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gerrit.omnirom.org / android_frameworks_native / 78c84d62bdc4ebe288c7cfaf6ddf9febc47d227d / . / libs / input / VelocityTracker.cpp
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/*
* 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"
#include <array>
#include <inttypes.h>
#include <limits.h>
#include <math.h>
#include <optional>
#include <android-base/stringprintf.h>
#include <input/VelocityTracker.h>
#include <utils/BitSet.h>
#include <utils/Timers.h>
using std::literals::chrono_literals::operator""ms;
namespace android {
/**
* Log debug messages about velocity tracking.
* Enable this via "adb shell setprop log.tag.VelocityTrackerVelocity DEBUG" (requires restart)
*/
const bool DEBUG_VELOCITY =
__android_log_is_loggable(ANDROID_LOG_DEBUG, LOG_TAG "Velocity", ANDROID_LOG_INFO);
/**
* Log debug messages about the progress of the algorithm itself.
* Enable this via "adb shell setprop log.tag.VelocityTrackerStrategy DEBUG" (requires restart)
*/
const bool DEBUG_STRATEGY =
__android_log_is_loggable(ANDROID_LOG_DEBUG, LOG_TAG "Strategy", ANDROID_LOG_INFO);
/**
* Log debug messages about the 'impulse' strategy.
* Enable this via "adb shell setprop log.tag.VelocityTrackerImpulse DEBUG" (requires restart)
*/
const bool DEBUG_IMPULSE =
__android_log_is_loggable(ANDROID_LOG_DEBUG, LOG_TAG "Impulse", ANDROID_LOG_INFO);
// Nanoseconds per milliseconds.
static const nsecs_t NANOS_PER_MS = 1000000;
// All axes supported for velocity tracking, mapped to their default strategies.
// Although other strategies are available for testing and comparison purposes,
// the default strategy is the one 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.
static const std::map<int32_t, VelocityTracker::Strategy> DEFAULT_STRATEGY_BY_AXIS =
{{AMOTION_EVENT_AXIS_X, VelocityTracker::Strategy::LSQ2},
{AMOTION_EVENT_AXIS_Y, VelocityTracker::Strategy::LSQ2},
{AMOTION_EVENT_AXIS_SCROLL, VelocityTracker::Strategy::IMPULSE}};
// Axes specifying location on a 2D plane (i.e. X and Y).
static const std::set<int32_t> PLANAR_AXES = {AMOTION_EVENT_AXIS_X, AMOTION_EVENT_AXIS_Y};
// Axes whose motion values are differential values (i.e. deltas).
static const std::set<int32_t> DIFFERENTIAL_AXES = {AMOTION_EVENT_AXIS_SCROLL};
// 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 std::chrono::duration ASSUME_POINTER_STOPPED_TIME = 40ms;
static std::string toString(std::chrono::nanoseconds t) {
std::stringstream stream;
stream.precision(1);
stream << std::fixed << std::chrono::duration<float, std::milli>(t).count() << " ms";
return stream.str();
}
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);
}
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;
}
static std::string vectorToString(const std::vector<float>& v) {
return vectorToString(v.data(), v.size());
}
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;
}
// --- VelocityTracker ---
VelocityTracker::VelocityTracker(const Strategy strategy)
: mLastEventTime(0),
mCurrentPointerIdBits(0),
mActivePointerId(-1),
mOverrideStrategy(strategy) {}
VelocityTracker::~VelocityTracker() {
}
bool VelocityTracker::isAxisSupported(int32_t axis) {
