From eb5b2c0b827b3452385d0d5ec87b879915eddfa1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Maro=C5=A1=20Grego?= Date: Wed, 26 Jan 2022 23:45:30 +0100 Subject: [PATCH 1/2] Use automatic differentiation and distance estimate to make details less noisy A simple automatic differentiation system is implemented, along with a distance estimate of the form `log(r) * r / dr`, where `r` is the iterated function and `dr` its derivative. --- Cargo.lock | 478 +++++++++++++------------------------------------ Cargo.toml | 16 +- README.md | 27 ++- examples/1.png | Bin 118253 -> 354229 bytes examples/2.png | Bin 61133 -> 171188 bytes src/ast.rs | 2 +- src/eval.rs | 101 ++++++----- src/lex.rs | 60 +++---- src/main.rs | 93 +++++----- src/parser.rs | 2 +- 10 files changed, 268 insertions(+), 511 deletions(-) diff --git a/Cargo.lock b/Cargo.lock index bb5779f..817ad3a 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -1,559 +1,327 @@ # This file is automatically @generated by Cargo. # It is not intended for manual 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"bmp"] diff --git a/README.md b/README.md index a3d20ac..668ee37 100644 --- a/README.md +++ b/README.md @@ -1,33 +1,46 @@ # multiman A parallel Mandelbrot and Julia set-style fractal renderer supporting custom user expressions. -It leverages all available CPU cores to render images in parallel. +It leverages automatic differentiation and a distance estimate to make the details less noisy. +All available CPU cores are used to render images in parallel. ## Usage ``` -multiman 0.1.0 +multiman 0.2.0 USAGE: - multiman + multiman FLAGS: -h, --help Prints help information -V, --version Prints version information ARGS: - Initialization expression + Initialization expression (the value of the pixel) + Start of the iteration Iteration expression Width of the image Height of the image Path of the resulting image ``` +In the expressions, the following variables are available: +``` +w The width of the image +h The height of the image +x The current x coordinate +y The current y coordinate +c The initial complex value of the current pixel +z The value of the previous iteration +``` +They can be combined using arithmetic operations. + ## Examples ``` -multiman "(X / WIDTH * 2 - 1) + (Y / HEIGHT * 2 - 1.0) * i" "Z * Z + (0.1 + 0.65i)" 500 500 examples/1.png +multiman "(x / w * 2 - 1) + (y / h * 2 - 1.0) * i" "c" "z * z + (0.1 + 0.65i)" 1000 1000 examples/1.png ``` ![1](examples/1.png) ``` -multiman "0i" "Z * Z + (X * 2 / WIDTH - 1.5 + (Y * 2 / HEIGHT - 1) * i)" 500 500 examples/2.png +multiman "x * 2 / w - 1.5 + (y * 2 / h - 1) * i" "0" "z * z + c" 1000 1000 examples/2.png ``` -![2](examples/2.png) \ No newline at end of file +![2](examples/2.png) diff --git a/examples/1.png b/examples/1.png index f4e2763b9398d710cb869a9ec768593a42d9fcfe..8c5edebcb4dfc36ca06a40d0e51651e428b80833 100644 GIT binary patch literal 354229 zcmYIQWmr{vvzL&TM!G>tQb3Sy5Tq4pBt$||X{4naMUX}%r9q@oq&uV=B&55!v(GvA zUY_^;;(@*QTI)YEznUGYuBvbgivsJ$jT^U=6lFDU+(21H{2v1u{^durO!VwoMKUDU_Bk`xX&VSQrzl`&@9Gp21wUord`# 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pub width: f64, + pub height: f64, + pub x: f64, + pub y: f64, + pub c: Value, + pub z: Value, } impl Context { - pub fn new() -> Context { - Context { - vars: HashMap::new(), - } - } - - pub fn set(&mut self, name: &'static str, value: impl Into) { - self.vars.insert(name, value.into()); + pub fn new() -> Self { + Default::default() } - pub fn update(&mut self, name: &str, value: impl Into) { - *self.vars.get_mut(name).unwrap() = value.into(); + #[inline] + fn get(&self, name: u8) -> Option { + match name { + b'w' => Some(self.width.into()), + b'h' => Some(self.height.into()), + b'x' => Some(self.x.into()), + b'y' => Some(self.y.into()), + b'c' => Some(self.c.into()), + b'z' => Some(self.z.into()), + _ => None, + } } pub fn eval(&self, expr: &Expr) -> Result { @@ -34,12 +42,7 @@ impl Context { BinOp::Sub => Ok(left - right), BinOp::Mul => Ok(left * right), BinOp::Div => { - let zero = match right { - Value::Real(num) => num == 0.0, - Value::Complex(num) => num.re == 0.0 && num.im == 0.0, - }; - - if zero { + if right.v == 0.0.into() { return Err(Error { message: "Divide by zero", position: expr.position, @@ -50,31 +53,39 @@ impl Context { } } } - ExprKind::Var(ref var) => self.vars.get(var.as_str()).cloned().ok_or_else(|| Error { + ExprKind::Var(var) => self.get(var).ok_or_else(|| Error { message: "Undefined variable", position: expr.position, }), - ExprKind::Real(num) => Ok(Value::Real(num)), - ExprKind::Imag(num) => Ok(Value::Complex(Complex { re: 0.0, im: num })), + ExprKind::Real(num) => Ok(num.into()), + ExprKind::Imag(num) => Ok(Complex { re: 0.0, im: num }.into()), } } } -#[derive(Clone, Copy, Debug)] -pub enum Value { - Real(f64), - Complex(Complex), +#[derive(Clone, Copy, Debug, Default)] +pub struct Value { + /// Value of the expression + pub v: Complex, + /// Derivative of the expression + pub d: Complex, } impl From for Value { fn from(value: f64) -> Value { - Value::Real(value) + Value { + v: value.into(), + d: 0.0.into(), + } } } impl From> for Value { fn from(value: Complex) -> Value { - Value::Complex(value) + Value { + v: value, + d: 0.0.into(), + } } } @@ -82,12 +93,9 @@ impl Add for Value { type Output = Value; fn add(self, other: Value) -> Value { - match (self, other) { - (Value::Real(a), Value::Real(b)) => Value::Real(a + b), - (Value::Complex(a), Value::Complex(b)) => Value::Complex(a + b), - (Value::Real(a), Value::Complex(b)) | (Value::Complex(b), Value::Real(a)) => { - Value::Complex(a + b) - } + Value { + v: self.v + other.v, + d: self.d + other.d, } } } @@ -96,12 +104,9 @@ impl Sub for Value { type Output = Value; fn sub(self, other: Value) -> Value { - match (self, other) { - (Value::Real(a), Value::Real(b)) => Value::Real(a - b), - (Value::Complex(a), Value::Complex(b)) => Value::Complex(a - b), - (Value::Real(a), Value::Complex(b)) | (Value::Complex(b), Value::Real(a)) => { - Value::Complex(a - b) - } + Value { + v: self.v - other.v, + d: self.d - other.d, } } } @@ -110,12 +115,9 @@ impl Mul for Value { type Output = Value; fn mul(self, other: Value) -> Value { - match (self, other) { - (Value::Real(a), Value::Real(b)) => Value::Real(a * b), - (Value::Complex(a), Value::Complex(b)) => Value::Complex(a * b), - (Value::Real(a), Value::Complex(b)) | (Value::Complex(b), Value::Real(a)) => { - Value::Complex(a * b) - } + Value { + v: self.v * other.v, + d: self.v * other.d + other.v * self.d, } } } @@ -124,12 +126,9 @@ impl Div for Value { type Output = Value; fn div(self, other: Value) -> Value { - match (self, other) { - (Value::Real(a), Value::Real(b)) => Value::Real(a / b), - (Value::Complex(a), Value::Complex(b)) => Value::Complex(a / b), - (Value::Real(a), Value::Complex(b)) | (Value::Complex(b), Value::Real(a)) => { - Value::Complex(a / b) - } + Value { + v: self.v / other.v, + d: (self.d * other.v - other.d * self.v) / (other.d * other.d), } } } diff --git a/src/lex.rs b/src/lex.rs index af21c03..c16e260 100644 --- a/src/lex.rs +++ b/src/lex.rs @@ -14,74 +14,58 @@ pub enum TokenKind { Sub, Mul, Div, - Ident(String), + Ident(u8), Real(f64), Imag(f64), } pub fn tokenize(input: &str) -> Result, Error> { let mut tokens = Vec::new(); - let mut chars = input.chars().enumerate().map(|(i, c)| (i + 1, c)); + let mut chars = input.as_bytes().iter().enumerate(); let mut last = None; while let Some((i, c)) = last.take().or_else(|| chars.next()) { let kind = match c { - '(' => TokenKind::LParen, - ')' => TokenKind::RParen, - '+' => TokenKind::Add, - '-' => TokenKind::Sub, - '*' => TokenKind::Mul, - '/' => TokenKind::Div, - 'a'..='z' | 'A'..='Z' | '_' => { - let mut data = c.to_string(); - - while let Some((i, c)) = chars.next() { - match c { - 'a'..='z' | 'A'..='Z' | '_' | '0'..='9' => data.push(c), - _ => { - last = Some((i, c)); - break; - } - } - } - - if data == "i" { - TokenKind::Imag(1.0) - } else { - TokenKind::Ident(data) - } - } - '0'..='9' => { + b'(' => TokenKind::LParen, + b')' => TokenKind::RParen, + b'+' => TokenKind::Add, + b'-' => TokenKind::Sub, + b'*' => TokenKind::Mul, + b'/' => TokenKind::Div, + b'w' | b'h' | b'x' | b'y' | b'c' | b'z' => TokenKind::Ident(*c), + b'i' => TokenKind::Imag(1.0), + b'0'..