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<!DOCTYPE html> <html lang="en-US"> <head> <meta charset="UTF-8"> <meta http-equiv="X-UA-Compatible" content="IE=Edge"> <title>Rig - </title> <link rel="shortcut icon" href="/favicon.ico" type="image/x-icon"> <link rel="stylesheet" href="/assets/css/just-the-docs-default.css"> <script type="text/javascript" src="/assets/js/vendor/lunr.min.js"></script> <script type="text/javascript" src="/assets/js/just-the-docs.js"></script> <meta name="viewport" content="width=device-width, initial-scale=1"> <!-- Begin Jekyll SEO tag v2.7.1 --> <title>Rig</title> <meta name="generator" content="Jekyll v4.2.0" /> <meta property="og:title" content="Rig" /> <meta property="og:locale" content="en_US" /> <meta name="twitter:card" content="summary" /> <meta property="twitter:title" content="Rig" /> <script type="application/ld+json"> {"headline":"Rig","@type":"WebPage","url":"/guide/rigging_mode/","@context":"https://schema.org"}</script> <!-- End Jekyll SEO tag --> </head> <body> <svg 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class="nav-list-link">Animate</a></li><li class="nav-list-item "><a href="/guide/layout_mode/" class="nav-list-link">Layout</a></li><li class="nav-list-item "><a href="/guide/model_mode/" class="nav-list-link">Model</a></li><li class="nav-list-item "><a href="/guide/render_mode/" class="nav-list-link">Render</a></li><li class="nav-list-item active"><a href="/guide/rigging_mode/" class="nav-list-link active">Rig</a></li><li class="nav-list-item "><a href="/guide/simulate_mode/" class="nav-list-link">Simulate</a></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/" class="nav-list-link">A2: MeshEdit</a><ul class="nav-list "><li class="nav-list-item "><a href="/meshedit/halfedge" class="nav-list-link">Halfedge Mesh</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/local/" class="nav-list-link">Local Operations</a><ul class="nav-list"><li class="nav-list-item "> <a href="/meshedit/local/edge_flip" class="nav-list-link">Edge Flip Tutorial</a> </li><li class="nav-list-item "> <a href="/meshedit/local/bevel/" class="nav-list-link">Bevelling</a> </li></ul></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/global/" class="nav-list-link">Global Operations</a><ul class="nav-list"><li class="nav-list-item "> <a href="/meshedit/global/catmull/" class="nav-list-link">Catmull-Clark Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/remesh/" class="nav-list-link">Isotropic Remeshing</a> </li><li class="nav-list-item "> <a href="/meshedit/global/linear/" class="nav-list-link">Linear Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/loop/" class="nav-list-link">Loop Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/simplify/" class="nav-list-link">Simplification</a> </li><li class="nav-list-item "> <a href="/meshedit/global/triangulate/" class="nav-list-link">Triangulation</a> </li></ul></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/" class="nav-list-link">A3: Pathtracer</a><ul class="nav-list "><li class="nav-list-item "><a href="/pathtracer/camera_rays" class="nav-list-link">(Task 1) Camera Rays</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/intersecting_objects" class="nav-list-link">(Task 2) Intersections</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/ray_triangle_intersection" class="nav-list-link">Ray Triangle Intersection</a> </li><li class="nav-list-item "> <a href="/pathtracer/ray_sphere_intersection" class="nav-list-link">Ray Sphere Intersection</a> </li></ul></li><li class="nav-list-item "><a href="/pathtracer/bounding_volume_hierarchy" class="nav-list-link">(Task 3) BVH</a></li><li class="nav-list-item "><a href="/pathtracer/shadow_rays" class="nav-list-link">(Task 4) Shadow Rays</a></li><li class="nav-list-item "><a href="/pathtracer/path_tracing" class="nav-list-link">(Task 5) Path Tracing</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/materials" class="nav-list-link">(Task 6) Materials</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/dielectrics_and_transmission" class="nav-list-link">Dielectrics and Transmission</a> </li></ul></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/environment_lighting" class="nav-list-link">(Task 7) Environment Lighting</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/importance_sampling" class="nav-list-link">Environment Light Importance Sampling</a> </li></ul></li><li class="nav-list-item "><a href="/pathtracer/visualization_of_normals" class="nav-list-link">Visualization of normals</a></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/animation/" class="nav-list-link">A4: Animation</a><ul class="nav-list "><li class="nav-list-item "><a href="/animation/splines" class="nav-list-link">Splines</a></li><li class="nav-list-item "><a href="/animation/skeleton_kinematics" class="nav-list-link">Skeleton Kinematics</a></li><li class="nav-list-item "><a href="/animation/skinning" class="nav-list-link">Skinning</a></li><li class="nav-list-item "><a href="/animation/particles" class="nav-list-link">Particles</a></li></ul></li></ul> </nav> <footer class="site-footer"> This site uses <a href="https://github.com/pmarsceill/just-the-docs">Just the Docs</a>, a documentation theme for Jekyll. </footer> </div> <div class="main" id="top"> <div id="main-header" class="main-header"> <div class="search"> <div class="search-input-wrap"> <input type="text" id="search-input" class="search-input" tabindex="0" placeholder="Search " aria-label="Search " autocomplete="off"> <label for="search-input" class="search-label"><svg viewBox="0 0 24 24" class="search-icon"><use xlink:href="#svg-search"></use></svg></label> </div> <div id="search-results" class="search-results"></div> </div> </div> <div id="main-content-wrap" class="main-content-wrap"> <nav aria-label="Breadcrumb" class="breadcrumb-nav"> <ol class="breadcrumb-nav-list"> <li class="breadcrumb-nav-list-item"><a href="/guide/">User Guide</a></li> <li class="breadcrumb-nav-list-item"><span>Rig</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="rig"> <a href="#rig" class="anchor-heading" aria-labelledby="rig"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Rig </h1> <h3 id="rigging-setup"> <a href="#rigging-setup" class="anchor-heading" aria-labelledby="rigging-setup"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Rigging Setup </h3> <p>Select the <code class="language-plaintext highlighter-rouge">Rig</code> tab to create a skeletal rig for an object.</p> <p>You can create new bone by first selecting a parent joint and pressing <code class="language-plaintext highlighter-rouge">New Bone</code>, then click anywhere else on the object to place the bone. From thereon, you can repeat this process to create a chain of bones connected along the selected joint. If you want to branch off at a joint, simply click on the joint to branch off of, then start another chain by adding a new bone from there.</p> <video src="/guide/rigging_mode/guide-rigging-1.mov" controls="" preload="" muted="" loop="" style="max-width: 100%; margin: 0 auto;"></video> <p>To view a rigged example, see <code class="language-plaintext highlighter-rouge">media/human.dae</code> example and select the object in the Rig tab to view its joints. Once you’ve implemented forward kinematics the skeleton should be setup like so:</p> <p><img src="guide-rigging-human.png" alt="rigged-human" /></p> <h3 id="editing-skinning-weight-threshold-radius"> <a href="#editing-skinning-weight-threshold-radius" class="anchor-heading" aria-labelledby="editing-skinning-weight-threshold-radius"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Editing Skinning Weight Threshold Radius </h3> <p>Each joint has an associated <code class="language-plaintext highlighter-rouge">Radius</code> which controls the part of the mesh influenced by the selected bone during animaton. The radius is visualized by the blue capsule around each bone and can be edited using the menu. The position of the joint can also be edited using the <code class="language-plaintext highlighter-rouge">Extent</code> values in the menu.