/*
* Copyright (C) 2012 The Android Open Source Project
*
* 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.
*/
#define LOG_TAG "VelocityTracker"
//#define LOG_NDEBUG 0
// Log debug messages about velocity tracking.
#define DEBUG_VELOCITY 0
// Log debug messages about the progress of the algorithm itself.
#define DEBUG_STRATEGY 0
#include <inttypes.h>
#include <limits.h>
#include <math.h>
#include <android-base/stringprintf.h>
#include <cutils/properties.h>
#include <input/VelocityTracker.h>
#include <utils/BitSet.h>
#include <utils/Timers.h>
namespace android {
// Nanoseconds per milliseconds.
static const nsecs_t NANOS_PER_MS = 1000000;
// Threshold for determining that a pointer has stopped moving.
// Some input devices do not send ACTION_MOVE events in the case where a pointer has
// stopped. We need to detect this case so that we can accurately predict the
// velocity after the pointer starts moving again.
static const nsecs_t ASSUME_POINTER_STOPPED_TIME = 40 * NANOS_PER_MS;
static float vectorDot(const float* a, const float* b, uint32_t m) {
float r = 0;
for (size_t i = 0; i < m; i++) {
r += *(a++) * *(b++);
}
return r;
}
static float vectorNorm(const float* a, uint32_t m) {
float r = 0;
for (size_t i = 0; i < m; i++) {
float t = *(a++);
r += t * t;
}
return sqrtf(r);
}
#if DEBUG_STRATEGY || DEBUG_VELOCITY
static std::string vectorToString(const float* a, uint32_t m) {
std::string str;
str += "[";
for (size_t i = 0; i < m; i++) {
if (i) {
str += ",";
}
str += android::base::StringPrintf(" %f", *(a++));
}
str += " ]";
return str;
}
#endif
#if DEBUG_STRATEGY
static std::string matrixToString(const float* a, uint32_t m, uint32_t n, bool rowMajor) {
std::string str;
str = "[";
for (size_t i = 0; i < m; i++) {
if (i) {
str += ",";
}
str += " [";
for (size_t j = 0; j < n; j++) {
if (j) {
str += ",";
}
str += android::base::StringPrintf(" %f", a[rowMajor ? i * n + j : j * m + i]);
}
str += " ]";
}
str += " ]";
return str;
}
#endif
// --- VelocityTracker ---
// The default velocity tracker strategy.
// Although other strategies are available for testing and comparison purposes,
// this is the strategy that applications will actually use. Be very careful
// when adjusting the default strategy because it can dramatically affect
// (often in a bad way) the user experience.
const char* VelocityTracker::DEFAULT_STRATEGY = "lsq2";
VelocityTracker::VelocityTracker(const char* strategy) :
mLastEventTime(0), mCurrentPointerIdBits(0), mActivePointerId(-1) {
char value[PROPERTY_VALUE_MAX];
// Allow the default strategy to be overridden using a system property for debugging.
if (!strategy) {
int length = property_get("debug.velocitytracker.strategy", value, NULL);
if (length > 0) {
strategy = value;
} else {
strategy = DEFAULT_STRATEGY;
}
}
// Configure the strategy.
if (!configureStrategy(strategy)) {
ALOGD("Unrecognized velocity tracker strategy name '%s'.", strategy);
if (!configureStrategy(DEFAULT_STRATEGY)) {
LOG_ALWAYS_FATAL("Could not create the default velocity tracker strategy '%s'!",
strategy);
}
}
}
VelocityTracker::~VelocityTracker() {
delete mStrategy;
}
bool VelocityTracker::configureStrategy(const char* strategy) {
mStrategy = createStrategy(strategy);
return mStrategy != NULL;
}
VelocityTrackerStrategy* VelocityTracker::createStrategy(const char* strategy) {
if (!strcmp("impulse", strategy)) {
// Physical model of pushing an object. Quality: VERY GOOD.
// Works with duplicate coordinates, unclean finger liftoff.
return new ImpulseVelocityTrackerStrategy();
}
if (!strcmp("lsq1", strategy)) {
// 1st order least squares. Quality: POOR.
// Frequently underfits the touch data especially when the finger accelerates
// or changes direction. Often underestimates velocity. The direction
// is overly influenced by historical touch points.
return new LeastSquaresVelocityTrackerStrategy(1);
}
if (!strcmp("lsq2", strategy)) {
// 2nd order least squares. Quality: VERY GOOD.
// Pretty much ideal, but can be confused by certain kinds of touch data,
// particularly if the panel has a tendency to generate delayed,
// duplicate or jittery touch coordinates when the finger is released.
return new LeastSquaresVelocityTrackerStrategy(2);
}
if (!strcmp("lsq3", strategy)) {
// 3rd order least squares. Quality: UNUSABLE.
// Frequently overfits the touch data yielding wildly divergent estimates
// of the velocity when the finger is released.
return new LeastSquaresVelocityTrackerStrategy(3);
}
if (!strcmp("wlsq2-delta", strategy)) {
// 2nd order weighted least squares, delta weighting. Quality: EXPERIMENTAL
return new LeastSquaresVelocityTrackerStrategy(2,
LeastSquaresVelocityTrackerStrategy::WEIGHTING_DELTA);
}
if (!strcmp("wlsq2-central", strategy)) {
// 2nd order weighted least squares, central weighting. Quality: EXPERIMENTAL
return new LeastSquaresVelocityTrackerStrategy(2,
LeastSquaresVelocityTrackerStrategy::WEIGHTING_CENTRAL);
}
if (!strcmp("wlsq2-recent", strategy)) {
// 2nd order weighted least squares, recent weighting. Quality: EXPERIMENTAL
return new LeastSquaresVelocityTrackerStrategy(2,
LeastSquaresVelocityTrackerStrategy::WEIGHTING_RECENT);
}
if (!strcmp("int1", strategy)) {
// 1st order integrating filter. Quality: GOOD.
