Merge branch 'master-upstream' into python_bindings
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Sebastian Koch
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@@ -45,6 +45,7 @@ lecture notes links to a cross-platform example application.</p>
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<li><a href="#scalarfieldvisualization">104 Scalar field visualization</a></li>
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<li><a href="#overlays">105 Overlays</a></li>
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<li><a href="#viewermenu">106 Viewer Menu</a></li>
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<li><a href="#screencapture">107 Screen Capture</a></li>
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</ul></li>
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<li><a href="#chapter2:discretegeometricquantitiesandoperators">Chapter 2: Discrete Geometric Quantities and
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Operators</a>
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@@ -145,6 +146,7 @@ lecture notes links to a cross-platform example application.</p>
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<li><a href="#signeddistances">704 Signed Distances</a></li>
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<li><a href="#marchingcubes">705 Marching Cubes</a></li>
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<li><a href="#facetorientation">706 Facet Orientation</a></li>
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<li><a href="#sweptvolume">707 Swept Volume</a></li>
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</ul></li>
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<li><a href="#future">Chapter 8: Outlook for continuing development</a></li>
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</ul>
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@@ -479,13 +481,13 @@ viewer.callback_init = [&](igl::viewer::Viewer& viewer)
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// Expose a variable directly ...
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viewer.ngui->addVariable("float",floatVariable);
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// Expose an enumaration type
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viewer.ngui->addVariable<Orientation>("Direction",dir)->setItems({"Up","Down","Left","Right"});
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// Add a button
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viewer.ngui->addButton("Print Hello",[](){ std::cout << "Hello\n"; });
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// call to generate menu
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viewer.ngui->layout();
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return false;
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@@ -515,6 +517,25 @@ viewer.ngui->addVariable<bool>("bool",[&](bool val) {
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<figcaption>(<a href="106_ViewerMenu/main.cpp">Example 106</a>) The UI of the viewer can be easily customized.</figcaption>
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</figure>
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<h2 id="screencapture"><a href="#screencapture">Screen capture</a></h2>
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<p>It is possible to render the scene in a memory buffer using the function draw_buffer:</p>
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<pre><code class="cpp">// Allocate temporary buffers
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Eigen::Matrix<unsigned char,Eigen::Dynamic,Eigen::Dynamic> R(1280,800);
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Eigen::Matrix<unsigned char,Eigen::Dynamic,Eigen::Dynamic> G(1280,800);
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Eigen::Matrix<unsigned char,Eigen::Dynamic,Eigen::Dynamic> B(1280,800);
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Eigen::Matrix<unsigned char,Eigen::Dynamic,Eigen::Dynamic> A(1280,800);
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// Draw the scene in the buffers
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viewer.core.draw_buffer(viewer.data,viewer.opengl,false,R,G,B,A);
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// Save it to a PNG
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igl::png::writePNG(R,G,B,A,"out.png");
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</code></pre>
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<p>In <a href="107_ScreenCapture/main.cpp">Example 107</a> a scene is rendered in a temporary png and used to texture a quadrilateral.</p>
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<h1 id="chapter2:discretegeometricquantitiesandoperators">Chapter 2: Discrete Geometric Quantities and Operators</h1>
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<p>This chapter illustrates a few discrete quantities that libigl can compute on a
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@@ -3353,6 +3374,65 @@ Alternatively, each individual triangle is considered a “patch” (mid
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and oriented outward independently.</figcaption>
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</figure>
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<h2 id="sweptvolume"><a href="#sweptvolume">Swept Volume</a></h2>
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<p>The swept volume <span class="math">\(S\)</span> of a moving solid object <span class="math">\(A\)</span> can be defined as any point in
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space such that at one moment in time the point lies inside the solid. In other
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words, it is the union of the solid object transformed by the rigid motion
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<span class="math">\(f(t)\)</span> over time:</p>
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<p><span class="math">\(S = \bigcup \limits_{t\in [0,1]} f(t) A.\)</span></p>
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<p>The surface of the swept volume of a solid bounded by a triangle mesh
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undergoing a rigid motion with non-trivial rotation is <em><strong>not</strong></em> a surface