return DEFAULT_STRATEGY_BY_AXIS.find(axis) != DEFAULT_STRATEGY_BY_AXIS.end();
}
void VelocityTracker::configureStrategy(int32_t axis) {
const bool isDifferentialAxis = DIFFERENTIAL_AXES.find(axis) != DIFFERENTIAL_AXES.end();
std::unique_ptr<VelocityTrackerStrategy> createdStrategy;
if (mOverrideStrategy != VelocityTracker::Strategy::DEFAULT) {
createdStrategy = createStrategy(mOverrideStrategy, isDifferentialAxis /* deltaValues */);
} else {
createdStrategy = createStrategy(DEFAULT_STRATEGY_BY_AXIS.at(axis),
isDifferentialAxis /* deltaValues */);
}
LOG_ALWAYS_FATAL_IF(createdStrategy == nullptr,
"Could not create velocity tracker strategy for axis '%" PRId32 "'!", axis);
mConfiguredStrategies[axis] = std::move(createdStrategy);
}
std::unique_ptr<VelocityTrackerStrategy> VelocityTracker::createStrategy(
VelocityTracker::Strategy strategy, bool deltaValues) {
switch (strategy) {
case VelocityTracker::Strategy::IMPULSE:
ALOGI_IF(DEBUG_STRATEGY, "Initializing impulse strategy");
return std::make_unique<ImpulseVelocityTrackerStrategy>(deltaValues);
case VelocityTracker::Strategy::LSQ1:
return std::make_unique<LeastSquaresVelocityTrackerStrategy>(1);
case VelocityTracker::Strategy::LSQ2:
ALOGI_IF(DEBUG_STRATEGY && !DEBUG_IMPULSE, "Initializing lsq2 strategy");
return std::make_unique<LeastSquaresVelocityTrackerStrategy>(2);
case VelocityTracker::Strategy::LSQ3:
return std::make_unique<LeastSquaresVelocityTrackerStrategy>(3);
case VelocityTracker::Strategy::WLSQ2_DELTA:
return std::make_unique<
LeastSquaresVelocityTrackerStrategy>(2,
LeastSquaresVelocityTrackerStrategy::
WEIGHTING_DELTA);
case VelocityTracker::Strategy::WLSQ2_CENTRAL:
return std::make_unique<
LeastSquaresVelocityTrackerStrategy>(2,
LeastSquaresVelocityTrackerStrategy::
WEIGHTING_CENTRAL);
case VelocityTracker::Strategy::WLSQ2_RECENT:
return std::make_unique<
LeastSquaresVelocityTrackerStrategy>(2,
LeastSquaresVelocityTrackerStrategy::
WEIGHTING_RECENT);
case VelocityTracker::Strategy::INT1:
return std::make_unique<IntegratingVelocityTrackerStrategy>(1);
case VelocityTracker::Strategy::INT2:
return std::make_unique<IntegratingVelocityTrackerStrategy>(2);
case VelocityTracker::Strategy::LEGACY:
return std::make_unique<LegacyVelocityTrackerStrategy>();
default:
break;
}
return nullptr;
}
void VelocityTracker::clear() {
mCurrentPointerIdBits.clear();
mActivePointerId = -1;
mConfiguredStrategies.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;
}
for (const auto& [_, strategy] : mConfiguredStrategies) {
strategy->clearPointers(idBits);
}
}
void VelocityTracker::addMovement(nsecs_t eventTime, BitSet32 idBits,
const std::map<int32_t /*axis*/, std::vector<float>>& positions) {
while (idBits.count() > MAX_POINTERS) {
idBits.clearLastMarkedBit();
}
if ((mCurrentPointerIdBits.value & idBits.value) &&
std::chrono::nanoseconds(eventTime - mLastEventTime) > ASSUME_POINTER_STOPPED_TIME) {
ALOGD_IF(DEBUG_VELOCITY, "VelocityTracker: stopped for %s, clearing state.",
toString(std::chrono::nanoseconds(eventTime - mLastEventTime)).c_str());
// We have not received any movements for too long. Assume that all pointers
// have stopped.
