1;
+    ++count;
+  }
+  for (j = 1; j < width; j++) {
+    if (data[pos] !== data[pos + 1]) {
+      points[j] = data[pos] ? 2 : 1;
+      ++count;
+    }
+    pos++;
+  }
+  if (data[pos] !== 0) {
+    points[j] = 2;
+    ++count;
+  }
+  for (i = 1; i < height; i++) {
+    pos = i * lineSize;
+    j0 = i * width1;
+    if (data[pos - lineSize] !== data[pos]) {
+      points[j0] = data[pos] ? 1 : 8;
+      ++count;
+    }
+    // 'sum' is the position of the current pixel configuration in the 'TYPES'
+    // array (in order 8-1-2-4, so we can use '>>2' to shift the column).
+    let sum = (data[pos] ? 4 : 0) + (data[pos - lineSize] ? 8 : 0);
+    for (j = 1; j < width; j++) {
+      sum =
+        (sum >> 2) +
+        (data[pos + 1] ? 4 : 0) +
+        (data[pos - lineSize + 1] ? 8 : 0);
+      if (POINT_TYPES[sum]) {
+        points[j0 + j] = POINT_TYPES[sum];
+        ++count;
+      }
+      pos++;
+    }
+    if (data[pos - lineSize] !== data[pos]) {
+      points[j0 + j] = data[pos] ? 2 : 4;
+      ++count;
+    }
+
+    if (count > POINT_TO_PROCESS_LIMIT) {
+      return null;
+    }
+  }
+
+  pos = lineSize * (height - 1);
+  j0 = i * width1;
+  if (data[pos] !== 0) {
+    points[j0] = 8;
+    ++count;
+  }
+  for (j = 1; j < width; j++) {
+    if (data[pos] !== data[pos + 1]) {
+      points[j0 + j] = data[pos] ? 4 : 8;
+      ++count;
+    }
+    pos++;
+  }
+  if (data[pos] !== 0) {
+    points[j0 + j] = 4;
+    ++count;
+  }
+  if (count > POINT_TO_PROCESS_LIMIT) {
+    return null;
+  }
+
+  // building outlines
+  const steps = new Int32Array([0, width1, -1, 0, -width1, 0, 0, 0, 1]);
+  const pathBuf = [];
+
+  // the path shall be painted in [0..1]x[0..1] space
+  const { a, b, c, d, e, f } = new DOMMatrix()
+    .scaleSelf(1 / width, -1 / height)
+    .translateSelf(0, -height);
+
+  for (i = 0; count && i <= height; i++) {
+    let p = i * width1;
+    const end = p + width;
+    while (p < end && !points[p]) {
+      p++;
+    }
+    if (p === end) {
+      continue;
+    }
+    let x = p % width1;
+    let y = i;
+    pathBuf.push(DrawOPS.moveTo, a * x + c * y + e, b * x + d * y + f);
+
+    const p0 = p;
+    let type = points[p];
+    do {
+      const step = steps[type];
+      do {
+        p += step;
+      } while (!points[p]);
+
+      const pp = points[p];
+      if (pp !== 5 && pp !== 10) {
+        // set new direction
+        type = pp;
+        // delete mark
+        points[p] = 0;
+      } else {
+        // type is 5 or 10, ie, a crossing
+        // set new direction
+        type = pp & ((0x33 * type) >> 4);
+        // set new type for "future hit"
+        points[p] &= (type >> 2) | (type << 2);
+      }
+      x = p % width1;
+      y = (p / width1) | 0;
+      pathBuf.push(DrawOPS.lineTo, a * x + c * y + e, b * x + d * y + f);
+
+      if (!points[p]) {
+        --count;
+      }
+    } while (p0 !== p);
+    --i;
+  }
+
+  return [
+    OPS.rawFillPath,
+    [new Float32Array(pathBuf)],
+    new Float32Array([0, 0, width, height]),
+  ];
+}
+
 export {
+  compileType3Glyph,
   FontFlags,
   getVerticalPresentationForm,
   MacStandardGlyphOrdering,

src/core/operator_list.js

@@ -13,7 +13,14 @@
  * limitations under the License.
  */
 
-import { ImageKind, OPS, RenderingIntentFlag, warn } from "../shared/util.js";
+import {
+  DrawOPS,
+  ImageKind,
+  OPS,
+  RenderingIntentFlag,
+  Util,
+  warn,
+} from "../shared/util.js";
 
 function addState(parentState, pattern, checkFn, iterateFn, processFn) {
   let state = parentState;
@@ -470,6 +477,70 @@ addState(
   }
 );
 
