copy to assignment 1c

This commit is contained in:
Michael Zhang 2023-02-18 18:28:55 -06:00
parent 87ba3b4cf4
commit b1c54826ab
31 changed files with 2721 additions and 0 deletions

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"tracing-attributes",
"tracing-core",
]
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]
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32
assignment-1c/Cargo.toml Normal file
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[package]
name = "assignment-1b"
authors = ["Michael Zhang <zhan4854@umn.edu>"]
version = "0.1.0"
edition = "2021"
# For profiling with flamegraphs
[profile.release]
debug = true
# Optimize for size when creating handin
[profile.release-handin]
inherits = "release"
strip = true
lto = true
[[bin]]
name = "raytracer1b"
path = "src/main.rs"
[dependencies]
anyhow = "1.0.68"
base64 = "0.21.0"
clap = { version = "4.1.4", features = ["cargo", "derive"] }
derivative = "2.2.0"
nalgebra = "0.32.1"
num = { version = "0.4.0", features = ["serde"] }
ordered-float = "3.4.0"
rand = "0.8.5"
rayon = "1.6.1"
tracing = "0.1.37"
tracing-subscriber = "0.3.16"

54
assignment-1c/Makefile Normal file
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@ -0,0 +1,54 @@
.PHONY: all clean
.PRECIOUS: $(EXAMPLES_PPM)
RAYTRACER_FLAGS :=
DOCKER := docker
ZIP := zip
PANDOC := pandoc
CONVERT := convert
HANDIN := ./hw1b.michael.zhang.zip
BINARY := ./raytracer1b
WRITEUP := ./writeup.pdf
SHOWCASE := ./showcase.png
SOURCES := Cargo.toml $(shell find -name "*.rs")
EXAMPLES := $(shell find examples -name "*.txt")
EXAMPLES_PPM := $(patsubst %.txt,%.ppm,$(EXAMPLES))
EXAMPLES_PNG := $(patsubst %.txt,%.png,$(EXAMPLES))
all: $(HANDIN)
$(BINARY): $(SOURCES)
mkdir -p target/docker
$(DOCKER) run \
--rm \
-v "$(shell pwd)":/usr/src/myapp \
-v cargo-registry:/usr/local/cargo \
--user "$(shell id -u)":"$(shell id -g)" \
-w /usr/src/myapp \
-e CARGO_TARGET_DIR=/usr/src/myapp/target/docker \
rust \
cargo build --profile release-handin
mv target/docker/release-handin/raytracer1b $@
$(HANDIN): $(BINARY) $(WRITEUP) Makefile Cargo.toml Cargo.lock README.md $(EXAMPLES_PNG) $(EXAMPLES_PPM) $(SHOWCASE)
$(ZIP) -r $@ src examples $^
$(SHOWCASE): examples/soft-shadow-demo.png
cp $< $@
examples/%.ppm: examples/%.txt $(SOURCES)
cargo run --release -- -o $@ $(RAYTRACER_FLAGS) $<
examples/%.png: examples/%.ppm
convert $< $@
writeup.pdf: writeup.md $(EXAMPLES_PNG)
$(PANDOC) -o $@ $<
clean:
rm -rf target/docker \
$(HANDIN) $(BINARY) $(WRITEUP) $(SHOWCASE) \
$(EXAMPLES_PPM) $(EXAMPLES_PNG)

29
assignment-1c/README.md Normal file
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# Raycaster
## Bundle contents
Writeup is located at `/writeup.pdf`.
The binary can be found at `/raytracer1b`. Run `./raytracer1b --help` to see
how to use it. The binary has been built using the Rust Docker image, which
should have an environment similar to CSELabs. If there is trouble running the
binary, try building from source, as documented below.
Examples are found in the `examples` directory. The text files are the input
sources, and the ppm files are the corresponding outputs. They have been
generated by running this program. For convenience, pngs have also been provided
using imagemagick.
## Showcase image
The showcase image can be found at `/showcase.png`.
## Building from source
The Makefile currently uses Docker to produce a more consistent build. If you
have a Rust+Cargo toolchain installed locally, it's also possible to build the
source using just:
cargo build --release
The binary will be found in `target/release`.

View file

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imsize 600 200
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hfov 90
updir 0 1 0
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updir 0 1 0
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@ -0,0 +1,41 @@
use std::io::{Result, Write};
use nalgebra::Vector3;
/// A pixel color represented by a red, green, and blue value in the range 0-1.
pub type Color = Vector3<f64>;
/// A representation of an image
pub struct Image {
/// Width in pixels
pub width: usize,
/// Height in pixels
pub height: usize,
/// Pixel data in row-major form.
pub data: Vec<Color>,
}
impl Image {
/// Write the image in PPM format to a file.
pub fn write(&self, mut w: impl Write) -> Result<()> {
// Header
let header = format!("P3 {} {} 255\n", self.width, self.height);
w.write_all(header.as_bytes())?;
// Pixel data
assert_eq!(self.data.len(), self.width * self.height);
for pixel in self.data.iter() {
let pixel = pixel * 256.0;
let red = pixel.x as u8;
let green = pixel.y as u8;
let blue = pixel.z as u8;
let pixel = format!("{red} {green} {blue}\n");
w.write_all(pixel.as_bytes())?;
}
Ok(())
}
}

13
assignment-1c/src/lib.rs Normal file
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@ -0,0 +1,13 @@
#![doc = include_str!("../README.md")]
#[macro_use]
extern crate anyhow;
#[macro_use]
extern crate derivative;
#[macro_use]
extern crate tracing;
pub mod image;
pub mod ray;
pub mod scene;
pub mod utils;

