From 7c22e959e2111db45be6c2d6d80294313f8a6115 Mon Sep 17 00:00:00 2001 From: anavmehta12 Date: Tue, 13 Feb 2024 01:44:41 -0800 Subject: [PATCH] finished hw1 webpage --- .DS_Store | Bin 0 -> 6148 bytes .vscode/launch.json | 15 ++ hw1/.DS_Store | Bin 0 -> 6148 bytes hw1/assets/.DS_Store | Bin 0 -> 6148 bytes hw1/assets/16pxSampleRate.png | Bin 0 -> 6827 bytes hw1/assets/1pxSampleRate.png | Bin 0 -> 3143 bytes hw1/assets/4pxSampleRate.png | Bin 0 -> 5879 bytes hw1/assets/Billinear16px.png | Bin 0 -> 143264 bytes hw1/assets/Billinear1px.png | Bin 0 -> 152167 bytes hw1/assets/BlendedTriangle.png | Bin 0 -> 10517 bytes hw1/assets/ColorPicker.png | Bin 0 -> 66328 bytes hw1/assets/L_NEAREST_P_LINEAR.png | Bin 0 -> 71337 bytes hw1/assets/L_NEAREST_P_NEAREST.png | Bin 0 -> 40832 bytes hw1/assets/L_ZERO_P_LINEAR.png | Bin 0 -> 64653 bytes hw1/assets/L_ZERO_P_NEAREST.png | Bin 0 -> 39145 bytes hw1/assets/Nearest16px.png | Bin 0 -> 144942 bytes hw1/assets/Nearest1px.png | Bin 0 -> 147427 bytes 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#005a9c; + margin-top: 20px; +} + +section { + margin-bottom: 40px; +} + +article { + margin-top: 10px; +} + +figure { + margin-top: 10px; + margin-bottom: 10px; +} + +img { + max-width: 100%; + height: auto; +} + +figcaption { + text-align: center; + font-style: italic; +} + +/* Additional styles can be added as needed */ +table { + width: 100%; + border-collapse: collapse; +} +table, +th, +td { + border: 1px solid black; +} +th, +td { + padding: 10px; + text-align: left; +} +th { + background-color: #f2f2f2; +} diff --git a/hw1/index.html b/hw1/index.html index a7458a3..61978db 100644 --- a/hw1/index.html +++ b/hw1/index.html @@ -1,7 +1,313 @@ - - - - - Homework 1 index.html here - + + CS184 Homework 1 Write Up + + + + + Link to website: Website + +

CS184 Homework 1 Report

+ +
+

Project Overview

+

+ In this Project, I implemented basic rasterization with anti-aliasing methods such as supersampling. I also + implemented basic hierarchical transforms including translation, rotation, and scaling. Another main idea of this + project was texture mapping where we mapped textures onto 2d objects through various techniques such as Barycentric + coordinates to interpolate the textures of given coordinates. For texture mapping, the project supported two kinds of + Pixel Sampling Nearest Neighbour and Billinear and three kinds of level sampling 0-th, Nearest, and Billinear + Interpolation. As for my thoughts on this assignment, I found it certainly cemented the techniques we learned + in the lecture as I had to spend hours debugging and learning what was going wrong. I understood the differences + between the frame and sample buffer and why each was important. I learned about the importance of defining the + unwinding direction of the vertices. I learned to understand the partial derivatives and why they were important in + calculating the specific mip map level. +

+
+
+

Task 1 - Drawing Single-Color Triangles

+
+

+ To render a triangle or polygon on a screen, the process begins by identifying the polygon's bounding + box. This is achieved by calculating the minimum and maximum values among the vertices' x and y coordinates. + The minimum values, after being floored, define the starting X and Y position of the bounding box, while the + maximum values, once ceiled, determine the ending X and Y positions. Following this, the algorithm + iterates from the bounding box's top left pixel’s center to its bottom right pixel’s center. For the center of + each subsequent pixel in the bounding box we determine through a point-in-triangle test if the center lies + within the triangle. If the test is positive, the pixel is rendered. This process is repeated across the entire + bounding box, ensuring that every potential pixel in the triangle is evaluated. +

+
+ +
+

+ My algorithm is no worse than one that checks each sample within the bounding box of the triangle since + it essentially checks each within the bounding box of the triangle. Therefore, it cannot be any worse by + design. +