</p> <video src="/guide/rigging_mode/guide-rigging-2.mov" controls="" preload="" muted="" loop="" style="max-width: 100%; margin: 0 auto;"></video> <p>Note that rigging only uses extents of the bone for skeleton setup, joint pose does not influence the skeleton. Once rigging is done, the object can be posed by changing joint rotations in the <a href="../animate_mode">animate</a> mode.</p> <h2 id="inverse-kinematics"> <a href="#inverse-kinematics" class="anchor-heading" aria-labelledby="inverse-kinematics"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Inverse Kinematics </h2> <p>Instead of computing the positions of the bones from the joint poses (forward kinematics), in inverse kinematics, joint positions are computed from target positions. To associate a target position with a joint, select <code class="language-plaintext highlighter-rouge">Add IK</code> and edit the target position. Multiple target positions can be associated with the same joint but targets need to be explicitly enabled using the checkbox.</p> <p>In the <a href="../animate_mode">animate</a> mode, once inverse kinematics is implemented, joint rotation(pose) is updated based on the enabled IK handles.</p> <video src="/guide/rigging_mode/guide-ik.mp4" controls="" preload="" muted="" loop="" style="max-width: 100%; margin: 0 auto;"></video> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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<!DOCTYPE html> <html lang="en-US"> <head> <meta charset="UTF-8"> <meta http-equiv="X-UA-Compatible" content="IE=Edge"> <title>Simulate - </title> <link rel="shortcut icon" href="/favicon.ico" type="image/x-icon"> <link rel="stylesheet" href="/assets/css/just-the-docs-default.css"> <script type="text/javascript" src="/assets/js/vendor/lunr.min.js"></script> <script type="text/javascript" src="/assets/js/just-the-docs.js"></script> <meta name="viewport" content="width=device-width, initial-scale=1"> <!-- Begin Jekyll SEO tag v2.7.1 --> <title>Simulate</title> <meta name="generator" content="Jekyll v4.2.0" /> <meta property="og:title" content="Simulate" /> <meta property="og:locale" content="en_US" /> <meta name="twitter:card" content="summary" /> <meta property="twitter:title" content="Simulate" /> <script type="application/ld+json"> {"headline":"Simulate","@type":"WebPage","url":"/guide/simulate_mode/","@context":"https://schema.org"}</script> <!-- End Jekyll SEO tag --> </head> <body> <svg xmlns="http://www.w3.org/2000/svg" style="display: none;"> <symbol id="svg-link" viewBox="0 0 24 24"> <title>Link</title> <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="feather feather-link"> <path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path> </svg> </symbol> <symbol id="svg-search" viewBox="0 0 24 24"> <title>Search</title> <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="feather feather-search"> <circle cx="11" cy="11" r="8"></circle><line x1="21" y1="21" x2="16.65" y2="16.65"></line> </svg> </symbol> <symbol id="svg-menu" viewBox="0 0 24 24"> <title>Menu</title> <svg 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class="nav-list-link">Animate</a></li><li class="nav-list-item "><a href="/guide/layout_mode/" class="nav-list-link">Layout</a></li><li class="nav-list-item "><a href="/guide/model_mode/" class="nav-list-link">Model</a></li><li class="nav-list-item "><a href="/guide/render_mode/" class="nav-list-link">Render</a></li><li class="nav-list-item "><a href="/guide/rigging_mode/" class="nav-list-link">Rig</a></li><li class="nav-list-item active"><a href="/guide/simulate_mode/" class="nav-list-link active">Simulate</a></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/" class="nav-list-link">A2: MeshEdit</a><ul class="nav-list "><li class="nav-list-item "><a href="/meshedit/halfedge" class="nav-list-link">Halfedge Mesh</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/local/" class="nav-list-link">Local Operations</a><ul class="nav-list"><li class="nav-list-item "> <a href="/meshedit/local/edge_flip" class="nav-list-link">Edge Flip Tutorial</a> </li><li class="nav-list-item "> <a href="/meshedit/local/bevel/" class="nav-list-link">Bevelling</a> </li></ul></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/global/" class="nav-list-link">Global Operations</a><ul class="nav-list"><li class="nav-list-item "> <a href="/meshedit/global/catmull/" class="nav-list-link">Catmull-Clark Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/remesh/" class="nav-list-link">Isotropic Remeshing</a> </li><li class="nav-list-item "> <a href="/meshedit/global/linear/" class="nav-list-link">Linear Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/loop/" class="nav-list-link">Loop Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/simplify/" class="nav-list-link">Simplification</a> </li><li class="nav-list-item "> <a href="/meshedit/global/triangulate/" class="nav-list-link">Triangulation</a> </li></ul></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/" class="nav-list-link">A3: Pathtracer</a><ul class="nav-list "><li class="nav-list-item "><a href="/pathtracer/camera_rays" class="nav-list-link">(Task 1) Camera Rays</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/intersecting_objects" class="nav-list-link">(Task 2) Intersections</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/ray_triangle_intersection" class="nav-list-link">Ray Triangle Intersection</a> </li><li class="nav-list-item "> <a href="/pathtracer/ray_sphere_intersection" class="nav-list-link">Ray Sphere Intersection</a> </li></ul></li><li class="nav-list-item "><a href="/pathtracer/bounding_volume_hierarchy" class="nav-list-link">(Task 3) BVH</a></li><li class="nav-list-item "><a href="/pathtracer/shadow_rays" class="nav-list-link">(Task 4) Shadow Rays</a></li><li class="nav-list-item "><a href="/pathtracer/path_tracing" class="nav-list-link">(Task 5) Path Tracing</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/materials" class="nav-list-link">(Task 6) Materials</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/dielectrics_and_transmission" class="nav-list-link">Dielectrics and Transmission</a> </li></ul></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/environment_lighting" class="nav-list-link">(Task 7) Environment Lighting</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/importance_sampling" class="nav-list-link">Environment Light Importance Sampling</a> </li></ul></li><li class="nav-list-item "><a href="/pathtracer/visualization_of_normals" class="nav-list-link">Visualization of normals</a></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/animation/" class="nav-list-link">A4: Animation</a><ul class="nav-list "><li class="nav-list-item "><a href="/animation/splines" class="nav-list-link">Splines</a></li><li class="nav-list-item "><a href="/animation/skeleton_kinematics" class="nav-list-link">Skeleton Kinematics</a></li><li class="nav-list-item "><a href="/animation/skinning" class="nav-list-link">Skinning</a></li><li class="nav-list-item "><a href="/animation/particles" class="nav-list-link">Particles</a></li></ul></li></ul> </nav> <footer class="site-footer"> This site uses <a href="https://github.com/pmarsceill/just-the-docs">Just the Docs</a>, a documentation theme for Jekyll. </footer> </div> <div class="main" id="top"> <div id="main-header" class="main-header"> <div class="search"> <div class="search-input-wrap"> <input type="text" id="search-input" class="search-input" tabindex="0" placeholder="Search " aria-label="Search " autocomplete="off"> <label for="search-input" class="search-label"><svg viewBox="0 0 24 24" class="search-icon"><use xlink:href="#svg-search"></use></svg></label> </div> <div id="search-results" class="search-results"></div> </div> </div> <div id="main-content-wrap" class="main-content-wrap"> <nav aria-label="Breadcrumb" class="breadcrumb-nav"> <ol class="breadcrumb-nav-list"> <li class="breadcrumb-nav-list-item"><a href="/guide/">User Guide</a></li> <li class="breadcrumb-nav-list-item"><span>Simulate</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="simulate"> <a href="#simulate" class="anchor-heading" aria-labelledby="simulate"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Simulate </h1> <p>The simulation view provides a way to create and manage particle emitters.