Google Git
Sign in
android / platform / frameworks / native / refs/heads/main / . / libs / input / VelocityTracker.cpp
blob: 613a0df040f340828342f510fe343bde71f38117 [file] [log] [blame]
/*
* 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 <android-base/logging.h>
#include <ftl/enum.h>
#include <inttypes.h>
#include <limits.h>
#include <math.h>
#include <array>
#include <optional>
#include <input/PrintTools.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;
// Seconds per nanosecond.
static const float SECONDS_PER_NANO = 1E-9;
// 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), mOverrideStrategy(strategy) {}
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();
if (isDifferentialAxis || mOverrideStrategy == VelocityTracker::Strategy::DEFAULT) {
// Do not allow overrides of strategies for differential axes, for now.
mConfiguredStrategies[axis] = createStrategy(DEFAULT_STRATEGY_BY_AXIS.at(axis),
/*deltaValues=*/isDifferentialAxis);
} else {
mConfiguredStrategies[axis] = createStrategy(mOverrideStrategy, /*deltaValues=*/false);
}
}
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;
}
LOG(FATAL) << "Invalid strategy: " << ftl::enum_string(strategy)
<< ", deltaValues = " << deltaValues;
return nullptr;
}
void VelocityTracker::clear() {
mCurrentPointerIdBits.clear();
mActivePointerId = std::nullopt;
mConfiguredStrategies.clear();
}
void VelocityTracker::clearPointer(int32_t pointerId) {
mCurrentPointerIdBits.clearBit(pointerId);
if (mActivePointerId && *mActivePointerId == pointerId) {
// The active pointer id is being removed. Mark it invalid and try to find a new one
// from the remaining pointers.
mActivePointerId = std::nullopt;
if (!mCurrentPointerIdBits.isEmpty()) {
mActivePointerId = mCurrentPointerIdBits.firstMarkedBit();
}
}
for (const auto& [_, strategy] : mConfiguredStrategies) {
strategy->clearPointer(pointerId);
}
}
void VelocityTracker::addMovement(nsecs_t eventTime, int32_t pointerId, int32_t axis,
float position) {
if (pointerId < 0 || pointerId > MAX_POINTER_ID) {
LOG(FATAL) << "Invalid pointer ID " << pointerId << " for axis "
<< MotionEvent::getLabel(axis);
}
if (mCurrentPointerIdBits.hasBit(pointerId) &&
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.markBit(pointerId);
if (!mActivePointerId) {
// Let this be the new active pointer if no active pointer is currently set
mActivePointerId = pointerId;
}
if (mConfiguredStrategies.find(axis) == mConfiguredStrategies.end()) {
configureStrategy(axis);
}
mConfiguredStrategies[axis]->addMovement(eventTime, pointerId, position);
if (DEBUG_VELOCITY) {
LOG(INFO) << "VelocityTracker: addMovement axis=" << MotionEvent::getLabel(axis)
<< ", eventTime=" << eventTime << ", pointerId=" << pointerId
<< ", activePointerId=" << toString(mActivePointerId) << ", position=" << position
<< ", velocity=" << toString(getVelocity(axis, pointerId));
}
}
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.
clearPointer(event.getPointerId(event.getActionIndex()));
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:
if (event.getFlags() & AMOTION_EVENT_FLAG_CANCELED) {
clearPointer(event.getPointerId(event.getActionIndex()));
return;
}
// Continue to ACTION_UP to ensure that the POINTER_STOPPED logic is triggered.
[[fallthrough]];
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;
case AMOTION_EVENT_ACTION_CANCEL: {
clear();
return;
}
default:
// Ignore all other actions.
return;
}
const size_t historySize = event.getHistorySize();
for (size_t h = 0; h <= historySize; h++) {
const nsecs_t eventTime = event.getHistoricalEventTime(h);
for (size_t i = 0; i < event.getPointerCount(); i++) {
if (event.isResampled(i, h)) {
continue; // skip resampled samples
}
const int32_t pointerId = event.getPointerId(i);
for (int32_t axis : axesToProcess) {
const float position = event.getHistoricalAxisValue(axis, i, h);
addMovement(eventTime, pointerId, axis, position);
}
}
}
}
std::optional<float> VelocityTracker::getVelocity(int32_t axis, int32_t pointerId) const {
const auto& it = mConfiguredStrategies.find(axis);
if (it != mConfiguredStrategies.end()) {
return it->second->getVelocity(pointerId);
}
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;
}
AccumulatingVelocityTrackerStrategy::AccumulatingVelocityTrackerStrategy(
nsecs_t horizonNanos, bool maintainHorizonDuringAdd)
: mHorizonNanos(horizonNanos), mMaintainHorizonDuringAdd(maintainHorizonDuringAdd) {}
void AccumulatingVelocityTrackerStrategy::clearPointer(int32_t pointerId) {
mMovements.erase(pointerId);
}
void AccumulatingVelocityTrackerStrategy::addMovement(nsecs_t eventTime, int32_t pointerId,
float position) {
auto [ringBufferIt, _] = mMovements.try_emplace(pointerId, HISTORY_SIZE);
RingBuffer<Movement>& movements = ringBufferIt->second;
const size_t size = movements.size();
if (size != 0 && movements[size - 1].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 (i.e. pop out the last element, and insert the updated movement).