// Not as good as 'lsq2' because it cannot estimate acceleration but it is
// more tolerant of errors. Like 'lsq1', this strategy tends to underestimate
// the velocity of a fling but this strategy tends to respond to changes in
// direction more quickly and accurately.
return new IntegratingVelocityTrackerStrategy(1);
}
if (!strcmp("int2", strategy)) {
// 2nd order integrating filter. Quality: EXPERIMENTAL.
// For comparison purposes only. Unlike 'int1' this strategy can compensate
// for acceleration but it typically overestimates the effect.
return new IntegratingVelocityTrackerStrategy(2);
}
if (!strcmp("legacy", strategy)) {
// Legacy velocity tracker algorithm. Quality: POOR.
// For comparison purposes only. This algorithm is strongly influenced by
// old data points, consistently underestimates velocity and takes a very long
// time to adjust to changes in direction.
return new LegacyVelocityTrackerStrategy();
}
return NULL;
}
void VelocityTracker::clear() {
mCurrentPointerIdBits.clear();
mActivePointerId = -1;
mStrategy->clear();
}
void VelocityTracker::clearPointers(BitSet32 idBits) {
BitSet32 remainingIdBits(mCurrentPointerIdBits.value & ~idBits.value);
mCurrentPointerIdBits = remainingIdBits;
if (mActivePointerId >= 0 && idBits.hasBit(mActivePointerId)) {
mActivePointerId = !remainingIdBits.isEmpty() ? remainingIdBits.firstMarkedBit() : -1;
}
mStrategy->clearPointers(idBits);
}
void VelocityTracker::addMovement(nsecs_t eventTime, BitSet32 idBits, const Position* positions) {
while (idBits.count() > MAX_POINTERS) {
idBits.clearLastMarkedBit();
}
if ((mCurrentPointerIdBits.value & idBits.value)
&& eventTime >= mLastEventTime + ASSUME_POINTER_STOPPED_TIME) {
#if DEBUG_VELOCITY
ALOGD("VelocityTracker: stopped for %0.3f ms, clearing state.",
(eventTime - mLastEventTime) * 0.000001f);
#endif
// We have not received any movements for too long. Assume that all pointers
// have stopped.
mStrategy->clear();
}
mLastEventTime = eventTime;
mCurrentPointerIdBits = idBits;
if (mActivePointerId < 0 || !idBits.hasBit(mActivePointerId)) {
mActivePointerId = idBits.isEmpty() ? -1 : idBits.firstMarkedBit();
}
mStrategy->addMovement(eventTime, idBits, positions);
#if DEBUG_VELOCITY
ALOGD("VelocityTracker: addMovement eventTime=%" PRId64 ", idBits=0x%08x, activePointerId=%d",
eventTime, idBits.value, mActivePointerId);
for (BitSet32 iterBits(idBits); !iterBits.isEmpty(); ) {
uint32_t id = iterBits.firstMarkedBit();
uint32_t index = idBits.getIndexOfBit(id);
iterBits.clearBit(id);
Estimator estimator;
getEstimator(id, &estimator);
ALOGD(" %d: position (%0.3f, %0.3f), "
"estimator (degree=%d, xCoeff=%s, yCoeff=%s, confidence=%f)",
id, positions[index].x, positions[index].y,
int(estimator.degree),
vectorToString(estimator.xCoeff, estimator.degree + 1).c_str(),
vectorToString(estimator.yCoeff, estimator.degree + 1).c_str(),
estimator.confidence);
}
#endif
}
void VelocityTracker::addMovement(const MotionEvent* event) {
int32_t actionMasked = event->getActionMasked();
switch (actionMasked) {
case AMOTION_EVENT_ACTION_DOWN:
case AMOTION_EVENT_ACTION_HOVER_ENTER:
// Clear all pointers on down before adding the new movement.
clear();
break;
case AMOTION_EVENT_ACTION_POINTER_DOWN: {
// Start a new movement trace for a pointer that just went down.
// We do this on down instead of on up because the client may want to query the
// final velocity for a pointer that just went up.
BitSet32 downIdBits;
downIdBits.markBit(event->getPointerId(event->getActionIndex()));
clearPointers(downIdBits);
break;
}
case AMOTION_EVENT_ACTION_MOVE:
case AMOTION_EVENT_ACTION_HOVER_MOVE:
break;
default:
// Ignore all other actions because they do not convey any new information about
// pointer movement. We also want to preserve the last known velocity of the pointers.