</p> <p>To add an emitter, open the dropdown menu, adjust desired parameters, and press <code class="language-plaintext highlighter-rouge">Add</code>.</p> <p><img src="simulate_mode/add_emitter.png" alt="add emitter" /></p> <ul> <li>Color: color with which to render the particles.</li> <li>Angle: angle of cone within which particles are generated (pointing in the emitter object’s direction).</li> <li>Scale: the scale factor to apply to the particle mesh when rendering particles.</li> <li>Lifetime: how long (in seconds) each particle should live before it is deleted.</li> <li>Particles/Sec: how many particles should be generated per second. The total amount of live particles is hence <code class="language-plaintext highlighter-rouge">lifetime * particles_per_second</code>.</li> <li>Particle: choose the shape of each particle. If mesh objects are present in the scene, they will also show up here, allowing the creation of particles with custom shapes.</li> <li>Enabled: whether to immediately enable the emitter</li> </ul> <p>Once an enabled emitter is added to the scene (and animation task 4: particle simulation is implemented), particles will start generating and following trajectories based on the emitter parameters. Particles should collide with scene objects. When moving existing objects that particles interact with, the simulation will not be updated until the movement is completed.</p> <p>For example, the <code class="language-plaintext highlighter-rouge">particles.dae</code> test scene:</p> <video src="/guide/simulate_mode/guide-simulate-1.mp4" controls="" preload="" muted="" loop="" style="max-width: 100%; margin: 0 auto;"></video> <p>Finally, note that you can render particles just like any other scene objects. In the path tracer, each particle is also a point light source! Rendering <code class="language-plaintext highlighter-rouge">particles.dae</code> with depth of field:</p> <p><img src="simulate_mode/render.png" alt="particles render" /></p> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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<!DOCTYPE html> <html lang="en-US"> <head> <meta charset="UTF-8"> <meta http-equiv="X-UA-Compatible" content="IE=Edge"> <title>Home - </title> <link rel="shortcut icon" href="/favicon.ico" type="image/x-icon"> <link rel="stylesheet" href="/assets/css/just-the-docs-default.css"> <script type="text/javascript" src="/assets/js/vendor/lunr.min.js"></script> <script type="text/javascript" src="/assets/js/just-the-docs.js"></script> <meta name="viewport" content="width=device-width, initial-scale=1"> <!-- Begin Jekyll SEO tag v2.7.1 --> <title>Home</title> <meta name="generator" content="Jekyll v4.2.0" /> <meta property="og:title" content="Home" /> <meta property="og:locale" content="en_US" /> <meta name="twitter:card" content="summary" /> <meta property="twitter:title" content="Home" /> <script type="application/ld+json"> {"headline":"Home","@type":"WebSite","url":"/","@context":"https://schema.org"}</script> <!-- End Jekyll SEO tag --> </head> <body> <svg xmlns="http://www.w3.org/2000/svg" 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points="13 2 13 9 20 9"></polyline> </svg> </symbol> </svg> <div class="side-bar"> <div class="site-header"> <a href="/" class="site-title lh-tight"> </a> <a href="#" id="menu-button" class="site-button"> <svg viewBox="0 0 24 24" class="icon"><use xlink:href="#svg-menu"></use></svg> </a> </div> <nav role="navigation" aria-label="Main" id="site-nav" class="site-nav"> <ul class="nav-list"><li class="nav-list-item active"><a href="/" class="nav-list-link active">Home</a></li><li class="nav-list-item"><a href="/git/" class="nav-list-link">GitHub Setup</a></li><li class="nav-list-item"><a href="/build/" class="nav-list-link">Building Scotty3D</a></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/guide/" class="nav-list-link">User Guide</a><ul class="nav-list "><li class="nav-list-item "><a href="/guide/animate_mode/" class="nav-list-link">Animate</a></li><li class="nav-list-item "><a href="/guide/layout_mode/" class="nav-list-link">Layout</a></li><li class="nav-list-item "><a href="/guide/model_mode/" class="nav-list-link">Model</a></li><li class="nav-list-item "><a href="/guide/render_mode/" class="nav-list-link">Render</a></li><li class="nav-list-item "><a href="/guide/rigging_mode/" class="nav-list-link">Rig</a></li><li class="nav-list-item "><a href="/guide/simulate_mode/" class="nav-list-link">Simulate</a></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/" class="nav-list-link">A2: MeshEdit</a><ul class="nav-list "><li class="nav-list-item "><a href="/meshedit/halfedge" class="nav-list-link">Halfedge Mesh</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/local/" class="nav-list-link">Local Operations</a><ul class="nav-list"><li class="nav-list-item "> <a href="/meshedit/local/edge_flip" class="nav-list-link">Edge Flip Tutorial</a> </li><li class="nav-list-item "> <a href="/meshedit/local/bevel/" class="nav-list-link">Bevelling</a> </li></ul></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/meshedit/global/" class="nav-list-link">Global Operations</a><ul class="nav-list"><li class="nav-list-item "> <a href="/meshedit/global/catmull/" class="nav-list-link">Catmull-Clark Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/remesh/" class="nav-list-link">Isotropic Remeshing</a> </li><li class="nav-list-item "> <a href="/meshedit/global/linear/" class="nav-list-link">Linear Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/loop/" class="nav-list-link">Loop Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/simplify/" class="nav-list-link">Simplification</a> </li><li class="nav-list-item "> <a href="/meshedit/global/triangulate/" class="nav-list-link">Triangulation</a> </li></ul></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/" class="nav-list-link">A3: Pathtracer</a><ul class="nav-list "><li class="nav-list-item "><a href="/pathtracer/camera_rays" class="nav-list-link">(Task 1) Camera Rays</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/intersecting_objects" class="nav-list-link">(Task 2) Intersections</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/ray_triangle_intersection" class="nav-list-link">Ray Triangle Intersection</a> </li><li class="nav-list-item "> <a href="/pathtracer/ray_sphere_intersection" class="nav-list-link">Ray Sphere Intersection</a> </li></ul></li><li class="nav-list-item "><a href="/pathtracer/bounding_volume_hierarchy" class="nav-list-link">(Task 3) BVH</a></li><li class="nav-list-item "><a href="/pathtracer/shadow_rays" class="nav-list-link">(Task 4) Shadow Rays</a></li><li class="nav-list-item "><a href="/pathtracer/path_tracing" class="nav-list-link">(Task 5) Path Tracing</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/materials" class="nav-list-link">(Task 6) Materials</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/dielectrics_and_transmission" class="nav-list-link">Dielectrics and Transmission</a> </li></ul></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/environment_lighting" class="nav-list-link">(Task 