1 /*
2  * Copyright (C) 2008-2009 The Android Open Source Project
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  *      http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
15  */
16 
17 package android.gesture;
18 
19 import android.graphics.RectF;
20 import android.util.Log;
21 
22 import java.util.ArrayList;
23 import java.util.Arrays;
24 import java.io.Closeable;
25 import java.io.IOException;
26 
27 import static android.gesture.GestureConstants.*;
28 
29 /**
30  * Utility functions for gesture processing & analysis, including methods for:
31  * <ul>
32  * <li>feature extraction (e.g., samplers and those for calculating bounding
33  * boxes and gesture path lengths);
34  * <li>geometric transformation (e.g., translation, rotation and scaling);
35  * <li>gesture similarity comparison (e.g., calculating Euclidean or Cosine
36  * distances between two gestures).
37  * </ul>
38  */
39 public final class GestureUtils {
40 
41     private static final float SCALING_THRESHOLD = 0.26f;
42     private static final float NONUNIFORM_SCALE = (float) Math.sqrt(2);
43 
GestureUtils()44     private GestureUtils() {
45     }
46 
47     /**
48      * Closes the specified stream.
49      *
50      * @param stream The stream to close.
51      */
closeStream(Closeable stream)52     static void closeStream(Closeable stream) {
53         if (stream != null) {
54             try {
55                 stream.close();
56             } catch (IOException e) {
57                 Log.e(LOG_TAG, "Could not close stream", e);
58             }
59         }
60     }
61 
62     /**
63      * Samples the gesture spatially by rendering the gesture into a 2D
64      * grayscale bitmap. Scales the gesture to fit the size of the bitmap.
65      * The scaling does not necessarily keep the aspect ratio of the gesture.
66      *
67      * @param gesture the gesture to be sampled
68      * @param bitmapSize the size of the bitmap
69      * @return a bitmapSize x bitmapSize grayscale bitmap that is represented
70      *         as a 1D array. The float at index i represents the grayscale
71      *         value at pixel [i%bitmapSize, i/bitmapSize]
72      */
spatialSampling(Gesture gesture, int bitmapSize)73     public static float[] spatialSampling(Gesture gesture, int bitmapSize) {
74         return spatialSampling(gesture, bitmapSize, false);
75     }
76 
77     /**
78      * Samples the gesture spatially by rendering the gesture into a 2D
79      * grayscale bitmap. Scales the gesture to fit the size of the bitmap.
80      *
81      * @param gesture the gesture to be sampled
82      * @param bitmapSize the size of the bitmap
83      * @param keepAspectRatio if the scaling should keep the gesture's
84      *        aspect ratio
85      *
86      * @return a bitmapSize x bitmapSize grayscale bitmap that is represented
87      *         as a 1D array. The float at index i represents the grayscale
88      *         value at pixel [i%bitmapSize, i/bitmapSize]
89      */
spatialSampling(Gesture gesture, int bitmapSize, boolean keepAspectRatio)90     public static float[] spatialSampling(Gesture gesture, int bitmapSize,
91             boolean keepAspectRatio) {
92         final float targetPatchSize = bitmapSize - 1;
93         float[] sample = new float[bitmapSize * bitmapSize];
94         Arrays.fill(sample, 0);
95 
96         RectF rect = gesture.getBoundingBox();
97         final float gestureWidth = rect.width();
98         final float gestureHeight = rect.height();
99         float sx = targetPatchSize / gestureWidth;
100         float sy = targetPatchSize / gestureHeight;
101 
102         if (keepAspectRatio) {
103             float scale = sx < sy ? sx : sy;
104             sx = scale;
105             sy = scale;
106         } else {
107 
108             float aspectRatio = gestureWidth / gestureHeight;
109             if (aspectRatio > 1) {
110                 aspectRatio = 1 / aspectRatio;
111             }
112             if (aspectRatio < SCALING_THRESHOLD) {
113                 float scale = sx < sy ? sx : sy;
114                 sx = scale;
115                 sy = scale;
116             } else {
117                 if (sx > sy) {
118                     float scale = sy * NONUNIFORM_SCALE;
119                     if (scale < sx) {
120                         sx = scale;
121                     }
122                 } else {
123                     float scale = sx * NONUNIFORM_SCALE;
124                     if (scale < sy) {
125                         sy = scale;
126                     }
127                 }
128             }
129         }
130         float preDx = -rect.centerX();
131         float preDy = -rect.centerY();
132         float postDx = targetPatchSize / 2;
133         float postDy = targetPatchSize / 2;
134         final ArrayList<GestureStroke> strokes = gesture.getStrokes();
135         final int count = strokes.size();
136         int size;
137         float xpos;
138         float ypos;
139         for (int index = 0; index < count; index++) {
140             final GestureStroke stroke = strokes.get(index);
141             float[] strokepoints = stroke.points;
142             size = strokepoints.length;
143             final float[] pts = new float[size];
144             for (int i = 0; i < size; i += 2) {
145                 pts[i] = (strokepoints[i] + preDx) * sx + postDx;
146                 pts[i + 1] = (strokepoints[i + 1] + preDy) * sy + postDy;
147             }
148             float segmentEndX = -1;
