Add writeup
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9 changed files with 114 additions and 19 deletions
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assignment-1/.gitignore
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assignment-1/.gitignore
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/target
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/assignment-1
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*.ppm
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*.zip
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*.pdf
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.PHONY: clean
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.PHONY: all clean
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DOCKER := docker
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ZIP := zip
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PANDOC := pandoc
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HANDIN := hw1a.michael.zhang.zip
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BINARY := target/release/assignment-1
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BINARY := assignment-1
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WRITEUP := writeup.pdf
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SOURCES := $(shell find -name "*.rs")
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all: $(HANDIN)
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$(BINARY):
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docker run \
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$(BINARY): $(SOURCES)
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$(DOCKER) run \
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--rm \
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-v "$(shell pwd)":/usr/src/myapp \
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-v cargo-registry:/usr/local/cargo \
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@ -15,9 +20,13 @@ $(BINARY):
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-w /usr/src/myapp \
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rust \
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cargo build --release
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mv target/release/assignment-1 $@
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$(HANDIN): $(BINARY) Cargo.toml Cargo.lock README.md
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zip -r $@ src $<
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$(HANDIN): $(BINARY) $(WRITEUP) Cargo.toml Cargo.lock README.md
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$(ZIP) -r $@ src $<
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writeup.pdf: writeup.md
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$(PANDOC) -o $@ $<
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clean:
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rm -f $(HANDIN) $(BINARY)
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rm -f $(HANDIN) $(BINARY) $(WRITEUP)
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# Raycaster
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BIN
assignment-1/doc/fov.jpg
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assignment-1/doc/fov.jpg
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assignment-1/doc/map.jpg
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assignment-1/doc/map.jpg
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assignment-1/doc/rot.jpg
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assignment-1/doc/rot.jpg
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@ -59,7 +59,13 @@ fn main() -> Result<()> {
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move |px: usize, py: usize| {
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let x_component = pixel_base_x * px as f64;
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let y_component = pixel_base_y * py as f64;
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view_window.upper_left + x_component + y_component
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// Without adding this, we would be getting the top-left of the pixel's
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// rectangle. We want the center, so add half of the pixel size as
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// well.
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let center_offset = (pixel_base_x + pixel_base_y) / 2.0;
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view_window.upper_left + x_component + y_component + center_offset
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}
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};
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73
assignment-1/writeup.md
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assignment-1/writeup.md
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---
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geometry: margin=2cm
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output: pdf_document
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---
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# Raycaster
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Determining the viewing window for the raycaster for this assignment involved
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creating a "virtual" screen in world coordinates, mapping image pixels into that
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virtual screen, and then casting a ray through each pixel's world coordinate to
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see where it would intersect objects.
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### Creating a virtual screen
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The virtual screen is determined first using the eye's position and where it's
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looking. This gives us a single 3d vector, but it doesn't give us a 2d screen in
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the world. This is where the field of view (FOV) comes in; the FOV determines
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how many degrees the screen should take up.
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![Field of view](doc/fov.jpg){width=180px}
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Changing the angle of the field of view would result in a wider or narrower
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screen, which when paired with the aspect ratio (width / height), would produce
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a bigger or smaller viewing screen, like the orange box in the above diagram
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shows. Simply put, FOV affects how _much_ of the frame you're able to see.
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Curiously, distance from the eye actually doesn't really affect the viewing
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screen very much. The reason is the screen is only used to determine how to
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project rays. As the two black rectangles in the diagram above demonstrates,
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changing the distance would still allow the viewer to see the same amount of the
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scene. (using the word _amount_ very loosely here to mean percentage of the
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landscape, rather than # of pixels, which is determined by the actual image
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dimensions)
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The up-direction vector controls the rotation of the scene. Without the
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up-direction, it would not be possible to tell which rotation the screen should
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be in:
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![Rotation determined by up direction](doc/rot.jpg){width=240px}
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Together, all of these parameters can uniquely determine a virtual screen
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location, that we can use to cast rays through and fill pixels. We can change
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any of these to produce an image with a more exaggerated view of the scene for
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example; simply move the eye position to be incredibly close to the object that
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we are observing, and increase the field of view to cover the entire object.
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Because the rays are going in much different directions and travelling different
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distances, the corners of the image will seem more stretched than if we were
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observing the object from afar and all the rays are in approximately the same
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part of the virtual screen.
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One other point to make is that we're currently using a rectangle for our
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virtual screen, which automatically does a bit of the distortion. If instead we
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were to use a curved lens-like shape, then the rays pointing to any pixel of the
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screen would be travelling the same distance. Moving the eye position closer to
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the object would still generate distortion, but to a lesser extent.
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### Mapping image pixels
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After the rectangle has been determined, we can simply pick one corner to start
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as an anchor, and then find out what pixel values would correspond to it. For
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example, in the image below:
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![Mapping image pixels](doc/map.jpg){width=240px}
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I would pick a starting point like $A$, and then take the vector $B-A$ and
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subdivide it into 4 pieces, letting $\Delta x = \frac{B-A}{4}$. Then, same thing
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for the $y$ direction, I would set $\Delta y = \frac{D-A}{4}$. Taking $A +
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x_i \times \Delta x + y_i \times \Delta y$ yields the precise coordinate
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location for any pixel.
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(Technically really we would want the middle of the pixel, so just add
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$\frac{\Delta x + \Delta y}{2}$ to the point to get that)
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12
flake.nix
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flake.nix
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toolchain = pkgs.fenix.stable;
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in rec {
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devShell = pkgs.mkShell {
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packages =
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(with pkgs; [ cargo-watch cargo-deny cargo-edit zip unzip ])
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++ (with toolchain; [
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packages = (with pkgs; [
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cargo-watch
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cargo-deny
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cargo-edit
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pandoc
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zip
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unzip
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texlive.combined.scheme-full
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]) ++ (with toolchain; [
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cargo
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rustc
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clippy
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