Source code
Revision control
Copy as Markdown
Other Tools
/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=8 sts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
#include "AndroidVelocityTracker.h"
#include "mozilla/StaticPrefs_apz.h"
namespace mozilla {
namespace layers {
// This velocity tracker implementation was adapted from Chromium's
// second-order unweighted least-squares velocity tracker strategy
// Threshold between position updates for determining that a pointer has
// stopped moving. Some input devices do not send 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 TimeDuration kAssumePointerMoveStoppedTime =
TimeDuration::FromMilliseconds(40);
// The degree of the approximation.
static const uint8_t kDegree = 2;
// The degree of the polynomial used in SolveLeastSquares().
// This should be the degree of the approximation plus one.
static const uint8_t kPolyDegree = kDegree + 1;
// Maximum size of position history.
static const uint8_t kHistorySize = 20;
AndroidVelocityTracker::AndroidVelocityTracker() {}
void AndroidVelocityTracker::StartTracking(ParentLayerCoord aPos,
TimeStamp aTimestamp) {
Clear();
mHistory.AppendElement(std::make_pair(aTimestamp, aPos));
mLastEventTime = aTimestamp;
}
Maybe<float> AndroidVelocityTracker::AddPosition(ParentLayerCoord aPos,
TimeStamp aTimestamp) {
if ((aTimestamp - mLastEventTime) >= kAssumePointerMoveStoppedTime) {
Clear();
}
if ((aTimestamp - mLastEventTime).ToMilliseconds() < 1.0) {
// If we get a sample within a millisecond of the previous one,
// just update its position. Two samples in the history with the
// same timestamp can lead to things like infinite velocities.
if (mHistory.Length() > 0) {
mHistory[mHistory.Length() - 1].second = aPos;
}
} else {
mHistory.AppendElement(std::make_pair(aTimestamp, aPos));
if (mHistory.Length() > kHistorySize) {
mHistory.RemoveElementAt(0);
}
}
mLastEventTime = aTimestamp;
if (mHistory.Length() < 2) {
return Nothing();
}
auto start = mHistory[mHistory.Length() - 2];
auto end = mHistory[mHistory.Length() - 1];
auto velocity =
(end.second - start.second) / (end.first - start.first).ToMilliseconds();
// The velocity needs to be negated because the positions represent
// touch positions, and the direction of scrolling is opposite to the
// direction of the finger's movement.
return Some(-velocity);
}
static float VectorDot(const float* a, const float* b, uint32_t m) {
float r = 0;
while (m--) {
r += *(a++) * *(b++);
}
return r;
}
static float VectorNorm(const float* a, uint32_t m) {
float r = 0;
while (m--) {
float t = *(a++);
r += t * t;
}
return sqrtf(r);
}
/**
* 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.
*
*/
static bool SolveLeastSquares(const float* x, const float* y, const float* w,
uint32_t m, uint32_t n, float* out_b) {
// MSVC does not support variable-length arrays (used by the original Android
// implementation of this function).
#if defined(COMPILER_MSVC)
const uint32_t M_ARRAY_LENGTH = VelocityTracker::kHistorySize;
const uint32_t N_ARRAY_LENGTH = VelocityTracker::kPolyDegree;
DCHECK_LE(m, M_ARRAY_LENGTH);
DCHECK_LE(n, N_ARRAY_LENGTH);
#else
const uint32_t M_ARRAY_LENGTH = m;
const uint32_t N_ARRAY_LENGTH = n;
#endif
// Expand the X vector to a matrix A, pre-multiplied by the weights.
float a[N_ARRAY_LENGTH][M_ARRAY_LENGTH]; // 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];
}
}
// Apply the Gram-Schmidt process to A to obtain its QR decomposition.
// Orthonormal basis, column-major order.
float q[N_ARRAY_LENGTH][M_ARRAY_LENGTH];
// Upper triangular matrix, row-major order.
float r[N_ARRAY_LENGTH][N_ARRAY_LENGTH];
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
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);
}
}
// 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_ARRAY_LENGTH];
for (uint32_t h = 0; h < m; h++) {
wy[h] = y[h] * w[h];
}
for (uint32_t i = n; i-- != 0;) {
out_b[i] = VectorDot(&q[i][0], wy, m);
for (uint32_t j = n - 1; j > i; j--) {
out_b[i] -= r[i][j] * out_b[j];
}
out_b[i] /= r[i][i];
}
return true;
}
Maybe<float> AndroidVelocityTracker::ComputeVelocity(TimeStamp aTimestamp) {
if (mHistory.IsEmpty()) {
return Nothing{};
}
// Polynomial coefficients describing motion along the axis.
float xcoeff[kPolyDegree + 1];
for (size_t i = 0; i <= kPolyDegree; i++) {
xcoeff[i] = 0;
}
// Iterate over movement samples in reverse time order and collect samples.
float pos[kHistorySize];
float w[kHistorySize];
float time[kHistorySize];
uint32_t m = 0;
int index = mHistory.Length() - 1;
const TimeDuration horizon = TimeDuration::FromMilliseconds(
StaticPrefs::apz_velocity_relevance_time_ms());
const auto& newest_movement = mHistory[index];
do {
const auto& movement = mHistory[index];
TimeDuration age = newest_movement.first - movement.first;
if (age > horizon) break;
ParentLayerCoord position = movement.second;
pos[m] = position;
w[m] = 1.0f;
time[m] =
-static_cast<float>(age.ToMilliseconds()) / 1000.0f; // in seconds
index--;
m++;
} while (index >= 0);
if (m == 0) {
return Nothing{}; // no data
}
// Calculate a least squares polynomial fit.
// Polynomial degree (number of coefficients), or zero if no information is
// available.
uint32_t degree = kDegree;
if (degree > m - 1) {
degree = m - 1;
}
if (degree >= 1) { // otherwise, no velocity data available
uint32_t n = degree + 1;
if (SolveLeastSquares(time, pos, w, m, n, xcoeff)) {
float velocity = xcoeff[1];
// The velocity needs to be negated because the positions represent
// touch positions, and the direction of scrolling is opposite to the
// direction of the finger's movement.
return Some(-velocity / 1000.0f); // convert to pixels per millisecond
}
}
return Nothing{};
}
void AndroidVelocityTracker::Clear() { mHistory.Clear(); }
} // namespace layers
} // namespace mozilla