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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>(Task 5) Path Tracing - </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>(Task 5) Path Tracing</title> <meta name="generator" content="Jekyll v4.2.0" /> <meta property="og:title" content="(Task 5) Path Tracing" /> <meta property="og:locale" content="en_US" /> <meta name="twitter:card" content="summary" /> <meta property="twitter:title" content="(Task 5) Path Tracing" /> <script type="application/ld+json"> {"headline":"(Task 5) Path 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<li class="breadcrumb-nav-list-item"><a href="/pathtracer/">A3: Pathtracer</a></li> <li class="breadcrumb-nav-list-item"><span>(Task 5) Path Tracing</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="task-5-path-tracing"> <a href="#task-5-path-tracing" class="anchor-heading" aria-labelledby="task-5-path-tracing"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> (Task 5) Path Tracing </h1> <p>Up to this point, your renderer simulates light which begins at a source, bounces off a surface, and hits a camera. However in the real world, light can take much more complicated paths, bouncing of many surfaces before eventually reaching the camera. Simulating this multi-bounce light is referred to as <em>indirect illumination</em>, and it is critical to producing realistic images, especially when specular surfaces are present. In this task you will modify your ray tracer to simulate multi-bounce light, adding support for indirect illumination.</p> <p>You must modify <code class="language-plaintext highlighter-rouge">Pathtracer::trace_ray</code> to simulate multiple bounces. We recommend using the <a href="http://15462.courses.cs.cmu.edu/spring2020/lecture/montecarloraytracing/slide_044">Russian Roulette</a> algorithm discussed in class.</p> <p>The basic structure will be as follows:</p> <ul> <li>(1) Randomly select a new ray direction using <code class="language-plaintext highlighter-rouge">bsdf.sample</code> (which you will implement in Step 2)</li> <li>(2) Potentially terminate the path (using Russian roulette)</li> <li>(3) Recursively trace the ray to evaluate weighted reflectance contribution due to light from this direction. Remember to respect the maximum number of bounces from <code class="language-plaintext highlighter-rouge">max_depth</code> (which is a member of class <code class="language-plaintext highlighter-rouge">Pathtracer</code>). Don’t forget to add in the BSDF emissive component!</li> </ul> <h2 id="step-2"> <a href="#step-2" class="anchor-heading" aria-labelledby="step-2"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Step 2 </h2> <p>Implement <code class="language-plaintext highlighter-rouge">BSDF_Lambertian::sample</code> for diffuse reflections, which randomly samples a direction from a uniform hemisphere distribution and returns a <code class="language-plaintext highlighter-rouge">BSDF_Sample</code>. Note that the interface is in <code class="language-plaintext highlighter-rouge">rays/bsdf.h</code>. Task 6 contains further discussion of sampling BSDFs, reading ahead may help your understanding. The implementation of <code class="language-plaintext highlighter-rouge">BSDF_Lambertian::evaluate</code> is already provided to you.</p> <p>Note:</p> <ul> <li> <p>When adding the recursive term to the total radiance, you will need to account for emissive materials, like the ceiling light in the Cornell Box (cbox.dae). To do this, simply add the BSDF sample’s emissive term to your total radiance, i.e. <code class="language-plaintext highlighter-rouge">L += sample.emisssive</code>.</p> </li> <li> <p>Functions in <code class="language-plaintext highlighter-rouge">student/sampler.cpp</code> from class <code class="language-plaintext highlighter-rouge">Sampler</code> contains helper functions for random sampling, which you will use for sampling. Our starter code uses uniform hemisphere sampling <code class="language-plaintext highlighter-rouge">Samplers::Hemisphere::Uniform sampler</code>(see <code class="language-plaintext highlighter-rouge">rays/bsdf.h</code> and <code class="language-plaintext highlighter-rouge">student/sampler.cpp</code>) which is already implemented. You are welcome to implement Cosine-Weighted Hemisphere sampling for extra credit, but it is not required. If you want to implement Cosine-Weighted Hemisphere sampling, fill in <code class="language-plaintext highlighter-rouge">Hemisphere::Cosine::sample</code> in <code class="language-plaintext highlighter-rouge">student/samplers.cpp</code> and then change <code class="language-plaintext highlighter-rouge">Samplers::Hemisphere::Uniform sampler</code> to <code class="language-plaintext highlighter-rouge">Samplers::Hemisphere::Cosine sampler</code> in <code class="language-plaintext highlighter-rouge">rays/bsdf.h</code>.</p> </li> </ul><hr /> <p>After correctly implementing path tracing, your renderer should be able to make a beautifully lit picture of the Cornell Box. Below is the rendering result of 1024 sample per pixel.