138
assignment-1c/src/main.rs Normal file
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@ -0,0 +1,138 @@
#[macro_use]
extern crate tracing;
use std::fs::File;
use std::path::PathBuf;
use anyhow::Result;
use assignment_1b::image::Image;
use assignment_1b::ray::Ray;
use assignment_1b::scene::Scene;
use clap::Parser;
use rayon::prelude::{IntoParallelIterator, ParallelIterator};
/// Simple raytracer with Blinn-Phong illumination and shadowing.
#[derive(Parser)]
#[clap(author, version, about, long_about = None)]
struct Opt {
/// Path to the input file to use.
#[clap()]
input_path: PathBuf,
/// Path to the output (defaults to the same file name as the input except
/// with an extension of .ppm)
#[clap(short = 'o', long = "output")]
output_path: Option<PathBuf>,
/// Force parallel projection to be used
#[clap(long = "parallel")]
force_parallel: bool,
/// Override distance from eye
#[clap(long = "distance", default_value = "1.0")]
distance: f64,
}
fn main() -> Result<()> {
let opt = Opt::parse();
// Set up logging
tracing_subscriber::fmt()
.with_target(false)
.with_timer(tracing_subscriber::fmt::time::uptime())
.with_level(true)
.init();
// Rename the output file if it's not provided
let out_file = opt
.output_path
.unwrap_or_else(|| opt.input_path.with_extension("ppm"));
let mut scene = Scene::from_input_file(&opt.input_path)?;
let distance = opt.distance;
// Force-override parallel projection
if opt.force_parallel {
scene.parallel_projection = true;
}
// Translate image pixels to real-world 3d coords
let translate_pixel = scene.pixel_translation_function(distance);
// Generate a parallel iterator for pixels
// The iterator preserves order and uses row-major order
let pixels_iter = (0..scene.image_height)
.into_par_iter()
.flat_map(|y| (0..scene.image_width).into_par_iter().map(move |x| (x, y)));
// Loop through every single pixel of the output file
let pixels = pixels_iter
.map(|(px, py)| {
let pixel_in_space = translate_pixel(px, py);
let ray_start = if scene.parallel_projection {
// For a parallel projection, we'll just take the view direction and
// subtract it from the target point. This means every single
// ray will be viewed from a point at infinity, rather than a single eye
// position.
let n = scene.view_dir.normalize();
let view_dir = n * distance;
pixel_in_space - view_dir
} else {
scene.eye_pos
};
let ray = Ray::from_endpoints(ray_start, pixel_in_space);
let intersections = scene
.objects
.iter()
.enumerate()
.filter_map(|(i, object)| {
match object.kind.intersects_ray_at(&ray) {
Ok(Some(t)) => {
// Return both the t and the sphere, because we want to sort on
// the t but later retrieve attributes from the sphere
Some(Ok((i, t, object)))
}
Ok(None) => None,
Err(err) => {
error!("Error: {err}");
Some(Err(err))
}
}
})
.collect::<Result<Vec<_>>>()?;
// Sort the list of intersection times by the lowest one.
let earliest_intersection =
intersections.into_iter().min_by_key(|(_, t, _)| t.time);
Ok(match earliest_intersection {
// Take the object's material color
Some((obj_idx, intersection_context, object)) => scene
.compute_pixel_color(obj_idx, object.material, intersection_context),
// There was no intersection, so this should default to the scene's
// background color
None => scene.bkg_color,
})
})
.collect::<Result<Vec<_>>>()?;
// Construct and emit image
let image = Image {
width: scene.image_width,
height: scene.image_height,
data: pixels,
};
{
let file = File::create(out_file)?;
image.write(file)?;
}
Ok(())
}

27
assignment-1c/src/ray.rs Normal file
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use nalgebra::Vector3;
/// A normalized parametric Ray of the form (origin + direction * time)
///
/// That means at any time t: f64, the point represented by origin + direction *
/// time occurs on the ray.
#[derive(Debug)]
pub struct Ray {
pub origin: Vector3<f64>,
pub direction: Vector3<f64>,
}
impl Ray {
/// Construct a ray from endpoints
pub fn from_endpoints(start: Vector3<f64>, end: Vector3<f64>) -> Self {
let delta = (end - start).normalize();
Ray {
origin: start,
direction: delta,
}
}
/// Evaluate the ray at a certain point in time, yielding a point
pub fn eval(&self, time: f64) -> Vector3<f64> {
self.origin + self.direction * time
}
}

