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Assignment 6 – Ray Tracer

Due Wednesday 4/24 at 11:59 pm. You must work individually.

• Goals
• Associated Labs
• Starting Point
• Task 1: Camera Setup
• Task 2: Spheres and Shadows
• Task 3: Ellipsoid
• Task 4: Reflections
• Task 5: Triangle Mesh
• Task 6: Transforming the Camera
• Bonus
• Rubric
• What to Hand in

Goals

In this assignment, you will be writing a ray tracer with the following features:

• Blinn-Phong shading
• Multiple lights
• Shadows
• Reflections
• Plus other bonus features

Associated Labs

• Lab -1 (required): Setting Up Your Development Environment (no OpenGL)
• Lab 13 (recommended): Ray Intersections

Starting Point

The skeleton code for Assignment 1 is a good starting point. Just like A1, this assignment does not use OpenGL and instead writes the result as an image file. You may also reuse any of your previous code from this course for this assignment. Even though you do not need OpenGL, you can still use the GLM library for matrices and vectors. Also, you do not need to load any obj files until Task 6.

The command line argument should be:

> ./A6 <SCENE> <IMAGE SIZE> <IMAGE FILENAME>

• <SCENE>: Scene description number 1, 2, …, described below.
• <IMAGE SIZE>: Width/height of the resulting image, e.g., 1024
• <IMAGE FILENAME>: Output filename, e.g., output.png.

Here’s the link to the 3D ray visualizer by Michael Stewart. Hitting the number key should produce the corresponding scene.

Task 1: Camera Setup

Set up the camera manually (using some trigonometry) with the following parameters:

• Position: (0, 0, 5)
• Rotation: None (i.e., Y up, -Z forward)
• Field of view: 45 degrees (see left image)
• Aspect ratio: \(1.0\) (i.e., square)
• Resolution of the image (width/height, indicating the number of pixels horizontally/vertically)

Imagine a virtual plane at Z=4.0 (i.e., one unit away from the camera, which is at Z=5.0). Our virtual rays will be starting at (0, 0, 5) and then will be going through the center of each pixel in the virtual plane. For example, in the center image, there are 9 rays, including one going straight out through the center of the middle pixel. The right image shows how these rays would look for a 10 by 10 image. (This was rendered with OpenGL for pedagogical purposes. Your code does not need to show the virtual scene in 3D.)

To start, write a function that can generate these rays given the camera specifications above, and the width/height of the output image from the commandline argument. With a 3x3 image, the 9 rays should have the following directions (each column is a unit direction vector):

 0.2572     0.0000     -0.2572      0.2662      0.0000     -0.2662      0.2572      0.0000     -0.2572
 0.2572     0.2662      0.2572      0.0000      0.0000      0.0000     -0.2572     -0.2662     -0.2572
-0.9315    -0.9639     -0.9315     -0.9639     -1.0000     -0.9639     -0.9315     -0.9639     -0.9315

(Click here for a screenshot of the data in case your screen is too small.) Since the camera is not rotated, the middle ray’s direction is (0, 0, -1), straight ahead along the negative Z direction. Due to round-off errors, the numbers you get may be slightly different.

Task 2: Spheres and Shadows (Scenes 1 & 2)

Your first scenes consist of three spheres and one light. Scene 1 is without shadows, and Scene 2 is with shadows. If you complete Scene 2, you do not need to keep the code for Scene 1. In other words, when the <SCENE> argument is set to 1, either of the images below will give you full points. When the <SCENE> argument is set to 2, only the right image below will give you full points.

To create the scene, you can hard code the values in your code. (You may also use a parser if you prefer.) These values must be used when the command line argument <SCENE> is set to 1 or 2. Make sure to use exactly these values, since they will be used to test your code with an automatic script.

Light

• Position: (-2.0, 1.0, 1.0)
• Intensity: 1.0

I highly recommend writing test cases for the collision functions. For example, place a unit-radius sphere at the origin and shoot a ray from (0, 0, 5) with direction (0, 0, -1). The ray should hit the sphere at (0, 0, 1) and (0, 0, -1). Try other test cases, with a different radius and/or position, as well as different rays.

Once your intersection functions have been tested, you’re ready to start implementing a ray tracer. First, shoot just the primary view rays and not the shadow rays (Scene 1, left image above). Once you get the correct result, add the shadow rays (Scene 2, right image above).