mConfiguredStrategies.clear();
}
mLastEventTime = eventTime;
mCurrentPointerIdBits = idBits;
if (mActivePointerId < 0 || !idBits.hasBit(mActivePointerId)) {
mActivePointerId = idBits.isEmpty() ? -1 : idBits.firstMarkedBit();
}
for (const auto& [axis, positionValues] : positions) {
LOG_ALWAYS_FATAL_IF(idBits.count() != positionValues.size(),
"Mismatching number of pointers, idBits=%" PRIu32 ", positions=%zu",
idBits.count(), positionValues.size());
if (mConfiguredStrategies.find(axis) == mConfiguredStrategies.end()) {
configureStrategy(axis);
}
mConfiguredStrategies[axis]->addMovement(eventTime, idBits, positionValues);
}
if (DEBUG_VELOCITY) {
ALOGD("VelocityTracker: addMovement eventTime=%" PRId64
", idBits=0x%08x, activePointerId=%d",
eventTime, idBits.value, mActivePointerId);
for (const auto& positionsEntry : positions) {
for (BitSet32 iterBits(idBits); !iterBits.isEmpty();) {
uint32_t id = iterBits.firstMarkedBit();
uint32_t index = idBits.getIndexOfBit(id);
iterBits.clearBit(id);
Estimator estimator;
getEstimator(positionsEntry.first, id, &estimator);
ALOGD(" %d: axis=%d, position=%0.3f, "
"estimator (degree=%d, coeff=%s, confidence=%f)",
id, positionsEntry.first, positionsEntry.second[index], int(estimator.degree),
vectorToString(estimator.coeff, estimator.degree + 1).c_str(),
estimator.confidence);
}
}
}
}
void VelocityTracker::addMovement(const MotionEvent* event) {
// Stores data about which axes to process based on the incoming motion event.
std::set<int32_t> axesToProcess;
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();
axesToProcess.insert(PLANAR_AXES.begin(), PLANAR_AXES.end());
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);
axesToProcess.insert(PLANAR_AXES.begin(), PLANAR_AXES.end());
break;
}
case AMOTION_EVENT_ACTION_MOVE:
case AMOTION_EVENT_ACTION_HOVER_MOVE:
axesToProcess.insert(PLANAR_AXES.begin(), PLANAR_AXES.end());
break;
case AMOTION_EVENT_ACTION_POINTER_UP:
case AMOTION_EVENT_ACTION_UP: {
std::chrono::nanoseconds delaySinceLastEvent(event->getEventTime() - mLastEventTime);
if (delaySinceLastEvent > ASSUME_POINTER_STOPPED_TIME) {
ALOGD_IF(DEBUG_VELOCITY,
"VelocityTracker: stopped for %s, clearing state upon pointer liftoff.",
toString(delaySinceLastEvent).c_str());
// We have not received any movements for too long. Assume that all pointers
// have stopped.
for (int32_t axis : PLANAR_AXES) {
mConfiguredStrategies.erase(axis);
}
}
// These 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;
}
case AMOTION_EVENT_ACTION_SCROLL:
axesToProcess.insert(AMOTION_EVENT_AXIS_SCROLL);
break;
default:
// Ignore all other actions.
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));
}
std::map<int32_t, std::vector<float>> positions;
for (int32_t axis : axesToProcess) {
positions[axis].resize(pointerCount);
}
size_t historySize = event->getHistorySize();
for (size_t h = 0; h <= historySize; h++) {
nsecs_t eventTime = event->getHistoricalEventTime(h);
for (int32_t axis : axesToProcess) {
for (size_t i = 0; i < pointerCount; i++) {
positions[axis][pointerIndex[i]] = event->getHistoricalAxisValue(axis, i, h);
}
}
addMovement(eventTime, idBits, positions);
}
}
std::optional<float> VelocityTracker::getVelocity(int32_t axis, uint32_t id) const {
Estimator estimator;
bool validVelocity = getEstimator(axis, id, &estimator) && estimator.degree >= 1;
if (validVelocity) {
return estimator.coeff[1];
}
return {};
}
VelocityTracker::ComputedVelocity VelocityTracker::getComputedVelocity(int32_t units,
float maxVelocity) {
ComputedVelocity computedVelocity;
for (const auto& [axis, _] : mConfiguredStrategies) {
BitSet32 copyIdBits = BitSet32(mCurrentPointerIdBits);
while (!copyIdBits.isEmpty()) {
