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- In this Project, I implemented a ray tracing pipeline, starting with generating sample camera rays for each - pixel in the image. To determine whether a ray intersected a primitive, I incorporated different ray-object - intersections such as ray-triangle and ray-sphere. To improev on the rendering speeds, we constructed a Bounding - Volume Heirachy where instead of checking if a ray intersects each primitive we check against a larger, encompassing - bounding volume. Initially the rendering only used normal shading; we expanded on this by implementing two - direct illumination techniques one being sampling from a uniform hemisphere and another being importance sampling of - light sources. These methods introduced zero and one bounce illumination creating a more realistic scene. We then - built on the illumination techniques by implementing global illumination, allowing light to reflect more than once in - a scene. The potential bias introduced limiting the number of bounces was combatted through Russian Roulette - global illumination, which probabilistically terminated light bounces with a 30% likelihood. Lastly, adaptive sampling - was adopted to reduce noise in the rendering, prioritizing areas requiring more intensive sampling to achieve - convergence. I faced plenty of debugging problems in this project the main ones being not allocating the vectors on - the heap when constructing the BVH, forgetting to normalize when notaccumulating bounces, and dealing with object and - world coordinate spaces. -
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- To generate one ray, we first had to map the image space coordinates onto the sensor in camera space. Since (0, 0) and
- (1, 1) represent the sensors bottom left corner (-tan(0.5 * hFov_radians), -tan(0.5 * vFov_radians)) and
- top right corner (tan(0.5 * hFov_radians), tan(0.5 * vFov_radians)) respectively, I was able to properly
- map through two formulas. The camera_space_x coordinate =
- (sensor_top_x - sensor_bottom_x) * x + sensor_bottom_x and camera_space_y =
- (sensor_top_y - sensor_bottom_y) * y + sensor_bottom_y. (camera_space_x, camera_space_y, -1) represented
- the direction of the generated ray. We normalize the direction and convert to world space. We finally generate the ray
- and set the min_t and max_t of the ray to the near clip and forward clip respectively. To raytrace a pixel, we then
- generate ns_aa rays to estimate the radiance for that pixel.
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- To determine if a ray intersected a triangle, I implemented the Möller-Trumbore Algortihm. By solving the matrix shown
- below we were able to solve for the time the ray intersected the triangle and barycentric coordinates b1 and b2. If
- the time intersected was between the bounds of ray min and max time and b1, b2, and (1 - b1 - b2) > 0 and less than 1
- then we can confirm it is an intersection and update the max_t of the ray. With our barycentric coordinates we can
- interpolate the surface normal using (1 - b1 - b2) * n1 + b1 * n2 + b2 * n3.
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- - To determine if a ray intersected a sphere, we can check for times where the (o + td - c) - R^2 = 0 where o + td is - the ray formula, c is the origin of the sphere, and R is the radius of the sphere. Since we know this will result in - the form at^2 + bt + c, we can solve for t by finding the coefficients a, b, c. Expanding out the terms, we get a = - dot(d, d), b = 2*dot(o - c, d), and c = dot(o - c, o - c) - R^2. We use the quadratic formulas to find the times where - the ray enters and exits the sphere denoted t1, t2 respectively. If the t1 and t2 are both valid, we can set the rays - max t to be the smaller of the two. We can then find the surface normal of the intersection using the formula (p - - o).unit(). -
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- To construct the BVH, we initiate a recursive process and for each recursive call we create a bounding box and - expand it for each primitves bounding box while simultaneously, we summming each primitives bounding boxes x, y and z. - A new BVHnode is then created. For a leaf node—identified when the primitive count is less than the max_leaf_size-we - just set the nodes start and end pointer to the passed in params. For inner nodes, we have to partition the primitives - into leftSet or rightSet based on each axis. The heuristic I chose to split on was the difference between the - primitives stored in the leftSet and rightSet splitting on the axis that had the most balance between the two sets. We - then recursively call the construction algorithm on the chosen left and right sets for the nodes left and right child. -
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- To show the acceleration that BVH provides, I rendered three scenes with and without BVH acceleration all rendered on - a M1 Mac of resolution 480x360. The first was cow.dae where without BVH acceleration took 17.4257s while with BVH - acceleration it took 0.0466s. The second was beetle.dae where without BVH acceleration took 21.7633s while with BVH - acceleration it took 0.0961s. And finally building.dae where without BVH acceleration took 121.8985s while with BVH - acceleration it took 0.0445s. -
-- The two direct lighting functions we implemented were direct lighting through uniform hemisphere sampling and direct - lighting through importance sampling. -
| - Uniform Hemisphere Sampling - | -- Light Sampling - | -
