BouncingBalls2014.h

//  BouncingBalls2014 is a program that lets you animate an LED strip
//  to look like a group of bouncing balls
//
//  https://github.com/fibonacci162/LEDs/blob/master/BouncingBalls2014/BouncingBalls2014.ino
// 
//  Daniel Wilson, 2014
//
//  With BIG thanks to the FastLED community!
///////////////////////////////////////////////////////////////////////////////////////////

#define GRAVITY           -9.81              // Downward (negative) acceleration of gravity in m/s^2
#define h0                1                  // Starting height, in meters, of the ball (strip length)
#define NUM_BALLS         3                  // Number of bouncing balls you want (recommend < 7, but 20 is fun in its own way)

float h[NUM_BALLS];                         // An array of heights
float vImpact0 = sqrt(-2 * GRAVITY * h0);  // Impact velocity of the ball when it hits the ground if "dropped" from the top of the strip
float vImpact[NUM_BALLS];                   // As time goes on the impact velocity will change, so make an array to store those values
float tCycle[NUM_BALLS];                    // The time since the last time the ball struck the ground
int   pos[NUM_BALLS];                       // The integer position of the dot on the strip (LED index)
long  tLast[NUM_BALLS];                     // The clock time of the last ground strike
float COR[NUM_BALLS];                       // Coefficient of Restitution (bounce damping)

bool initialized = false;

uint32_t bouncingBalls2014() {
    if (!initialized) {
        initialized = true;

        for (int i = 0; i < NUM_BALLS; i++) {    // Initialize variables
            tLast[i] = millis();
            h[i] = h0;
            pos[i] = 0;                              // Balls start on the ground
            vImpact[i] = vImpact0;                   // And "pop" up at vImpact0
            tCycle[i] = 0;
            COR[i] = 0.90 - float(i) / pow(NUM_BALLS, 2);
        }
    }

    dimAll(120);

    for (int i = 0; i < NUM_BALLS; i++) {
        tCycle[i] = millis() - tLast[i];     // Calculate the time since the last time the ball was on the ground

        // A little kinematics equation calculates positon as a function of time, acceleration (gravity) and intial velocity
        h[i] = 0.5 * GRAVITY * pow(tCycle[i] / 1000, 2.0) + vImpact[i] * tCycle[i] / 1000;

        if (h[i] < 0) {
            h[i] = 0;                            // If the ball crossed the threshold of the "ground," put it back on the ground
            vImpact[i] = COR[i] * vImpact[i];   // and recalculate its new upward velocity as it's old velocity * COR
            tLast[i] = millis();

            if (vImpact[i] < 0.01) vImpact[i] = vImpact0;  // If the ball is barely moving, "pop" it back up at vImpact0
        }
        pos[i] = round(h[i] * (NUM_LEDS - 1) / h0);       // Map "h" to a "pos" integer index position on the LED strip
    }

    //Choose color of LEDs, then the "pos" LED on
    for (int i = 0; i < NUM_BALLS; i++)
        leds[pos[i]] = CHSV(uint8_t(i * 40), 255, 255);

    return 0;
}