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use anyhow::Result;
use nalgebra::Vector3;
use ordered_float::NotNan;
use crate::ray::Ray;
use crate::utils::compute_rotation_matrix;
use super::{illumination::IntersectionContext};
#[derive(Debug)]
pub struct Cylinder {
pub center: Vector3<f64>,
pub direction: Vector3<f64>,
pub radius: f64,
pub length: f64,
}
impl Cylinder {
/// Given a cylinder, returns the first time at which this ray intersects the
/// cylinder.
///
/// If there is no intersection point, returns None.
pub fn intersects_ray_at(
&self,
ray: &Ray,
) -> Result<Option<IntersectionContext>> {
// Determine rotation matrix for turning the cylinder upright along the
// Z-axis
let target_direction = Vector3::new(0.0, 0.0, 1.0);
let rotation_matrix =
compute_rotation_matrix(self.direction, target_direction)?;
let inverse_rotation_matrix =
rotation_matrix.try_inverse().ok_or_else(|| {
anyhow!("Rotation matrix for some reason does not have an inverse?")
})?;
// Transform all parameters according to this rotation matrix
let rotated_cylinder_center = rotation_matrix * self.center;
let rotated_ray_origin = rotation_matrix * ray.origin;
let rotated_ray_direction = rotation_matrix * ray.direction;
// Now that we know the cylinder is upright, we can start checking against
// the formula:
//
// (ox + t*rx - cx)^2 + (oy + t*ry - cy)^2 = r^2
//
// where o{xy} is the ray origin, r{xy} is the ray direction, and c{xy} is
// the cylinder center. The z will be taken care of after the fact. To
// solve, we must put it into the form At^2 + Bt + c = 0. The variables
// are:
//
// A: rx^2 + ry^2
// B: 2(rx(ox - cx) + ry(oy - cy))
// C: (cx - ox)^2 + (cy - oy)^2 - r^2
let (a, b, c) = {
let o = rotated_ray_origin;
let r = rotated_ray_direction;
let c = rotated_cylinder_center;
(
r.x.powi(2) + r.y.powi(2),
2.0 * (r.x * (o.x - c.x) + r.y * (o.y - c.y)),
(c.x - o.x).powi(2) + (c.y - o.y).powi(2) - self.radius.powi(2),
)
};
let discriminant = b * b - 4.0 * a * c;
let possible_side_solutions = match discriminant {
// Discriminant < 0, means the equation has no solutions.
d if d < 0.0 => vec![],
// Discriminant == 0
d if d == 0.0 => vec![-b / 2.0 * a],
// Discriminant > 0, 2 solutions available.
d if d > 0.0 => {
vec![
(-b + discriminant.sqrt()) / (2.0 * a),
(-b - discriminant.sqrt()) / (2.0 * a),
]
}
// Probably hit some NaN or Infinity value due to faulty inputs...
_ => bail!("Invalid determinant value: {discriminant}"),
};
// Filter out solutions that don't have a valid Z position.
let side_solutions = possible_side_solutions.into_iter().filter_map(|t| {
let ray_point = ray.eval(t);
let rotated_ray_point = rotation_matrix * ray_point;
let z = rotated_ray_point.z - rotated_cylinder_center.z;
// Check to see if z is between -len/2 and len/2
if z.abs() > self.length / 2.0 {
return None;
}
let time = NotNan::new(t).ok()?;
// The point on the center of the cylinder that corresponds to the z-axis
// point of the intersection
let center_at_z = {
let mut center_point = rotation_matrix * ray_point;
center_point.x = rotated_cylinder_center.x;
center_point.y = rotated_cylinder_center.y;
inverse_rotation_matrix * center_point
};
let normal = (ray_point - center_at_z).normalize();
Some(IntersectionContext {
time,
point: ray_point,
normal,
})
});
// We also need to add solutions for the two ends of the cylinder, which
// uses a similar method except backwards: check intersection points
// with the correct z-plane and then see if the points are within the
// circle.
//
// Luckily, this means we only need to care about one dimension at first,
// and don't need to perform the quadratic equation method above.
//
// oz + t * rz = cz +- (len / 2)
// t = (-oz + cz +- (len / 2)) / rz
let possible_z_intersections = {
let o = rotated_ray_origin;
let r = rotated_ray_direction;
let c = rotated_cylinder_center;
if r.z == 0.0 {
Vec::new() // No solutions here
} else {
vec![
(-o.z + c.z + self.length / 2.0) / r.z,
(-o.z + c.z - self.length / 2.0) / r.z,
]
}
};
let end_solutions = possible_z_intersections.into_iter().filter_map(|t| {
let ray_point = ray.eval(t);
let rotated_point = rotation_matrix * ray_point;
// Filter out all the solutions where the intersection point does not lie
// in the circle
if rotated_point.x.powi(2) + rotated_point.y.powi(2) > self.radius.powi(2)
{
return None;
}
let normal_rotated =
Vector3::new(0.0, 0.0, rotated_point.z - rotated_cylinder_center.z)
.normalize();
let normal = inverse_rotation_matrix * normal_rotated;
let time = NotNan::new(t).ok()?;
Some(IntersectionContext {
time,
point: ray_point,
normal,
})
});
let solutions = side_solutions
.into_iter()
.chain(end_solutions.into_iter())
// Remove any t < 0, since that means it's behind the viewer and we
// can't see it.
.filter(|ctx| *ctx.time >= 0.0);
// Return the minimum solution
Ok(solutions.min_by_key(|ctx| ctx.time))
}
}
#[cfg(test)]
mod tests {
use nalgebra::Vector3;
use crate::{ray::Ray};
use super::Cylinder;
#[test]
fn test_cylinder() {
let cylinder = Cylinder {
center: Vector3::new(0.0, 0.0, 0.0),
direction: Vector3::new(0.0, 1.0, 0.0),
radius: 3.0,
length: 4.0,
};
let eye = Vector3::new(0.0, 3.0, 3.0);
let end = Vector3::new(0.0, 2.0, 2.0);
let ray = Ray::from_endpoints(eye, end);
let res = cylinder.intersects_ray_at(&ray);
panic!("Result: {res:?}");
}
}