// Note that ACTION_UP and ACTION_POINTER_UP always report the last known position
// of the pointers that went up. ACTION_POINTER_UP does include the new position of
// pointers that remained down but we will also receive an ACTION_MOVE with this
// information if any of them actually moved. Since we don't know how many pointers
// will be going up at once it makes sense to just wait for the following ACTION_MOVE
// before adding the movement.
return;
}
size_t pointerCount = event->getPointerCount();
if (pointerCount > MAX_POINTERS) {
pointerCount = MAX_POINTERS;
}
BitSet32 idBits;
for (size_t i = 0; i < pointerCount; i++) {
idBits.markBit(event->getPointerId(i));
}
uint32_t pointerIndex[MAX_POINTERS];
for (size_t i = 0; i < pointerCount; i++) {
pointerIndex[i] = idBits.getIndexOfBit(event->getPointerId(i));
}
nsecs_t eventTime;
Position positions[pointerCount];
size_t historySize = event->getHistorySize();
for (size_t h = 0; h < historySize; h++) {
eventTime = event->getHistoricalEventTime(h);
for (size_t i = 0; i < pointerCount; i++) {
uint32_t index = pointerIndex[i];
positions[index].x = event->getHistoricalRawX(i, h);
positions[index].y = event->getHistoricalRawY(i, h);
}
addMovement(eventTime, idBits, positions);
}
eventTime = event->getEventTime();
for (size_t i = 0; i < pointerCount; i++) {
uint32_t index = pointerIndex[i];
positions[index].x = event->getRawX(i);
positions[index].y = event->getRawY(i);
}
addMovement(eventTime, idBits, positions);
}
bool VelocityTracker::getVelocity(uint32_t id, float* outVx, float* outVy) const {
Estimator estimator;
if (getEstimator(id, &estimator) && estimator.degree >= 1) {
*outVx = estimator.xCoeff[1];
*outVy = estimator.yCoeff[1];
return true;
}
*outVx = 0;
*outVy = 0;
return false;
}
bool VelocityTracker::getEstimator(uint32_t id, Estimator* outEstimator) const {
return mStrategy->getEstimator(id, outEstimator);
}
// --- LeastSquaresVelocityTrackerStrategy ---
LeastSquaresVelocityTrackerStrategy::LeastSquaresVelocityTrackerStrategy(
uint32_t degree, Weighting weighting) :
mDegree(degree), mWeighting(weighting) {
clear();
}
LeastSquaresVelocityTrackerStrategy::~LeastSquaresVelocityTrackerStrategy() {
}
void LeastSquaresVelocityTrackerStrategy::clear() {
mIndex = 0;
mMovements[0].idBits.clear();
}
void LeastSquaresVelocityTrackerStrategy::clearPointers(BitSet32 idBits) {
BitSet32 remainingIdBits(mMovements[mIndex].idBits.value & ~idBits.value);
mMovements[mIndex].idBits = remainingIdBits;
}
void LeastSquaresVelocityTrackerStrategy::addMovement(nsecs_t eventTime, BitSet32 idBits,
const VelocityTracker::Position* positions) {
if (++mIndex == HISTORY_SIZE) {
mIndex = 0;
}
Movement& movement = mMovements[mIndex];
movement.eventTime = eventTime;
movement.idBits = idBits;
uint32_t count = idBits.count();
for (uint32_t i = 0; i < count; i++) {
movement.positions[i] = positions[i];
}
}
/**
* Solves a linear least squares problem to obtain a N degree polynomial that fits
* the specified input data as nearly as possible.
*
* Returns true if a solution is found, false otherwise.
*
* The input consists of two vectors of data points X and Y with indices 0..m-1
* along with a weight vector W of the same size.
*
* The output is a vector B with indices 0..n that describes a polynomial
* that fits the data, such the sum of W[i] * W[i] * abs(Y[i] - (B[0] + B[1] X[i]
* + B[2] X[i]^2 ... B[n] X[i]^n)) for all i between 0 and m-1 is minimized.
*
* Accordingly, the weight vector W should be initialized by the caller with the
* reciprocal square root of the variance of the error in each input data point.
* In other words, an ideal choice for W would be W[i] = 1 / var(Y[i]) = 1 / stddev(Y[i]).
* The weights express the relative importance of each data point. If the weights are
* all 1, then the data points are considered to be of equal importance when fitting
* the polynomial. It is a good idea to choose weights that diminish the importance
* of data points that may have higher than usual error margins.
*
* Errors among data points are assumed to be independent. W is represented here
* as a vector although in the literature it is typically taken to be a diagonal matrix.
*
* That is to say, the function that generated the input data can be approximated
* by y(x) ~= B[0] + B[1] x + B[2] x^2 + ... + B[n] x^n.
*
* The coefficient of determination (R^2) is also returned to describe the goodness
* of fit of the model for the given data. It is a value between 0 and 1, where 1
* indicates perfect correspondence.
*
* This function first expands the X vector to a m by n matrix A such that
* A[i][0] = 1, A[i][1] = X[i], A[i][2] = X[i]^2, ..., A[i][n] = X[i]^n, then
* multiplies it by w[i]./
*
* Then it calculates the QR decomposition of A yielding an m by m orthonormal matrix Q
* and an m by n upper triangular matrix R. Because R is upper triangular (lower
* part is all zeroes), we can simplify the decomposition into an m by n matrix
* Q1 and a n by n matrix R1 such that A = Q1 R1.
*
* Finally we solve the system of linear equations given by R1 B = (Qtranspose W Y)
* to find B.
*
* For efficiency, we lay out A and Q column-wise in memory because we frequently
* operate on the column vectors. Conversely, we lay out R row-wise.