7) Environment Lighting</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/importance_sampling" class="nav-list-link">Environment Light Importance Sampling</a> </li></ul></li><li class="nav-list-item "><a href="/pathtracer/visualization_of_normals" class="nav-list-link">Visualization of normals</a></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/animation/" class="nav-list-link">A4: Animation</a><ul class="nav-list "><li class="nav-list-item "><a href="/animation/splines" class="nav-list-link">Splines</a></li><li class="nav-list-item "><a href="/animation/skeleton_kinematics" class="nav-list-link">Skeleton Kinematics</a></li><li class="nav-list-item "><a href="/animation/skinning" class="nav-list-link">Skinning</a></li><li class="nav-list-item "><a href="/animation/particles" class="nav-list-link">Particles</a></li></ul></li></ul> </nav> <footer class="site-footer"> This site uses <a href="https://github.com/pmarsceill/just-the-docs">Just the Docs</a>, a documentation theme for Jekyll. </footer> </div> <div class="main" id="top"> <div id="main-header" class="main-header"> <div class="search"> <div class="search-input-wrap"> <input type="text" id="search-input" class="search-input" tabindex="0" placeholder="Search " aria-label="Search " autocomplete="off"> <label for="search-input" class="search-label"><svg viewBox="0 0 24 24" class="search-icon"><use xlink:href="#svg-search"></use></svg></label> </div> <div id="search-results" class="search-results"></div> </div> </div> <div id="main-content-wrap" class="main-content-wrap"> <div id="main-content" class="main-content" role="main"> <!--![15-462 F20 Renders](results/me_f20.png)--> <!--![15-462 F20 Renders](results/pt_f20_2.png)--> <p><img src="results/me_f20_crop.png" alt="15-462 F20 Renders" /></p> <h1 id="scotty3d"> <a href="#scotty3d" class="anchor-heading" aria-labelledby="scotty3d"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Scotty3D </h1> <p>Welcome to Scotty3D! This 3D graphics software package includes components for interactive mesh editing, realistic path tracing, and dynamic animation. Implementing functionality in each of these areas constitutes the majority of the coursework for 15-462/662 (Computer Graphics) at Carnegie Mellon University</p> <p>These pages describe how to set up and use Scotty3D. Start here!</p> <ul> <li><a href="git">Git Setup</a>: create a private git mirror that can pull changes from Scotty3D.</li> <li><a href="build">Building Scotty3D</a>: build and run Scotty3D on various platforms.</li> <li><a href="guide">User Guide</a>: learn the intended functionality for end users.</li> </ul> <p>The developer manual describes what you must implement to complete Scotty3D. It is organized under the three main components of the software:</p> <ul> <li><a href="meshedit">MeshEdit</a></li> <li><a href="pathtracer">PathTracer</a></li> <li><a href="animation">Animation</a></li> </ul> <h2 id="project-philosophy"> <a href="#project-philosophy" class="anchor-heading" aria-labelledby="project-philosophy"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Project Philosophy </h2> <p>Welcome to your first day of work at Scotty Industries! Over the next few months you will implement core features in Scotty Industries’ flagship product Scotty3D, which is a modern package for 3D modeling, rendering, and animation. In terms of basic structure, this package doesn’t look much different from “real” 3D tools like Maya, Blender, modo, or Houdini. Your overarching goal is to use the developer manual to implement a package that works as described in the <a href="guide">User Guide</a>, much as you would at a real software company (more details below).</p> <p>Note that the User Guide is <strong>not</strong> an Assignment Writeup. The User Guide contains only instructions on how to use the software, and serves as a high-level specification of <em>what the software should do</em>. The Developer Guide contains information about the internals of the code, i.e., <em>how the software works</em>. This division is quite common in software development: there is a <strong>design specification</strong> or “design spec”, and an <strong>implementation</strong> that implements that spec. Also, as in the real world, the design spec does <em>not</em> necessarily specify every tiny detail of how the software should behave! Some behaviors may be undefined, and some of these details are left up to the party who implements the specification. A good example you have already seen is OpenGL, which defines some important rules about how rasterization should behave, but is not a “pixel-exact” specification. In other words, two different OpenGL implementations from two different vendors (Intel and NVIDIA, say) may produce images that differ by a number of pixels. Likewise, in this assignment, your implementation may differ from the implementation of your classmates in terms of the exact values it produces, or the particular collection of corner-cases it handles. However, as a developer you should strive to provide a solution that meets a few fundamental criteria:</p> <ul> <li><a href="https://en.wikipedia.org/wiki/Fault_tolerance">Failing gracefully</a> is preferable to failing utterly—for instance, if a rare corner case is difficult to handle, it is far better to simply refuse to perform the operation than to let the program crash!</li> <li>Your implementation should follow the <a href="https://en.wikipedia.org/wiki/Principle_of_least_astonishment">principle of least surprise</a>. A user should be able to expect that things behave more or less as they are described in the User Guide.</li> <li>You should not use an algorithm whose performance is <a href="https://en.wikipedia.org/wiki/Asymptotic_computational_complexity">asymptotically worse</a> just because it makes your code easier to write (for instance, using <a href="https://en.wikipedia.org/wiki/Bubble_sort">bubble sort</a> rather than <a href="https://en.wikipedia.org/wiki/Merge_sort">merge sort</a> on large data sets).</li> <li>That being said, when it comes to performance, <a href="https://en.wikipedia.org/wiki/Program_optimization#When_to_optimize">premature optimization is the root of all evil!</a> The only way to know whether an optimization matters is to <a href="https://en.wikipedia.org/wiki/Profiling_(computer_programming)">measure performance</a>, and understand <a href="https://en.wikipedia.org/wiki/Program_optimization#Bottlenecks">bottlenecks</a>.</li> <li>Finally, you should take pride in your craft. Beautiful things just tend to work better.</li> </ul> <p>Just to reiterate the main point above:</p> <p><strong>As in real-world software development, we will not specify every little detail about how methods in this assignment should work!</strong></p> <p>If you encounter a tough corner case (e.g., “how should edge flip behave for a tetrahedron”), we want you to <em>think about what a good <strong>design choice</strong> might be</em>, and implement it to the best of your ability. This activity is part of becoming a world-class developer. However, we are more than happy to discuss good design choices with you, and you should also feel free to discuss these choices with your classmates. Practically speaking, it is ok for routines to simply show an error if they encounter a rare and difficult corner case—as long as it does not interfere with successful operation of the program (i.e., if it does not crash or yield bizarre behavior). Your main goal here above all else should be to develop <em>effective tool for modeling, rendering, and animation</em>.