+
+ Rasterizer Screenshot +
Base Rasterization of Triangles
+ +
+
+
+ +
+

Task 2 - Antialiasing by Supersampling

+
+

+ For my supersampling algorithm, I dynamically increased the sample buffer size in response to increases + in the sample rate to accommodate for the subsamples. The modified rasterize triangle function now + populates the sample buffer with sub samples, coloring them if it passes the point in triangle test. I stored the + subsamples linearly for efficient and easier access during restoration to the frame buffer. As I + restored the sample buffer to the frame buffer I aggregated the RGB values across all subsamples for each pixel. + Supersampling smoothes out the jaggedness of the triangles by minimizing the rapid color shifts from the + background to the edges of the triangle creating a more balanced color representation. +

+
+
+
+ Supersampling Screenshot at 1px sample rate +
Supersampling at 1px
+ +
+
+ Supersampling Screenshot at 4px sample rate +
Supersampling at 4px
+ +
+
+ Supersampling Screenshot at 16px sample rate +
Supersampling at 16px
+ +
+

+ When our sample rate is 1px we can see that the tip of the triangle is disconnected while as we increase + the sample rate from 1 -> 16 the edge becomes more and more continuous. This is caused because when we only + have one subsample we just check whether that pixel is in the triangle leaving us to a very + unbalanced image but as we increase the number of subsamples and start averaging out the colors we + increase the probability that these pixels will lie in the triangle allowing for a more smooth image. +

+
+
+ +
+

Task 3 - Transforms

+
+
+ Robot +
+ +

+ I rotated the right leg by -90 degrees and the left leg by 90 degrees, and adjusted both arms to a + 45-degree + angle, aiming to give the robot a splits-like appearance. +

+
+
+ + +
+

Task 4 - Barycentric Coordinates

+
+

+ Barycentric coordinates are coordinates used to interpolate different attributes such as textures, + coordinates, colors by weighting the distance from a given point to the vertices of the triangle where a + point closer to vertex A is biased heavily more on A's values then B or C. +

+ +
+ Blended Triangle showing how Red, Green, and Blue colors blend using barycentric coordinates +
Illustration of color interpolation in a triangle using barycentric coordinates.
+
+ +

+ I created this SVG image to illustrate how Red, Green, Blue blend using barycentric coordinates + emphasizing the influence of proximity to the triangle vertices on the resulting color. The method assigns greater + weight to the vertex nearest to the given point, making the point’s color more influenced by that vertex + color. As a result, points near the vertex associated with Red, for example, exhibit a color closer to + Red. And at the midpoint between the Red and Blue vertices, we observe a purplish hue, signifying a blend of + the two colors. The midpoint between Green and Blue reveals a tealish shade, and the midpoint between Green and + Red presents a brownish color. These colors align with the expected results of mixing the given colors, showcasing + how barycentric coordinates can interpolate colors. +

+ +
+ Color Picker showing the result of color blending +
Image of a color wheel using barycentric coordinates for color interpolation.
+
+
+
+ +
+

Task 5 - Pixel Sampling for Texture Mapping

+
+

+ Pixel sampling involves determining the color and intensity of pixels to display to the screen from a + given source material. +

+

Nearest Neighbor Sampling

+

+ Nearest neighbor sampling takes the nearest texture sample colors to the (u, v) + coordinate. I achieved this by converting screen (x, y) coordinates to their corresponding texture coordinates + (u,v) through Barycentric coordinates, scaling by the mipmaps dimensions, and then fetching the texel color + at the scaled coordinates. +

+

Bilinear Sampling

+

+ Bilinear sampling on the other hand interpolates between the nearest four texel + samples to achieve a more refined texture color by factoring in the distances to each of the texel + samples. For this method, after scaling the Barycentric coordinates (p) the four closest texel samples are: +

+
    +
  • Top Left (u01): Flooring both u and v.
  • +
  • Top Right (u11): Ceiling u and flooring v.
  • +
  • Bottom Left (u00): Flooring u and ceiling v.
  • +
  • Bottom Right (u10): Ceiling both u and v.
  • +
+

+ The relative positions of p within this bounding box, denoted as s and t, are then calculated. Horizontal + interpolation between u00 and u10 using s as the weighting gives u0, while interpolation between u01 and u11 gives + u1. The final texture color is determined by vertically interpolating between u0 and u1 using t as the + weighting. +