uint32_t id = copyIdBits.clearFirstMarkedBit();
std::optional<float> velocity = getVelocity(axis, id);
if (velocity) {
float adjustedVelocity =
std::clamp(*velocity * units / 1000, -maxVelocity, maxVelocity);
computedVelocity.addVelocity(axis, id, adjustedVelocity);
}
}
}
return computedVelocity;
}
bool VelocityTracker::getEstimator(int32_t axis, uint32_t id, Estimator* outEstimator) const {
const auto& it = mConfiguredStrategies.find(axis);
if (it == mConfiguredStrategies.end()) {
return false;
}
return it->second->getEstimator(id, outEstimator);
}
// --- LeastSquaresVelocityTrackerStrategy ---
LeastSquaresVelocityTrackerStrategy::LeastSquaresVelocityTrackerStrategy(uint32_t degree,
Weighting weighting)
: mDegree(degree), mWeighting(weighting), mIndex(0) {}
LeastSquaresVelocityTrackerStrategy::~LeastSquaresVelocityTrackerStrategy() {
}
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 std::vector<float>& positions) {
if (mMovements[mIndex].eventTime != eventTime) {
// When ACTION_POINTER_DOWN happens, we will first receive ACTION_MOVE with the coordinates
// of the existing pointers, and then ACTION_POINTER_DOWN with the coordinates that include
// the new pointer. If the eventtimes for both events are identical, just update the data
// for this time.
// We only compare against the last value, as it is likely that addMovement is called
// in chronological order as events occur.
mIndex++;
}
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 std::vector<float>& x, const std::vector<float>& y,
const std::vector<float>& w, uint32_t n, float* outB, float* outDet) {
const size_t m = x.size();
ALOGD_IF(DEBUG_STRATEGY, "solveLeastSquares: m=%d, n=%d, x=%s, y=%s, w=%s", int(m), int(n),
vectorToString(x).c_str(), vectorToString(y).c_str(), vectorToString(w).c_str());
LOG_ALWAYS_FATAL_IF(m != y.size() || m != w.size(), "Mismatched vector sizes");
// 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];
}
}
ALOGD_IF(DEBUG_STRATEGY, " - a=%s",
matrixToString(&a[0][0], m, n, false /*rowMajor*/).c_str());
// 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
ALOGD_IF(DEBUG_STRATEGY, " - no solution, norm=%f", norm);
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());
}
// 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];
}
ALOGD_IF(DEBUG_STRATEGY, " - b=%s", vectorToString(outB, n).c_str());
// 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;
ALOGD_IF(DEBUG_STRATEGY, " - sserr=%f", sserr);
ALOGD_IF(DEBUG_STRATEGY, " - sstot=%f", sstot);
ALOGD_IF(DEBUG_STRATEGY, " - det=%f", *outDet);
return true;
}
/*
* Optimized unweighted second-order least squares fit. About 2x speed improvement compared to
* the default implementation
*/
static std::optional<std::array<float, 3>> solveUnweightedLeastSquaresDeg2(
const std::vector<float>& x, const std::vector<float>& y) {
const size_t count = x.size();
LOG_ALWAYS_FATAL_IF(count != y.size(), "Mismatching array sizes");
// Solving y = a*x^2 + b*x + c
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 xiyi = xi*yi;
float xi2yi = xi2*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 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 std::nullopt;
}
// Compute a
float numerator = Sx2y*Sxx - Sxy*Sxx2;
float a = numerator / denominator;
// Compute b
numerator = Sxy*Sx2x2 - Sx2y*Sxx2;
float b = numerator / denominator;
// Compute c
float c = syi/count - b * sxi/count - a * sxi2/count;
return std::make_optional(std::array<float, 3>({c, b, a}));
}
bool LeastSquaresVelocityTrackerStrategy::getEstimator(uint32_t id,
VelocityTracker::Estimator* outEstimator) const {
outEstimator->clear();
// Iterate over movement samples in reverse time order and collect samples.