</p> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/loop/" class="nav-list-link">Loop Subdivision</a> </li><li class="nav-list-item "> <a href="/meshedit/global/simplify/" class="nav-list-link">Simplification</a> </li><li class="nav-list-item "> <a href="/meshedit/global/triangulate/" class="nav-list-link">Triangulation</a> </li></ul></li></ul></li><li class="nav-list-item"><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/" class="nav-list-link">A3: Pathtracer</a><ul class="nav-list "><li class="nav-list-item "><a href="/pathtracer/camera_rays" class="nav-list-link">(Task 1) Camera Rays</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/intersecting_objects" class="nav-list-link">(Task 2) Intersections</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/ray_triangle_intersection" class="nav-list-link">Ray Triangle Intersection</a> </li><li class="nav-list-item "> <a href="/pathtracer/ray_sphere_intersection" class="nav-list-link">Ray Sphere Intersection</a> </li></ul></li><li class="nav-list-item "><a href="/pathtracer/bounding_volume_hierarchy" class="nav-list-link">(Task 3) BVH</a></li><li class="nav-list-item "><a href="/pathtracer/shadow_rays" class="nav-list-link">(Task 4) Shadow Rays</a></li><li class="nav-list-item "><a href="/pathtracer/path_tracing" class="nav-list-link">(Task 5) Path Tracing</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/materials" class="nav-list-link">(Task 6) Materials</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/dielectrics_and_transmission" class="nav-list-link">Dielectrics and Transmission</a> </li></ul></li><li class="nav-list-item 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class="breadcrumb-nav-list-item"><a href="/meshedit/">A2: MeshEdit</a></li> <li class="breadcrumb-nav-list-item"><a href="/meshedit/global/">Global Operations</a></li> <li class="breadcrumb-nav-list-item"><span>Catmull-Clark Subdivision</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="catmull-clark-subdivision"> <a href="#catmull-clark-subdivision" class="anchor-heading" aria-labelledby="catmull-clark-subdivision"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Catmull-Clark Subdivision </h1> <p>For an in-practice example, see the <a href="/Scotty3D/guide/model">User Guide</a>.</p> <p>The only difference between Catmull-Clark and <a href="../linear">linear</a> subdivision is the choice of positions for new vertices. Whereas linear subdivision simply takes a uniform average of the old vertex positions, Catmull-Clark uses a very carefully-designed <em>weighted</em> average to ensure that the surface converges to a nice, round surface as the number of subdivision steps increases. The original scheme is described in the paper <em>“Recursively generated B-spline surfaces on arbitrary topological meshes”</em> by (Pixar co-founder) Ed Catmull and James Clark. Since then, the scheme has been thoroughly discussed, extended, and analyzed; more modern descriptions of the algorithm may be easier to read, including those from the <a href="https://en.wikipedia.org/wiki/Catmull-Clark_subdivision_surface">Wikipedia</a> and <a href="http://www.rorydriscoll.com/2008/08/01/catmull-clark-subdivision-the-basics/">this webpage</a>. In short, the new vertex positions can be calculated by:</p> <ol> <li>setting the new vertex position at each face f to the average of all its original vertices (exactly as in linear subdivision),</li> <li>setting the new vertex position at each edge e to the average of the new face positions (from step 1) and the original endpoint positions, and</li> <li>setting the new vertex position at each vertex v to the weighted sum</li> </ol> <center><img src="catmull_clark_positions.png" style="height:80px" /></center> <p>where <em>n</em> is the degree of vertex <em>v</em> (i.e., the number of faces containing <em>v</em>), and</p> <ul> <li><em>Q</em> is the average of all new face position for faces containing <em>v</em>,</li> <li><em>R</em> is the average of all original edge midpoints for edges containing <em>v</em>, and</li> <li><em>S</em> is the original vertex position for vertex <em>v</em>.</li> </ul> <p>In other words, the new vertex positions are an “average of averages.” (Note that you <em>will</em> need to divide by <em>n</em> <em>both</em> when computing <em>Q</em> and <em>R</em>, <em>and</em> when computing the final, weighted value—this is not a typo!)</p> <p>Apart from changing the way vertex positions are computed, there should be no difference in your implementation of linear and Catmull-Clark subdivision.</p> <p>This step should be implemented in the method <code class="language-plaintext highlighter-rouge">HalfedgeMesh::catmullclark_subdivide_positions</code> in <code class="language-plaintext highlighter-rouge">student/meshedit.cpp</code>.</p> <p>This subdivision rule <strong>is not</strong> required to support meshes with boundary, unless the implementer wishes to go above and beyond.</p> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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class="nav-list-link">Ray Triangle Intersection</a> </li><li class="nav-list-item "> <a href="/pathtracer/ray_sphere_intersection" class="nav-list-link">Ray Sphere Intersection</a> </li></ul></li><li class="nav-list-item "><a href="/pathtracer/bounding_volume_hierarchy" class="nav-list-link">(Task 3) BVH</a></li><li class="nav-list-item "><a href="/pathtracer/shadow_rays" class="nav-list-link">(Task 4) Shadow Rays</a></li><li class="nav-list-item "><a href="/pathtracer/path_tracing" class="nav-list-link">(Task 5) Path Tracing</a></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg viewBox="0 0 24 24"><use xlink:href="#svg-arrow-right"></use></svg></a><a href="/pathtracer/materials" class="nav-list-link">(Task 6) Materials</a><ul class="nav-list"><li class="nav-list-item "> <a href="/pathtracer/dielectrics_and_transmission" class="nav-list-link">Dielectrics and Transmission</a> </li></ul></li><li class="nav-list-item "><a href="#" class="nav-list-expander"><svg 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class="nav-list-link">Skinning</a></li><li class="nav-list-item "><a href="/animation/particles" class="nav-list-link">Particles</a></li></ul></li></ul> </nav> <footer class="site-footer"> This site uses <a href="https://github.com/pmarsceill/just-the-docs">Just the Docs</a>, a documentation theme for Jekyll. </footer> </div> <div class="main" id="top"> <div id="main-header" class="main-header"> <div class="search"> <div class="search-input-wrap"> <input type="text" id="search-input" class="search-input" tabindex="0" placeholder="Search " aria-label="Search " autocomplete="off"> <label for="search-input" class="search-label"><svg viewBox="0 0 24 24" class="search-icon"><use xlink:href="#svg-search"></use></svg></label> </div> <div id="search-results" class="search-results"></div> </div> </div> <div id="main-content-wrap" class="main-content-wrap"> <nav aria-label="Breadcrumb" class="breadcrumb-nav"> <ol class="breadcrumb-nav-list"> <li class="breadcrumb-nav-list-item"><a href="/meshedit/">A2: MeshEdit</a></li> <li class="breadcrumb-nav-list-item"><span>Global Operations</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="global-mesh-operations"> <a href="#global-mesh-operations" class="anchor-heading" aria-labelledby="global-mesh-operations"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Global Mesh Operations </h1> <p>In addition to local operations on mesh connectivity, Scotty3D provides several global remeshing operations (as outlined in the <a href="/Scotty3D/guide/model">User Guide</a>). Two different mechanisms are used to implement global operations:</p> <ul> <li><em>Repeated application of local operations.</em> Some mesh operations are most easily expressed by applying local operations (edge flips, etc.) to a sequence of mesh elements until the target output is achieved. A good example is <a href="simplify">mesh simplification</a>, which is a greedy algorithm that collapses one edge at a time.