*
* http://en.wikipedia.org/wiki/Numerical_methods_for_linear_least_squares
* http://en.wikipedia.org/wiki/Gram-Schmidt
*/
static bool solveLeastSquares(const float* x, const float* y,
const float* w, uint32_t m, uint32_t n, float* outB, float* outDet) {
#if DEBUG_STRATEGY
ALOGD("solveLeastSquares: m=%d, n=%d, x=%s, y=%s, w=%s", int(m), int(n),
vectorToString(x, m).c_str(), vectorToString(y, m).c_str(),
vectorToString(w, m).c_str());
#endif
// Expand the X vector to a matrix A, pre-multiplied by the weights.
float a[n][m]; // column-major order
for (uint32_t h = 0; h < m; h++) {
a[0][h] = w[h];
for (uint32_t i = 1; i < n; i++) {
a[i][h] = a[i - 1][h] * x[h];
}
}
#if DEBUG_STRATEGY
ALOGD(" - a=%s", matrixToString(&a[0][0], m, n, false /*rowMajor*/).c_str());
#endif
// Apply the Gram-Schmidt process to A to obtain its QR decomposition.
float q[n][m]; // orthonormal basis, column-major order
float r[n][n]; // upper triangular matrix, row-major order
for (uint32_t j = 0; j < n; j++) {
for (uint32_t h = 0; h < m; h++) {
q[j][h] = a[j][h];
}
for (uint32_t i = 0; i < j; i++) {
float dot = vectorDot(&q[j][0], &q[i][0], m);
for (uint32_t h = 0; h < m; h++) {
q[j][h] -= dot * q[i][h];
}
}
float norm = vectorNorm(&q[j][0], m);
if (norm < 0.000001f) {
// vectors are linearly dependent or zero so no solution
#if DEBUG_STRATEGY
ALOGD(" - no solution, norm=%f", norm);
#endif
return false;
}
float invNorm = 1.0f / norm;
for (uint32_t h = 0; h < m; h++) {
q[j][h] *= invNorm;
}
for (uint32_t i = 0; i < n; i++) {
r[j][i] = i < j ? 0 : vectorDot(&q[j][0], &a[i][0], m);
}
}
#if DEBUG_STRATEGY
ALOGD(" - q=%s", matrixToString(&q[0][0], m, n, false /*rowMajor*/).c_str());
ALOGD(" - r=%s", matrixToString(&r[0][0], n, n, true /*rowMajor*/).c_str());
// calculate QR, if we factored A correctly then QR should equal A
float qr[n][m];
for (uint32_t h = 0; h < m; h++) {
for (uint32_t i = 0; i < n; i++) {
qr[i][h] = 0;
for (uint32_t j = 0; j < n; j++) {
qr[i][h] += q[j][h] * r[j][i];
}
}
}
ALOGD(" - qr=%s", matrixToString(&qr[0][0], m, n, false /*rowMajor*/).c_str());
#endif
// Solve R B = Qt W Y to find B. This is easy because R is upper triangular.
// We just work from bottom-right to top-left calculating B's coefficients.
float wy[m];
for (uint32_t h = 0; h < m; h++) {
wy[h] = y[h] * w[h];
}
for (uint32_t i = n; i != 0; ) {
i--;
outB[i] = vectorDot(&q[i][0], wy, m);
for (uint32_t j = n - 1; j > i; j--) {
outB[i] -= r[i][j] * outB[j];
}
outB[i] /= r[i][i];
}
#if DEBUG_STRATEGY
ALOGD(" - b=%s", vectorToString(outB, n).c_str());
#endif
// Calculate the coefficient of determination as 1 - (SSerr / SStot) where
// SSerr is the residual sum of squares (variance of the error),
// and SStot is the total sum of squares (variance of the data) where each
// has been weighted.
float ymean = 0;
for (uint32_t h = 0; h < m; h++) {
ymean += y[h];
}
ymean /= m;
float sserr = 0;
float sstot = 0;
for (uint32_t h = 0; h < m; h++) {
float err = y[h] - outB[0];
float term = 1;
for (uint32_t i = 1; i < n; i++) {
term *= x[h];
err -= term * outB[i];
}
sserr += w[h] * w[h] * err * err;
float var = y[h] - ymean;
sstot += w[h] * w[h] * var * var;
}
*outDet = sstot > 0.000001f ? 1.0f - (sserr / sstot) : 1;
#if DEBUG_STRATEGY
ALOGD(" - sserr=%f", sserr);
ALOGD(" - sstot=%f", sstot);
ALOGD(" - det=%f", *outDet);
#endif
return true;
}
/*
* Optimized unweighted second-order least squares fit. About 2x speed improvement compared to
* the default implementation
*/
static float solveUnweightedLeastSquaresDeg2(const float* x, const float* y, size_t count) {
float sxi = 0, sxiyi = 0, syi = 0, sxi2 = 0, sxi3 = 0, sxi2yi = 0, sxi4 = 0;
for (size_t i = 0; i < count; i++) {
float xi = x[i];
float yi = y[i];
float xi2 = xi*xi;
float xi3 = xi2*xi;
float xi4 = xi3*xi;
float xi2yi = xi2*yi;
float xiyi = xi*yi;
sxi += xi;
sxi2 += xi2;
sxiyi += xiyi;
sxi2yi += xi2yi;
syi += yi;
sxi3 += xi3;
sxi4 += xi4;
}
float Sxx = sxi2 - sxi*sxi / count;
float Sxy = sxiyi - sxi*syi / count;
float Sxx2 = sxi3 - sxi*sxi2 / count;
float Sx2y = sxi2yi - sxi2*syi / count;
float Sx2x2 = sxi4 - sxi2*sxi2 / count;
float numerator = Sxy*Sx2x2 - Sx2y*Sxx2;
float denominator = Sxx*Sx2x2 - Sxx2*Sxx2;
if (denominator == 0) {
ALOGW("division by 0 when computing velocity, Sxx=%f, Sx2x2=%f, Sxx2=%f", Sxx, Sx2x2, Sxx2);
return 0;
}
return numerator/denominator;
}
bool LeastSquaresVelocityTrackerStrategy::getEstimator(uint32_t id,
VelocityTracker::Estimator* outEstimator) const {
outEstimator->clear();
// Iterate over movement samples in reverse time order and collect samples.