+
+ + +
+
+ Color Picker +
Nearest (1px)
+
+ +
+ Color Picker +
Billinear (1px)
+
+ +
+ Color Picker +
Nearest (16px)
+
+
+ Color Picker +
Billinear (16px)
+ +
+ +

+ Sampling at a rate of 1px demonstrates the superiority of Bilinear filtering over Nearest neighbor + sampling. This is evident as Bilinear filtering more effectively incorporates surrounding pixels, which is + highlighted by its ability to accurately identify Latitude lines—a task at which Nearest sampling fails. As the + sampling rate increases to 16px, differences between the two methods become less noticeable from afar. + However, when we take a look using the pixel inspector it reveals that Bilinear filtering still maintains a more + balanced pixel distribution. This proves that at lower sampling rates, it is more obvious to view the + advantages of Bilinear over Nearest filtering. +

+ +
+ +
+
+

Level 6 - "Level sampling" with mipmaps for texture mapping

+

+ Level sampling involves sampling from mipmaps from corresponding mipmaps based on how much on the texture + coordinates change based off a small increment in screen space coordinates. +

+

+ Magnification: When there is a steep change in texture coordinates relative to screen + space coordinates, it indicates that the screen is magnified. This calls for higher mipmap levels to + provide more detail. +

+

+ Minification: Conversely, shallower gradients suggest that the screen is minified, + requiring lower mipmap levels thus less detail to represent without noticeable loss in quality +

+

+ For nearest level sampling, it is necessary to calculate the Barycentric coordinates + corresponding to (x + increment, y) and (x, y + increment), where the increment + is determined by the sampling rate. The next step involves calculating the difference between these + Barycentric coordinates and the original (u, v) coordinate to find the partial derivatives. +

+

+ The Mipmap level is calculated by taking the logarithm of the maximum of two expressions: + sqrt(pow(dudx.x, 2) + pow(dudx.y, 2)) and sqrt(pow(dvdy.x, 2) + pow(dvdy.y, 2)). +

+

+ For linear level sampling, the process involves flooring and + ceiling the calculated Mipmap level to determine the adjacent stored Mipmap levels. The colors from the + floored and ceiling Mipmap levels are then linearly interpolated to derive the resulting color. +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
TechniqueSpeedMemory UsageAntialiasing Power
Pixel SamplingVery fast when using just a one sample per pixel due to its simplicity, but the speed decreases as more + samples per pixel are taken to improve quality.Minimal when using a single sample as it requires access to only one pixel value at a time, but increases with + multiple samples due to the need for more pixel information.Basic with a single sample, resulting in jagged edges.
Level SamplingGenerally faster, especially at oblique angles or in distant views, because it uses pre-calculated, lower + resolution textures that require less computational power.Stores more memory as we need to store several levels of pre-filtered textures.Reduces aliasing during texture minification and magnification as it chooses the appropriately + sized mipmap level to balance between detail and rendering speed.
Number of samples per pixelSubstantially slower due to the increase in samples per pixel meaning we must calculate for 4x, 9x, + or even 16x more pixelsConsiderably higher because it stores multiple samples for each pixel, which increases with the square of the + sample count.Offers the highest antialiasing power by averaging many samples to simulate sub-pixel details, leading to the + smoothest edge and texture details.
+ +

Below I rendered a Dice Texture Map

+ +

+ Our most aliased result arises when setting the default sampling technique at level 0 with nearest pixel sampling. + This approach yields blocky and discontinous edges, leading to a distinctly pixelated image. In contrast, when we + switch to billinear sampling it creates smoother transition between edges and colors. And moreso exemplified + when we billinearly sample and level sample, we see an even cleaner and smoother edge definition. As for just level + sampling we see that the edges are continous but do not transition well between colors. Evidently, the combo of + billinear pixel sampling and nearest level sampling emerges as the superior technique. +

+
+ L_ZERO_P_NEAREST +
L_ZERO P_NEAREST
+
+ +
+ L_ZERO_P_LINEAR +
L_ZERO P_LINEAR
+
+ +
+ L_NEAREST_P_NEAREST +
L_NEAREST P_NEAREST
+
+
+ L_NEAREST_P_LINEAR +
L_NEAREST P_LINEAR
+ +
+ + +
+ + + \ No newline at end of file