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exactly representably by triangle mesh: it will be a piecewise-ruled surface.</p>
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<p>To see this, consider the surface swept by a single edge’s line segment as it
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performs a screw motion. </p>
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<p>This means that if we’d like to the surface of the swept volume of a triangle
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mesh undergoing a rigid motion and we’d like the output to be another triangle
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mesh, then we’re going to have to be happy with some amount of approximation
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error.</p>
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<p>With this in mind, the simplest method for computing an approximate swept
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volume is by exploiting an alternative definition of the swept volume based on
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signed distances:</p>
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<p><span class="math">\(S = \left\{ \mathbf{p}\ \middle| \ d(\mathbf{p},\partial S) < 0 \right\} = \left\{ \mathbf{p}\
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\middle|\
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\min\limits_{t \in [0,1]} d(\mathbf{p},f(t)\ \partial A) < 0 \right\}\)</span></p>
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<p>If <span class="math">\(\partial A\)</span> is a triangle mesh, then we can approximate this by 1)
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discretizing time at a finite step of steps <span class="math">\([0,\Delta t,2\Delta t, \dots, 1]\)</span>
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and by 2) discretizing space with a regular grid and representing the distance
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field using trilinear interpolation of grid values. Finally the output mesh,
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<span class="math">\(\partial S\)</span> is approximated by contouring using Marching Cubes
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<a class="citation" href="#fn:38" title="Jump to citation">[38]<span class="citekey" style="display:none">lorensen_1987</span></a>.</p>
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<p>This method is similar to one described by Schroeder et al. in 1994
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<a class="citation" href="#fn:40" title="Jump to citation">[40]<span class="citekey" style="display:none">schroeder_1994</span></a>, and the one used in conjunction with boolean operations by
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Garg et al. 2016 <a class="citation" href="#fn:41" title="Jump to citation">[41]<span class="citekey" style="display:none">garg_2016</span></a>.</p>
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<p>In libigl, if your input solid’s surface is represented by <code>(V,F)</code> then the
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output surface mesh will be <code>(SV,SF)</code> after calling:</p>
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<pre><code class="cpp">igl::copyleft::swept_volume(V,F,num_time_steps,grid_size,isolevel,SV,SF);
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</code></pre>
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<p>The <code>isolevel</code> parameter can be set to zero to approximate the exact swept
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volume, greater than zero to approximate a positive offset of the swept volume
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or less than zero to approximate a negative offset.</p>
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<figure>
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<img src="images/bunny-swept-volume.gif" alt="(Example 707) computes
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the surface of the swept volume (silver) of the bunny model undergoing a rigid
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motion (gold)." />
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<figcaption>(<a href="707_SweptVolume/main.cpp">Example 707</a>) computes
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the surface of the swept volume (silver) of the bunny model undergoing a rigid
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motion (gold).</figcaption>
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</figure>
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<h1 id="future">Outlook for continuing development</h1>
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<p>Libigl is in active development, and we plan to focus on the following features
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@@ -3603,6 +3683,18 @@ pseudonormal</a>,
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2014.</p>
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</li>
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<li id="fn:40" class="citation"><span class="citekey" style="display:none">schroeder_1994</span><p>William J. Schroeder, William E. Lorensen, and Steve
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Linthicum. <a href="https://www.google.com/search?q=implicit+modeling+of+swept+surfaces+and+volumes">Implicit Modeling of Swept Surfaces and
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Volumes</a>,
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1994.</p>
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</li>
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<li id="fn:41" class="citation"><span class="citekey" style="display:none">garg_2016</span><p>Akash Garg, Alec Jacobson, Eitan Grinspun. <a href="https://www.google.com/search?q=Computational+Design+of+Reconfigurables">Computational Design
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of
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Reconfigurables</a>,
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2016</p>
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</li>
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</ol>
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</div>
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