float x[HISTORY_SIZE];
float y[HISTORY_SIZE];
float w[HISTORY_SIZE];
float time[HISTORY_SIZE];
uint32_t m = 0;
uint32_t index = mIndex;
const Movement& newestMovement = mMovements[mIndex];
do {
const Movement& movement = mMovements[index];
if (!movement.idBits.hasBit(id)) {
break;
}
nsecs_t age = newestMovement.eventTime - movement.eventTime;
if (age > HORIZON) {
break;
}
const VelocityTracker::Position& position = movement.getPosition(id);
x[m] = position.x;
y[m] = position.y;
w[m] = chooseWeight(index);
time[m] = -age * 0.000000001f;
index = (index == 0 ? HISTORY_SIZE : index) - 1;
} while (++m < HISTORY_SIZE);
if (m == 0) {
return false; // no data
}
// Calculate a least squares polynomial fit.
uint32_t degree = mDegree;
if (degree > m - 1) {
degree = m - 1;
}
if (degree >= 1) {
if (degree == 2 && mWeighting == WEIGHTING_NONE) { // optimize unweighted, degree=2 fit
outEstimator->time = newestMovement.eventTime;
outEstimator->degree = 2;
outEstimator->confidence = 1;
outEstimator->xCoeff[0] = 0; // only slope is calculated, set rest of coefficients = 0
outEstimator->yCoeff[0] = 0;
outEstimator->xCoeff[1] = solveUnweightedLeastSquaresDeg2(time, x, m);
outEstimator->yCoeff[1] = solveUnweightedLeastSquaresDeg2(time, y, m);
outEstimator->xCoeff[2] = 0;
outEstimator->yCoeff[2] = 0;
return true;
}
float xdet, ydet;
uint32_t n = degree + 1;
if (solveLeastSquares(time, x, w, m, n, outEstimator->xCoeff, &xdet)
&& solveLeastSquares(time, y, w, m, n, outEstimator->yCoeff, &ydet)) {
outEstimator->time = newestMovement.eventTime;
outEstimator->degree = degree;
outEstimator->confidence = xdet * ydet;
#if DEBUG_STRATEGY
ALOGD("estimate: degree=%d, xCoeff=%s, yCoeff=%s, confidence=%f",
int(outEstimator->degree),
vectorToString(outEstimator->xCoeff, n).c_str(),
vectorToString(outEstimator->yCoeff, n).c_str(),
outEstimator->confidence);
#endif
return true;
}
}
// No velocity data available for this pointer, but we do have its current position.
outEstimator->xCoeff[0] = x[0];
outEstimator->yCoeff[0] = y[0];
outEstimator->time = newestMovement.eventTime;
outEstimator->degree = 0;
outEstimator->confidence = 1;
return true;
}
float LeastSquaresVelocityTrackerStrategy::chooseWeight(uint32_t index) const {
switch (mWeighting) {
case WEIGHTING_DELTA: {
// Weight points based on how much time elapsed between them and the next
// point so that points that "cover" a shorter time span are weighed less.
// delta 0ms: 0.5
// delta 10ms: 1.0
if (index == mIndex) {
return 1.0f;
}
uint32_t nextIndex = (index + 1) % HISTORY_SIZE;
float deltaMillis = (mMovements[nextIndex].eventTime- mMovements[index].eventTime)
* 0.000001f;
if (deltaMillis < 0) {
return 0.5f;
}
if (deltaMillis < 10) {
return 0.5f + deltaMillis * 0.05;
}
return 1.0f;
}
case WEIGHTING_CENTRAL: {
// Weight points based on their age, weighing very recent and very old points less.
// age 0ms: 0.5
// age 10ms: 1.0
// age 50ms: 1.0
// age 60ms: 0.5
float ageMillis = (mMovements[mIndex].eventTime - mMovements[index].eventTime)
* 0.000001f;
if (ageMillis < 0) {
return 0.5f;
}
if (ageMillis < 10) {
return 0.5f + ageMillis * 0.05;
}
if (ageMillis < 50) {
return 1.0f;
}
if (ageMillis < 60) {
return 0.5f + (60 - ageMillis) * 0.05;
}
return 0.5f;
}
case WEIGHTING_RECENT: {
// Weight points based on their age, weighing older points less.