</p> <p><img src="new_results/lambertian.png" alt="cornell_lambertian" /></p> <p>Note the time-quality tradeoff here. With these commandline arguments, your path tracer will be running with 8 worker threads at a sample rate of 1024 camera rays per pixel, with a max ray depth of 4. This will produce an image with relatively high quality but will take quite some time to render. Rendering a high quality image will take a very long time as indicated by the image sequence below, so start testing your path tracer early! Below are the result and runtime of rendering cornell box with different sample per pixel at 640 by 430 on Macbook Pro(3.1 GHz Dual-Core Intel Core i5).</p> <p><img src="new_results/timing.png" alt="spheres" /></p> <p>Also note that if you have enabled Russian Roulette, your result may seem noisier, but should complete faster. The point of Russian roulette is not to increase sample quality, but to allow the computation of more samples in the same amount of time, resulting in a higher quality result.</p> <p>Here are a few tips:</p> <ul> <li>The path termination probability should be computed based on the <a href="http://15462.courses.cs.cmu.edu/fall2015/lecture/globalillum/slide_044">overall throughput</a> of the path. The throughput of the ray is recorded in its <code class="language-plaintext highlighter-rouge">throughput</code> member, which represents the multiplicative factor the current radiance will be affected by before contributing to the final pixel color. Hence, you should both use and update this field. To update it, simply multiply in the rendering equation factors: BSDF attenuation, <code class="language-plaintext highlighter-rouge">cos(theta)</code>, and (inverse) BSDF PDF. Remember to apply the coefficients from the current step before deriving the termination probability. Finally, note that the updated throughput should be copied to the recursive ray for later steps.</li> </ul> <p>Keep in mind that delta function BSDFs can take on values greater than one, so clamping termination probabilities derived from BSDF values to 1 is wise.</p> <ul> <li> <p>To convert a Spectrum to a termination probability, we recommend you use the luminance (overall brightness) of the Spectrum, which is available via <code class="language-plaintext highlighter-rouge">Spectrum::luma</code></p> </li> <li> <p>We’ve given you some <a href="http://15462.courses.cs.cmu.edu/fall2015/lecture/globalillum/slide_047">pretty good notes</a> on how to do this part of the assignment, but it can still be tricky to get correct.</p> </li> </ul> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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<li class="breadcrumb-nav-list-item"><a href="/pathtracer/">A3: Pathtracer</a></li> <li class="breadcrumb-nav-list-item"><a href="/pathtracer/intersecting_objects">(Task 2) Intersections</a></li> <li class="breadcrumb-nav-list-item"><span>Ray Sphere Intersection</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="ray-sphere-intersection"> <a href="#ray-sphere-intersection" class="anchor-heading" aria-labelledby="ray-sphere-intersection"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Ray Sphere Intersection </h1> <center><img src="sphere_intersect_diagram.png" style="height:320px" /></center> <center><img src="sphere_intersect_eqns.png" style="height:400px" /></center> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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href="/pathtracer/ray_triangle_intersection" class="nav-list-link active">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 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<li class="breadcrumb-nav-list-item"><a href="/pathtracer/">A3: Pathtracer</a></li> <li class="breadcrumb-nav-list-item"><a href="/pathtracer/intersecting_objects">(Task 2) Intersections</a></li> <li class="breadcrumb-nav-list-item"><span>Ray Triangle Intersection</span></li> </ol> </nav> <div id="main-content" class="main-content" role="main"> <h1 id="ray-triangle-intersection"> <a href="#ray-triangle-intersection" class="anchor-heading" aria-labelledby="ray-triangle-intersection"><svg viewBox="0 0 16 16" aria-hidden="true"><use xlink:href="#svg-link"></use></svg></a> Ray Triangle Intersection </h1> <p>We recommend that you implement the <em>Moller-Trumbore algorithm</em>, a fast algorithm that takes advantage of a barycentric coordinates parameterization of the intersection point, for ray-triangle intersection.</p> <center><img src="triangle_intersect_diagram.png" style="height:320px" /></center> <center><img src="triangle_intersect_eqns.png" style="height:400px" /></center> <p>A few final notes and thoughts:</p> <p>If the denominator <em>dot((e1 x d), e2)</em> is zero, what does that mean about the relationship of the ray and the triangle? Can a triangle with this area be hit by a ray? Given <em>u</em> and <em>v</em>, how do you know if the ray hits the triangle? Don’t forget that the intersection point on the ray should be within the ray’s <code class="language-plaintext highlighter-rouge">time_bound</code>.</p> </div> </div> <div class="search-overlay"></div> </div> </body> </html>
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