+// This replaces (save, transform, constructPath, restore)
+// sequences with |constructPath| operation.
+addState(
+  InitialState,
+  [OPS.save, OPS.transform, OPS.constructPath, OPS.restore],
+  context => {
+    const argsArray = context.argsArray;
+    const iFirstConstructPath = context.iCurr - 1;
+    const op = argsArray[iFirstConstructPath][0];
+
+    // When stroking the transform has to be applied to the line width too.
+    // So we can only optimize if the transform is an identity.
+    if (
+      op !== OPS.stroke &&
+      op !== OPS.closeStroke &&
+      op !== OPS.fillStroke &&
+      op !== OPS.eoFillStroke &&
+      op !== OPS.closeFillStroke &&
+      op !== OPS.closeEOFillStroke
+    ) {
+      return true;
+    }
+    const iFirstTransform = context.iCurr - 2;
+    const transform = argsArray[iFirstTransform];
+    return (
+      transform[0] === 1 &&
+      transform[1] === 0 &&
+      transform[2] === 0 &&
+      transform[3] === 1
+    );
+  },
+  () => false,
+  (context, i) => {
+    const { fnArray, argsArray } = context;
+    const curr = context.iCurr;
+    const iFirstSave = curr - 3;
+    const iFirstTransform = curr - 2;
+    const iFirstConstructPath = curr - 1;
+    const args = argsArray[iFirstConstructPath];
+    const transform = argsArray[iFirstTransform];
+    const [, [buffer], minMax] = args;
+
+    Util.scaleMinMax(transform, minMax);
+    for (let k = 0, kk = buffer.length; k < kk; ) {
+      switch (buffer[k++]) {
+        case DrawOPS.moveTo:
+        case DrawOPS.lineTo:
+          Util.applyTransformInPlace(buffer.subarray(k), transform);
+          k += 2;
+          break;
+        case DrawOPS.curveTo:
+          Util.applyTransformToBezierInPlace(buffer.subarray(k), transform);
+          k += 6;
+          break;
+      }
+    }
+    // Replace queue items.
+    fnArray.splice(iFirstSave, 4, OPS.constructPath);
+    argsArray.splice(iFirstSave, 4, args);
+
+    return iFirstSave + 1;
+  }
+);
+
 class NullOptimizer {
   constructor(queue) {
     this.queue = queue;
@@ -699,7 +770,7 @@ class OperatorList {
         case OPS.paintInlineImageXObjectGroup:
         case OPS.paintImageMaskXObject:
           const arg = argsArray[i][0]; // First parameter in imgData.
-          if (!arg.cached && arg.data?.buffer instanceof ArrayBuffer) {
+          if (arg.data?.buffer instanceof ArrayBuffer) {
             transfers.push(arg.data.buffer);
           }
           break;

src/display/canvas.js

@@ -54,9 +54,6 @@ const EXECUTION_TIME = 15; // ms
 // Defines the number of steps before checking the execution time.
 const EXECUTION_STEPS = 10;
 
-// To disable Type3 compilation, set the value to `-1`.
-const MAX_SIZE_TO_COMPILE = 1000;
-
 const FULL_CHUNK_HEIGHT = 16;
 
 // Only used in rescaleAndStroke. The goal is to avoid
@@ -299,169 +296,6 @@ function drawImageAtIntegerCoords(
   return [scaleX * destW, scaleY * destH];
 }
 