// age 0ms: 1.0
// age 50ms: 1.0
// age 100ms: 0.5
float ageMillis = (mMovements[mIndex].eventTime - mMovements[index].eventTime)
* 0.000001f;
if (ageMillis < 50) {
return 1.0f;
}
if (ageMillis < 100) {
return 0.5f + (100 - ageMillis) * 0.01f;
}
return 0.5f;
}
case WEIGHTING_NONE:
default:
return 1.0f;
}
}
// --- IntegratingVelocityTrackerStrategy ---
IntegratingVelocityTrackerStrategy::IntegratingVelocityTrackerStrategy(uint32_t degree) :
mDegree(degree) {
}
IntegratingVelocityTrackerStrategy::~IntegratingVelocityTrackerStrategy() {
}
void IntegratingVelocityTrackerStrategy::clear() {
mPointerIdBits.clear();
}
void IntegratingVelocityTrackerStrategy::clearPointers(BitSet32 idBits) {
mPointerIdBits.value &= ~idBits.value;
}
void IntegratingVelocityTrackerStrategy::addMovement(nsecs_t eventTime, BitSet32 idBits,
const VelocityTracker::Position* positions) {
uint32_t index = 0;
for (BitSet32 iterIdBits(idBits); !iterIdBits.isEmpty();) {
uint32_t id = iterIdBits.clearFirstMarkedBit();
State& state = mPointerState[id];
const VelocityTracker::Position& position = positions[index++];
if (mPointerIdBits.hasBit(id)) {
updateState(state, eventTime, position.x, position.y);
} else {
initState(state, eventTime, position.x, position.y);
}
}
mPointerIdBits = idBits;
}
bool IntegratingVelocityTrackerStrategy::getEstimator(uint32_t id,
VelocityTracker::Estimator* outEstimator) const {
outEstimator->clear();
if (mPointerIdBits.hasBit(id)) {
const State& state = mPointerState[id];
populateEstimator(state, outEstimator);
return true;
}
return false;
}
void IntegratingVelocityTrackerStrategy::initState(State& state,
nsecs_t eventTime, float xpos, float ypos) const {
state.updateTime = eventTime;
state.degree = 0;
state.xpos = xpos;
state.xvel = 0;
state.xaccel = 0;
state.ypos = ypos;
state.yvel = 0;
state.yaccel = 0;
}
void IntegratingVelocityTrackerStrategy::updateState(State& state,
nsecs_t eventTime, float xpos, float ypos) const {
const nsecs_t MIN_TIME_DELTA = 2 * NANOS_PER_MS;
const float FILTER_TIME_CONSTANT = 0.010f; // 10 milliseconds
if (eventTime <= state.updateTime + MIN_TIME_DELTA) {
return;
}
float dt = (eventTime - state.updateTime) * 0.000000001f;
state.updateTime = eventTime;
float xvel = (xpos - state.xpos) / dt;
float yvel = (ypos - state.ypos) / dt;
if (state.degree == 0) {
state.xvel = xvel;
state.yvel = yvel;
state.degree = 1;
} else {
float alpha = dt / (FILTER_TIME_CONSTANT + dt);
if (mDegree == 1) {
state.xvel += (xvel - state.xvel) * alpha;
state.yvel += (yvel - state.yvel) * alpha;
} else {
float xaccel = (xvel - state.xvel) / dt;
float yaccel = (yvel - state.yvel) / dt;
if (state.degree == 1) {
state.xaccel = xaccel;
state.yaccel = yaccel;
state.degree = 2;
} else {
state.xaccel += (xaccel - state.xaccel) * alpha;
state.yaccel += (yaccel - state.yaccel) * alpha;
}
state.xvel += (state.xaccel * dt) * alpha;
state.yvel += (state.yaccel * dt) * alpha;
}
}
state.xpos = xpos;
state.ypos = ypos;
}
void IntegratingVelocityTrackerStrategy::populateEstimator(const State& state,
VelocityTracker::Estimator* outEstimator) const {
outEstimator->time = state.updateTime;
outEstimator->confidence = 1.0f;
outEstimator->degree = state.degree;
outEstimator->xCoeff[0] = state.xpos;
outEstimator->xCoeff[1] = state.xvel;
outEstimator->xCoeff[2] = state.xaccel / 2;
outEstimator->yCoeff[0] = state.ypos;
outEstimator->yCoeff[1] = state.yvel;
outEstimator->yCoeff[2] = state.yaccel / 2;
}
// --- LegacyVelocityTrackerStrategy ---
LegacyVelocityTrackerStrategy::LegacyVelocityTrackerStrategy() {
clear();
}
LegacyVelocityTrackerStrategy::~LegacyVelocityTrackerStrategy() {
}
void LegacyVelocityTrackerStrategy::clear() {
mIndex = 0;
mMovements[0].idBits.clear();
}
void LegacyVelocityTrackerStrategy::clearPointers(BitSet32 idBits) {
BitSet32 remainingIdBits(mMovements[mIndex].idBits.value & ~idBits.value);
mMovements[mIndex].idBits = remainingIdBits;
}
void LegacyVelocityTrackerStrategy::addMovement(nsecs_t eventTime, BitSet32 idBits,
const VelocityTracker::Position* positions) {
if (++mIndex == HISTORY_SIZE) {
mIndex = 0;
}
Movement& movement = mMovements[mIndex];
movement.eventTime = eventTime;
movement.idBits = idBits;
uint32_t count = idBits.count();
for (uint32_t i = 0; i < count; i++) {
movement.positions[i] = positions[i];
}
}
bool LegacyVelocityTrackerStrategy::getEstimator(uint32_t id,
VelocityTracker::Estimator* outEstimator) const {
outEstimator->clear();
const Movement& newestMovement = mMovements[mIndex];
if (!newestMovement.idBits.hasBit(id)) {
return false; // no data
}
// Find the oldest sample that contains the pointer and that is not older than HORIZON.
nsecs_t minTime = newestMovement.eventTime - HORIZON;
uint32_t oldestIndex = mIndex;
uint32_t numTouches = 1;
do {
uint32_t nextOldestIndex = (oldestIndex == 0 ? HISTORY_SIZE : oldestIndex) - 1;
const Movement& nextOldestMovement = mMovements[nextOldestIndex];
if (!nextOldestMovement.idBits.hasBit(id)
|| nextOldestMovement.eventTime < minTime) {
break;
}
oldestIndex = nextOldestIndex;
} while (++numTouches < HISTORY_SIZE);
// Calculate an exponentially weighted moving average of the velocity estimate
// at different points in time measured relative to the oldest sample.