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use std::fmt::Debug;
use anyhow::Result;
use nalgebra::Vector3;
use crate::image::Color;
use crate::ray::Ray;
use crate::utils::cross;
use super::cylinder::Cylinder;
use super::illumination::IntersectionContext;
use super::sphere::Sphere;
use super::Scene;
#[derive(Debug)]
pub enum ObjectKind {
Sphere(Sphere),
Cylinder(Cylinder),
}
impl ObjectKind {
/// Determine where the ray intersects this object, returning the earliest
/// time this happens. Returns None if no intersection occurs.
///
/// Also known as Trace_Ray in the slides, except not the part where it calls
/// Shade_Ray.
pub fn intersects_ray_at(
&self,
ray: &Ray,
) -> Result<Option<IntersectionContext>> {
match self {
ObjectKind::Sphere(sphere) => sphere.intersects_ray_at(ray),
ObjectKind::Cylinder(cylinder) => cylinder.intersects_ray_at(ray),
}
}
}
/// An object in the scene
#[derive(Debug)]
pub struct Object {
pub kind: ObjectKind,
/// Index into the scene's material color list
pub material: usize,
}
#[derive(Debug)]
pub struct Rect {
pub upper_left: Vector3<f64>,
pub upper_right: Vector3<f64>,
pub lower_left: Vector3<f64>,
pub lower_right: Vector3<f64>,
}
#[derive(Debug)]
pub struct Material {
pub diffuse_color: Vector3<f64>,
pub specular_color: Vector3<f64>,
pub k_a: f64,
pub k_d: f64,
pub k_s: f64,
pub exponent: f64,
}
#[derive(Debug)]
pub enum LightKind {
/// A point light source exists at a point and emits light in all directions
Point {
location: Vector3<f64>,
/// Whether light attenuation is enabled for this light
attenuation: Option<Attenuation>,
},
/// A directional light source exists at an infinitely far location but emits
/// light in a specific direction
Directional { direction: Vector3<f64> },
}
#[derive(Debug)]
pub struct Light {
/// The kind of light source, as well as its associated information
pub kind: LightKind,
/// The color, or intensity, of the light source
pub color: Vector3<f64>,
}
impl Light {
/// Get the unit directional vector pointing from the given point to this
/// light source
pub fn direction_from(&self, point: Vector3<f64>) -> Vector3<f64> {
match self.kind {
LightKind::Point { location, .. } => location - point,
LightKind::Directional { direction } => -direction,
}
.normalize()
}
}
#[derive(Debug)]
pub struct DepthCueing {
/// The color to tint (should be the same as the background color, to avoid
/// bizarre visual effects)
pub color: Color,
/// Proportion of the color influenced by the depth tint when the distance is
/// maxed (caps at 1.0)
pub a_max: f64,
/// Proportion of the color influenced by the depth tint when the distance is
/// at the minimum (caps at 1.0)
pub a_min: f64,
/// The max distance that should be affected by the depth tint
pub dist_max: f64,
/// The min distance that should be affected by the depth tint
pub dist_min: f64,
}
/// A default implementation here needs to simulate what would happen if there
/// was no depth cueing. In this case, if we have both a_max and a_min be 1.0,
/// then the original color will always apply and there will be no need for
/// depth color
impl Default for DepthCueing {
fn default() -> Self {
Self {
color: Default::default(),
a_max: 1.0,
a_min: 1.0,
dist_max: 0.0,
dist_min: 0.0,
}
}
}
/// Light attenuation dropoff coefficients
#[derive(Debug)]
pub struct Attenuation {
pub c1: f64,
pub c2: f64,
pub c3: f64,
}
/// A default implementation here needs to simulate what would happen if there
/// was no light attenuation specified. In this case, c1 would just be a
/// constant of 1 and all the coefficients for anything involving distance would
/// be zeroed out
impl Default for Attenuation {
fn default() -> Self {
Self {
c1: 1.0,
c2: 0.0,
c3: 0.0,
}
}
}
impl Scene {
/// Determine the boundaries of the viewing window in world coordinates
pub fn compute_viewing_window(&self, distance: f64) -> Rect {
// Compute viewing directions
let u = cross(self.view_dir, self.up_dir).normalize();
let v = cross(u, self.view_dir).normalize();
// Compute dimensions of viewing window based on field of view
let viewing_width = {
// Divide the angle in 2 since we are trying to use trig rules so we must
// get it from a right triangle
let half_hfov = self.hfov.to_radians() / 2.0;
// tan(hfov / 2) = w / 2d
let w_over_2d = half_hfov.tan();
// To find the viewing width we must multiply by 2d now
w_over_2d * 2.0 * distance
};
let aspect_ratio = self.image_width as f64 / self.image_height as f64;
let viewing_height = viewing_width / aspect_ratio;
// Compute viewing window corners
let n = self.view_dir.normalize();
#[rustfmt::skip] // Don't format, or else this line wraps over
let view_window = Rect {
upper_left: self.eye_pos + n * distance - u * (viewing_width / 2.0) + v * (viewing_height / 2.0),
upper_right: self.eye_pos + n * distance + u * (viewing_width / 2.0) + v * (viewing_height / 2.0),
lower_left: self.eye_pos + n * distance - u * (viewing_width / 2.0) - v * (viewing_height / 2.0),
lower_right: self.eye_pos + n * distance + u * (viewing_width / 2.0) - v * (viewing_height / 2.0),
};
view_window
}
/// Create a pixel translation function based on the viewing window of the
/// current scene
pub fn pixel_translation_function(
&self,
distance: f64,
) -> impl Fn(usize, usize) -> Vector3<f64> {
let view_window = self.compute_viewing_window(distance);
let dx = view_window.upper_right - view_window.upper_left;
let pixel_base_x = dx / self.image_width as f64;
let dy = view_window.lower_left - view_window.upper_left;
let pixel_base_y = dy / self.image_height as f64;
// The final function to be returned
move |px: usize, py: usize| {
let x_component = pixel_base_x * px as f64;
let y_component = pixel_base_y * py as f64;
// Without adding this, we would be getting the top-left of the pixel's
// rectangle. We want the center, so add half of the pixel size as
// well.
let center_offset = (pixel_base_x + pixel_base_y) / 2.0;
view_window.upper_left + x_component + y_component + center_offset
}
}
}