149             float segmentEndY = -1;
150             for (int i = 0; i < size; i += 2) {
151                 float segmentStartX = pts[i] < 0 ? 0 : pts[i];
152                 float segmentStartY = pts[i + 1] < 0 ? 0 : pts[i + 1];
153                 if (segmentStartX > targetPatchSize) {
154                     segmentStartX = targetPatchSize;
155                 }
156                 if (segmentStartY > targetPatchSize) {
157                     segmentStartY = targetPatchSize;
158                 }
159                 plot(segmentStartX, segmentStartY, sample, bitmapSize);
160                 if (segmentEndX != -1) {
161                     // Evaluate horizontally
162                     if (segmentEndX > segmentStartX) {
163                         xpos = (float) Math.ceil(segmentStartX);
164                         float slope = (segmentEndY - segmentStartY) /
165                                       (segmentEndX - segmentStartX);
166                         while (xpos < segmentEndX) {
167                             ypos = slope * (xpos - segmentStartX) + segmentStartY;
168                             plot(xpos, ypos, sample, bitmapSize);
169                             xpos++;
170                         }
171                     } else if (segmentEndX < segmentStartX){
172                         xpos = (float) Math.ceil(segmentEndX);
173                         float slope = (segmentEndY - segmentStartY) /
174                                       (segmentEndX - segmentStartX);
175                         while (xpos < segmentStartX) {
176                             ypos = slope * (xpos - segmentStartX) + segmentStartY;
177                             plot(xpos, ypos, sample, bitmapSize);
178                             xpos++;
179                         }
180                     }
181                     // Evaluate vertically
182                     if (segmentEndY > segmentStartY) {
183                         ypos = (float) Math.ceil(segmentStartY);
184                         float invertSlope = (segmentEndX - segmentStartX) /
185                                             (segmentEndY - segmentStartY);
186                         while (ypos < segmentEndY) {
187                             xpos = invertSlope * (ypos - segmentStartY) + segmentStartX;
188                             plot(xpos, ypos, sample, bitmapSize);
189                             ypos++;
190                         }
191                     } else if (segmentEndY < segmentStartY) {
192                         ypos = (float) Math.ceil(segmentEndY);
193                         float invertSlope = (segmentEndX - segmentStartX) /
194                                             (segmentEndY - segmentStartY);
195                         while (ypos < segmentStartY) {
196                             xpos = invertSlope * (ypos - segmentStartY) + segmentStartX;
197                             plot(xpos, ypos, sample, bitmapSize);
198                             ypos++;
199                         }
200                     }
201                 }
202                 segmentEndX = segmentStartX;
203                 segmentEndY = segmentStartY;
204             }
205         }
206         return sample;
207     }
208 
plot(float x, float y, float[] sample, int sampleSize)209     private static void plot(float x, float y, float[] sample, int sampleSize) {
210         x = x < 0 ? 0 : x;
211         y = y < 0 ? 0 : y;
212         int xFloor = (int) Math.floor(x);
213         int xCeiling = (int) Math.ceil(x);
214         int yFloor = (int) Math.floor(y);
215         int yCeiling = (int) Math.ceil(y);
216 
217         // if it's an integer
218         if (x == xFloor && y == yFloor) {
219             int index = yCeiling * sampleSize + xCeiling;
220             if (sample[index] < 1){
221                 sample[index] = 1;
222             }
223         } else {
224             final double xFloorSq = Math.pow(xFloor - x, 2);
225             final double yFloorSq = Math.pow(yFloor - y, 2);
226             final double xCeilingSq = Math.pow(xCeiling - x, 2);
227             final double yCeilingSq = Math.pow(yCeiling - y, 2);
228             float topLeft = (float) Math.sqrt(xFloorSq + yFloorSq);
229             float topRight = (float) Math.sqrt(xCeilingSq + yFloorSq);
230             float btmLeft = (float) Math.sqrt(xFloorSq + yCeilingSq);
231             float btmRight = (float) Math.sqrt(xCeilingSq + yCeilingSq);
232             float sum = topLeft + topRight + btmLeft + btmRight;
233 
234             float value = topLeft / sum;
235             int index = yFloor * sampleSize + xFloor;
236             if (value > sample[index]){
237                 sample[index] = value;
238             }
239 
240             value = topRight / sum;
241             index = yFloor * sampleSize + xCeiling;
242             if (value > sample[index]){
243                 sample[index] = value;
244             }
245 
246             value = btmLeft / sum;
247             index = yCeiling * sampleSize + xFloor;
248             if (value > sample[index]){
249                 sample[index] = value;
250             }
251 
252             value = btmRight / sum;
253             index = yCeiling * sampleSize + xCeiling;
254             if (value > sample[index]){
255                 sample[index] = value;
256             }
257         }
258     }
259 
260     /**
261      * Samples a stroke temporally into a given number of evenly-distributed
262      * points.