The color should be computed using the Blinn-Phong equation we used in our previous assignments: \[ \vec{k}_a + \sum_i \vec{L}_i \odot \left( \vec{k}_d \max(0, \hat{n} \cdot \hat{l}_i) + \vec{k}_s \max(0, (\hat{n} \cdot \hat{h}_i)^s) \right). \] For Scene 2, if the shadow ray hits an object before reaching the light, the color contribution corresponding to that light should be set to zero.

Note: When setting pixel colors, cap each of the R, G, and B values to the range [0, 255].

Your code should be efficient enough to generate a 1024 by 1024 image without having to wait a long time. It should only take a few seconds at most, even on an older computer. If your code is slow, make sure you are not passing big STL vectors by value and that you are running your code in release mode. Excessively slow code will be penalized.

Also, use object-oriented design to organize your code. There should be a superclass that represents all shapes. The subclasses should implement specific intersection tests. For example, a subclass that represents an infinite plane should implement Task 2 from Lab 13, and another subclass that represents a sphere should implement Task 3 from Lab 13.

Task 3: Ellipsoid (Scene 3)

The next scene consists of one sphere, one ellipsoid, one infinite plane, and two lights.

With two lights, you should be able to see areas that are occluded from both or just one light. Also note that the ellipsoid casts a shadow on the sphere.

Task 4: Reflections (Scenes 4 & 5)

Your next scenes consist of two lights, two Phong spheres, two reflective spheres, and two infinite planes. Scene 4 is with a single reflection, and Scene 5 is with multiple (recursive) reflections. If you complete Scene 5, you do not need to keep the code for Scene 4. In other words, when the <SCENE> argument is set to 4, either of the images below will give you full points. When the <SCENE> argument is set to 5, only the right image below will give you full points.

Task 5: Triangle Mesh (Scenes 6 & 7)

For these scenes, import an obj mesh. Scene 6 is without model transformation, and Scene 7 is with model transformation. Once you finish Scene 7, you should set up your code so that Scene 6 uses the identity transform.

For triangle-ray tests, use the optimized code by Thomas Akenine-Moller. Some hints for this piece of code:

• The return value is 1 or 0 depending on whether there was a hit.
• Input arguments orig and dir are the ray origin and direction, respectively.
• Input arguments vert0, vert1, and vert2 are the three vertex positions of the triangle.
• Output argument t is the distance along the ray where the hit occurred.
  • Make sure to check that t > 0 to deal with collisions happening behind the ray.
• Output arguments u and v are the barycentric coordinates of the triangle where the hit occurred.
  • u corresponds to vert1, and v corresponds to vert2.

Without any optimizations, using the bunny mesh will take a very long time to render, since each ray will need to be tested against every single triangle. Add a simple optimization by putting a bounding sphere around the bunny and testing the ray against the sphere first. If the ray does not hit the sphere, you do not need to test against any of the triangles. It should not take more than a minute to render a bunny with a single light at 512x512 resolution. Make sure to run your code in release mode. We will be testing your submission with the bunny mesh.

There should be a single light in the scene, and the material should be the same as the blue sphere from the previous task.

Now add the ability to transform the obj mesh. To do this, you need to transform the ray into local coordinates, perform collision detection, and then transform the result back to world coordinates. Let \(E\) be the 4x4 transformation matrix of the obj mesh. Then:

1. Transform ray to local coordinates.
   • Ray origin: multiply by \(E^{-1}\).
   • Ray direction: multiply by \(E^{-1}\) and normalize.
2. Perform collision detection in local coordinates, using the transformed ray.
3. Transform results to world coordinates.
   • Hit position: multiply by \(E\).
   • Hit normal: multiply by \(E^{-\top}\) (inverse transpose) and normalize.
   • Hit distance: compute from ray origin and hit position; \(t = \| \vec{x} - \vec{p} \|\), where \(\vec{x}\) is the hit position, and \(\vec{p}\) is the ray origin, both in world coords. Remember to check if the hit point is behind the ray – see the last part of Lab 13.

For Task 7, there should be a single light in the scene:

• Position: (1.0, 1.0, 2.0)
• Intensity: 1.0

We will be testing your submission with the bunny mesh with the following model transform:

E =

    1.5000         0         0    0.3000
         0    1.4095   -0.5130   -1.5000
         0    0.5130    1.4095         0
         0         0         0    1.0000

This transformation matrix can also be constructed as the product E = T * R * S, where

• T is a translation by (0.3, -1.5, 0.0).
• R is a rotation about the X-axis by \(20\) degrees.
• S is a uniform scale by 1.5.

(The teapot figure is for illustration purposes only; it uses a different transform.)