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use std::iter;
use nalgebra::Vector3;
use ordered_float::NotNan;
use rand::Rng;
use rayon::prelude::{
IndexedParallelIterator, IntoParallelIterator, IntoParallelRefIterator,
ParallelIterator,
};
use crate::{image::Color, ray::Ray, utils::dot};
use super::{
data::{DepthCueing, Light, LightKind, Object},
Scene,
};
impl Scene {
/// Determine the color that should be used to fill this pixel.
///
/// - material_idx is the index into the materials list.
/// - intersection_context contains information on vectors where the
/// intersection occurred
///
/// Also known as Shade_Ray in the slides.
pub fn compute_pixel_color(
&self,
obj_idx: usize,
material_idx: usize,
intersection_context: IntersectionContext,
) -> Color {
// TODO: Does it make sense to make this function fallible from an API
// design standpoint?
let material = match self.materials.get(material_idx) {
Some(v) => v,
None => return self.bkg_color,
};
let ambient_component = material.k_a * material.diffuse_color;
// Diffuse and specular lighting for each separate light
let diffuse_and_specular: Vector3<f64> = self
.lights
.par_iter()
.map(|light| {
// The vector pointing in the direction of the light
let light_direction = light.direction_from(intersection_context.point);
let normal = intersection_context.normal.normalize();
let viewer_direction = self.eye_pos - intersection_context.point;
let halfway_direction =
((light_direction + viewer_direction) / 2.0).normalize();
let diffuse_component = material.k_d
* material.diffuse_color
* dot(normal, light_direction).max(0.0);
let specular_component = material.k_s
* material.specular_color
* dot(normal, halfway_direction)
.max(0.0)
.powf(material.exponent);
// Shadow coefficient between 0 and 1 to control how bright this pixel
// should be from being in the shadow of another object (could be
// between 0 and 1 when applying soft shadows)
let shadow_coefficient = self.compute_shadow_coefficient(
obj_idx,
intersection_context.point,
light,
);
let attenuation_coefficient = match &light.kind {
LightKind::Point {
location,
attenuation: Some(att),
} => {
let dist = (location - intersection_context.point).norm();
let denom = att.c1 + att.c2 * dist + att.c3 * dist.powi(2);
if denom == 0.0 {
warn!("Light attenuation coefficients produced a denominator of 0. Check your inputs...");
1.0 // Some kind of graceful fallback here
} else {
1.0 / denom
}
}
_ => 1.0,
};
let diffuse_and_specular = diffuse_component + specular_component;
attenuation_coefficient
* shadow_coefficient
* light.color.component_mul(&diffuse_and_specular)
})
.sum();
let color = ambient_component + diffuse_and_specular;
// Apply depth cueing to the result
let a_dc = {
// Distance from the viewer
let d_obj = (intersection_context.point - self.eye_pos).norm();
let DepthCueing {
dist_max,
dist_min,
a_max,
a_min,
..
} = self.depth_cueing;
if d_obj < dist_min {
a_max
} else if d_obj < dist_max {
a_min + (a_max - a_min) * (dist_max - d_obj) / (dist_max - dist_min)
} else {
a_min
}
};
let color = a_dc * color + (1.0 - a_dc) * self.depth_cueing.color;
// Need to clamp the result so none of the components goes over 1
let clamped_result = color.map(|v| v.min(1.0));
clamped_result
}
/// Perform another ray casting to see if there are any objects obstructing
/// the light source to this particular point
pub fn compute_shadow_coefficient(
&self,
obj_idx: usize,
point: Vector3<f64>,
light: &Light,
) -> f64 {
let light_direction = light.direction_from(point);
let ray = Ray {
origin: point,
direction: light_direction.normalize(),
};
// Small helper for iterating over all of the objects in the scene except
// for the current one
let other_objects = self
.objects
.par_iter()
.enumerate()
.filter(|(i, _)| *i != obj_idx);
// Get the list of intersections with all the other objects in the scene
// This list will be a set of opacities
let intersections = other_objects
.filter_map(|(_, object)| {
let intersection_context = match object.kind.intersects_ray_at(&ray) {
Ok(v) => v,
Err(err) => {
error!("Error while performing shadow casting: {err}");
None
}
}?;
let intersection_time = *intersection_context.time;
match light.kind {
// In the case of point lights, we must check to see if both t > 0 and
// t is less than the time it took to even get to the light.
LightKind::Point { location, .. } => {
let light_time = (location - ray.origin).norm();
if intersection_time <= 0.0 || intersection_time >= light_time {
None
} else {
let soft_shadow_coefficient =
self.compute_soft_shadow_coefficient(location, point, object);
Some(soft_shadow_coefficient)
}
}
// In the case of directional lights, only t > 0 needs to be checked,
// otherwise
LightKind::Directional { .. } => {
if intersection_time <= 0.0 {
None
} else {
Some(0.0) // complete obstruction
}
}
}
})
.collect::<Vec<_>>();
let average =
intersections.iter().cloned().sum::<f64>() / intersections.len() as f64;
match intersections.is_empty() {
true => 1.0,
false => average,
}
}
fn compute_soft_shadow_coefficient(
&self,
light_location: Vector3<f64>,
original_intersection_point: Vector3<f64>,
object: &Object,
) -> f64 {
// Soft shadows: jitter some rays here to somewhere close to the
// actual location as well, and measure the proportion
// of them that intersect any objects
const JITTER_RADIUS: f64 = 1.0;
const JITTER_RAYS: usize = 75;
let mut rng = rand::thread_rng();
let locations = iter::repeat_with(|| {
let x = rng.gen_range(0.0..JITTER_RADIUS);
let y = rng.gen_range(0.0..JITTER_RADIUS);
let z = rng.gen_range(0.0..JITTER_RADIUS);
let delta = Vector3::new(x, y, z);
light_location + delta
})
.take(JITTER_RAYS)
.collect::<Vec<_>>();
let num_obstructed_rays = locations
.into_par_iter()
.filter(|location| {
let direction = (location - original_intersection_point).normalize();
let ray = Ray {
origin: original_intersection_point,
direction,
};
let intersection_context = match object.kind.intersects_ray_at(&ray) {
Ok(Some(v)) => v,
Ok(None) => return false,
Err(err) => {
error!("Error while performing shadow casting: {err}");
return false;
}
};
let light_time = (location - ray.origin).norm();
let intersection_time = *intersection_context.time;
0.0 < intersection_time && intersection_time < light_time
})
.count();
(JITTER_RAYS - num_obstructed_rays) as f64 / JITTER_RAYS as f64
}
}
/// Information about an intersection
#[derive(Derivative)]
#[derivative(Debug, PartialEq, PartialOrd, Ord)]
pub struct IntersectionContext {
/// The time of the intersection in the parametric ray
///
/// Unfortunately, IEEE floats in Rust don't have total ordering, because
/// NaNs violate ordering properties. The way to remedy this is to ensure we
/// don't have NaNs by wrapping it into this type, which then implements
/// total ordering.
pub time: NotNan<f64>,
/// The intersection point.
#[derivative(PartialEq = "ignore", Ord = "ignore")]
pub point: Vector3<f64>,
/// The normal vector protruding from the surface of the object at the
/// intersection point
#[derivative(PartialEq = "ignore", Ord = "ignore")]
pub normal: Vector3<f64>,
}
impl Eq for IntersectionContext {}
impl IntersectionContext {}

