forked from joejulian/gio
all: rename the gioui.org/ui module to gioui.org
The "ui" is redundant and stutters. Signed-off-by: Elias Naur <mail@eliasnaur.com>
This commit is contained in:
Elias Naur
@@ -0,0 +1,98 @@
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// SPDX-License-Identifier: Unlicense OR MIT
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package fling
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import (
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"math"
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"runtime"
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"time"
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"gioui.org/ui"
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)
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type Animation struct {
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// Current offset in pixels.
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x float32
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// Initial time.
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t0 time.Time
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// Initial velocity in pixels pr second.
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v0 float32
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}
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var (
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// Pixels/second.
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minFlingVelocity = ui.Dp(50)
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maxFlingVelocity = ui.Dp(8000)
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)
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const (
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thresholdVelocity = 1
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)
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// Start a fling given a starting velocity. Returns whether a
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// fling was started.
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func (f *Animation) Start(c ui.Config, velocity float32) bool {
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min := float32(c.Px(minFlingVelocity))
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v := velocity
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if -min <= v && v <= min {
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return false
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}
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max := float32(c.Px(maxFlingVelocity))
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if v > max {
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v = max
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} else if v < -max {
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v = -max
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}
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f.init(c.Now(), v)
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return true
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}
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func (f *Animation) init(now time.Time, v0 float32) {
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f.t0 = now
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f.v0 = v0
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f.x = 0
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}
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func (f *Animation) Active() bool {
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return f.v0 != 0
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}
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// Tick computes and returns a fling distance since
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// the last time Tick was called.
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func (f *Animation) Tick(now time.Time) int {
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if !f.Active() {
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return 0
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}
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var k float32
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if runtime.GOOS == "darwin" {
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k = -2 // iOS
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} else {
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k = -4.2 // Android and default
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}
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t := now.Sub(f.t0)
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// The acceleration x''(t) of a point mass with a drag
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// force, f, proportional with velocity, x'(t), is
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// governed by the equation
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//
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// x''(t) = kx'(t)
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//
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// Given the starting position x(0) = 0, the starting
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// velocity x'(0) = v0, the position is then
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// given by
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//
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// x(t) = v0*e^(k*t)/k - v0/k
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//
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ekt := float32(math.Exp(float64(k) * t.Seconds()))
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x := f.v0*ekt/k - f.v0/k
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dist := x - f.x
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idist := int(math.Round(float64(dist)))
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f.x += float32(idist)
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// Solving for the velocity x'(t) gives us
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//
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// x'(t) = v0*e^(k*t)
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v := f.v0 * ekt
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if -thresholdVelocity < v && v < thresholdVelocity {
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f.v0 = 0
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}
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return idist
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}
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@@ -0,0 +1,332 @@
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// SPDX-License-Identifier: Unlicense OR MIT
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package fling
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import (
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"math"
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"strconv"
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"strings"
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"time"
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)
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// Extrapolation computes a 1-dimensional velocity estimate
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// for a set of timestamped points using the least squares
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// fit of a 2nd order polynomial. The same method is used
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// by Android.
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type Extrapolation struct {
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// Index into points.
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idx int
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// Circular buffer of samples.
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samples []sample
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lastValue float32
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// Pre-allocated cache for samples.
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cache [historySize]sample
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// Filtered values and times
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values [historySize]float32
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times [historySize]float32
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}
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type sample struct {
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t time.Duration
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v float32
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}
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type matrix struct {
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rows, cols int
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data []float32
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}
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type Estimate struct {
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Velocity float32
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Distance float32
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}
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type coefficients [degree + 1]float32
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const (
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degree = 2
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historySize = 20
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maxAge = 100 * time.Millisecond
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maxSampleGap = 40 * time.Millisecond
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)
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// SampleDelta adds a relative sample to the estimation.
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func (e *Extrapolation) SampleDelta(t time.Duration, delta float32) {
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val := delta + e.lastValue
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e.Sample(t, val)
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}
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// Sample adds an absolute sample to the estimation.
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func (e *Extrapolation) Sample(t time.Duration, val float32) {
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e.lastValue = val
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if e.samples == nil {
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e.samples = e.cache[:0]
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}
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s := sample{
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t: t,
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v: val,
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}
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if e.idx == len(e.samples) && e.idx < cap(e.samples) {
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e.samples = append(e.samples, s)
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} else {
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e.samples[e.idx] = s
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}
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e.idx++
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if e.idx == cap(e.samples) {
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e.idx = 0
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}
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}
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// Velocity returns an estimate of the implied velocity and
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// distance for the points sampled, or zero if the estimation method
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// failed.