263      *
264      * @param stroke the gesture stroke to be sampled
265      * @param numPoints the number of points
266      * @return the sampled points in the form of [x1, y1, x2, y2, ..., xn, yn]
267      */
temporalSampling(GestureStroke stroke, int numPoints)268     public static float[] temporalSampling(GestureStroke stroke, int numPoints) {
269         final float increment = stroke.length / (numPoints - 1);
270         int vectorLength = numPoints * 2;
271         float[] vector = new float[vectorLength];
272         float distanceSoFar = 0;
273         float[] pts = stroke.points;
274         float lstPointX = pts[0];
275         float lstPointY = pts[1];
276         int index = 0;
277         float currentPointX = Float.MIN_VALUE;
278         float currentPointY = Float.MIN_VALUE;
279         vector[index] = lstPointX;
280         index++;
281         vector[index] = lstPointY;
282         index++;
283         int i = 0;
284         int count = pts.length / 2;
285         while (i < count) {
286             if (currentPointX == Float.MIN_VALUE) {
287                 i++;
288                 if (i >= count) {
289                     break;
290                 }
291                 currentPointX = pts[i * 2];
292                 currentPointY = pts[i * 2 + 1];
293             }
294             float deltaX = currentPointX - lstPointX;
295             float deltaY = currentPointY - lstPointY;
296             float distance = (float) Math.hypot(deltaX, deltaY);
297             if (distanceSoFar + distance >= increment) {
298                 float ratio = (increment - distanceSoFar) / distance;
299                 float nx = lstPointX + ratio * deltaX;
300                 float ny = lstPointY + ratio * deltaY;
301                 vector[index] = nx;
302                 index++;
303                 vector[index] = ny;
304                 index++;
305                 lstPointX = nx;
306                 lstPointY = ny;
307                 distanceSoFar = 0;
308             } else {
309                 lstPointX = currentPointX;
310                 lstPointY = currentPointY;
311                 currentPointX = Float.MIN_VALUE;
312                 currentPointY = Float.MIN_VALUE;
313                 distanceSoFar += distance;
314             }
315         }
316 
317         for (i = index; i < vectorLength; i += 2) {
318             vector[i] = lstPointX;
319             vector[i + 1] = lstPointY;
320         }
321         return vector;
322     }
323 
324     /**
325      * Calculates the centroid of a set of points.
326      *
327      * @param points the points in the form of [x1, y1, x2, y2, ..., xn, yn]
328      * @return the centroid
329      */
computeCentroid(float[] points)330     static float[] computeCentroid(float[] points) {
331         float centerX = 0;
332         float centerY = 0;
333         int count = points.length;
334         for (int i = 0; i < count; i++) {
335             centerX += points[i];
336             i++;
337             centerY += points[i];
338         }
339         float[] center = new float[2];
340         center[0] = 2 * centerX / count;
341         center[1] = 2 * centerY / count;
342 
343         return center;
344     }
345 
346     /**
347      * Calculates the variance-covariance matrix of a set of points.
