Hacked-together KaTeX support
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@ -19,6 +19,15 @@
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<style>{{ page.custom_css }}</style>
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<!--noformat-->
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{% endif %}
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{% if page.enable_katex %}
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<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.css"
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integrity="sha512-fHwaWebuwA7NSF5Qg/af4UeDx9XqUpYpOGgubo3yWu+b2IQR4UeQwbb42Ti7gVAjNtVoI/I9TEoYeu9omwcC6g=="
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crossorigin="anonymous" referrerpolicy="no-referrer" />
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<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.js"
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integrity="sha512-LQNxIMR5rXv7o+b1l8+N1EZMfhG7iFZ9HhnbJkTp4zjNr5Wvst75AqUeFDxeRUa7l5vEDyUiAip//r+EFLLCyA=="
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crossorigin="anonymous" referrerpolicy="no-referrer"></script>
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{% endif %}
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</head>
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<body>
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@ -31,7 +40,8 @@
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<ul>
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<li>
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<a href="mailto:evan@ewpratten.com">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 32 32" style="height: 1em; width: 1em;">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 32 32"
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style="height: 1em; width: 1em;">
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<path
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d="M 3 8 L 3 26 L 29 26 L 29 8 Z M 7.3125 10 L 24.6875 10 L 16 15.78125 Z M 5 10.875 L 15.4375 17.84375 L 16 18.1875 L 16.5625 17.84375 L 27 10.875 L 27 24 L 5 24 Z" />
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</svg>
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@ -40,7 +50,8 @@
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</li>
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<li>
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<a href="https://linkedin.com/in/ewpratten">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 32 32" style="height: 1em; width: 1em;">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 32 32"
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style="height: 1em; width: 1em;">
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<path
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d="M 7.5 5 C 6.132813 5 5 6.132813 5 7.5 L 5 24.5 C 5 25.867188 6.132813 27 7.5 27 L 24.5 27 C 25.867188 27 27 25.867188 27 24.5 L 27 7.5 C 27 6.132813 25.867188 5 24.5 5 Z M 7.5 7 L 24.5 7 C 24.785156 7 25 7.214844 25 7.5 L 25 24.5 C 25 24.785156 24.785156 25 24.5 25 L 7.5 25 C 7.214844 25 7 24.785156 7 24.5 L 7 7.5 C 7 7.214844 7.214844 7 7.5 7 Z M 10.4375 8.71875 C 9.488281 8.71875 8.71875 9.488281 8.71875 10.4375 C 8.71875 11.386719 9.488281 12.15625 10.4375 12.15625 C 11.386719 12.15625 12.15625 11.386719 12.15625 10.4375 C 12.15625 9.488281 11.386719 8.71875 10.4375 8.71875 Z M 19.46875 13.28125 C 18.035156 13.28125 17.082031 14.066406 16.6875 14.8125 L 16.625 14.8125 L 16.625 13.5 L 13.8125 13.5 L 13.8125 23 L 16.75 23 L 16.75 18.3125 C 16.75 17.074219 16.996094 15.875 18.53125 15.875 C 20.042969 15.875 20.0625 17.273438 20.0625 18.375 L 20.0625 23 L 23 23 L 23 17.78125 C 23 15.226563 22.457031 13.28125 19.46875 13.28125 Z M 9 13.5 L 9 23 L 11.96875 23 L 11.96875 13.5 Z" />
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</svg>
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@ -84,6 +95,24 @@
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</footer>
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{% include goatcounter.html %}
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{% if page.enable_katex %}
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<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/contrib/auto-render.min.js"
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integrity="sha512-iWiuBS5nt6r60fCz26Nd0Zqe0nbk1ZTIQbl3Kv7kYsX+yKMUFHzjaH2+AnM6vp2Xs+gNmaBAVWJjSmuPw76Efg=="
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crossorigin="anonymous" referrerpolicy="no-referrer"></script>
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<script>
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document.addEventListener("DOMContentLoaded", function () {
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renderMathInElement(document.body, {
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delimiters: [
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{ left: '$$', right: '$$', display: true },
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{ left: '$', right: '$', display: false },
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{ left: '\\(', right: '\\)', display: false },
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{ left: '\\[', right: '\\]', display: true }
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],
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throwOnError: false
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});
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});
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</script>
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{% endif %}
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</body>
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</html>
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@ -3,18 +3,7 @@ layout: default
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title: 'Notes from FRC: Converting joystick data to tank-drive outputs'
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description: and making a tank-based robot's movements look natural
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date: 2020-08-03
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tags:
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- frc
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- math
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- python
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aliases:
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- /blog/2020/08/03/joystick-to-voltage
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- /blog/joystick-to-voltage
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extra:
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uses:
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- katex
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excerpt: This post covers the algorithm I devised for converting joystick data to
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motor commands at Raider Robotics
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enable_katex: true
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---
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I am starting a new little series here called "Notes from FRC". The idea is that I am going to write about what I have learned over the past three years of working (almost daily) with robots, and hopefully someone in the future will find them useful. The production source code I based this post around is available [here](https://github.com/frc5024/lib5k/blob/cd8ad407146b514cf857c1d8ac82ac8f3067812b/common_drive/src/main/java/io/github/frc5024/common_drive/calculation/DifferentialDriveCalculation.java).