// We only compare against the last value, as it is likely that addMovement is called
// in chronological order as events occur.
movements.popBack();
}
movements.pushBack({eventTime, position});
// Clear movements that do not fall within `mHorizonNanos` of the latest movement.
// Note that, if in the future we decide to use more movements (i.e. increase HISTORY_SIZE),
// we can consider making this step binary-search based, which will give us some improvement.
if (mMaintainHorizonDuringAdd) {
while (eventTime - movements[0].eventTime > mHorizonNanos) {
movements.popFront();
}
}
}
// --- LeastSquaresVelocityTrackerStrategy ---
LeastSquaresVelocityTrackerStrategy::LeastSquaresVelocityTrackerStrategy(uint32_t degree,
Weighting weighting)
: AccumulatingVelocityTrackerStrategy(HORIZON /*horizonNanos*/,
true /*maintainHorizonDuringAdd*/),
mDegree(degree),
mWeighting(weighting) {}
LeastSquaresVelocityTrackerStrategy::~LeastSquaresVelocityTrackerStrategy() {}
/**
* 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 std::optional<float> solveLeastSquares(const std::vector<float>& x,
const std::vector<float>& y,
const std::vector<float>& w, uint32_t n) {
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, /*rowMajor=*/false).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 {};
}
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, /*rowMajor=*/false).c_str());
ALOGD(" - r=%s", matrixToString(&r[0][0], n, n, /*rowMajor=*/true).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, /*rowMajor=*/false).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];
}
std::array<float, VelocityTracker::MAX_DEGREE + 1> outB;
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.data(), 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;
if (DEBUG_STRATEGY) {
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;
}
ALOGD(" - sserr=%f", sserr);
ALOGD(" - sstot=%f", sstot);
}
return outB[1];
}
/*
* Optimized unweighted second-order least squares fit. About 2x speed improvement compared to
* the default implementation
*/
std::optional<float> LeastSquaresVelocityTrackerStrategy::solveUnweightedLeastSquaresDeg2(
const RingBuffer<Movement>& movements) const {
// Solving y = a*x^2 + b*x + c, where
// - "x" is age (i.e. duration since latest movement) of the movemnets
// - "y" is positions of the movements.
float sxi = 0, sxiyi = 0, syi = 0, sxi2 = 0, sxi3 = 0, sxi2yi = 0, sxi4 = 0;
const size_t count = movements.size();
const Movement& newestMovement = movements[count - 1];
for (size_t i = 0; i < count; i++) {
const Movement& movement = movements[i];
nsecs_t age = newestMovement.eventTime - movement.eventTime;
float xi = -age * SECONDS_PER_NANO;
float yi = movement.position;
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;
}
return (Sxy * Sx2x2 - Sx2y * Sxx2) / denominator;
}
std::optional<float> LeastSquaresVelocityTrackerStrategy::getVelocity(int32_t pointerId) const {
const auto movementIt = mMovements.find(pointerId);
if (movementIt == mMovements.end()) {
return std::nullopt; // no data
}
const RingBuffer<Movement>& movements = movementIt->second;
const size_t size = movements.size();
if (size == 0) {
return std::nullopt; // no data
}
uint32_t degree = mDegree;
if (degree > size - 1) {
degree = size - 1;
}
if (degree <= 0) {
return std::nullopt;
}
if (degree == 2 && mWeighting == Weighting::NONE) {
// Optimize unweighted, quadratic polynomial fit
return solveUnweightedLeastSquaresDeg2(movements);
}
// Iterate over movement samples in reverse time order and collect samples.