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- For the 1 light ray image we can see the very large and apparent amount of noise near the bottom of the bunny's shadow - as there aren't enough samples per light. Increasing the number of light rays to 4 provides a bit more detail and less - noise but the shadows aren't very soft. With 16 rays, we can see definite softness in the shadow edges and a large - reduction in noise compared to both the 1 and 4 ray image. At 64 rays, the noise within the shadow region is greatly - reduced and the edges of the shadows are much softer, creating a more realistic representation of the shadows. -
-- The major difference between uniform hemisphere sampling and importance sampling is that uniform hemisphere sampling - exhibits a lot more noise on the walls and especially near the shadows which makes sense as any ray is equally likely - to be sampled including rays that are heavily attenuated near the horizon causing noise. However in importance - lighting sampling we sample directly from light sources, thus giving us a less noisy image. Additionally, point light - sources cannot be hemisphere sampled as the probability of picking a single point in a PDF is 0 which is why on the - left we see a black image for the bench. Importance sampling from light sources allows us to render point light - sources correctly. -
-- To implement the indirect lighting function, we first sample an incident light direction and the pdf of that sampled - direction. Using the incoming wi and outgoing w_out light directions, we compute the BRDF. We then transform the - sampled direction to world space and cast a shadow ray from the intersection point, decreasing its depth by one. - If the shadow ray intersects an object and we are accumulating bounces we accumulate the indirect illumination by - adding to L_out and make a recursive call to the indirect lighting function using the shadow ray and shadow - intersection. However, if we are not accumulating bounces and the shadow ray's depth has reached zero, we return - this mth bounce and return the radiance given by the one_bounce_radiance function. If russian roulette is used, we - determine whether to terminate the ray's path via a coin flip function with p = 0.3 and if the path continues we must - scale by the continution probability. -
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- When comparing Direct Illumination which encompasses only zero + one bounce illumination, with Indirect Illumination, - all illumination provided by more than one bounce we can see that Direct Illumination results in much more pronounced - shadows due to substantial impact of the initial light rays. This also leads to much darker areas where light must - need more than one bounce to reach such as the ceiling. For the indirect illumination image, we can see no effect from - the zero bounce light rays which is why the area light is essenitally turned off. We also notice the scene is much - more uniformly lit and dimmer as the later light rays are much less intense. -
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- In the rendered images, the second bounce of light is visible as soft shadows and color bleeding on the rabbit, - indicating light reflecting from the colored walls and floor. The third bounce contributes to the nuanced global - illumination in corners and subtle light gradations across the rabbit and the room, enhancing the depth and realism. - These bounces add layers of complexity and detail that rasterization cannot replicate as rasterization calculates - the color of each pixel based on direct light sources and simple shading models without simulating the - physical interactions of light rays in an environment. -
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- Comparing images with max_ray_depth equal to 0, 1, 2, 3, 4, and 5, we can see that as we increase the max - ray depth the image becomes brighter. With zero bounce illumination, we can see that only rays that arrive directly - from the light source are included which is why only the area light shines. With one bounce, we illuminate the scene - but we can still see that the ceiling is not lit as it takes two bounces of light to shine the ceiling. As we start to - add more indirect illumination, the scene becomes brighter and brighter and the shadows start to show more of a - penumbra. -
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- When comparing different per pixel sample rates, we can clearly see as we increase the sample rate, the amount of - noise in the image decreases. We can see the large amount of noise when we sample at 1, 2, or 4 samples per pixel and - with a much higher sample rate in 1024 samples we can see the apparent lack of noise. -
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- Adaptive sampling is a technique to create noise-free images by increasing the per pixel sample rate and concentrating
- the pixels on more difficult parts of the image. My implementation of adaptive sampling consisted of keeping track of
- two sums for the pixel s1 and s2, one for the sample illuminance and one for the sample illuminance squared. Every
- samplesPerBatch I calculate the mean u of the current n samples by dividing s1 / n and the variance o^2 of the current
- n samples through (1 / (n - 1)) * (s2 * (s1**2)/n). I then I = 1.96 * sqrt(o^2)/sqrt(n) and
- if I <= maxTolerance * u, we can stop generate rays and assume the pixel has converged. We then must divide the calcualted
- radiance by the number of samples taken.
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