std::vector<float> positions;
std::vector<float> w;
std::vector<float> time;
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;
}
positions.push_back(movement.getPosition(id));
w.push_back(chooseWeight(index));
time.push_back(-age * 0.000000001f);
index = (index == 0 ? HISTORY_SIZE : index) - 1;
} while (positions.size() < HISTORY_SIZE);
const size_t m = positions.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 == 2 && mWeighting == WEIGHTING_NONE) {
// Optimize unweighted, quadratic polynomial fit
std::optional<std::array<float, 3>> coeff =
solveUnweightedLeastSquaresDeg2(time, positions);
if (coeff) {
outEstimator->time = newestMovement.eventTime;
outEstimator->degree = 2;
outEstimator->confidence = 1;
for (size_t i = 0; i <= outEstimator->degree; i++) {
outEstimator->coeff[i] = (*coeff)[i];
}
return true;
}
} else if (degree >= 1) {
// General case for an Nth degree polynomial fit
float det;
uint32_t n = degree + 1;
if (solveLeastSquares(time, positions, w, n, outEstimator->coeff, &det)) {
outEstimator->time = newestMovement.eventTime;
outEstimator->degree = degree;
outEstimator->confidence = det;
ALOGD_IF(DEBUG_STRATEGY, "estimate: degree=%d, coeff=%s, confidence=%f",
int(outEstimator->degree), vectorToString(outEstimator->coeff, n).c_str(),
outEstimator->confidence);
return true;
}
}
// No velocity data available for this pointer, but we do have its current position.
outEstimator->coeff[0] = positions[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::clearPointers(BitSet32 idBits) {
mPointerIdBits.value &= ~idBits.value;
}
void IntegratingVelocityTrackerStrategy::addMovement(nsecs_t eventTime, BitSet32 idBits,
const std::vector<float>& positions) {
uint32_t index = 0;
for (BitSet32 iterIdBits(idBits); !iterIdBits.isEmpty();) {
uint32_t id = iterIdBits.clearFirstMarkedBit();
State& state = mPointerState[id];
const float position = positions[index++];
if (mPointerIdBits.hasBit(id)) {
updateState(state, eventTime, position);
} else {
initState(state, eventTime, position);
}
}
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 pos) const {
state.updateTime = eventTime;
state.degree = 0;
state.pos = pos;
state.accel = 0;
state.vel = 0;
}
void IntegratingVelocityTrackerStrategy::updateState(State& state, nsecs_t eventTime,
float pos) 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 vel = (pos - state.pos) / dt;
if (state.degree == 0) {
state.vel = vel;
state.degree = 1;
} else {
float alpha = dt / (FILTER_TIME_CONSTANT + dt);
if (mDegree == 1) {
state.vel += (vel - state.vel) * alpha;
} else {
float accel = (vel - state.vel) / dt;
if (state.degree == 1) {
state.accel = accel;
state.degree = 2;
} else {
state.accel += (accel - state.accel) * alpha;
}
state.vel += (state.accel * dt) * alpha;
}
}
state.pos = pos;
}
void IntegratingVelocityTrackerStrategy::populateEstimator(const State& state,
VelocityTracker::Estimator* outEstimator) const {
outEstimator->time = state.updateTime;
outEstimator->confidence = 1.0f;
outEstimator->degree = state.degree;
outEstimator->coeff[0] = state.pos;
outEstimator->coeff[1] = state.vel;
outEstimator->coeff[2] = state.accel / 2;
}
// --- LegacyVelocityTrackerStrategy ---
LegacyVelocityTrackerStrategy::LegacyVelocityTrackerStrategy() : mIndex(0) {}
LegacyVelocityTrackerStrategy::~LegacyVelocityTrackerStrategy() {
}
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 std::vector<float>& 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 accumV = 0;
uint32_t index = oldestIndex;
uint32_t samplesUsed = 0;
const Movement& oldestMovement = mMovements[oldestIndex];
float 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) {
float position = movement.getPosition(id);
float scale = 1000000000.0f / duration; // one over time delta in seconds
float v = (position - oldestPosition) * scale;
accumV = (accumV * lastDuration + v * duration) / (duration + lastDuration);
lastDuration = duration;
samplesUsed += 1;
}
}
// Report velocity.