std::vector<float> positions;
std::vector<float> w;
std::vector<float> time;
const Movement& newestMovement = movements[size - 1];
for (ssize_t i = size - 1; i >= 0; i--) {
const Movement& movement = movements[i];
nsecs_t age = newestMovement.eventTime - movement.eventTime;
positions.push_back(movement.position);
w.push_back(chooseWeight(pointerId, i));
time.push_back(-age * 0.000000001f);
}
// General case for an Nth degree polynomial fit
return solveLeastSquares(time, positions, w, degree + 1);
}
float LeastSquaresVelocityTrackerStrategy::chooseWeight(int32_t pointerId, uint32_t index) const {
const RingBuffer<Movement>& movements = mMovements.at(pointerId);
const size_t size = movements.size();
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 == size - 1) {
return 1.0f;
}
float deltaMillis =
(movements[index + 1].eventTime - movements[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 =
(movements[size - 1].eventTime - movements[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 =
(movements[size - 1].eventTime - movements[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:
return 1.0f;
}
}
// --- IntegratingVelocityTrackerStrategy ---
IntegratingVelocityTrackerStrategy::IntegratingVelocityTrackerStrategy(uint32_t degree) :
mDegree(degree) {
}
IntegratingVelocityTrackerStrategy::~IntegratingVelocityTrackerStrategy() {
}
void IntegratingVelocityTrackerStrategy::clearPointer(int32_t pointerId) {
mPointerIdBits.clearBit(pointerId);
}
void IntegratingVelocityTrackerStrategy::addMovement(nsecs_t eventTime, int32_t pointerId,
float position) {
State& state = mPointerState[pointerId];
if (mPointerIdBits.hasBit(pointerId)) {
updateState(state, eventTime, position);
} else {
initState(state, eventTime, position);
}
mPointerIdBits.markBit(pointerId);
}
std::optional<float> IntegratingVelocityTrackerStrategy::getVelocity(int32_t pointerId) const {
if (mPointerIdBits.hasBit(pointerId)) {
return mPointerState[pointerId].vel;
}
return std::nullopt;
}
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;
}
// --- LegacyVelocityTrackerStrategy ---
LegacyVelocityTrackerStrategy::LegacyVelocityTrackerStrategy()
: AccumulatingVelocityTrackerStrategy(HORIZON /*horizonNanos*/,
false /*maintainHorizonDuringAdd*/) {}
LegacyVelocityTrackerStrategy::~LegacyVelocityTrackerStrategy() {
}
std::optional<float> LegacyVelocityTrackerStrategy::getVelocity(int32_t pointerId) const {
const auto movementIt = mMovements.find(pointerId);
if (movementIt == mMovements.end()) {
return std::nullopt; // no data
}
const RingBuffer<Movement>& movements = movementIt->second;
const size_t size = movements.size();
if (size == 0) {
return std::nullopt; // no data
}
const Movement& newestMovement = movements[size - 1];
// Find the oldest sample that contains the pointer and that is not older than HORIZON.
nsecs_t minTime = newestMovement.eventTime - HORIZON;
uint32_t oldestIndex = size - 1;
for (ssize_t i = size - 1; i >= 0; i--) {
const Movement& nextOldestMovement = movements[i];
if (nextOldestMovement.eventTime < minTime) {
break;
}
oldestIndex = i;
}
// 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 samplesUsed = 0;
const Movement& oldestMovement = movements[oldestIndex];
float oldestPosition = oldestMovement.position;
nsecs_t lastDuration = 0;
for (size_t i = oldestIndex; i < size; i++) {
const Movement& movement = movements[i];
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.position;
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;
}
}
if (samplesUsed) {
return accumV;
}
return std::nullopt;
}
// --- ImpulseVelocityTrackerStrategy ---
ImpulseVelocityTrackerStrategy::ImpulseVelocityTrackerStrategy(bool deltaValues)
: AccumulatingVelocityTrackerStrategy(HORIZON /*horizonNanos*/,
true /*maintainHorizonDuringAdd*/),
mDeltaValues(deltaValues) {}
ImpulseVelocityTrackerStrategy::~ImpulseVelocityTrackerStrategy() {
}
/**
* 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;
}
std::optional<float> ImpulseVelocityTrackerStrategy::getVelocity(int32_t pointerId) const {
const auto movementIt = mMovements.find(pointerId);
if (movementIt == mMovements.end()) {
return std::nullopt; // no data
}
const RingBuffer<Movement>& movements = movementIt->second;
const size_t size = movements.size();
if (size == 0) {
return std::nullopt; // no data
}
float work = 0;
for (size_t i = 0; i < size - 1; i++) {
const Movement& mvt = movements[i];
const Movement& nextMvt = movements[i + 1];
float vprev = kineticEnergyToVelocity(work);
float delta = mDeltaValues ? nextMvt.position : nextMvt.position - mvt.position;
float vcurr = delta / (SECONDS_PER_NANO * (nextMvt.eventTime - mvt.eventTime));
work += (vcurr - vprev) * fabsf(vcurr);
if (i == 0) {
work *= 0.5; // initial condition, case 2) above
}
}
const float velocity = kineticEnergyToVelocity(work);
ALOGD_IF(DEBUG_STRATEGY, "velocity: %.1f", velocity);
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);
for (size_t i = 0; i < size; i++) {
const Movement& mvt = movements[i];
lsq2.addMovement(mvt.eventTime, pointerId, AMOTION_EVENT_AXIS_X, mvt.position);
}
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 velocity;
}
} // namespace android