348      *
349      * @param points the points in the form of [x1, y1, x2, y2, ..., xn, yn]
350      * @return the variance-covariance matrix
351      */
computeCoVariance(float[] points)352     private static float[][] computeCoVariance(float[] points) {
353         float[][] array = new float[2][2];
354         array[0][0] = 0;
355         array[0][1] = 0;
356         array[1][0] = 0;
357         array[1][1] = 0;
358         int count = points.length;
359         for (int i = 0; i < count; i++) {
360             float x = points[i];
361             i++;
362             float y = points[i];
363             array[0][0] += x * x;
364             array[0][1] += x * y;
365             array[1][0] = array[0][1];
366             array[1][1] += y * y;
367         }
368         array[0][0] /= (count / 2);
369         array[0][1] /= (count / 2);
370         array[1][0] /= (count / 2);
371         array[1][1] /= (count / 2);
372 
373         return array;
374     }
375 
computeTotalLength(float[] points)376     static float computeTotalLength(float[] points) {
377         float sum = 0;
378         int count = points.length - 4;
379         for (int i = 0; i < count; i += 2) {
380             float dx = points[i + 2] - points[i];
381             float dy = points[i + 3] - points[i + 1];
382             sum += Math.hypot(dx, dy);
383         }
384         return sum;
385     }
386 
computeStraightness(float[] points)387     static float computeStraightness(float[] points) {
388         float totalLen = computeTotalLength(points);
389         float dx = points[2] - points[0];
390         float dy = points[3] - points[1];
391         return (float) Math.hypot(dx, dy) / totalLen;
392     }
393 
computeStraightness(float[] points, float totalLen)394     static float computeStraightness(float[] points, float totalLen) {
395         float dx = points[2] - points[0];
396         float dy = points[3] - points[1];
397         return (float) Math.hypot(dx, dy) / totalLen;
398     }
399 
400     /**
401      * Calculates the squared Euclidean distance between two vectors.
402      *
403      * @param vector1
404      * @param vector2
405      * @return the distance
406      */
squaredEuclideanDistance(float[] vector1, float[] vector2)407     static float squaredEuclideanDistance(float[] vector1, float[] vector2) {
408         float squaredDistance = 0;
409         int size = vector1.length;
410         for (int i = 0; i < size; i++) {
411             float difference = vector1[i] - vector2[i];
412             squaredDistance += difference * difference;
413         }
414         return squaredDistance / size;
415     }
416 
417     /**
418      * Calculates the cosine distance between two instances.
419      *
420      * @param vector1
421      * @param vector2
422      * @return the distance between 0 and Math.PI
423      */
cosineDistance(float[] vector1, float[] vector2)424     static float cosineDistance(float[] vector1, float[] vector2) {
425         float sum = 0;
426         int len = vector1.length;
427         for (int i = 0; i < len; i++) {
428             sum += vector1[i] * vector2[i];
429         }
430         return (float) Math.acos(sum);
431     }
432 
433     /**
434      * Calculates the "minimum" cosine distance between two instances.
435      *
436      * @param vector1
437      * @param vector2
438      * @param numOrientations the maximum number of orientation allowed
439      * @return the distance between the two instances (between 0 and Math.PI)
440      */
minimumCosineDistance(float[] vector1, float[] vector2, int numOrientations)441     static float minimumCosineDistance(float[] vector1, float[] vector2, int numOrientations) {
442         final int len = vector1.length;
443         float a = 0;
444         float b = 0;
445         for (int i = 0; i < len; i += 2) {
446             a += vector1[i] * vector2[i] + vector1[i + 1] * vector2[i + 1];
447             b += vector1[i] * vector2[i + 1] - vector1[i + 1] * vector2[i];
448         }
449         if (a != 0) {
450             final float tan = b/a;
451             final double angle = Math.atan(tan);
452             if (numOrientations > 2 && Math.abs(angle) >= Math.PI / numOrientations) {
453                 return (float) Math.acos(a);
454             } else {
455                 final double cosine = Math.cos(angle);
456                 final double sine = cosine * tan;
457                 return (float) Math.acos(a * cosine + b * sine);
458             }
459         } else {
460             return (float) Math.PI / 2;
461         }
462     }
463 
464     /**
465      * Computes an oriented, minimum bounding box of a set of points.
466      *
467      * @param originalPoints
468      * @return an oriented bounding box
469      */
computeOrientedBoundingBox(ArrayList<GesturePoint> originalPoints)470     public static OrientedBoundingBox computeOrientedBoundingBox(ArrayList<GesturePoint> originalPoints) {
471         final int count = originalPoints.size();
472         float[] points = new float[count * 2];
473         for (int i = 0; i < count; i++) {
474             GesturePoint point = originalPoints.get(i);
475             int index = i * 2;
476             points[index] = point.x;
477             points[index + 1] = point.y;
478         }
479         float[] meanVector = computeCentroid(points);
480         return computeOrientedBoundingBox(points, meanVector);
481     }
482 
483     /**
484      * Computes an oriented, minimum bounding box of a set of points.