-function compileType3Glyph(imgData) {
-  const { width, height } = imgData;
-  if (width > MAX_SIZE_TO_COMPILE || height > MAX_SIZE_TO_COMPILE) {
-    return null;
-  }
-
-  const POINT_TO_PROCESS_LIMIT = 1000;
-  const POINT_TYPES = new Uint8Array([
-    0, 2, 4, 0, 1, 0, 5, 4, 8, 10, 0, 8, 0, 2, 1, 0,
-  ]);
-
-  const width1 = width + 1;
-  const points = new Uint8Array(width1 * (height + 1));
-  let i, j, j0;
-
-  // decodes bit-packed mask data
-  const lineSize = (width + 7) & ~7;
-  const data = new Uint8Array(lineSize * height);
-  let pos = 0;
-  for (const elem of imgData.data) {
-    let mask = 128;
-    while (mask > 0) {
-      data[pos++] = elem & mask ? 0 : 255;
-      mask >>= 1;
-    }
-  }
-
-  // finding interesting points: every point is located between mask pixels,
-  // so there will be points of the (width + 1)x(height + 1) grid. Every point
-  // will have flags assigned based on neighboring mask pixels:
-  //   4 | 8
-  //   --P--
-  //   2 | 1
-  // We are interested only in points with the flags:
-  //   - outside corners: 1, 2, 4, 8;
-  //   - inside corners: 7, 11, 13, 14;
-  //   - and, intersections: 5, 10.
-  let count = 0;
-  pos = 0;
-  if (data[pos] !== 0) {
-    points[0] = 1;
-    ++count;
-  }
-  for (j = 1; j < width; j++) {
-    if (data[pos] !== data[pos + 1]) {
-      points[j] = data[pos] ? 2 : 1;
-      ++count;
-    }
-    pos++;
-  }
-  if (data[pos] !== 0) {
-    points[j] = 2;
-    ++count;
-  }
-  for (i = 1; i < height; i++) {
-    pos = i * lineSize;
-    j0 = i * width1;
-    if (data[pos - lineSize] !== data[pos]) {
-      points[j0] = data[pos] ? 1 : 8;
-      ++count;
-    }
-    // 'sum' is the position of the current pixel configuration in the 'TYPES'
-    // array (in order 8-1-2-4, so we can use '>>2' to shift the column).
-    let sum = (data[pos] ? 4 : 0) + (data[pos - lineSize] ? 8 : 0);
-    for (j = 1; j < width; j++) {
-      sum =
-        (sum >> 2) +
-        (data[pos + 1] ? 4 : 0) +
-        (data[pos - lineSize + 1] ? 8 : 0);
-      if (POINT_TYPES[sum]) {
-        points[j0 + j] = POINT_TYPES[sum];
-        ++count;
-      }
-      pos++;
-    }
-    if (data[pos - lineSize] !== data[pos]) {
-      points[j0 + j] = data[pos] ? 2 : 4;
-      ++count;
-    }
-
-    if (count > POINT_TO_PROCESS_LIMIT) {
-      return null;
-    }
-  }
-
-  pos = lineSize * (height - 1);
-  j0 = i * width1;
-  if (data[pos] !== 0) {
-    points[j0] = 8;
-    ++count;
-  }
-  for (j = 1; j < width; j++) {
-    if (data[pos] !== data[pos + 1]) {
-      points[j0 + j] = data[pos] ? 4 : 8;
-      ++count;
-    }
-    pos++;
-  }
-  if (data[pos] !== 0) {
-    points[j0 + j] = 4;
-    ++count;
-  }
-  if (count > POINT_TO_PROCESS_LIMIT) {
-    return null;
-  }
-
-  // building outlines
-  const steps = new Int32Array([0, width1, -1, 0, -width1, 0, 0, 0, 1]);
-  const path = new Path2D();
-
-  // the path shall be painted in [0..1]x[0..1] space
-  const { a, b, c, d, e, f } = new DOMMatrix()
-    .scaleSelf(1 / width, -1 / height)
-    .translateSelf(0, -height);
-
-  for (i = 0; count && i <= height; i++) {
-    let p = i * width1;
-    const end = p + width;
-    while (p < end && !points[p]) {
-      p++;
-    }
-    if (p === end) {
-      continue;
-    }
-    let x = p % width1;
-    let y = i;
-    path.moveTo(a * x + c * y + e, b * x + d * y + f);
-
-    const p0 = p;
-    let type = points[p];
-    do {
-      const step = steps[type];
-      do {
-        p += step;
-      } while (!points[p]);
-
-      const pp = points[p];
-      if (pp !== 5 && pp !== 10) {
-        // set new direction
-        type = pp;
-        // delete mark
-        points[p] = 0;
-      } else {
-        // type is 5 or 10, ie, a crossing
-        // set new direction
-        type = pp & ((0x33 * type) >> 4);
-        // set new type for "future hit"
-        points[p] &= (type >> 2) | (type << 2);
-      }
-      x = p % width1;
-      y = (p / width1) | 0;
-      path.lineTo(a * x + c * y + e, b * x + d * y + f);
-
-      if (!points[p]) {
-        --count;
-      }
-    } while (p0 !== p);
-    --i;
-  }
-
-  return path;
-}
-
 class CanvasExtraState {
   constructor(width, height) {
     // Are soft masks and alpha values shapes or opacities?
@@ -821,7 +655,6 @@ class CanvasGraphics {
     this.canvasFactory = canvasFactory;
     this.filterFactory = filterFactory;
     this.groupStack = [];
-    this.processingType3 = null;
     // Patterns are painted relative to the initial page/form transform, see
     // PDF spec 8.7.2 NOTE 1.
     this.baseTransform = null;
@@ -1747,6 +1580,10 @@ class CanvasGraphics {
     this.consumePath(path);
   }
 
