弹跳球.让它在高度高峰时减速 [英] Bouncing Ball. Making it slow down at peak of height

问题描述

我在 x3d 中创建了一个弹跳球动画.我只是很好奇如何让球在其高度达到顶峰时放慢速度，使其看起来更逼真.提前致谢.

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>

推荐答案

为此使用真实"物理.

1. 球有参数

• 加速度 a(ax,ay,az) [m/s^2]...这是所有推动球的力的总和除以它的质量
• velocity v(vx,vy,vz) [m/s]...实际速度=加速度的积分v += a * dt
• position p(x,y,z) [m]... 实际位置=速度积分p += v * dt
• 半径 r [m]
• 质量 m [kg]
• dt [s] ... 迭代步长(更新时间)

• 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 值到 (0,0,0) 和 p 到起始位置

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

应用重力、摩擦、碰撞

• 重力例如g(gx=0,gy=-9.81,gz=0)
• friction f2 = -(|v|^2)*c2 * (v/|v|) ... in gas
• 摩擦 f3 = -(|v|^3)*c3 * (v/|v|) ... 在液体中

• 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

如果交叉碰撞边界前后的位置反映速度 * 碰撞系数 <=1 碰撞法线，如果无法跨越边界，您也可以反映位置.

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.

将它们全部放在一些带有 dt 间隔的定时器/更新代码中

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()

用于手动更改位置

只需设置p(x,y,z)到新的位置，也可以设置v=(0,0,0)来停止球

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

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