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<td align="center" valign="middle" width="75%"><font color="#ffccaa" size="+3"><b><i>第39课</i></b></font></td>
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<td width="75%"><p><font class="head">物理模拟简介:</font></p>
<p><font size="3">还记得高中的物理吧，直线运动，自由落体运动，弹簧。在这一课里，我们将创造这一切。</font></p></td>
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<td valign="top" width="100%"><u>物理模拟介绍</u><br> <br>
如果你很熟悉物理规律，并且想实现它，这篇文章很适合你。<br> <br>
在这篇教程里，你会创建一个非常简单的物理引擎，我们将创建以下类：<br> <br> <u>内容:</u> <br> <br> <table border="0">
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<th align="left">位置类</th>
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<td><font color="#aaffaa">* class Vector3D</font></td>
<td>---> </td>
<td><font color="#ffffaa">用来记录物体的三维坐标的类</font></td>
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<th align="left">力和运动</th>
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<td><font color="#aaffaa">* class Mass</font></td>
<td>---> </td>
<td><font color="#ffffaa">表示一个物体的物理属性</font></td>
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<th align="left">模拟类</th>
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<td><font color="#aaffaa">* class Simulation</font></td>
<td>---> </td>
<td><font color="#ffffaa">模拟物理规律</font></td>
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<th align="left">模拟匀速运动</th>
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<td><font color="#aaffaa">* class ConstantVelocity : public Simulation</font></td>
<td>---> </td>
<td><font color="#ffffaa">模拟匀速运动</font></td>
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<th align="left">模拟在力的作用下运动</th>
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<td><font color="#aaffaa">* class MotionUnderGravitation : public Simulation</font></td>
<td>---> </td>
<td><font color="#ffffaa">模拟在引力的作用下运动</font></td>
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<td><font color="#aaffaa">* class MassConnectedWithSpring : public Simulation</font></td>
<td>---> </td>
<td><font color="#ffffaa">模拟在弹簧的作用下运动</font></td>
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<pre>class Mass
{
public:
float m; <font color="#ffffaa">// 质量</font>
Vector3D pos; <font color="#ffffaa">// 位置</font>
Vector3D vel; <font color="#ffffaa">// 速度</font>
Vector3D force; <font color="#ffffaa">// 力</font>
Mass(float m) <font color="#ffffaa">// 构造函数</font>
{
this->m = m;
}
...
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<td valign="top" width="100%"><p>下面的代码给物体增加一个力，在初始时这个力为0</p>
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<pre> void applyForce(Vector3D force)
{
this->force += force; <font color="#ffffaa">// 增加一个力</font>
}
void init() <font color="#ffffaa">// 初始时设为0</font>
{
force.x = 0;
force.y = 0;
force.z = 0;
}
...
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<td valign="top" width="100%"><p>下面的步骤完成一个模拟：</p>
<p>1.设置力<br>
2.应用外力<br>
3.根据力的时间，计算物体的位置和速度</p>
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<pre> void simulate(float dt)
{
vel += (force / m) * dt; <font color="#ffffaa">// 更新速度</font>
pos += vel * dt; <font color="#ffffaa">// 更新位置</font>
}
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<td valign="top" width="100%"><u>模拟类怎样运作:</u> <br> <br>
在一个物理模拟中，我们按以下规律进行模拟，设置力，更新物体的位置和速度，按时间一次又一次的进行模拟。下面是它的实现代码：</td>
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<pre>class Simulation
{
public:
int numOfMasses; <font color="#ffffaa">// 物体的个数</font>
Mass** masses; <font color="#ffffaa">// 指向物体结构的指针</font>
Simulation(int numOfMasses, float m) <font color="#ffffaa">// 构造函数</font>
{
this->numOfMasses = numOfMasses;
masses = new Mass*[numOfMasses];
for (int a = 0; a < numOfMasses; ++a)
masses[a] = new Mass(m);
}
virtual void release() <font color="#ffffaa">// 释放所有的物体</font>
{
for (int a = 0; a < numOfMasses; ++a)
{
delete(masses[a]);
masses[a] = NULL;
}
delete(masses);
masses = NULL;
}
Mass* getMass(int index)
{
if (index < 0 || index >= numOfMasses) <font color="#ffffaa">// 返回第i个物体</font>
return NULL;
return masses[index];
}
...
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</font> <font color="#aaffaa" size="3">
<pre> (class Simulation continued)
virtual void init() <font color="#ffffaa">// 初始化所有的物体</font>
{
for (int a = 0; a < numOfMasses; ++a)
masses[a]->init();
}
virtual void solve() <font color="#ffffaa">//虚函数，在具体的应用中设置各个施加给各个物体的力 </font>
{
}
virtual void simulate(float dt) <font color="#ffffaa">//让所有的物体模拟一步</font>
{
for (int a = 0; a < numOfMasses; ++a)
masses[a]->simulate(dt);
}
...
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<td valign="top" width="100%">整个模拟的部分被封装到下面的函数中</td>
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</font><pre><font color="#aaffaa" size="3"> (class Simulation continued)
virtual void operate(float dt) <font color="#ffffaa">// 完整的模拟过程</font>
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