/en/tags/affine/Recent content in Affine on Feynman's BlogHugoen-USSun, 09 Aug 2026 12:00:00 +0800/en/posts/games101-transformations/Sun, 09 Aug 2026 12:00:00 +0800/en/posts/games101-transformations/<blockquote class="blockquote-regular"> <p>Instructor: Lingqi Yan | UCSB Bilibili: <a href="https://www.bilibili.com/video/BV1X7411F744">https://www.bilibili.com/video/BV1X7411F744</a></p> </blockquote> <h2 id="1-why-study-transformations">1 Why Study Transformations</h2> <p>Transformations have two core applications in graphics:</p> <table> <thead> <tr> <th style="text-align: center">Application</th> <th style="text-align: left">Description</th> <th style="text-align: left">Example</th> </tr> </thead> <tbody> <tr> <td style="text-align: center"><strong>Modeling</strong></td> <td style="text-align: left">Place objects in a scene</td> <td style="text-align: left">Translate, rotate, scale objects</td> </tr> <tr> <td style="text-align: center"><strong>Viewing</strong></td> <td style="text-align: left">Project 3D scene onto a 2D image</td> <td style="text-align: left">Camera transform, projection transform</td> </tr> </tbody> </table> <hr> <h2 id="2-2d-transformations">2 2D Transformations</h2> <h3 id="scale">Scale</h3> <p><strong>Uniform scale</strong> (all directions scaled equally):</p> <p><img src="/images/2026-07-21_series_games101/03_transforms/chap3_01.png" alt="Uniform Scale"></p> <p>$x' = sx \qquad y' = sy$</p> $$ \begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} s & 0 \\ 0 & s \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} $$<p>For example: $x = 2, \; y = 2, \; s = 0.5$</p>