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b/hw1/index.html @@ -1,7 +1,372 @@ - - - - - Homework 1 index.html here - + + + + + + CS 184/284A Rasterizer + + + + + + + +

    CS 184/284A: Computer Graphics and Imaging, Spring 2024

    +

    Homework 1

    +

    Ian Dong

    + +
    + +

    Overview

    +

    Give a high-level overview of what you implemented in this homework. Think about what you've built as a whole. + Share your thoughts on what interesting things you've learned from completing the homework.

    + +

    Section I: Rasterization

    + +

    Part 1: Rasterizing Single-Color Triangles

    + +

    +

      +
    • + I first found the rectangular bounding box of the triangle by calculating the min and the max of the x and y + coordinates of the three vertices. Then, I iterated through each of these pixel locations and found their + centers. I defined a function that took in the sample point along with two vertices of the triangle and found + the dot product between the norm of the two vertices and the vector from the first vertex to the sample point. I + repeated this with all three pairs of the triangle vertices. These dot products will determine which side the + sample point lies on and it will be inside the triangle if all three dot products have the same sign or are all + zero. If this sample point is inside of the triangle, I filled the pixel with the function argument color. +
    • +
    • + My algorithm is no worse than one that checks every pixel in the bounding box of the triangle because it is + linear with respect to the number of pixels in this box as I used two nested for loops to iterate through the + min of x to the max of x and the min of y to the max of y + coordinates. Thus, my algorithm took into account every pixel in + the bounding + box of the triangle. +
    • +
    • + Here, I chose to center it around the long magenta shape because it has a little bit of jaggies. +
    • +
      + + + + +
      +
      + +
      Rasterizing Triangles
      +
      +
      +
    + +
      +
    • + Extra Credit: I had implemented a few different optimization methods. The first method was to + reduce repetitive + calculations by storing the six perpendicular vectors of the triangle as well as the base x and + y coordinates with step size outside of the for loop. I wanted to move calculations + that I was doing over and over that did not depend on the inner for loops outside of them. The + second method was to use + #pragma omp parallel for to parallelize the outer for loops. The third method was to + combine + the last two methods above. I used the C++ clock() library to time the execution of each method by + placing it before and after the svg.draw() in DrawRend::redraw() and subtracting the + two recorded times. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      ImageMethod 1: No OptimizationMethod 2: Reduce Repetitive Calculations OnlyMethod 3: Pragma Parallelization OnlyMethod 4: Methods 2 & 3 Combined
      Basic Test 332.172 ms26.906 ms31.964 ms27.112 ms
      Basic Test 764.232 ms43.85 ms63.857 ms43.61 ms
      Basic Test 815.193 ms14.438 ms14.468 ms14.178 ms
      +
    • +
    +

    + + + +

    + +

    Part 2: Antialiasing Triangles

    +

    +

      +
    • + I implemented supersampling by dividing each pixel into sample_rate number of subpixels. From + there, I + resized the sample_buffer to be sample_rate times larger than before so that I could + store each of the individual subpixels for each original pixel in the image and created a helper function to + figure out the index that each subpixel was supposed to be in the sample_buffer. I then iterated + through each of the subpixels, found the center of each subpixel, and used the same algorithm as in part 1 to + determine if the subpixel was inside of the triangle. If it was, I filled the subpixel with the color of the + triangle. In resolve_to_framebuffer, I averaged the colors of the subpixels to get the color of the + original pixel. Supersampling is very useful because it helps to improve the quality of the images by sampling + at a higher resolution and then downsampling to the original resolution. This will reduce aliasing and smooth + out any jaggies. A few modifications that I made to the original rasterizer pipeline was to change the + sample_buffer size and to calculate the new subpixels where each width and height became a multiple + of sqrt(sample_rate) away from the original pixel. I aslo had to change the + resolve_to_framebuffer to average the colors of the subpixels. These modifications helped antialias + my triangle because it helped smooth out the jaggies due to the blurring and connected subpixels together that + would have been otherwise disconnected. +
    • +
    • + Here, I have decided to zoom into the thin red part of the triangle to show the effects that supersampling has + on antialiasing our image. As I increase the sample_rate, there seems to be less gaps between the + different regions. The reason why there are missing gaps at lower sample_rates is because the + triangle is so thin that only parts of the pixel lies within the triangle and because it is an "all-or-nothing" + policy each pixel has its own color and there is no blending between them. As the sample_rate + increases, I am able to sample at a higher frequency and on smaller subpixels and because they are so small and + close together they lie within the triangle and are able to blend together to create a smoother image. This in + turn allows the original pixel to have a more faded color based on the saturation and thus is able to reduce + some of the jaggies and smooth out the fragmentations. +
    • +
      + + + + + +
      + + + + +
      + +
      Supersampling Rate of 1
      +
      + +
      Supersampling Rate of 4
      +
      + +
      Sampling Rate of 9
      +
      + +
      Sampling Rate of 16
      +
      +
      +
    +

    + +

    +

    Part 3: Transforms

    +

    +

      +
    • + Here, I have transformed our cubeman robot into a basketball player, fully equipped with a basketball and the + necessary gear to become the next great Michael Jordan. He is shown dribbling the basketball and calling a play + for his teammates. +
    • +
      + + + + + +
      +
      + +
      Basketball Cubeman
      +
      +
      +
    + +

    + +
    +

    + +

    Section II: Sampling

    + +

    Part 4: Barycentric Coordinates

    +

    +

      +
    • + Barycentric coordinates essentially is a way to represent points within a geometric figure. In other words, + they tell us how much each vertex of the three + vertices + contributes to a + sample + point inside of the triangle, where these weights indicate how important each vertex is in determining the + location of the sample point. Any point inside of the triangle can be represented as a linear combination of the + three vertices, where the weights must sum to one. This constraint will ensure that the sample point will lie + within the triangle since each weight is essentially the proportion of the area of the triangle that the + corresponding vertex contributes to the overall area. Another way to think about this is that we are + distributing the area of the triangle to the three vertices based on the sample point's location. The closer the + sample point is to a vertex, the larger the weight of that vertex will be. The further the sample point is from + a vertex, the smaller the weight of that vertex will be. To illustrate how barycentric coordinates work, I + created an svg file with a triangle and each of the vertices is a different color: red, green or + blue. +
    • +
      + + + + + +
      +
      + +
      Smoothly Blended Triangle
      +
      +
      + +
    + +
      +
    • + Here is svg/basic/test7.svg with default viewing parameters and sample rate 1. +
    • +
      + + + + + +
      +
      + +
      Smoothly Blended Circle
      +
      +
      +
    + +

    + +

    +

    Part 5: "Pixel Sampling" for Texture Mapping

    +

    +

      +
    • + Pixel sampling is this process to help determine which pixel within the texture image to sample from and use + based on the barycentric coordinates for the sample point in the original image; it is a translation from the pixel (x, y) coordinates into the texels (u, v) coordinates. I implemented this algorithm by first calculating the barycentric coordinates of the sample points before multiplying them by the width and the height +
    • +
    +

    + +

    +

    Part 6: "Level Sampling" with Mipmaps for Texture Mapping

    + + + +

    Section III: Art Competition

    +

    If you are not participating in the optional art competition, don't worry about this section!

    + +

    Part 7: Draw something interesting!

    + + + \ No newline at end of file
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