class SimulationView extends View implements SensorEventListener {
// diameter of the balls in meters
private static final float sBallDiameter = 0.004f;
private static final float sBallDiameter2 = sBallDiameter * sBallDiameter;
// friction of the virtual table and air
private static final float sFriction = 0.1f;
private Sensor mAccelerometer;
private long mLastT;
private float mLastDeltaT;
private float mXDpi;
private float mYDpi;
private float mMetersToPixelsX;
private float mMetersToPixelsY;
private Bitmap mBitmap;
private Bitmap mWood;
private float mXOrigin;
private float mYOrigin;
private float mSensorX;
private float mSensorY;
private long mSensorTimeStamp;
private long mCpuTimeStamp;
private float mHorizontalBound;
private float mVerticalBound;
private final ParticleSystem mParticleSystem = new ParticleSystem();
/*
* Each of our particle holds its previous and current position, its
* acceleration. for added realism each particle has its own friction
* coefficient.
*/
class Particle {
private float mPosX;
private float mPosY;
private float mAccelX;
private float mAccelY;
private float mLastPosX;
private float mLastPosY;
private float mOneMinusFriction;
Particle() {
// make each particle a bit different by randomizing its
// coefficient of friction
final float r = ((float) Math.random() - 0.5f) * 0.2f;
mOneMinusFriction = 1.0f - sFriction + r;
}
public void computePhysics(float sx, float sy, float dT, float dTC) {
// Force of gravity applied to our virtual object
final float m = 1000.0f; // mass of our virtual object
final float gx = -sx * m;
final float gy = -sy * m;
/*
* F = mA <=> A = F / m We could simplify the code by
* completely eliminating "m" (the mass) from all the equations,
* but it would hide the concepts from this sample code.
*/
final float invm = 1.0f / m;
final float ax = gx * invm;
final float ay = gy * invm;
/*
* Time-corrected Verlet integration The position Verlet
* integrator is defined as x(t+dt) = x(t) + x(t) - x(t-dt) +
* a(t).t^2 However, the above equation doesn't handle variable
* dt very well, a time-corrected version is needed: x(t+dt) =
* x(t) + (x(t) - x(t-dt)) * (dt/dt_prev) + a(t).t^2 We also add
* a simple friction term (f) to the equation: x(t+dt) = x(t) +
* (1-f) * (x(t) - x(t-dt)) * (dt/dt_prev) + a(t)t^2
*/
final float dTdT = dT * dT;
final float x = mPosX + mOneMinusFriction * dTC * (mPosX - mLastPosX) + mAccelX
* dTdT;
final float y = mPosY + mOneMinusFriction * dTC * (mPosY - mLastPosY) + mAccelY
* dTdT;
mLastPosX = mPosX;
mLastPosY = mPosY;
mPosX = x;
mPosY = y;
mAccelX = ax;
mAccelY = ay;
}
/*
* Resolving constraints and collisions with the Verlet integrator
* can be very simple, we simply need to move a colliding or
* constrained particle in such way that the constraint is
* satisfied.
*/
public void resolveCollisionWithBounds() {
final float xmax = mHorizontalBound;
final float ymax = mVerticalBound;
final float x = mPosX;
final float y = mPosY;
if (x > xmax) {
mPosX = xmax;
} else if (x < -xmax) {
mPosX = -xmax;
}
if (y > ymax) {
mPosY = ymax;
} else if (y < -ymax) {
mPosY = -ymax;
}
}
}
/*
* A particle system is just a collection of particles
*/
class ParticleSystem {
static final int NUM_PARTICLES = 15;
private Particle mBalls[] = new Particle[NUM_PARTICLES];
ParticleSystem() {
/*
* Initially our particles have no speed or acceleration
*/
for (int i = 0; i < mBalls.length; i++) {
mBalls[i] = new Particle();
}
}
/*
* Update the position of each particle in the system using the
* Verlet integrator.
*/
private void updatePositions(float sx, float sy, long timestamp) {
final long t = timestamp;
if (mLastT != 0) {
final float dT = (float) (t - mLastT) * (1.0f / 1000000000.0f);
if (mLastDeltaT != 0) {
final float dTC = dT / mLastDeltaT;
final int count = mBalls.length;
for (int i = 0; i < count; i++) {
Particle ball = mBalls[i];
ball.computePhysics(sx, sy, dT, dTC);
}
}
mLastDeltaT = dT;
}
mLastT = t;
}
/*
* Performs one iteration of the simulation. First updating the
* position of all the particles and resolving the constraints and
* collisions.
*/
public void update(float sx, float sy, long now) {
// update the system's positions
updatePositions(sx, sy, now);
// We do no more than a limited number of iterations
final int NUM_MAX_ITERATIONS = 10;
/*
* Resolve collisions, each particle is tested against every
* other particle for collision. If a collision is detected the
* particle is moved away using a virtual spring of infinite
* stiffness.
*/
boolean more = true;
final int count = mBalls.length;
for (int k = 0; k < NUM_MAX_ITERATIONS && more; k++) {
more = false;
for (int i = 0; i < count; i++) {
Particle curr = mBalls[i];
for (int j = i + 1; j < count; j++) {
Particle ball = mBalls[j];
float dx = ball.mPosX - curr.mPosX;
float dy = ball.mPosY - curr.mPosY;
float dd = dx * dx + dy * dy;
// Check for collisions
if (dd <= sBallDiameter2) {
/*
* add a little bit of entropy, after nothing is
* perfect in the universe.
