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<!DOCTYPE html>
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<title>Physics for Games</title>
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<body>
<header>
<h1>Physics for Games</h1>
</header>
<nav>
<a href="/">Home</a>
<a href="rigidbody.html">Rigid Body</a>
<a href="references.html">Books n' References</a>
</nav>
<main>
<section>
<p>
<ul>
<li><a href="#introduction">Introduction</a></li>
<li><a href="#linear-forces">Part 1: Linear Forces</a></li>
<li><a href="#rotational-forces">Part 2: Rotational Forces</a></li>
<li><a href="#collisions">Part 3: Collisions</a></li>
</ul>
</p>
</section>
<section id='introduction'>
<h2>Introduction: Rigid Body Physics</h2>
<p>
You're most likely here because you have some interest in the world of rigid body physics. Maybe you have some knowledge of rendering via OpenGL or Vulkan,
and you want to begin watching your up-until-now static scene come to life. Well, you're in the right place! In the course of this tutorial series I will walk
you through the entirety of a 2D rigid body physics system entirely in the web. All of this information will be extendable to other languages, but we will use
JavaScript and WebGL in these blog posts. Additionally, much of the information presented here can be extended to 3 dimensions, but 3D carries some complications
with it, that we will discuss in future blog posts.
</p>
<p>
In implementing a rigidy body physics system, we're primarily interested in two sub-fields of physics, namely <b>dynamics</b> and <b>kinematics</b>. Although I'm
far as can be from being an expert in either of these fields, I will explain - from a programmer's persepctive - what they mean to me:
<ul>
<li>
<b>Kinematics</b> is the study of how an object's movement changes over time. These are the classic position, velocity, and acceleration equations
that you're most likely familiar with from high school or college physics.
</li>
<li>
<b>Dynamics</b> is the study of whats <i>causes</i> kinematic movement. These are the classic force and momentum equations that you may already be familiar
with as well.
</li>
</ul>
</p>
<p>
Finally, I must provide a disclaimer that all of rigid body systems are very math-y. You will need to know a decent amount of vector calculus and linear algebra to really understand
what's going on here. I am going to assume that you have this knowledge. If you don't already have this knowledge, I will try and provide some resources on the Books
n' References page of the website.
</p>
</section>
<hr />
<section id="linear-forces">
<h2>Part 1: Linear Forces</h2>
<p>
The first - and perhaps easiest - part of implementing any rigid body physics system is getting the entities in your scene to move in response to linear forces.
With this implementation alone, you can achieve an interesting level of realism in your 2D (and even 3D) scene.
</p>
<p>
Let's begin by recalling the relationships between acceleration, velocity, and position.
</p>
<p>
Knowing all this, you should be able to understand the following source code fairly easily;
<pre>
<code>
<span class="code_keyword">function</span> update(dtSeconds) {
<span class="code_comment">// Add up the forces acting on the circle</span>
<span class="code_keyword">const</span> GRAVITY = 9.8;
<span class="code_keyword">const</span> lGravityForce = vec2(0, -1.0 * (lCircle.mass * <span class="code_constant">GRAVITY</span>));
lCircle.force = addVec2(lCircle.force, lGravityForce);
<span class="code_comment">// Figure out acceleration (a = F / m)</span>
<span class="code_keyword">const</span> lCurrentAcceleration = scaleVec2(lCircle.force, 1.0 / lCircle.mass);
<span class="code_comment">// Calculate the new velocity: v = v0 + a * t</span>
lCircle.velocity = addVec2(lCircle.velocity, scaleVec2(lCurrentAcceleration, dtSeconds));
<span class="code_comment">// Update the position based on velocity: x = x0 + v * t</span>
lCircle.position = addVec2(lCircle.position, scaleVec2(lCircle.velocity, dtSeconds));
<span class="code_comment">// Update the model matrix accordingly</span>
lCircle.model = translateMatrix(mat4(), lCircle.position.x, lCircle.position.y, 0);
<span class="code_comment">// Reset the force vector for the next update</span>
lCircle.force = vec2()
}
</code>
</pre>
</p>
<div id="rigidbody_1" class="opengl_canvas_container">
<canvas width="640" height="480"></canvas>
<div class="opengl_canvas_sidebar">
<ul class="opengl_value_tracker">
<li><b>Linear Force:</b><span id="rigidbody_1_force_field">N/A</span></li>
<li><b>Linear Acceleration:</b><span id="rigidbody_1_acceleration_field">N/A</span></li>
<li><b>Linear Velocity:</b><span id="rigidbody_1_velocity_field">N/A</span></li>
<li><b>Linear Position:</b><span id="rigidbody_1_position_field">N/A</span></li>
</ul>
<form id="rigidbody_1_force_submit_button" style="text-align: right; padding: 0.5rem;">
<div class="vec2_input_group">
<label>Force Vector</label>
<input class="vec2_x_input" type="number" placeholder="X (Default 0)"/>
<input class="vec2_y_input" type="number" placeholder="Y (Default 5000 N)"/>
</div>
<input type="submit" value="Apply Force"></input>
</form>
</div>
<button class="play_button">
Play
</button>
<button class="stop_button">
Stop
</button>
</div>
</section>
<hr />
<section id="rotational-forces">
<h2>Part 2: Rotational Forces</h2>
<p>
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
</p>
<div id="rigidbody_2" class="opengl_canvas_container">
<canvas width="640" height="480"></canvas>
<div class="opengl_canvas_sidebar">
<ul class="opengl_value_tracker">
<li><b>Angular Force:</b><span id="rigidbody_2_force_field">N/A</span></li>
<li><b>Angular Acceleration:</b><span id="rigidbody_2_acceleration_field">N/A</span></li>
<li><b>Angular Velocity:</b><span id="rigidbody_2_velocity_field">N/A</span></li>
<li><b>Angular Position:</b><span id="rigidbody_2_position_field">N/A</span></li>
</ul>
<form id="rigidbody_2_force_submit_button" style="text-align: right; padding: 0.5rem;">
<div id="rigidbody_2_force_input" class="vec2_input_group">
<label>Force Vector</label>
<input class="vec2_x_input" type="number" placeholder="X (Default 0)"/>
<input class="vec2_y_input" type="number" placeholder="Y (Default 5000 N)"/>
</div>
<div id="rigidbody_2_position_input" class="vec2_input_group">
<label>Point of Application (Unit Vector)</label>
<input class="vec2_x_input" type="number" placeholder="X (Default 2 Root 2)"/>
<input class="vec2_y_input" type="number" placeholder="Y (Default 2 Root 2)"/>
</div>
<input type="submit" value="Apply Force"></input>
</form>
</div>
<button class="play_button">
Play
</button>
<button class="stop_button">
Stop
</button>
</div>
</section>
<section id="collisions">
<h2>Part 3: Collisions</h2>
<p>
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
</p>
<div id="rigidbody_3" class="opengl_canvas_container">
<canvas width="640" height="480"></canvas>
<div class="opengl_canvas_sidebar">
</div>
<button class="play_button">
Play
</button>
<button class="stop_button">
Stop
</button>
</div>
</section>
<section style="height: 50vh;"></section>
</main>
</body>
</html>
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