+  rawFillPath(path) {
+    this.ctx.fill(path);
+  }
+
   // Clipping
   clip() {
     this.pendingClip = NORMAL_CLIP;
@@ -2267,7 +2104,6 @@ class CanvasGraphics {
       if (!operatorList) {
         warn(`Type3 character "${glyph.operatorListId}" is not available.`);
       } else if (this.contentVisible) {
-        this.processingType3 = glyph;
         this.save();
         ctx.scale(fontSize, fontSize);
         ctx.transform(...fontMatrix);
@@ -2282,7 +2118,6 @@ class CanvasGraphics {
       current.x += width * textHScale;
     }
     ctx.restore();
-    this.processingType3 = null;
   }
 
   // Type3 fonts
@@ -2703,18 +2538,6 @@ class CanvasGraphics {
     img.count = count;
 
     const ctx = this.ctx;
-    const glyph = this.processingType3;
-
-    if (glyph) {
-      if (glyph.compiled === undefined) {
-        glyph.compiled = compileType3Glyph(img);
-      }
-
-      if (glyph.compiled) {
-        ctx.fill(glyph.compiled);
-        return;
-      }
-    }
     const mask = this._createMaskCanvas(img);
     const maskCanvas = mask.canvas;
 

src/shared/util.js

@@ -339,6 +339,7 @@ const OPS = {
   constructPath: 91,
   setStrokeTransparent: 92,
   setFillTransparent: 93,
+  rawFillPath: 94,
 };
 
 // In order to have a switch statement that is fast (i.e. which use a jump
@@ -676,6 +677,57 @@ class Util {
     return `#${hexNumbers[r]}${hexNumbers[g]}${hexNumbers[b]}`;
   }
 
+  // Apply a scaling matrix to some min/max values.
+  // If a scaling factor is negative then min and max must be
+  // swapped.
+  static scaleMinMax(transform, minMax) {
+    let temp;
+    if (transform[0]) {
+      if (transform[0] < 0) {
+        temp = minMax[0];
+        minMax[0] = minMax[2];
+        minMax[2] = temp;
+      }
+      minMax[0] *= transform[0];
+      minMax[2] *= transform[0];
+
+      if (transform[3] < 0) {
+        temp = minMax[1];
+        minMax[1] = minMax[3];
+        minMax[3] = temp;
+      }
+      minMax[1] *= transform[3];
+      minMax[3] *= transform[3];
+    } else {
+      temp = minMax[0];
+      minMax[0] = minMax[1];
+      minMax[1] = temp;
+      temp = minMax[2];
+      minMax[2] = minMax[3];
+      minMax[3] = temp;
+
+      if (transform[1] < 0) {
+        temp = minMax[1];
+        minMax[1] = minMax[3];
+        minMax[3] = temp;
+      }
+      minMax[1] *= transform[1];
+      minMax[3] *= transform[1];
+
+      if (transform[2] < 0) {
+        temp = minMax[0];
+        minMax[0] = minMax[2];
+        minMax[2] = temp;
+      }
+      minMax[0] *= transform[2];
+      minMax[2] *= transform[2];
+    }
+    minMax[0] += transform[4];
+    minMax[1] += transform[5];
+    minMax[2] += transform[4];
+    minMax[3] += transform[5];
+  }
+
   // Concatenates two transformation matrices together and returns the result.
   static transform(m1, m2) {
     return [
@@ -695,6 +747,22 @@ class Util {
     return [xt, yt];
   }
 
+  static applyTransformInPlace(p, m) {
+    const [p0, p1] = p;
+    p[0] = p0 * m[0] + p1 * m[2] + m[4];
+    p[1] = p0 * m[1] + p1 * m[3] + m[5];
+  }
+
+  // For 2d affine transforms
+  static applyTransformToBezierInPlace(p, [m0, m1, m2, m3, m4, m5]) {
+    for (let i = 0; i < 6; i += 2) {
+      const pI = p[i];
+      const pI1 = p[i + 1];
+      p[i] = pI * m0 + pI1 * m2 + m4;
+      p[i + 1] = pI * m1 + pI1 * m3 + m5;
+    }
+  }
+
   static applyInverseTransform(p, m) {
     const d = m[0] * m[3] - m[1] * m[2];
     const xt = (p[0] * m[3] - p[1] * m[2] + m[2] * m[5] - m[4] * m[3]) / d;