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<!DOCTYPE html><html lang="en-US"><head><title>Math. Unity Math classes</title><meta property="og:title" content="Math. 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/*!
* Marp default theme.
*
* @theme default
* @author Yuki Hattori
*
* @auto-scaling true
* @size 16:9 1280px 720px
* @size 4:3 960px 720px
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class="bespoke-marp-osc"><button data-bespoke-marp-osc="prev" tabindex="-1" title="Previous slide">Previous slide</button><span data-bespoke-marp-osc="page"></span><button data-bespoke-marp-osc="next" tabindex="-1" title="Next slide">Next slide</button><button data-bespoke-marp-osc="fullscreen" tabindex="-1" title="Toggle fullscreen (f)">Toggle fullscreen</button><button data-bespoke-marp-osc="presenter" tabindex="-1" title="Open presenter view (p)">Open presenter view</button></div><div id=":$p"><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="1" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="1" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h1 id="unity-math-classes-mathf-random-quaternion">Unity Math classes: Mathf, Random, Quaternion</h1>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="2" data-marpit-fragments="4" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="2" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h2 id="mathf-class"><code>Mathf</code> class</h2>
<ul>
<li data-marpit-fragment="1"><a href="https://docs.unity3d.com/Manual/class-Mathf.html">Manual: Mathf class</a></li>
<li data-marpit-fragment="2"><a href="https://docs.unity3d.com/ScriptReference/Mathf.html">Script Reference: Mathf class</a></li>
<li data-marpit-fragment="3">Min, Max, Clamp, Abs: See <a href="0-mathf">Helpful Math functions</a></li>
<li data-marpit-fragment="4">See <a href="3-interpolation">Interpolation</a> (lerp, slerp...)</li>
</ul>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="3" data-marpit-fragments="3" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="3" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h3 id="trigonometric-functions">Trigonometric functions</h3>
<ul>
<li data-marpit-fragment="1">Sin, Cos, Tan, Asin, Acos, Atan, Atan2</li>
<li data-marpit-fragment="2">Rad2Deg, Deg2Rad</li>
<li data-marpit-fragment="3">PI</li>
</ul>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="4" data-marpit-fragments="2" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="4" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h3 id="other-functions">Other functions</h3>
<ul>
<li data-marpit-fragment="1">Pow, Sqrt, Exp, Log</li>
<li data-marpit-fragment="2">Abs</li>
</ul>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="5" data-marpit-fragments="6" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="5" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h3 id="limits--repeats">Limits & repeats</h3>
<ul>
<li data-marpit-fragment="1">Max, Min</li>
<li data-marpit-fragment="2">Clamp, Clamp01
<ul>
<li data-marpit-fragment="3">(value, min, max)</li>
</ul>
</li>
<li data-marpit-fragment="4">Repeat, PingPong</li>
<li data-marpit-fragment="5">Ceil, Floor</li>
<li data-marpit-fragment="6"><a href="https://docs.unity3d.com/ScriptReference/Mathf.DeltaAngle.html">Mathf.DeltaAngle(a,b)</a>: Shortest difference between two given angles</li>
</ul>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="6" data-marpit-fragments="3" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="6" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h2 id="random-class"><code>Random</code> class</h2>
<ul>
<li data-marpit-fragment="1"><a href="https://docs.unity3d.com/Manual/class-Random.html">Important classes: Random</a>
<ul>
<li data-marpit-fragment="2">This page has all the random examples you need</li>
</ul>
</li>
<li data-marpit-fragment="3"><a href="https://docs.unity3d.com/ScriptReference/Random.html">Script Reference: Random class</a></li>
</ul>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="7" data-marpit-fragments="6" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="7" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h3 id="randomrange"><code>Random.Range</code></h3>
<ul>
<li data-marpit-fragment="1"><a href="https://docs.unity3d.com/ScriptReference/Random.Range.html">Script Reference: Random.Range</a></li>
<li data-marpit-fragment="2"><strong>Note:</strong> For integers, the maximum value is <em><strong>exclusive</strong></em> (it's not included!)