</li> <li><em>Global replacement of the mesh.</em> Other mesh operations are better expressed by temporarily storing new mesh elements in a simpler mesh data structure (e.g., an indexed list of faces) and completely re-building the halfedge data structure from this data. A good example is <a href="catmull">Catmull-Clark subdivision</a>, where every polygon must be simultaneously split into quadrilaterals.</li> </ul> <p>Note that in general there are no inter-dependencies among global remeshing operations (except that some of them require a triangle mesh as input, which can be achieved via the method <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::triangulate</code>).</p> <h2 id="subdivision"> <a href="#subdivision" class="anchor-heading" aria-labelledby="subdivision"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Subdivision </h2> <p>In image processing, we often have a low resolution image that we want to display at a higher resolution. Since we only have a few samples of the original signal, we need to somehow interpolate or <em>upsample</em> the image. One idea would be to simply cut each pixel into four, leaving the color values unchanged, but this leads to a blocky appearance. Instead we might try a more sophisticated scheme (like bilinear or trilinear interpolation) that yields a smoother appearance.</p> <p>In geometry processing, one encounters the same situation: we may have a low-resolution polygon mesh that we wish to upsample for display, simulation, etc. Simply splitting each polygon into smaller pieces doesn’t help, because it does nothing to alleviate blocky silhouettes or chunky features. Instead, we need an upsampling scheme that nicely interpolates or approximates the original data. Polygon meshes are quite a bit trickier than images, however, since our sample points are generally at <em>irregular</em> locations, i.e., they are no longer found at regular intervals on a grid.</p> <p>Three subdivision schemes are supported by Scotty3D: <a href="linear">Linear</a>, <a href="catmull">Catmull-Clark</a>, and <a href="loop">Loop</a>. The first two can be used on any polygon mesh without boundary, and should be implemented via the global replacement strategy described above. Loop subdivision can be implemented using repeated application of local operations. For further details, see the linked pages.</p> <h2 id="performance"> <a href="#performance" class="anchor-heading" aria-labelledby="performance"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Performance </h2> <p>All subdivision operations, as well as re-meshing and simplification, should complete almost instantaneously (no more than a second) on meshes of a few hundred polygons or fewer. If performance is worse than this, ensure that implementations are not repeatedly iterating over more elements than needed, or allocating/deallocating more memory than necessary. A useful debugging technique is to print out (or otherwise keep track of, e.g., via an integer counter or a profiler) the number of times basic methods like <code class="language-plaintext highlighter-rouge">Halfedge::next()</code> or <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::new_vertex()</code> are called during a single execution of one of the methods; for most methods this number should be some reasonably small constant (no more than, say, 1000!) times the number of elements in the mesh.</p> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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href="/animation/skinning" class="nav-list-link">Skinning</a></li><li class="nav-list-item "><a href="/animation/particles" class="nav-list-link">Particles</a></li></ul></li></ul> </nav> <footer class="site-footer"> This site uses <a href="https://github.com/pmarsceill/just-the-docs">Just the Docs</a>, a documentation theme for Jekyll. </footer> </div> <div class="main" id="top"> <div id="main-header" class="main-header"> <div class="search"> <div class="search-input-wrap"> <input type="text" id="search-input" class="search-input" tabindex="0" placeholder="Search " aria-label="Search " autocomplete="off"> <label for="search-input" class="search-label"><svg viewBox="0 0 24 24" class="search-icon"><use xlink:href="#svg-search"></use></svg></label> </div> <div id="search-results" class="search-results"></div> </div> </div> <div id="main-content-wrap" class="main-content-wrap"> <nav aria-label="Breadcrumb" class="breadcrumb-nav"> <ol class="breadcrumb-nav-list"> <li class="breadcrumb-nav-list-item"><a href="/meshedit/">A2: MeshEdit</a></li> <li class="breadcrumb-nav-list-item"><a href="/meshedit/global/">Global Operations</a></li> <li class="breadcrumb-nav-list-item"><span>Linear Subdivision</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="linear-subdivision"> <a href="#linear-subdivision" class="anchor-heading" aria-labelledby="linear-subdivision"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Linear Subdivision </h1> <p>For an in-practice example, see the <a href="/Scotty3D/guide/model">User Guide</a>.</p> <p>Unlike most other global remeshing operations, linear (and Catmull-Clark) subdivision will proceed by completely replacing the original halfedge mesh with a new one. The high-level procedure is:</p> <ol> <li>Generate a list of vertex positions for the new mesh.</li> <li>Generate a list of polygons for the new mesh, as a list of indices into the new vertex list (a la “polygon soup”).</li> <li>Using these two lists, rebuild the halfedge connectivity from scratch.</li> </ol> <p>Given these lists, <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::from_poly</code> will take care of allocating halfedges, setting up <code class="language-plaintext highlighter-rouge">next</code> and <code class="language-plaintext highlighter-rouge">twin</code> pointers, etc., based on the list of polygons generated in step 2—this routine is already implemented in the Scotty3D skeleton code.</p> <p>Both linear and Catmull-Clark subdivision schemes will handle general <em>n</em>-gons (i.e., polygons with <em>n</em> sides) rather than, say, quads only or triangles only. Each <em>n</em>-gon (including but not limited to quadrilaterals) will be split into <em>n</em> quadrilaterals according to the following template:</p> <center><img src="subdivide_quad.png" style="height:220px" /></center> <p>The high-level procedure is outlined in greater detail in <code class="language-plaintext highlighter-rouge">student/meshedit.cpp</code>.</p> <h3 id="vertex-positions"> <a href="#vertex-positions" class="anchor-heading" aria-labelledby="vertex-positions"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Vertex Positions </h3> <p>For global linear or Catmull-Clark subdivision, the strategy for assigning new vertex positions may at first appear a bit strange: in addition to updating positions at vertices, we will also calculate vertex positions associated with the <em>edges</em> and <em>faces</em> of the original mesh. Storing new vertex positions on edges and faces will make it extremely convenient to generate the polygons in our new mesh, since we can still use the halfedge data structure to decide which four positions get connected up to form a quadrilateral. In particular, each quad in the new mesh will consist of:</p> <ul> <li>one new vertex associated with a face from the original mesh,</li> <li>two new vertices associated with edges from the original mesh, and</li> <li>one vertex from the original mesh.</li> </ul> <p>For linear subdivision, the rules for computing new vertex positions are very simple:</p> <ul> <li>New vertices at original faces are assigned the average coordinates of all corners of that face (i.e., the arithmetic mean).</li> <li>New vertices at original edges are assigned the average coordinates of the two edge endpoints.