https://benjamin.ahlbrand.me/tags/laplacian/LaplacianHugo Blox Builder (https://hugoblox.com)en-usWed, 03 Feb 2021 00:00:00 +0000https://benjamin.ahlbrand.me/media/sharing.pnghttps://benjamin.ahlbrand.me/tags/laplacian/https://benjamin.ahlbrand.me/post/2021-12-03-laplacian-smoothing/Wed, 03 Feb 2021 00:00:00 +0000https://benjamin.ahlbrand.me/post/2021-12-03-laplacian-smoothing/<p>I implemented laplacian smoothing in my core c++ pipeline using the discrete formulation of the cotangent laplace <strong><a href="https://en.wikipedia.org/wiki/Laplace%E2%80%93Beltrami_operator" target="_blank" rel="noopener">operator</a></strong>.</p> <p>As a test case, I tried &ldquo;over-smoothing&rdquo; a typical mesh to see it reduce along the medial axes. Below you see my source mesh before smoothing:</p> <p> <figure > <div class="flex justify-center "> <div class="w-100" ><img src="https://benjamin.ahlbrand.me/assets/elephant.png" alt="elephant" loading="lazy" data-zoomable /></div> </div></figure> </p> <p>And after several iterations:</p> <p> <figure > <div class="flex justify-center "> <div class="w-100" ><img src="https://benjamin.ahlbrand.me/assets/elephant-semi-smoothed.png" alt="elephant smoothed" loading="lazy" data-zoomable /></div> </div></figure> </p> <p>And now several more:</p> <p># <figure > <div class="flex justify-center "> <div class="w-100" ><img src="https://benjamin.ahlbrand.me/assets/elephant-smoothed.png" alt="" loading="lazy" data-zoomable /></div> </div></figure> </p>