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func (e *Extrapolation) Estimate() Estimate {
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if len(e.samples) == 0 {
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return Estimate{}
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}
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values := e.values[:0]
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times := e.times[:0]
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first := e.get(0)
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t := first.t
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// Walk backwards collecting samples.
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for i := 0; i < len(e.samples); i++ {
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p := e.get(-i)
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age := first.t - p.t
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if age >= maxAge || t-p.t >= maxSampleGap {
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// If the samples are too old or
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// too much time passed between samples
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// assume they're not part of the fling.
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break
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}
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t = p.t
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values = append(values, first.v-p.v)
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times = append(times, float32((-age).Seconds()))
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}
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coef, ok := polyFit(times, values)
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if !ok {
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return Estimate{}
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}
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dist := values[len(values)-1] - values[0]
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return Estimate{
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Velocity: coef[1],
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Distance: dist,
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}
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}
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func (e *Extrapolation) get(i int) sample {
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idx := (e.idx + i - 1 + len(e.samples)) % len(e.samples)
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return e.samples[idx]
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}
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// fit computes the least squares polynomial fit for
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// the set of points in X, Y. If the fitting fails
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// because of contradicting or insufficient data,
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// fit returns false.
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func polyFit(X, Y []float32) (coefficients, bool) {
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if len(X) != len(Y) {
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panic("X and Y lengths differ")
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}
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if len(X) <= degree {
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// Not enough points to fit a curve.
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return coefficients{}, false
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}
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// Use a method similar to Android's VelocityTracker.cpp:
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// https://android.googlesource.com/platform/frameworks/base/+/56a2301/libs/androidfw/VelocityTracker.cpp
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// where all weights are 1.
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// First, expand the X vector to the matrix A in column-major order.
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A := newMatrix(degree+1, len(X))
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for i, x := range X {
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A.set(0, i, 1)
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for j := 1; j < A.rows; j++ {
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A.set(j, i, A.get(j-1, i)*x)
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}
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}
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Q, Rt, ok := decomposeQR(A)
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if !ok {
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return coefficients{}, false
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}
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// Solve R*B = Qt*Y for B, which is then the polynomial coefficients.
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// Since R is upper triangular, we can proceed from bottom right to
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// upper left.
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// https://en.wikipedia.org/wiki/Non-linear_least_squares
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var B coefficients
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for i := Q.rows - 1; i >= 0; i-- {
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B[i] = dot(Q.col(i), Y)
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for j := Q.rows - 1; j > i; j-- {
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B[i] -= Rt.get(i, j) * B[j]
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}
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B[i] /= Rt.get(i, i)
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}
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return B, true
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}
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// decomposeQR computes and returns Q, Rt where Q*transpose(Rt) = A, if
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// possible. R is guaranteed to be upper triangular and only the square
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// part of Rt is returned.
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func decomposeQR(A *matrix) (*matrix, *matrix, bool) {
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// Gram-Schmidt QR decompose A where Q*R = A.
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// https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
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Q := newMatrix(A.rows, A.cols) // Column-major.
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Rt := newMatrix(A.rows, A.rows) // R transposed, row-major.
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for i := 0; i < Q.rows; i++ {
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// Copy A column.
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for j := 0; j < Q.cols; j++ {
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Q.set(i, j, A.get(i, j))
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}
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// Subtract projections. Note that int the projection
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//
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// proju a = <u, a>/<u, u> u
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//
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// the normalized column e replaces u, where <e, e> = 1:
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//
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// proje a = <e, a>/<e, e> e = <e, a> e
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for j := 0; j < i; j++ {
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d := dot(Q.col(j), Q.col(i))
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for k := 0; k < Q.cols; k++ {
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Q.set(i, k, Q.get(i, k)-d*Q.get(j, k))
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}
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}
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// Normalize Q columns.
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n := norm(Q.col(i))
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if n < 0.000001 {
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// Degenerate data, no solution.
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return nil, nil, false
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}
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invNorm := 1 / n
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for j := 0; j < Q.cols; j++ {
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Q.set(i, j, Q.get(i, j)*invNorm)
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}
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// Update Rt.