// This is essentially an IIR filter. Newer samples are weighted more heavily
// than older samples. Samples at equal time points are weighted more or less
// equally.
//
// One tricky problem is that the sample data may be poorly conditioned.
// Sometimes samples arrive very close together in time which can cause us to
// overestimate the velocity at that time point. Most samples might be measured
// 16ms apart but some consecutive samples could be only 0.5sm apart because
// the hardware or driver reports them irregularly or in bursts.
float accumVx = 0;
float accumVy = 0;
uint32_t index = oldestIndex;
uint32_t samplesUsed = 0;
const Movement& oldestMovement = mMovements[oldestIndex];
const VelocityTracker::Position& oldestPosition = oldestMovement.getPosition(id);
nsecs_t lastDuration = 0;
while (numTouches-- > 1) {
if (++index == HISTORY_SIZE) {
index = 0;
}
const Movement& movement = mMovements[index];
nsecs_t duration = movement.eventTime - oldestMovement.eventTime;
// If the duration between samples is small, we may significantly overestimate
// the velocity. Consequently, we impose a minimum duration constraint on the
// samples that we include in the calculation.
if (duration >= MIN_DURATION) {
const VelocityTracker::Position& position = movement.getPosition(id);
float scale = 1000000000.0f / duration; // one over time delta in seconds
float vx = (position.x - oldestPosition.x) * scale;
float vy = (position.y - oldestPosition.y) * scale;
accumVx = (accumVx * lastDuration + vx * duration) / (duration + lastDuration);
accumVy = (accumVy * lastDuration + vy * duration) / (duration + lastDuration);
lastDuration = duration;
samplesUsed += 1;
}
}
// Report velocity.
const VelocityTracker::Position& newestPosition = newestMovement.getPosition(id);
outEstimator->time = newestMovement.eventTime;
outEstimator->confidence = 1;
outEstimator->xCoeff[0] = newestPosition.x;
outEstimator->yCoeff[0] = newestPosition.y;
if (samplesUsed) {
outEstimator->xCoeff[1] = accumVx;
outEstimator->yCoeff[1] = accumVy;
outEstimator->degree = 1;
} else {
outEstimator->degree = 0;
}
return true;
}
// --- ImpulseVelocityTrackerStrategy ---
ImpulseVelocityTrackerStrategy::ImpulseVelocityTrackerStrategy() {
clear();
}
ImpulseVelocityTrackerStrategy::~ImpulseVelocityTrackerStrategy() {
}
void ImpulseVelocityTrackerStrategy::clear() {
mIndex = 0;
mMovements[0].idBits.clear();
}
void ImpulseVelocityTrackerStrategy::clearPointers(BitSet32 idBits) {
BitSet32 remainingIdBits(mMovements[mIndex].idBits.value & ~idBits.value);
mMovements[mIndex].idBits = remainingIdBits;
}
void ImpulseVelocityTrackerStrategy::addMovement(nsecs_t eventTime, BitSet32 idBits,
const VelocityTracker::Position* positions) {
if (++mIndex == HISTORY_SIZE) {
mIndex = 0;
}
Movement& movement = mMovements[mIndex];
movement.eventTime = eventTime;
movement.idBits = idBits;
uint32_t count = idBits.count();
for (uint32_t i = 0; i < count; i++) {
movement.positions[i] = positions[i];
}
}
/**
* Calculate the total impulse provided to the screen and the resulting velocity.
*
* The touchscreen is modeled as a physical object.
* Initial condition is discussed below, but for now suppose that v(t=0) = 0
*
* The kinetic energy of the object at the release is E=0.5*m*v^2
* Then vfinal = sqrt(2E/m). The goal is to calculate E.
*
* The kinetic energy at the release is equal to the total work done on the object by the finger.
* The total work W is the sum of all dW along the path.
*
* dW = F*dx, where dx is the piece of path traveled.
* Force is change of momentum over time, F = dp/dt = m dv/dt.
* Then substituting:
* dW = m (dv/dt) * dx = m * v * dv
*
* Summing along the path, we get:
* W = sum(dW) = sum(m * v * dv) = m * sum(v * dv)
* Since the mass stays constant, the equation for final velocity is:
* vfinal = sqrt(2*sum(v * dv))
*
* Here,
* dv : change of velocity = (v[i+1]-v[i])
* dx : change of distance = (x[i+1]-x[i])
* dt : change of time = (t[i+1]-t[i])
* v : instantaneous velocity = dx/dt
*
* The final formula is:
* vfinal = sqrt(2) * sqrt(sum((v[i]-v[i-1])*|v[i]|)) for all i
* The absolute value is needed to properly account for the sign. If the velocity over a
* particular segment descreases, then this indicates braking, which means that negative
* work was done. So for two positive, but decreasing, velocities, this contribution would be
* negative and will cause a smaller final velocity.