<ul>
<li data-marpit-fragment="3">For floats it's <em><strong>inclusive</strong></em> (it IS included!)</li>
</ul>
</li>
<li data-marpit-fragment="4">For example:
<ul>
<li data-marpit-fragment="5"><code>Random.Range(0,10)</code> returns random integer values <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="7.303ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 3228 860"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(500,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mo" transform="translate(944.7,0)"><path data-c="2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path></g><g data-mml-node="mo" transform="translate(2283.3,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(2728,0)"><path data-c="39" d="M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z"></path></g></g></g></svg></mjx-container> (not <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="2.262ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 1000 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z" transform="translate(500,0)"></path></g></g></g></svg></mjx-container>!)</li>
<li data-marpit-fragment="6"><code>Random.Range(0f,10f)</code> returns random float values <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="8.434ex" height="1.946ex" role="img" focusable="false" viewBox="0 -666 3728 860"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mo" transform="translate(500,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mo" transform="translate(944.7,0)"><path data-c="2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path></g><g data-mml-node="mo" transform="translate(2283.3,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mn" transform="translate(2728,0)"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z" transform="translate(500,0)"></path></g></g></g></svg></mjx-container></li>
</ul>
</li>
</ul>
</section>
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<h2 id="quaternion-class"><code>Quaternion</code> class</h2>
<ul>
<li data-marpit-fragment="1"><a href="https://docs.unity3d.com/Manual/QuaternionAndEulerRotationsInUnity.html">Manual: Rotation and Orientation in Unity</a></li>
<li data-marpit-fragment="2"><em><strong>Euler angles</strong></em> are a rather simple way of representing rotation with three X,Y,Z values</li>
<li data-marpit-fragment="3"><em><strong>Quaternions</strong></em>: A four-dimensional extension of complex numbers with three imaginary axes</li>
</ul>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="9" data-marpit-fragments="5" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="9" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h3 id="what-you-really-need-to-know-about-quaternions">What you <em>really</em> need to know about Quaternions</h3>
<ul>
<li data-marpit-fragment="1">
<p>They're used for representing rotation angles instead of Euler angles that can result in a <em>gimbal lock</em></p>
</li>
<li data-marpit-fragment="2">
<p>Most Unity devs don't <em>really</em> need to understand the underlying maths</p>
</li>
<li data-marpit-fragment="3">
<p>Even though rotation is <em>stored</em> as a quaternion...</p>
<ul>
<li data-marpit-fragment="4">four components: x, y, z, w</li>
</ul>
</li>
<li data-marpit-fragment="5">
<p>...it is <em>shown</em> in Inspector with Euler angles</p>
</li>
</ul>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="10" data-marpit-fragments="3" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="10" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h3 id="quaternion-note">Quaternion note</h3>
<ul>
<li data-marpit-fragment="1">Never adjust Quaternion components independently, use ready-made functions from the Quaternion class</li>
<li data-marpit-fragment="2"><code>transform.rotation = Quaternion.LookRotation(target.position - transform.position)</code></li>
<li data-marpit-fragment="3"><code>transform.rotation = Quaternion.LookRotation(target.position - transform.position, new Vector3.Up)</code></li>
</ul>
</section>
</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="11" data-marpit-fragments="1" data-paginate="true" data-class="invert" data-heading-divider="3" lang="en-US" class="invert" data-marpit-pagination="11" style="--paginate:true;--class:invert;--heading-divider:3;" data-marpit-pagination-total="11">
<h2 id="reading">Reading</h2>
<ul>
<li data-marpit-fragment="1"><a href="https://www.youtube.com/watch?v=dwI5b-wRLic">GMTK: The two types of random in game design</a></li>
</ul>
</section>
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