Task 6: Transforming the Camera (Scene 8) (Optional for honors students)

Implement a camera that can be translated/rotated arbitrarily in the world and whose field of view can be modified. Use the same setup as Scene 1 but from a different camera location/orientation. The camera should be placed at (-3,0,0) looking along the positive X axis, with a field of view of 60 degrees. One way to move/orient the camera is to use the glm::lookAt(...) function to obtain the view matrix, and then to transform everything in the scene by this view matrix.

The left image is the 3D view from the original viewpoint of Scene 1, and the right image is the resulting ray traced image.

Bonus (Honors students: implement at least 10 points from here)

Once you finish the base assignment, you can earn up to 20 bonus points by implementing the following features (in no particular order):

• [+3] Infinite cylinders – you may use online code as long as you cite it in the README.
• [+3] Boxes – you may use online code as long as you cite it in the README.
• [+3] Include an object or region that will attenuate light (reduce certain color of light based on distance traveled through that region – e.g., think colored glass, or fog).
• [+5] Multithreading – process the image pixels in parallel.
• [+5] Motion blur – have a moving object, and average the result of multiple renders.
• [+5] Blend reflection with Blinn-Phong lighting – e.g., 30% reflection and 70% Blinn-Phong.
• [+5] Find code online to accelerate the ray-triangle intersection. You can use a sphere-tree, OBB-tree, oct-tree, KD-tree, BSP-tree, etc. Remember to cite the source in the code and in the README.
• [+5] Constructive solid geometry – intersection, union, and difference.
• [+5] Perform antialiasing by generating multiple primary rays per pixel and averaging.
• [+5] Create “area” light sources that consist of multiple nearby points.
• [+5] Generate multiple reflection rays that spread out around the “exact” reflection to simulate surface roughness. The reflection calculation for the point is the average of these reflection rays.
• [+5] Include a texture-mapped object.
• [+8] Refraction
• [+10] Ambient occlusion
• [+20] Monte Carlo path tracing

Special Bonus: Hardware Acceleration

• [+50] Use your ray tracing hardware and include the speedups in your readme. Since the implementation will depend on your specific hardware, we will not be able to compile your code. You will need to set up a grading session with the grader.

Please use Scene 0 or 9 for the bonus scenes. The other scene numbers must work as if no bonus were implemented.

Rubric

In each task, you must use object-oriented design to obtain full points.

• [10] Scene 1: without shadows
• [15] Scene 2: with shadows
• [15] Scene 3: with multiple lights
• [15] Scene 4: with a single reflection
• [15] Scene 5: with multiple reflections
• [10] Scene 6: without transform
• [10] Scene 7: with transform
• [10] Scene 8: transformed camera
• [+20] Bonus up to 20 points
• [+50] Hardware Acceleration

Total: 100 plus bonus points

For honors students: you must complete at least 10 bonus points. (Otherwise, you will receive a \(0\) on this assignment.) Like all other students, you can still finish Scene 8 and earn up to 20 bonus points to end up with 120 total points.

What to hand in

Failing to follow these points may decrease your final score. On Linux/Mac, make sure that your code compiles and runs by typing:

> mkdir build
> cd build
> cmake ..
> make
> ./A6 <SCENE> <IMAGE SIZE> <IMAGE FILENAME>

If you’re on Windows, make sure that you can build your code using the same procedure as in Lab -1.

• Do not include any raytraced images (unless you have the instructor’s permission).
• Make sure the arguments are exactly as specified.
• We will be running the code in release mode.
• Include a README file (README.txt or README.md) that includes:
  • Your name, UID, and email
  • The highest task you’ve completed
  • Citations for any downloaded code
  • Plus anything else of note
• Make sure you don’t get any compiler warnings.
• Remove unnecessary debug printouts.
• Remove unnecessary debug code that has been commented out.
• Hand in src/, resources/, CMakeLists.txt, and your readme file. The resources folder should contain the obj files (if necessary).
• Do not hand in:
  • The build directory
  • The executable
  • Old save files (*.~)
  • Object files (*.o)
  • Visual Studio files (.vs)
  • Git folder (.git)
• Create a single zip file of all the required files.
  • The filename of this zip file should be UIN.zip (e.g., 12345678.zip).
  • The zip file should extract a single top-level folder named UIN/ (e.g. 12345678/).
  • This top-level folder should contain your README, src/, CMakeLists.txt, etc.
  • Use the standard .zip format (not .gz, .7z, .rar, etc.).