For use in JUDO5

GravityBall.js

function main() {
    var shipX = 50;
    var shipY = 100;
    var shipMass = 100;
    var shipSize = 20;
    var shipDirection = Pi * 1.5;
    var shipSpeed = 1.8;

    var earthX = 210;
    var earthY = 140;
    var earthMass = 2000;
    var earthSize = 50;

    var gravityMagnitude;
    var gravityDirection;

    setBackgroundColor(coral);

    while (true) {
        // calculate gravity
        gravityMagnitude = computeGravityMagnitude(earthX, earthY, earthMass, shipX, shipY, shipMass);
        gravityDirection = computeGravityDirection(earthX, earthY, shipX, shipY);

        // add gravity to ships current velocity
        shipSpeed = vectorAddMagnitude(gravityDirection, gravityMagnitude, shipDirection, shipSpeed);
        shipDirection = vectorAddTheta(gravityDirection, gravityMagnitude, shipDirection, shipSpeed);

        // move the ship
        shipX += getXComponent(shipSpeed, shipDirection);
        shipY -= getYComponent(shipSpeed, shipDirection);

        // draw the next frame in the animation
        clearDrawing();
        setColor(yellow);
        fillCircle(earthX - (earthSize / 2), earthY - (earthSize / 2), earthSize);
        setColor(blue);
        fillCircle(shipX - (shipSize / 2), shipY - (shipSize / 2), shipSize);
        delay(.03);

        if (getMouseEvent()) {
            earthX = getMouseX();
            earthY = getMouseY();
        }

        if (shipX > getDrawingWidth()) {
            shipX = getDrawingWidth() - 1;
            shipDirection = flipHorizontally(shipDirection);
        }
        if (shipX < 0) {
            shipX = 1;
            shipDirection = flipHorizontally(shipDirection);
        }
        if (shipY > getDrawingHeight()) {
            shipY = getDrawingHeight() - 1;
            shipDirection = flipVertically(shipDirection);
        }
        if (shipY < 0) {
            shipY = 1;
            shipDirection = flipVertically(shipDirection);
        }
    }
}

// gravitational constant
var G = 0.01;

// computes the magnitude of the gravitational force of
// one object (stationaryObject) on another (movingObject)
function computeGravityMagnitude(stationaryObjectX, stationaryObjectY,
                               stationaryObjectMass, movingObjectX,
                               movingObjectY, movingObjectMass) {

    var distance = getDistance(stationaryObjectX, stationaryObjectY,
                              movingObjectX, movingObjectY);

    return (G * stationaryObjectMass * movingObjectMass) / (distance * distance);
}

// computes the direction of the gravitational force of
// one object (stationaryObject) on another (movingObject)
function computeGravityDirection(stationaryObjectX, stationaryObjectY,
                               movingObjectX, movingObjectY) {

    var xComponent = stationaryObjectX - movingObjectX;
    var yComponent = -(stationaryObjectY - movingObjectY);
    var direction = Math.atan(yComponent / xComponent);

    return correctTheta(direction, xComponent, yComponent);
}

// computes the distance between two povars (x1, y1) and (x2, y2)
function getDistance(x1, y1, x2, y2) {
    return squareRoot(((x2 - x1) * (x2 - x1)) + ((y2 - y1) * (y2 - y1)));
}

// add two vectors and return resultant vector's magnitude
function vectorAddMagnitude(v1Theta, v1Magnitude, 
v2Theta, v2Magnitude) {
    var v1MagnitudeX = getXComponent(v1Magnitude, v1Theta);
    var v1MagnitudeY = getYComponent(v1Magnitude, v1Theta);
    var v2MagnitudeX = getXComponent(v2Magnitude, v2Theta);
    var v2MagnitudeY = getYComponent(v2Magnitude, v2Theta);
    var newXComponent = v1MagnitudeX + v2MagnitudeX;
    var newYComponent = v1MagnitudeY + v2MagnitudeY;
    var newMagnitude = squareRoot(
        (newXComponent * newXComponent) +
        (newYComponent * newYComponent));
    return newMagnitude;
}

// add two vectors return resultant vector's theta
function vectorAddTheta(v1Theta, v1Magnitude, 
v2Theta, v2Magnitude) {
    var v1MagnitudeX = getXComponent(v1Magnitude, v1Theta);
    var v1MagnitudeY = getYComponent(v1Magnitude, v1Theta);
    var v2MagnitudeX = getXComponent(v2Magnitude, v2Theta);
    var v2MagnitudeY = getYComponent(v2Magnitude, v2Theta);
    var newXComponent = v1MagnitudeX + v2MagnitudeX;
    var newYComponent = v1MagnitudeY + v2MagnitudeY;
    var newTheta = Math.atan(newYComponent / newXComponent);
    return correctTheta(newTheta, newXComponent, newYComponent);
}

// returns the X-component of the vector given by magnitude and theta
function getXComponent(magnitude, theta) {
    return magnitude * cos(theta);
}

// returns the Y-component of the vector given by magnitude and theta
function getYComponent(magnitude, theta) {
    return magnitude * sin(theta);
}

// Since there are two thetas for any given tangent (180 degrees off of one
// another), make sure we are using the correct one when doing vector addition
function correctTheta(theta, xComponent, yComponent) 
{
    // keep theta in the 0 .. 2 Pi range
    theta = theta % (2 * Pi);

    // first quadrant
    if (xComponent > 0 && yComponent > 0) {
        if (theta < (Pi / 2) && theta > 0) {
            return theta;
        }
        else {
            return theta + Pi;
        }
    }
    // second quadrant
    else if (xComponent < 0 && yComponent > 0) {
        if (theta < Pi && theta > (Pi / 2)) {
            return theta;
        }
        else {
            return theta + Pi;
        }
    }
    // third quadrant
    else if (xComponent < 0 && yComponent < 0) {
        if (theta < (3 * Pi / 2) && theta > Pi) {
            return theta;
        }
        else {
            return theta + Pi;
        }
    }

    return theta;
}

// flips theta over the horizontal axis
function flipVertically(theta) {
    return theta + 2 * (Pi - theta);
}

// flips theta over the vertical axis
function flipHorizontally(theta) {
    return (theta + Pi) - (2 * theta);
}