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use std::{fs::File, io::Read, path::Path};
use anyhow::Result;
use nalgebra::Vector3;
use crate::scene::{
cylinder::Cylinder,
data::{Attenuation, Light, LightKind, Material, Object},
sphere::Sphere,
Scene,
};
use super::data::{DepthCueing, ObjectKind};
impl Scene {
/// Parse the input file into a scene
pub fn from_input_file(path: impl AsRef<Path>) -> Result<Self> {
// Scope the read so the file is dropped and closed immediately after the
// contents have been read to memory
let contents = {
let mut contents = String::new();
let mut file = File::open(path.as_ref())?;
file.read_to_string(&mut contents)?;
contents
};
let mut scene = Scene::default();
let mut material_color = None;
for line in contents.lines() {
let mut parts = line.split_whitespace();
let keyword = match parts.next() {
Some(v) => v,
None => continue,
};
if keyword == "imsize" {
let parts = parts
.map(|s| s.parse::<usize>().map_err(|e| e.into()))
.collect::<Result<Vec<_>>>()?;
if let [width, height] = parts[..] {
scene.image_width = width;
scene.image_height = height;
}
} else if keyword == "projection" {
if let Some("parallel") = parts.next() {
scene.parallel_projection = true;
}
}
// Do float parsing instead
else {
let parts = parts
.map(|s| s.parse::<f64>().map_err(|e| e.into()))
.collect::<Result<Vec<_>>>()?;
let read_vec3 = |start: usize| {
ensure!(parts.len() >= start + 3, "Vec3 requires 3 components.");
Ok(Vector3::new(
parts[start],
parts[start + 1],
parts[start + 2],
))
};
match keyword {
"eye" => scene.eye_pos = read_vec3(0)?,
"viewdir" => scene.view_dir = read_vec3(0)?,
"updir" => scene.up_dir = read_vec3(0)?,
"hfov" => scene.hfov = parts[0],
"bkgcolor" => scene.bkg_color = read_vec3(0)?,
// light x y z w r g b
"light" => {
ensure!(parts.len() == 7, "Light requires 7 params");
let kind = match parts[3] as usize {
0 => LightKind::Directional {
direction: read_vec3(0)?,
},
1 => LightKind::Point {
location: read_vec3(0)?,
attenuation: None,
},
_ => bail!("Invalid w; must be either 0 or 1"),
};
let light = Light {
kind,
color: read_vec3(4)?,
};
scene.lights.push(light);
}
// attlight x y z w r g b c1 c2 c3
"attlight" => {
ensure!(parts.len() == 10, "Attenuated light requires 10 params");
let kind = match parts[3] as usize {
// TODO: Is this even defined? Pending TA answer
0 => LightKind::Directional {
direction: read_vec3(0)?,
},
1 => LightKind::Point {
location: read_vec3(0)?,
attenuation: Some(Attenuation {
c1: parts[7],
c2: parts[8],
c3: parts[9],
}),
},
_ => bail!("Invalid w; must be either 0 or 1"),
};
let light = Light {
kind,
color: read_vec3(4)?,
};
scene.lights.push(light);
}
// depthcueing dcr dcg dcb amax amin distmax distmin
"depthcueing" => {
ensure!(parts.len() == 7, "Depth cueing requires 7 params");
let color = read_vec3(0)?;
scene.depth_cueing = DepthCueing {
color,
a_max: parts[3],
a_min: parts[4],
dist_max: parts[5],
dist_min: parts[6],
};
}
// mtlcolor Odr Odg Odb Osr Osg Osb ka kd ks n
"mtlcolor" => {
ensure!(parts.len() == 10, "Material color requires 10 params");
let diffuse_color = read_vec3(0)?;
let specular_color = read_vec3(3)?;
let material = Material {
diffuse_color,
specular_color,
k_a: parts[6],
k_d: parts[7],
k_s: parts[8],
exponent: parts[9],
};
let idx = scene.materials.len();
material_color = Some(idx);
scene.materials.push(material);
}
"sphere" => scene.objects.push(Object {
kind: ObjectKind::Sphere(Sphere {
center: read_vec3(0)?,
radius: parts[3],
}),
material: match material_color {
Some(v) => v,
None => {
bail!("Each sphere must be preceded by a `mtlcolor` line")
}
},
}),
"cylinder" => scene.objects.push(Object {
kind: ObjectKind::Cylinder(Cylinder {
center: read_vec3(0)?,
direction: read_vec3(3)?,
radius: parts[6],
length: parts[7],
}),
material: match material_color {
Some(v) => v,
None => {
bail!("Each sphere must be preceded by a `mtlcolor` line")
}
},
}),
_ => bail!("Unknown keyword {keyword}"),
}
}
}
Ok(scene)
}
}

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@ -0,0 +1,34 @@
pub mod cylinder;
pub mod data;
pub mod illumination;
pub mod input_file;
pub mod sphere;
use nalgebra::Vector3;
use crate::image::Color;
use self::data::{DepthCueing, Light, Material, Object, Attenuation};
#[derive(Debug, Default)]
pub struct Scene {
pub eye_pos: Vector3<f64>,
pub view_dir: Vector3<f64>,
pub up_dir: Vector3<f64>,
/// Horizontal field of view (in degrees)
pub hfov: f64,
pub parallel_projection: bool,
pub image_width: usize,
pub image_height: usize,
/// Background color
pub bkg_color: Color,
pub depth_cueing: DepthCueing,
pub attenuation: Attenuation,
pub materials: Vec<Material>,
pub lights: Vec<Light>,
pub objects: Vec<Object>,
}

