Bouncing Ball. Making it slow down at peak of height

Question

I have created a bouncing ball animation in x3d. I am just curious how I could make the ball slow down at the peak of its height to make it look more realistic. Thank you in advance.

<X3D profile="interactive">
    <Scene>
        <Background skyColor='0.5 0.5 1'/>

    <Transform DEF="Ball" translation="0 1 0" >
    <TouchSensor DEF="Touch"/>
            <Shape>
                <Appearance>
                    <Material diffuseColor="1 0 0 "/>
                </Appearance>
                <Sphere radius='1'/>
            </Shape>
        </Transform>

    <TimeTrigger DEF="Trigger"/>
        <TimeSensor DEF="Clock" loop="false" cycleInterval="5" />    
        <PositionInterpolator DEF="Position" key="0.0 0.5 1.0" keyValue="0 1 0 0 5 0 0 1 0"/>

        <ROUTE fromNode="Clock" fromField="fraction_changed" toNode="Position" toField="set_fraction"/> 
        <ROUTE fromNode="Position" fromField="value_changed" toNode="Ball" toField="set_translation"/>
    <ROUTE fromNode="Touch" fromField="isActive" toNode="Trigger" toField="set_boolean"/>
    <ROUTE fromNode="Trigger" fromField="triggerTime" toNode="Clock" toField="startTime"/>

</Scene>

Answer 1

Use 'real' physics for that.

1. ball have parameters

   • acceleration a(ax,ay,az) [m/s^2]... this is sum of all forces driving ball divided by its mass
   • velocity v(vx,vy,vz) [m/s]... actual speed = integration of acceleration v += a * dt
   • position p(x,y,z) [m]... actual position = integration of velocity p += v * dt
   • radius r [m]
   • mass m [kg]
   • dt [s] ... iteration step (update time)

   init start a,v values to (0,0,0) and p to start position

2. apply gravity, friction, collision

   • gravity for example g(gx=0,gy=-9.81,gz=0)
   • friction f2 = -(|v|^2)*c2 * (v/|v|) ... in gas
   • friction f3 = -(|v|^3)*c3 * (v/|v|) ... in liquid

   if position before and after cross collision border reflect velocity * collision coef <=1 by impact normal also you can reflect position if crossing border is not possible.

3. put it all together in some timer / updating code with dt interval

   a =g+(f2+f3+(driving force))/m
   v+=a*dt
   p+=v*dt
   test_collisions()
   redraw()
   

4. for manual change of position

   just set p(x,y,z) to new position and also can set v=(0,0,0) to stop the ball