</li> <li>New vertices at original vertices are assigned the same coordinates as in the original mesh.</li> </ul> <p>These values should be assigned to the members <code class="language-plaintext highlighter-rouge">Face::new_pos</code>, <code class="language-plaintext highlighter-rouge">Edge::new_pos</code>, and <code class="language-plaintext highlighter-rouge">Vertex::new_pos</code>, respectively. For instance, <code class="language-plaintext highlighter-rouge">f-&gt;new_pos = Vec3( x, y, z );</code> will assign the coordinates (x,y,z) to the new vertex associated with face <code class="language-plaintext highlighter-rouge">f</code>. The general strategy for assigning these new positions is to iterate over all vertices, then all edges, then all faces, assigning appropriate values to <code class="language-plaintext highlighter-rouge">new_pos</code>. <strong>Note:</strong> you <em>must</em> copy the original vertex position <code class="language-plaintext highlighter-rouge">Vertex::pos</code> to the new vertex position <code class="language-plaintext highlighter-rouge">Vertex::new_pos</code>; these values will not be used automatically.</p> <p>This step should be implemented in the method <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::linear_subdivide_positions</code> in <code class="language-plaintext highlighter-rouge">student/meshedit.cpp</code>.</p> <p>Steps 2 and 3 are already implemented by <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::subdivide</code> in <code class="language-plaintext highlighter-rouge">geometry/halfedge.cpp</code>. For your understanding, an explanation of how these are implemented is provided below:</p> <h3 id="polygons"> <a href="#polygons" class="anchor-heading" aria-labelledby="polygons"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Polygons </h3> <p>Recall that in linear and Catmull-Clark subdivision <em>all polygons are subdivided simultaneously</em>. In other words, if we focus on the whole mesh (rather than a single polygon), then we are globally</p> <ul> <li>creating one new vertex for each edge,</li> <li>creating one new vertex for each face, and</li> <li>keeping all the vertices of the original mesh.</li> </ul> <p>These vertices are then connected up to form quadrilaterals (<em>n</em> quadrilaterals for each <em>n</em>-gon in the input mesh). Rather than directly modifying the halfedge connectivity, these new quads will be collected in a much simpler mesh data structure: a list of polygons. Note that with this subdivision scheme, <em>every</em> polygon in the output mesh will be a quadrilateral, even if the input contains triangles, pentagons, etc.</p> <p>In Scotty3D, a list of polygons can be declared as</p> <div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>std::vector&lt;std::vector&lt;Index&gt;&gt; quads;
</code></pre></div></div> <p>where <code class="language-plaintext highlighter-rouge">std::vector</code> is a <a href="http://en.cppreference.com/w/cpp/container/vector">class from the C++ standard template library</a>, representing a dynamically-sized array. An <code class="language-plaintext highlighter-rouge">Index</code> is just another name for a <code class="language-plaintext highlighter-rouge">size_t</code>, which is the standard C++ type for integers that specify an element of an array. Polygons can be created by allocating a list of appropriate size, then specifying the indices of each vertex in the polygon. For example:</p> <div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>std::vector&lt;Index&gt; quad( 4 ); // allocate an array with four elements
// Build a quad with vertices specified by integers (a,b,c,d), starting at zero.
// These indices should correspond to the indices computing when assigning vertex
// positions, as described above.
quad[0] = a;
quad[1] = b;
quad[2] = c;
quad[3] = d;
</code></pre></div></div> <p>Once a quad has been created, it can be added to the list of quads by using the method <code class="language-plaintext highlighter-rouge">vector::push_back</code>, which appends an item to a vector:</p> <div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>std::vector&lt;std::vector&lt;Index&gt;&gt; newPolygons;
newPolygons.push_back( quad );
</code></pre></div></div> <p>The full array of new polygons will then be passed to the method <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::from_poly</code>, together with the new vertex positions.</p> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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class="nav-list-link">Skinning</a></li><li class="nav-list-item "><a href="/animation/particles" class="nav-list-link">Particles</a></li></ul></li></ul> </nav> <footer class="site-footer"> This site uses <a href="https://github.com/pmarsceill/just-the-docs">Just the Docs</a>, a documentation theme for Jekyll. </footer> </div> <div class="main" id="top"> <div id="main-header" class="main-header"> <div class="search"> <div class="search-input-wrap"> <input type="text" id="search-input" class="search-input" tabindex="0" placeholder="Search " aria-label="Search " autocomplete="off"> <label for="search-input" class="search-label"><svg viewBox="0 0 24 24" class="search-icon"><use xlink:href="#svg-search"></use></svg></label> </div> <div id="search-results" class="search-results"></div> </div> </div> <div id="main-content-wrap" class="main-content-wrap"> <nav aria-label="Breadcrumb" class="breadcrumb-nav"> <ol class="breadcrumb-nav-list"> <li class="breadcrumb-nav-list-item"><a href="/meshedit/">A2: MeshEdit</a></li> <li class="breadcrumb-nav-list-item"><a href="/meshedit/global/">Global Operations</a></li> <li class="breadcrumb-nav-list-item"><span>Loop Subdivision</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="loop-subdivision"> <a href="#loop-subdivision" class="anchor-heading" aria-labelledby="loop-subdivision"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Loop Subdivision </h1> <p>For an in-practice example, see the <a href="/Scotty3D/guide/model">User Guide</a>.</p> <p>Loop subdivision (named after <a href="http://charlesloop.com/">Charles Loop</a>) is a standard approximating subdivision scheme for triangle meshes. At a high level, it consists of two basic steps:</p> <ol> <li>Split each triangle into four by connecting edge midpoints (sometimes called “4-1 subdivision”).</li> <li>Update vertex positions as a particular weighted average of neighboring positions.</li> </ol> <p>The 4-1 subdivision looks like this:</p> <p><img src="loop_41.png" alt="4-1 Subdivision" /></p> <p>And the following picture illustrates the weighted average:</p> <p><img src="loop_weights.png" alt="Loop subdivision weights" /></p> <p>In words, the new position of an old vertex is (1 - nu) times the old position + u times the sum of the positions of all of its neighbors. The new position for a newly created vertex v that splits Edge AB and is flanked by opposite vertices C and D across the two faces connected to AB in the original mesh will be 3/8 * (A + B) + 1/8 * (C + D). If we repeatedly apply these two steps, we will converge to a fairly smooth approximation of our original mesh.</p> <p>We will implement Loop subdivision as the <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::loop_subdivide()</code> method. In contrast to linear and Catmull-Clark subdivision, Loop subdivision <strong>must</strong> be implemented using the local mesh operations described above (simply because it provides an alternative perspective on subdivision implementation, which can be useful in different scenarios). In particular, 4-1 subdivision can be achieved by applying the following strategy:</p> <ol> <li>Split every edge of the mesh <em>in any order whatsoever</em>.</li> <li>Flip any new edge that touches a new vertex and an old vertex.</li> </ol> <p>The following pictures (courtesy Denis Zorin) illustrate this idea:</p> <p><img src="loop_flipping.png" alt="Subdivision via flipping" /></p> <p>Notice that only blue (and not black) edges are flipped in this procedure; as described above, edges in the split mesh should be flipped if and only if they touch both an original vertex <em>and</em> a new vertex (i.e., a midpoint of an original edge).</p> <p>When working with dynamic mesh data structures (like a halfedge mesh), one must think <strong>very carefully</strong> about the order in which mesh elements are processed—it is quite easy to delete an element at one point in the code, then try to access it later (typically resulting in a crash!). For instance, suppose we write a loop like this:</p> <div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>// iterate over all edges in the mesh