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@ -0,0 +1,74 @@
use anyhow::Result;
use nalgebra::Vector3;
use ordered_float::NotNan;
use crate::{ray::Ray, utils::min_f64};
use super::illumination::IntersectionContext;
#[derive(Debug)]
pub struct Sphere {
pub center: Vector3<f64>,
pub radius: f64,
}
impl Sphere {
/// Given a sphere, returns the first time at which this ray intersects the
/// sphere.
///
/// If there is no intersection point, returns None.
pub fn intersects_ray_at(
&self,
ray: &Ray,
) -> Result<Option<IntersectionContext>> {
let a = ray.direction.norm();
let b = 2.0
* (ray.direction.x * (ray.origin.x - self.center.x)
+ ray.direction.y * (ray.origin.y - self.center.y)
+ ray.direction.z * (ray.origin.z - self.center.z));
let c = (ray.origin.x - self.center.x).powi(2)
+ (ray.origin.y - self.center.y).powi(2)
+ (ray.origin.z - self.center.z).powi(2)
- self.radius.powi(2);
let discriminant = b * b - 4.0 * a * c;
let time = match discriminant {
// Discriminant < 0, means the equation has no solutions.
d if d < 0.0 => None,
// Discriminant == 0
d if d == 0.0 => Some(-b / (2.0 * a)),
d if d > 0.0 => {
let solution_1 = (-b + discriminant.sqrt()) / (2.0 * a);
let solution_2 = (-b - discriminant.sqrt()) / (2.0 * a);
let solutions = [solution_1, solution_2]
.into_iter()
// Remove any t < 0, since that means it's behind the viewer and we
// can't see it.
.filter(|t| *t >= 0.0);
// Return the minimum solution
min_f64(solutions)
}
// Probably hit some NaN or Infinity value due to faulty inputs...
_ => unreachable!("Invalid determinant value: {discriminant}"),
};
let time = match time.and_then(|t| NotNan::new(t).ok()) {
Some(v) => v,
None => return Ok(None),
};
let point = ray.eval(*time);
let normal = (point - self.center).normalize();
Ok(Some(IntersectionContext {
time,
point,
normal,
}))
}
}

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@ -0,0 +1,93 @@
use anyhow::Result;
use nalgebra::{Matrix3, Vector3};
use ordered_float::NotNan;
/// Finds the minimum of an iterator of f64s, ignoring any NaN values
#[inline]
pub fn min_f64<I>(i: I) -> Option<f64>
where
I: Iterator<Item = f64>,
{
i.filter_map(|i| NotNan::new(i).ok())
.min()
.map(|i| i.into_inner())
}
/// Finds the minimum of an iterator of f64s using the given predicate, ignoring
/// any NaN values
#[inline]
pub fn min_f64_by_key<I, F>(i: I, f: F) -> Option<f64>
where
I: Iterator<Item = f64>,
F: FnMut(&NotNan<f64>),
{
i.filter_map(|i| NotNan::new(i).ok())
.min_by_key(f)
.map(|i| i.into_inner())
}
/// Dot-product between two 3D vectors.
#[inline]
pub fn dot(a: Vector3<f64>, b: Vector3<f64>) -> f64 {
a.x * b.x + a.y * b.y + a.z * b.z
}
/// Cross-product between two 3D vectors.
#[inline]
pub fn cross(a: Vector3<f64>, b: Vector3<f64>) -> Vector3<f64> {
let x = a.y * b.z - a.z * b.y;
let y = a.z * b.x - a.x * b.z;
let z = a.x * b.y - a.y * b.x;
Vector3::new(x, y, z)
}
/// Calculate the rotation matrix between the 2 given vectors
///
/// Based on the method given [here][1].
///
/// [1]: https://math.stackexchange.com/a/897677
pub fn compute_rotation_matrix(
a: Vector3<f64>,
b: Vector3<f64>,
) -> Result<Matrix3<f64>> {
// Special case: if a and b are in the same direction, just return the
// identity matrix.
if a.normalize() == b.normalize() {
return Ok(Matrix3::identity());
}
let cos_t = dot(a, b);
let sin_t = cross(a, b).norm();
let g = Matrix3::new(cos_t, -sin_t, 0.0, sin_t, cos_t, 0.0, 0.0, 0.0, 1.0);
// New basis vectors
let u = a;
let v = (b - cos_t * a).normalize();
let w = cross(b, a);
// Not sure if this is required to be invertible?
let f_inverse = Matrix3::from_columns(&[u, v, w]);
let f = match f_inverse.try_inverse() {
Some(v) => v,
None => {
// So I ran into this case trying to compute the rotation matrix where one
// of the vector endpoints was (0, 0, 0). I'm pretty sure this case makes
// no sense in reality, which means if I ever encounter this case, I
// probably made a mistake somewhere before. So going to just error
// out here and screw recovering.
//
// println!("Failed to compute inverse matrix.");
// println!("- Initial: a = {a}, b = {b}");
// println!("- cos(t) = {cos_t}, sin(t) = {sin_t}");
// println!("- Basis: u = {u}, v = {v}, w = {w}");
bail!("Failed to compute inverse matrix of {f_inverse}\na = {a}\nb = {b}")
}
};
// if (f_inverse * g * f).norm() != 1.0 {
// bail!("WTF {}", (f_inverse * g * f).norm());
// }
Ok(f_inverse * g * f)
}