485      *
486      * @param originalPoints
487      * @return an oriented bounding box
488      */
computeOrientedBoundingBox(float[] originalPoints)489     public static OrientedBoundingBox computeOrientedBoundingBox(float[] originalPoints) {
490         int size = originalPoints.length;
491         float[] points = new float[size];
492         for (int i = 0; i < size; i++) {
493             points[i] = originalPoints[i];
494         }
495         float[] meanVector = computeCentroid(points);
496         return computeOrientedBoundingBox(points, meanVector);
497     }
498 
computeOrientedBoundingBox(float[] points, float[] centroid)499     private static OrientedBoundingBox computeOrientedBoundingBox(float[] points, float[] centroid) {
500         translate(points, -centroid[0], -centroid[1]);
501 
502         float[][] array = computeCoVariance(points);
503         float[] targetVector = computeOrientation(array);
504 
505         float angle;
506         if (targetVector[0] == 0 && targetVector[1] == 0) {
507             angle = (float) -Math.PI/2;
508         } else { // -PI<alpha<PI
509             angle = (float) Math.atan2(targetVector[1], targetVector[0]);
510             rotate(points, -angle);
511         }
512 
513         float minx = Float.MAX_VALUE;
514         float miny = Float.MAX_VALUE;
515         float maxx = Float.MIN_VALUE;
516         float maxy = Float.MIN_VALUE;
517         int count = points.length;
518         for (int i = 0; i < count; i++) {
519             if (points[i] < minx) {
520                 minx = points[i];
521             }
522             if (points[i] > maxx) {
523                 maxx = points[i];
524             }
525             i++;
526             if (points[i] < miny) {
527                 miny = points[i];
528             }
529             if (points[i] > maxy) {
530                 maxy = points[i];
531             }
532         }
533 
534         return new OrientedBoundingBox((float) (angle * 180 / Math.PI), centroid[0], centroid[1], maxx - minx, maxy - miny);
535     }
536 
computeOrientation(float[][] covarianceMatrix)537     private static float[] computeOrientation(float[][] covarianceMatrix) {
538         float[] targetVector = new float[2];
539         if (covarianceMatrix[0][1] == 0 || covarianceMatrix[1][0] == 0) {
540             targetVector[0] = 1;
541             targetVector[1] = 0;
542         }
543 
544         float a = -covarianceMatrix[0][0] - covarianceMatrix[1][1];
545         float b = covarianceMatrix[0][0] * covarianceMatrix[1][1] - covarianceMatrix[0][1]
546                 * covarianceMatrix[1][0];
547         float value = a / 2;
548         float rightside = (float) Math.sqrt(Math.pow(value, 2) - b);
549         float lambda1 = -value + rightside;
550         float lambda2 = -value - rightside;
551         if (lambda1 == lambda2) {
552             targetVector[0] = 0;
553             targetVector[1] = 0;
554         } else {
555             float lambda = lambda1 > lambda2 ? lambda1 : lambda2;
556             targetVector[0] = 1;
557             targetVector[1] = (lambda - covarianceMatrix[0][0]) / covarianceMatrix[0][1];
558         }
559         return targetVector;
560     }
561 
562 
rotate(float[] points, float angle)563     static float[] rotate(float[] points, float angle) {
564         float cos = (float) Math.cos(angle);
565         float sin = (float) Math.sin(angle);
566         int size = points.length;
567         for (int i = 0; i < size; i += 2) {
568             float x = points[i] * cos - points[i + 1] * sin;
569             float y = points[i] * sin + points[i + 1] * cos;
570             points[i] = x;
571             points[i + 1] = y;
572         }
573         return points;
574     }
575 
translate(float[] points, float dx, float dy)576     static float[] translate(float[] points, float dx, float dy) {
577         int size = points.length;
578         for (int i = 0; i < size; i += 2) {
579             points[i] += dx;
580             points[i + 1] += dy;
581         }
582         return points;
583     }
584 
scale(float[] points, float sx, float sy)585     static float[] scale(float[] points, float sx, float sy) {
586         int size = points.length;
587         for (int i = 0; i < size; i += 2) {
588             points[i] *= sx;
589             points[i + 1] *= sy;
590         }
591         return points;
592     }
593 }
594