*/
dx += ((float) Math.random() - 0.5f) * 0.0001f;
dy += ((float) Math.random() - 0.5f) * 0.0001f;
dd = dx * dx + dy * dy;
// simulate the spring
final float d = (float) Math.sqrt(dd);
final float c = (0.5f * (sBallDiameter - d)) / d;
curr.mPosX -= dx * c;
curr.mPosY -= dy * c;
ball.mPosX += dx * c;
ball.mPosY += dy * c;
more = true;
}
}
/*
* Finally make sure the particle doesn't intersects
* with the walls.
*/
curr.resolveCollisionWithBounds();
}
}
}
public int getParticleCount() {
return mBalls.length;
}
public float getPosX(int i) {
return mBalls[i].mPosX;
}
public float getPosY(int i) {
return mBalls[i].mPosY;
}
}
public void startSimulation() {
/*
* It is not necessary to get accelerometer events at a very high
* rate, by using a slower rate (SENSOR_DELAY_UI), we get an
* automatic low-pass filter, which "extracts" the gravity component
* of the acceleration. As an added benefit, we use less power and
* CPU resources.
*/
mSensorManager.registerListener(this, mAccelerometer, SensorManager.SENSOR_DELAY_UI);
}
public void stopSimulation() {
mSensorManager.unregisterListener(this);
}
public SimulationView(Context context) {
super(context);
mAccelerometer = mSensorManager.getDefaultSensor(Sensor.TYPE_ACCELEROMETER);
DisplayMetrics metrics = new DisplayMetrics();
getWindowManager().getDefaultDisplay().getMetrics(metrics);
mXDpi = metrics.xdpi;
mYDpi = metrics.ydpi;
mMetersToPixelsX = mXDpi / 0.0254f;
mMetersToPixelsY = mYDpi / 0.0254f;
// rescale the ball so it's about 0.5 cm on screen
Bitmap ball = BitmapFactory.decodeResource(getResources(), R.drawable.ball);
final int dstWidth = (int) (sBallDiameter * mMetersToPixelsX + 0.5f);
final int dstHeight = (int) (sBallDiameter * mMetersToPixelsY + 0.5f);
mBitmap = Bitmap.createScaledBitmap(ball, dstWidth, dstHeight, true);
Options opts = new Options();
opts.inDither = true;
opts.inPreferredConfig = Bitmap.Config.RGB_565;
mWood = BitmapFactory.decodeResource(getResources(), R.drawable.wood, opts);
}
@Override
protected void onSizeChanged(int w, int h, int oldw, int oldh) {
// compute the origin of the screen relative to the origin of
// the bitmap
mXOrigin = (w - mBitmap.getWidth()) * 0.5f;
mYOrigin = (h - mBitmap.getHeight()) * 0.5f;
mHorizontalBound = ((w / mMetersToPixelsX - sBallDiameter) * 0.5f);
mVerticalBound = ((h / mMetersToPixelsY - sBallDiameter) * 0.5f);
}
@Override
public void onSensorChanged(SensorEvent event) {
if (event.sensor.getType() != Sensor.TYPE_ACCELEROMETER)
return;
/*
* record the accelerometer data, the event's timestamp as well as
* the current time. The latter is needed so we can calculate the
* "present" time during rendering. In this application, we need to
* take into account how the screen is rotated with respect to the
* sensors (which always return data in a coordinate space aligned
* to with the screen in its native orientation).
*/
switch (mDisplay.getRotation()) {
case Surface.ROTATION_0:
mSensorX = event.values[0];
mSensorY = event.values[1];
break;
case Surface.ROTATION_90:
mSensorX = -event.values[1];
mSensorY = event.values[0];
break;
case Surface.ROTATION_180:
mSensorX = -event.values[0];
mSensorY = -event.values[1];
break;
case Surface.ROTATION_270:
mSensorX = event.values[1];
mSensorY = -event.values[0];
break;
}
mSensorTimeStamp = event.timestamp;
mCpuTimeStamp = System.nanoTime();
}
@Override
protected void onDraw(Canvas canvas) {
/*
* draw the background
*/
canvas.drawBitmap(mWood, 0, 0, null);
/*
* compute the new position of our object, based on accelerometer
* data and present time.
*/
final ParticleSystem particleSystem = mParticleSystem;
final long now = mSensorTimeStamp + (System.nanoTime() - mCpuTimeStamp);
final float sx = mSensorX;
final float sy = mSensorY;
particleSystem.update(sx, sy, now);
final float xc = mXOrigin;
final float yc = mYOrigin;
final float xs = mMetersToPixelsX;
final float ys = mMetersToPixelsY;
final Bitmap bitmap = mBitmap;
final int count = particleSystem.getParticleCount();
for (int i = 0; i < count; i++) {
/*
* We transform the canvas so that the coordinate system matches
* the sensors coordinate system with the origin in the center
* of the screen and the unit is the meter.
*/
final float x = xc + particleSystem.getPosX(i) * xs;
final float y = yc - particleSystem.getPosY(i) * ys;
canvas.drawBitmap(bitmap, x, y, null);
}
// and make sure to redraw asap
invalidate();
}
@Override
public void onAccuracyChanged(Sensor sensor, int accuracy) {
}
}