*
* Initial condition
* There are two ways to deal with initial condition:
* 1) Assume that v(0) = 0, which would mean that the screen is initially at rest.
* This is not entirely accurate. We are only taking the past X ms of touch data, where X is
* currently equal to 100. However, a touch event that created a fling probably lasted for longer
* than that, which would mean that the user has already been interacting with the touchscreen
* and it has probably already been moving.
* 2) Assume that the touchscreen has already been moving at a certain velocity, calculate this
* initial velocity and the equivalent energy, and start with this initial energy.
* Consider an example where we have the following data, consisting of 3 points:
* time: t0, t1, t2
* x : x0, x1, x2
* v : 0 , v1, v2
* Here is what will happen in each of these scenarios:
* 1) By directly applying the formula above with the v(0) = 0 boundary condition, we will get
* vfinal = sqrt(2*(|v1|*(v1-v0) + |v2|*(v2-v1))). This can be simplified since v0=0
* vfinal = sqrt(2*(|v1|*v1 + |v2|*(v2-v1))) = sqrt(2*(v1^2 + |v2|*(v2 - v1)))
* since velocity is a real number
* 2) If we treat the screen as already moving, then it must already have an energy (per mass)
* equal to 1/2*v1^2. Then the initial energy should be 1/2*v1*2, and only the second segment
* will contribute to the total kinetic energy (since we can effectively consider that v0=v1).
* This will give the following expression for the final velocity:
* vfinal = sqrt(2*(1/2*v1^2 + |v2|*(v2-v1)))
* This analysis can be generalized to an arbitrary number of samples.
*
*
* Comparing the two equations above, we see that the only mathematical difference
* is the factor of 1/2 in front of the first velocity term.
* This boundary condition would allow for the "proper" calculation of the case when all of the
* samples are equally spaced in time and distance, which should suggest a constant velocity.
*
* Note that approach 2) is sensitive to the proper ordering of the data in time, since
* the boundary condition must be applied to the oldest sample to be accurate.
*/
static float kineticEnergyToVelocity(float work) {
static constexpr float sqrt2 = 1.41421356237;
return (work < 0 ? -1.0 : 1.0) * sqrtf(fabsf(work)) * sqrt2;
}
static float calculateImpulseVelocity(const nsecs_t* t, const float* x, size_t count) {
// The input should be in reversed time order (most recent sample at index i=0)
// t[i] is in nanoseconds, but due to FP arithmetic, convert to seconds inside this function
static constexpr float SECONDS_PER_NANO = 1E-9;
if (count < 2) {
return 0; // if 0 or 1 points, velocity is zero
}
if (t[1] > t[0]) { // Algorithm will still work, but not perfectly
ALOGE("Samples provided to calculateImpulseVelocity in the wrong order");
}
if (count == 2) { // if 2 points, basic linear calculation
if (t[1] == t[0]) {
ALOGE("Events have identical time stamps t=%" PRId64 ", setting velocity = 0", t[0]);
return 0;
}
return (x[1] - x[0]) / (SECONDS_PER_NANO * (t[1] - t[0]));
}
// Guaranteed to have at least 3 points here
float work = 0;
for (size_t i = count - 1; i > 0 ; i--) { // start with the oldest sample and go forward in time
if (t[i] == t[i-1]) {
ALOGE("Events have identical time stamps t=%" PRId64 ", skipping sample", t[i]);
continue;
}
float vprev = kineticEnergyToVelocity(work); // v[i-1]
float vcurr = (x[i] - x[i-1]) / (SECONDS_PER_NANO * (t[i] - t[i-1])); // v[i]
work += (vcurr - vprev) * fabsf(vcurr);
if (i == count - 1) {
work *= 0.5; // initial condition, case 2) above
}
}
return kineticEnergyToVelocity(work);
}
bool ImpulseVelocityTrackerStrategy::getEstimator(uint32_t id,
VelocityTracker::Estimator* outEstimator) const {
outEstimator->clear();
// Iterate over movement samples in reverse time order and collect samples.
float x[HISTORY_SIZE];
float y[HISTORY_SIZE];
nsecs_t time[HISTORY_SIZE];
size_t m = 0; // number of points that will be used for fitting
size_t index = mIndex;
const Movement& newestMovement = mMovements[mIndex];
do {
const Movement& movement = mMovements[index];
if (!movement.idBits.hasBit(id)) {
break;
}
nsecs_t age = newestMovement.eventTime - movement.eventTime;
if (age > HORIZON) {
break;
}
const VelocityTracker::Position& position = movement.getPosition(id);
x[m] = position.x;
y[m] = position.y;
time[m] = movement.eventTime;
index = (index == 0 ? HISTORY_SIZE : index) - 1;
} while (++m < HISTORY_SIZE);
if (m == 0) {
return false; // no data
}
outEstimator->xCoeff[0] = 0;
outEstimator->yCoeff[0] = 0;
outEstimator->xCoeff[1] = calculateImpulseVelocity(time, x, m);
outEstimator->yCoeff[1] = calculateImpulseVelocity(time, y, m);
outEstimator->xCoeff[2] = 0;
outEstimator->yCoeff[2] = 0;
outEstimator->time = newestMovement.eventTime;
outEstimator->degree = 2; // similar results to 2nd degree fit
outEstimator->confidence = 1;
#if DEBUG_STRATEGY
ALOGD("velocity: (%f, %f)", outEstimator->xCoeff[1], outEstimator->yCoeff[1]);
#endif
return true;
}
} // namespace android