173
assignment-1c/writeup.md Normal file
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@ -0,0 +1,173 @@
---
geometry: margin=2cm
output: pdf_document
---
# Raytracer part B
This project implements a raytracer with Blinn-Phong illumination and shadows
implemented. The primary formula that is used by this implementation is:
\begin{equation}
I_{\lambda} =
k_a O_{d\lambda} +
\sum_{i=1}^{n_\textrm{lights}} \left(
f_\textrm{att} \cdot
S_i \cdot
IL_{i\lambda} \left[
k_d O_{d\lambda} \max ( 0, \vec{N} \cdot \vec{L_i} ) +
k_s O_{s\lambda} \max ( 0, \vec{N} \cdot \vec{H_i} )^n
\right]
\right)
\end{equation}
Where:
- $I_{\lambda}$ is the final illumination of the pixel on an object
- $k_a$ is the material's ambient reflectivity
- $k_d$ is the material's diffuse reflectivity
- $k_s$ is the material's specular reflectivity
- $n_\textrm{lights}$ is the number of lights
- $f_\textrm{att}$ is the light attenuation factor (1.0 if attenuation is not on)
- $S_i$ is the shadow coefficient for light $i$
- $IL_{i\lambda}$ is the intensity of light $i$
- $O_{d\lambda}$ is the object's diffuse color
- $O_{s\lambda}$ is the object's specular color
- $\vec{N}$ is the normal vector to the object's surface
- $\vec{L_i}$ is the direction from the intersection point to the light $i$
- $\vec{H_i}$ is halfway between the direction to the light $i$ and the
direction to the viewer
- $n$ is the exponent for the specular component
In this report we will look through how these various factors influence the
rendering of the scene. All the images along with their source `.txt` files,
rendered `.ppm` files, and converted `.png` files can be found in the `examples`
directory of this handin.
## Varying $k_a$
$k_a$ is the strength of ambient light. It's used as a coefficient for the
object's diffuse color, which keeps a constant value independent of the
positions of the object, light, and the viewer. In the image below, I varied
$k_a$ between 0.2 and 1. Note how the overall color of the ball increases or
decreases in brightness when all other factors remain constant.
![Varying $k_a$](examples/ka-demo.png){width=360px}
\
## Varying $k_d$
$k_d$ is the strength of the diffuse component. It also affects an object's
diffuse color, but at a strength that's affected by how much of it faces the
light. Much like the dark side of the moon, the parts of the object that aren't
pointed at the light will not receive as much of the light's influence. In the
image below, I varied $k_d$ between 0.2 and 1. Note how the part pointed to the
light changes the strength of the brightness as all other factors remain
constant.
![Varying $k_d$](examples/kd-demo.png){width=360px}
\
## Varying $k_s$
$k_s$ is the specular strength. It uses the object's specular color, which is
like its reflective component. When there is a large specular $k_s$, there's a
shine that appears on the object with a greater intensity. In the image below, I
varied $k_s$ between 0.2 and 1. Note how the whiteness of the light is more
reflective in higher $k_s$ values as other factors remain constant.
![Varying $k_s$](examples/ks-demo.png){width=360px}
\
## Varying $n$
$n$ is the exponent saying how big the radius of the specular highlight should
be. In the equation, increasing the exponent usually leads to smaller shines. In
the image below, I varied $n$ between 2 and 100. Note how the size of the shine
is the same intensity, but more focused but covers a smaller area as $n$
increases.
![Varying $n$](examples/n-demo.png){width=360px}
\
## Multiple lights
Multiple lights are handled by multiplying each light against an intensity
level, and then added together. Unfortunately, this means that the intensity of
each light can't be too bright. We rely on the image to not use lights that are
too bright. Because this may result in color values above 1.0, the final value
is clamped against 1.0. Below is an example of a scene with two lights; one to
the left and one to the right:
![Multiple lights](examples/multiple-lights-demo.png){width=360px}
\
## Shadows
Shadows are implemented by pointing a second ray between the intersection point
of the original view ray and each light. If the light has something obstructing
it in the middle, the light's effect is not used.
The soft shadow effect is realized by jittering rays across an area. In my
implementation, a jitter radius of about 1.0 is used, and 75 rays are shot into
uniformly sampled points within that radius. This also has the side effect that
rays that are closer to the original ray are sampled more frequently. Each of
these rays produces either 0 or 1 depending on if it was obstructed by the
object. Taking the proportion of rays that hit as a coefficient for the shadow,
we can get some soft shadow effects like this:
![Soft shadows](examples/soft-shadow-demo.png){width=360px}
\
## Light attenuation
Light attenuation is when more of the light is applied for objects that are
closer to a particular light source. The function that's applied is an inverse
quadratic formula with respect to the distance the object is from the light:
\begin{equation}
f_\textrm{att}(d) = \frac{1}{c_1 + c_2 d + c_3 d^2}
\end{equation}
Where:
- $f_\textrm{att}$ is the attenuation factor
- $d$ is the distance the object is from the light
- $c_1$, $c_2$, and $c_3$ are user-supplied coefficients
As you can see below, the effect of the light drops off with the distance from
the light (light coming from the left):
![Light attenuation](examples/attenuation-demo.png){width=360px}
\
## Depth Cueing
Depth cueing is when the objects further from the viewer have a lower opacity to
"fade" into the background in some sense. A good example of this can be seen in
the image below; note how the objects are less and less bright the further they
are away from the eye.
![Depth cueing](examples/depth-cueing-demo.png){width=360px}
\
## Shortcomings of the model
The Phong formula is just a model of how light works, and doesn't actually
represent reality. There's not actually rays physically escaping our eyes and
hitting objects; it's actually the other way around, but computing it that way
would not be efficient since we would be factoring in a lot of rays that don't
ever get rendered.
Also, one needs to take care to use reasonable constants. For example, if using
a different specular light color than the diffuse color, then it may produce
some bizarre lighting effects that may not actually look right compare to
reality.
# Arbitrary Objects
Here is an example scene with some objects that demonstrates some of the
features of the raytracer.
![Objects in the scene](examples/objects.png){width=360px}
\

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@ -5,7 +5,14 @@ the points on the side of the triangle in the triangle or not?**
_Hint: Two triangles that share a border may have problems._
If the triangles share a border, then you will have to decide whether points on
the border belong to one or the other. I think there might need to be some kind
of average function or something that decides how different values might be
reconciled, but I think omitting the border from either might also not be the
right solution because you really don't want there to be a gap.
# Participation Question 2
**When d11 \* d22 - d12 \* d12 = 0, the system will have no solution. When might
this happen, and what does it mean?**