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for j := i; j < Rt.cols; j++ {
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Rt.set(i, j, dot(Q.col(i), A.col(j)))
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}
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}
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return Q, Rt, true
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}
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func norm(V []float32) float32 {
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var n float32
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for _, v := range V {
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n += v * v
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}
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return float32(math.Sqrt(float64(n)))
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}
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func dot(V1, V2 []float32) float32 {
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var d float32
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for i, v1 := range V1 {
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d += v1 * V2[i]
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}
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return d
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}
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func newMatrix(rows, cols int) *matrix {
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return &matrix{
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rows: rows,
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cols: cols,
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data: make([]float32, rows*cols),
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}
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}
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func (m *matrix) set(row, col int, v float32) {
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if row < 0 || row >= m.rows {
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panic("row out of range")
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}
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if col < 0 || col >= m.cols {
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panic("col out of range")
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}
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m.data[row*m.cols+col] = v
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}
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func (m *matrix) get(row, col int) float32 {
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if row < 0 || row >= m.rows {
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panic("row out of range")
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}
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if col < 0 || col >= m.cols {
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panic("col out of range")
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}
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return m.data[row*m.cols+col]
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}
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func (m *matrix) col(c int) []float32 {
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return m.data[c*m.cols : (c+1)*m.cols]
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}
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func (m *matrix) approxEqual(m2 *matrix) bool {
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if m.rows != m2.rows || m.cols != m2.cols {
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return false
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}
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const epsilon = 0.00001
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for row := 0; row < m.rows; row++ {
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for col := 0; col < m.cols; col++ {
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d := m2.get(row, col) - m.get(row, col)
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if d < -epsilon || d > epsilon {
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return false
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}
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}
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}
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return true
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}
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func (m *matrix) transpose() *matrix {
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t := &matrix{
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rows: m.cols,
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cols: m.rows,
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data: make([]float32, len(m.data)),
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}
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for i := 0; i < m.rows; i++ {
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for j := 0; j < m.cols; j++ {
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t.set(j, i, m.get(i, j))
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}
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}
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return t
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}
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func (m *matrix) mul(m2 *matrix) *matrix {
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if m.rows != m2.cols {
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panic("mismatched matrices")
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}
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mm := &matrix{
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rows: m.rows,
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cols: m2.cols,
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data: make([]float32, m.rows*m2.cols),
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}
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for i := 0; i < mm.rows; i++ {
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for j := 0; j < mm.cols; j++ {
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var v float32
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for k := 0; k < m.rows; k++ {
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v += m.get(k, j) * m2.get(i, k)
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}
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mm.set(i, j, v)
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}
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}
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return mm
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}
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func (m *matrix) String() string {
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var b strings.Builder
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for i := 0; i < m.rows; i++ {
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for j := 0; j < m.cols; j++ {
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v := m.get(i, j)
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b.WriteString(strconv.FormatFloat(float64(v), 'g', -1, 32))
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b.WriteString(", ")
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}
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b.WriteString("\n")
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}
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return b.String()
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}
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func (c coefficients) approxEqual(c2 coefficients) bool {
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const epsilon = 0.00001
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for i, v := range c {
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d := v - c2[i]
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if d < -epsilon || d > epsilon {
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return false
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}
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}
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return true
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}
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@@ -0,0 +1,43 @@
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// SPDX-License-Identifier: Unlicense OR MIT
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package fling
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import "testing"
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func TestDecomposeQR(t *testing.T) {
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A := &matrix{
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rows: 3, cols: 3,
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data: []float32{
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12, 6, -4,
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-51, 167, 24,
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4, -68, -41,
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},
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}
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Q, Rt, ok := decomposeQR(A)
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if !ok {
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t.Fatal("decomposeQR failed")
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}
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R := Rt.transpose()
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QR := Q.mul(R)
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if !A.approxEqual(QR) {
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t.Log("A\n", A)
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t.Log("Q\n", Q)
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t.Log("R\n", R)
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t.Log("QR\n", QR)
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t.Fatal("Q*R not approximately equal to A")
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}
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}
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func TestFit(t *testing.T) {
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X := []float32{-1, 0, 1}
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Y := []float32{2, 0, 2}
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got, ok := polyFit(X, Y)
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if !ok {
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t.Fatal("polyFit failed")
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}
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want := coefficients{0, 0, 2}
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if !got.approxEqual(want) {
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t.Fatalf("polyFit: got %v want %v", got, want)
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}
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}
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Reference in New Issue
Block a user