Accelerometer - Rolling Ball in Ball

问题

i want to use the phones accelerometer for rolling a Ball in a Ball. The movement works correctly, the problem is that when the ball hits the Wall. How can i get a smooth rolling animation that the ball slides along the inner side of the bigger ball?

This is my current code to move the Ball and check the intersection:

    onSuccess: function(acceleration) {
        var xPos = this.xPos + (-1 * (acceleration.x * 0.5));
        var yPos = this.yPos + (acceleration.y * 0.5);

        var intersect = this.intersection(xPos + 32, 
                                          yPos + 32, 
                                          32, 
                                          self.canvas.width * 0.5, 
                                          self.canvas.height * 0.5, 
                                          self.canvas.width * 0.5);
        if (!intersect) {
            this.yPos = yPos;
            this.xPos = xPos;
        }

        this.cnv.clearRect(0.0, 0.0, this.canvas.width, this.canvas.height);    
        this.cnv.drawImage(this.target, this.xPos, this.yPos);
    },

    intersection: function(x0, y0, r0, x1, y1, r1) {

        var a, dx, dy, d, h, rx, ry;
        var x2, y2;

        /* dx and dy are the vertical and horizontal distances between
         * the circle centers.
         */
        dx = x1 - x0;
        dy = y1 - y0;

        /* Determine the straight-line distance between the centers. */
        d = Math.sqrt((dy*dy) + (dx*dx));

        /* Check for solvability. */
        if (d > (r0 + r1)) {
            /* no solution. circles do not intersect. */
            return false;
        }
        if (d < Math.abs(r0 - r1)) {
            /* no solution. one circle is contained in the other */
            return false;
        }

        /* 'point 2' is the point where the line through the circle
         * intersection points crosses the line between the circle
         * centers.  
         */

        /* Determine the distance from point 0 to point 2. */
        a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ;

        /* Determine the coordinates of point 2. */
        x2 = x0 + (dx * a/d);
        y2 = y0 + (dy * a/d);

        /* Determine the distance from point 2 to either of the
         * intersection points.
         */
        h = Math.sqrt((r0*r0) - (a*a));

        /* Now determine the offsets of the intersection points from
         * point 2.
         */
        rx = -dy * (h/d);
        ry = dx * (h/d);

        /* Determine the absolute intersection points. */
        var xi = x2 + rx;
        var xi_prime = x2 - rx;
        var yi = y2 + ry;
        var yi_prime = y2 - ry;

        return [xi, xi_prime, yi, yi_prime];
    }
};

Thanks for Helping :)

回答1:

in just sliding case use parametric circle equation

x=x0+r*cos(a)
y=y0+r*sin(a)

where:

x0,y0 is the big circle center
r = R0-R1
R0 is big circle radius
R1 is small circle radius

Now the angle a

the simplest would be to place a=gravity directionso:

a=atanxy(acceleration.x,acceleration.y)

the atanxy is atan2 which is 4-quadrant arcus tangens. If you don't have it use mine

atanxy C++ implementation

and correct the angle to your coordinate systems (maybe negate and or add some 90degree multiple)

[notes]

If you have compatible coordinate systems between screen and device accelerometer then just scale acceleration vector to size |r| and add (x0,y0) to it and you have the same result without any goniometric function ...

For proper simulation use D'ALembert equations + circle boundary

so the 2D movement is pretty easy:

// in some timer with interval dt [sec]
velocity.x+=acceleration.x*dt;
velocity.y+=acceleration.y*dt;
position.x+=velocity.x*dt;
position.y+=velocity.y*dt;

now if (|position-big_circle_center|>big_circle_radius) an collision occurred so when you do not want any bounce (all energy was absorbed) then:

position-=big_circle_center;
position*=big_circle_radius/|position|;
position+=big_circle_center;

Now you need remove the radial speed and left just tangent speed:

normal=position-big_circle_center; // normal vector to surface
normal*=dot(velocity,normal);      // this is the normal speed part
velocity-=normal;                  // now just tangential speed should be left

so after this just tangent (Yellow) part of velocity remains ... Hope I did not forget something (like make unit vector or +/- somewhere...)

来源：https://stackoverflow.com/questions/26216173/accelerometer-rolling-ball-in-ball

标签

javascript

jquery

math

vector