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@ -3,18 +3,7 @@ layout: default
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title: 'Notes from FRC: Autonomous point-to-point navigation'
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description: The tale of some very curvy math
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date: 2020-08-13
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tags:
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- frc
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- math
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extra:
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excerpt: This post is a continuation on my "Notes from FRC" series. This time, I
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cover an extremely simple, yet very effective way to get a tank-drive robot from
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A to B autonomously.
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uses:
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- katex
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aliases:
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- /blog/2020/08/13/drivetrain-navigation
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- /blog/drivetrain-navigation
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enable_katex: true
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---
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This post is a continuation on my "Notes from FRC" series. If you haven't already, I recommend reading my post on [Converting joystick data to tank-drive outputs](@/blog/2020-08-03-Joystick-to-Voltage.md). Some concepts in this post were introduced there. Like last time, to see the production code behind this post, check [here](https://github.com/frc5024/lib5k/blob/ab90994b2a0c769abfdde9a834133725c3ce3a38/common_drive/src/main/java/io/github/frc5024/common_drive/DriveTrainBase.java) and [here](https://github.com/frc5024/lib5k/tree/master/purepursuit/src/main/java/io/github/frc5024/purepursuit/pathgen).
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@ -3,17 +3,7 @@ layout: default
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title: A rusty guide to quaternions
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description: Fast and efficient 3D object manipulation
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date: 2021-12-03
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tags:
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- reference
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- math
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draft: false
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extra:
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uses:
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- katex
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excerpt: This post is an overview of Quaternions for Rust programmers, and anyone
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willing to learn.
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aliases:
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- /blog/quaternions
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enable_katex: true
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---
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The running joke in the graphics programming world is that nobody understands quaternions. These big scary math-filled types are always <em>someone else's problem</em>. While quaternions <del>are</del> may be scary, they serve an important purpose in the world of computing as they
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@ -121,19 +111,19 @@ $$
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As you can see, a pure quaternion is a quaternion with a real part of $0$ and a vector part equal to the vector it is being made of.
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Next, you need the conjugate of the quaternion (which is called $q^\*$). The following are both the expressions for a quaternion, and a conjugate quaternion:
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Next, you need the conjugate of the quaternion (which is called $q^*$). The following are both the expressions for a quaternion, and a conjugate quaternion:
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$$
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\begin{aligned}
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q &= w + x \mathbf{i} + y \mathbf{j} + z \mathbf{k} \\\\
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q^\* &= w - x \mathbf{i} - y \mathbf{j} - z \mathbf{k}
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q^* &= w - x \mathbf{i} - y \mathbf{j} - z \mathbf{k}
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\end{aligned}
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$$
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With all the required parts, the transformed vector ($p$) is equal to:
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$$
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p = q^\*kq
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p = q^*kq
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$$
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<strong>NOTE:</strong> Quaternion multiplicaiton is [noncommutative](https://en.wikipedia.org/wiki/Commutative_property), meaning that the order you multiply things <em>matters</em>. This is not normal multiplication.
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