for (EdgeRef e = mesh.edges_begin(); e != mesh.edges_end(); e++) {
if (some condition is met) {
mesh.split_edge(e);
}
}
</code></pre></div></div> <p>Although this routine looks straightforward, it can very easily crash! The reason is fairly subtle: we are iterating over edges in the mesh by incrementing the iterator <code class="language-plaintext highlighter-rouge">e</code> (via the expression <code class="language-plaintext highlighter-rouge">e++</code>). But since <code class="language-plaintext highlighter-rouge">split_edge()</code> is allowed to create and delete mesh elements, it might deallocate the edge pointed to by <code class="language-plaintext highlighter-rouge">e</code> before we increment it! To be safe, one should instead write a loop like this:</p> <div class="language-plaintext highlighter-rouge"><div class="highlight"><pre class="highlight"><code>// iterate over all edges in the mesh
int n = mesh.n_edges();
EdgeRef e = mesh.edges_begin();
for (int i = 0; i &lt; n; i++) {
// get the next edge NOW!
EdgeRef nextEdge = e;
nextEdge++;
// now, even if splitting the edge deletes it...
if (some condition is met) {
mesh.split_edge(e);
}
// ...we still have a valid reference to the next edge.
e = nextEdge;
}
</code></pre></div></div> <p>Note that this loop is just a representative example, the implementer must consider which elements might be affected by a local mesh operation when writing such loops. We recommend ensuring that your atomic edge operations provide certain guarantees. For instance, if the implementation of <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::flip_edge()</code> guarantees that no edges will be created or destroyed (as it should), then you can safely do edge flips inside a loop without worrying about these kinds of side effects.</p> <p>For Loop subdivision, there are some additional data members that will make it easy to keep track of the data needed to update the connectivity and vertex positions. In particular:</p> <ul> <li><code class="language-plaintext highlighter-rouge">Vertex::new_pos</code> can be used as temporary storage for the new position (computed via the weighted average above). Note that one should <em>not</em> change the value of <code class="language-plaintext highlighter-rouge">Vertex::pos</code> until <em>all</em> the new vertex positions have been computed – otherwise, subsequent computation will take averages of values that have already been averaged!</li> <li>Likewise, <code class="language-plaintext highlighter-rouge">Edge::new_pos</code> can be used to store the position of the vertices that will ultimately be inserted at edge midpoints. Again, these values should be computed from the original values (before subdivision), and applied to the new vertices only at the very end. The <code class="language-plaintext highlighter-rouge">Edge::new_pos</code> value will be used for the position of the vertex that will appear along the old edge after the edge is split. We precompute the position of the new vertex before splitting the edges and allocating the new vertices because it is easier to traverse the simpler original mesh to find the positions for the weighted average that determines the positions of the new vertices.</li> <li><code class="language-plaintext highlighter-rouge">Vertex::is_new</code> can be used to flag whether a vertex was part of the original mesh, or is a vertex newly inserted by subdivision (at an edge midpoint).</li> <li><code class="language-plaintext highlighter-rouge">Edge::is_new</code> likewise flags whether an edge is a piece of an edge in the original mesh, or is an entirely new edge created during the subdivision step.</li> </ul> <p>Given this setup, we strongly suggest that it will be easiest to implement subdivision according to the following “recipe” (though the implementer is of course welcome to try doing things a different way!). The basic strategy is to <em>first</em> compute the new vertex positions (storing the results in the <code class="language-plaintext highlighter-rouge">new_pos</code> members of both vertices and edges), and only <em>then</em> update the connectivity. Doing it this way will be much easier, since traversal of the original (coarse) connectivity is much simpler than traversing the new (fine) connectivity. In more detail:</p> <ol> <li>Mark all vertices as belonging to the original mesh by setting <code class="language-plaintext highlighter-rouge">Vertex::is_new</code> to <code class="language-plaintext highlighter-rouge">false</code> for all vertices in the mesh.</li> <li>Compute updated positions for all vertices in the original mesh using the vertex subdivision rule, and store them in <code class="language-plaintext highlighter-rouge">Vertex::new_pos</code>.</li> <li>Compute new positions associated with the vertices that will be inserted at edge midpoints, and store them in <code class="language-plaintext highlighter-rouge">Edge::new_pos</code>.</li> <li>Split every edge in the mesh, being careful about how the loop is written. In particular, you should make sure to iterate only over edges of the original mesh. Otherwise, the loop will keep splitting edges that you just created!</li> <li>Flip any new edge that connects an old and new vertex.</li> <li>Finally, copy the new vertex positions (<code class="language-plaintext highlighter-rouge">Vertex::new_pos</code>) into the usual vertex positions (<code class="language-plaintext highlighter-rouge">Vertex::pos</code>).</li> </ol> <p>It may be useful to ensure <code class="language-plaintext highlighter-rouge">Halfedge_Mesh::split_edge()</code> will now return an iterator to the newly inserted vertex, and particularly that the halfedge of this vertex will point along the edge of the original mesh. This iterator is useful because it can be used to (i) flag the vertex returned by the split operation as a new vertex, and (ii) flag each outgoing edge as either being new or part of the original mesh. (In other words, Step 3 is a great time to set the members <code class="language-plaintext highlighter-rouge">is_new</code> for vertices and edges created by the split. It is also a good time to copy the <code class="language-plaintext highlighter-rouge">new_pos</code> field from the edge being split into the <code class="language-plaintext highlighter-rouge">new_pos</code> field of the newly inserted vertex.)</p> <p>We recommend implementing this algorithm in stages, e.g., <em>first</em> see if you can correctly update the connectivity, <em>then</em> worry about getting the vertex positions right. Some examples below illustrate the correct behavior of the algorithm.</p> <p>This subdivision rule <strong>is not</strong> required to support meshes with boundary, unless the implementer wishes to go above and beyond.</p> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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