float newestPosition = newestMovement.getPosition(id);
outEstimator->time = newestMovement.eventTime;
outEstimator->confidence = 1;
outEstimator->coeff[0] = newestPosition;
if (samplesUsed) {
outEstimator->coeff[1] = accumV;
outEstimator->degree = 1;
} else {
outEstimator->degree = 0;
}
return true;
}
// --- ImpulseVelocityTrackerStrategy ---
ImpulseVelocityTrackerStrategy::ImpulseVelocityTrackerStrategy(bool deltaValues)
: mDeltaValues(deltaValues), mIndex(0) {}
ImpulseVelocityTrackerStrategy::~ImpulseVelocityTrackerStrategy() {
}
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 std::vector<float>& positions) {
if (mMovements[mIndex].eventTime != eventTime) {
// When ACTION_POINTER_DOWN happens, we will first receive ACTION_MOVE with the coordinates
// of the existing pointers, and then ACTION_POINTER_DOWN with the coordinates that include
// the new pointer. If the eventtimes for both events are identical, just update the data
// for this time.
// We only compare against the last value, as it is likely that addMovement is called
// in chronological order as events occur.
mIndex++;
}
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,
bool deltaValues) {
// 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 the data values are delta values, we do not have to calculate deltas here.
// We can use the delta values directly, along with the calculated time deltas.
// Since the data value input is in reversed time order:
// [a] for non-delta inputs, instantenous velocity = (x[i] - x[i-1])/(t[i] - t[i-1])
// [b] for delta inputs, instantenous velocity = -x[i-1]/(t[i] - t[i - 1])
// e.g., let the non-delta values are: V = [2, 3, 7], the equivalent deltas are D = [2, 1, 4].
// Since the input is in reversed time order, the input values for this function would be
// V'=[7, 3, 2] and D'=[4, 1, 2] for the non-delta and delta values, respectively.
//
// The equivalent of {(V'[2] - V'[1]) = 2 - 3 = -1} would be {-D'[1] = -1}
// Similarly, the equivalent of {(V'[1] - V'[0]) = 3 - 7 = -4} would be {-D'[0] = -4}
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;
}
const float deltaX = deltaValues ? -x[0] : x[1] - x[0];
return deltaX / (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]
const float deltaX = deltaValues ? -x[i-1] : x[i] - x[i-1];
float vcurr = deltaX / (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 positions[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;
}
positions[m] = movement.getPosition(id);
time[m] = movement.eventTime;
index = (index == 0 ? HISTORY_SIZE : index) - 1;
} while (++m < HISTORY_SIZE);
if (m == 0) {
return false; // no data
}
outEstimator->coeff[0] = 0;
outEstimator->coeff[1] = calculateImpulseVelocity(time, positions, m, mDeltaValues);
outEstimator->coeff[2] = 0;
outEstimator->time = newestMovement.eventTime;
outEstimator->degree = 2; // similar results to 2nd degree fit
outEstimator->confidence = 1;
ALOGD_IF(DEBUG_STRATEGY, "velocity: %.1f", outEstimator->coeff[1]);
if (DEBUG_IMPULSE) {
// TODO(b/134179997): delete this block once the switch to 'impulse' is complete.
// Calculate the lsq2 velocity for the same inputs to allow runtime comparisons.
// X axis chosen arbitrarily for velocity comparisons.
VelocityTracker lsq2(VelocityTracker::Strategy::LSQ2);
BitSet32 idBits;
const uint32_t pointerId = 0;
idBits.markBit(pointerId);
for (ssize_t i = m - 1; i >= 0; i--) {
lsq2.addMovement(time[i], idBits, {{AMOTION_EVENT_AXIS_X, {positions[i]}}});
}
std::optional<float> v = lsq2.getVelocity(AMOTION_EVENT_AXIS_X, pointerId);
if (v) {
ALOGD("lsq2 velocity: %.1f", *v);
} else {
ALOGD("lsq2 velocity: could not compute velocity");
}
}
return true;
}
} // namespace android