=b'9' => { let mut dot = false; let mut complex = false; - let mut data = c.to_string(); + let mut end = i + 1; while let Some((i, c)) = chars.next() { match c { - '.' => { + b'.' => { if dot { last = Some((i, c)); break; } dot = true; - data.push(c); } - 'i' => { + b'i' => { complex = true; + end = i; break; } - '0'..='9' => data.push(c), + b'0'..=b'9' => continue, _ => { last = Some((i, c)); + end = i; break; } } } - let n = data.parse::().map_err(|_| Error { + let n = input[i..end].parse::().map_err(|_| Error { message: "Invalid floating point literal", - position: i, + position: i + 1, })?; if complex { @@ -90,18 +74,18 @@ pub fn tokenize(input: &str) -> Result, Error> { TokenKind::Real(n) } } - ' ' | '\t' => continue, + b' ' | b'\t' => continue, _ => { return Err(Error { message: "Unexpected character", - position: i, + position: i + 1, }); } }; tokens.push(Token { kind: kind, - position: i, + position: i + 1, }); } diff --git a/src/main.rs b/src/main.rs index 1fadcfa..50e1212 100644 --- a/src/main.rs +++ b/src/main.rs @@ -1,4 +1,3 @@ -#![feature(process_exitcode_placeholder)] mod ast; mod error; mod eval; @@ -6,14 +5,13 @@ mod lex; mod parser; use error::Error; -use eval::{Context, Value}; +use eval::Context; use image::{Rgb, RgbImage}; use num_complex::Complex; use std::cmp; use std::env; use std::num::NonZeroU32; use std::path::PathBuf; -use std::process::ExitCode; use std::str::FromStr; use std::sync::Arc; use std::thread; @@ -23,8 +21,10 @@ const ITERATIONS: u32 = 200; #[derive(StructOpt)] struct Args { - #[structopt(help = "Initialization expression")] + #[structopt(help = "Initialization expression (the value of the pixel)")] init: Expr, + #[structopt(help = "Start of the iteration")] + first: Expr, #[structopt(help = "Iteration expression")] iter: Expr, #[structopt(help = "Width of the image")] @@ -53,6 +53,7 @@ fn abs(num: Complex) -> f64 { fn work( init: &ast::Expr, + first: &ast::Expr, iter: &ast::Expr, start: u32, length: u32, @@ -60,61 +61,50 @@ fn work( height: u32, ) -> Result>, Error> { let mut context = Context::new(); - context.set("WIDTH", width as f64); - context.set("HEIGHT", height as f64); - context.set("X", 0.0); - context.set("Y", 0.0); - context.set("Z", 0.0); + context.width = width as f64; + context.height = height as f64; let mut pixels = Vec::with_capacity(length as usize); for (x, y) in (start..start + length).map(|n| (n % width, n / height)) { - context.update("X", x as f64); - context.update("Y", y as f64); - - let mut z = match context.eval(&init)? { - Value::Complex(z) => z, - _ => { - return Err(Error { - message: "Init did not evaluate to a complex number", - position: init.position, - }); - } - }; - - let mut pixel = Rgb([0, 0, 0]); - for i in 0..ITERATIONS { - context.update("Z", z); - - z = match context.eval(&iter)? { - Value::Complex(z) => z, - _ => { - return Err(Error { - message: "Iter did not evaluate to a complex number", - position: init.position, - }); - } - }; - - if abs(z) >= 2.0 { - let pv = (i as f64 / ITERATIONS as f64 * 255.0) as u8; - - pixel = Rgb([pv, 0, 0]); + context.x = x as f64; + context.y = y as f64; + + let mut init = context.eval(&init)?; + init.d = 1.0.into(); + context.c = init; + + let mut z = context.eval(&first)?; + for _ in 0..ITERATIONS { + context.z = z; + + z = context.eval(&iter)?; + + if abs(z.v) >= 2.0 { break; } } - pixels.push(pixel); + let (r, dr) = (abs(z.v), abs(z.d)); + let distance = width as f64 * 0.7 * f64::ln(r) * r / dr; + let pv = std::cmp::min(f64::floor(255.0 * distance) as u8, 255); + pixels.push(Rgb([pv, pv, pv])); } Ok(pixels) } -fn render(init: ast::Expr, iter: ast::Expr, width: u32, height: u32) -> Result { +fn render( + init: ast::Expr, + first: ast::Expr, + iter: ast::Expr, + width: u32, + height: u32, +) -> Result { let total = width * height; let length = total / num_cpus::get() as u32; let pixels = if length != 0 { - let exprs = Arc::new((init, iter)); + let exprs = Arc::new((init, first, iter)); let mut threads = Vec::new(); let mut position = 0; while position < total { @@ -122,7 +112,9 @@ fn render(init: ast::Expr, iter: ast::Expr, width: u32, height: u32) -> Result Result Result ExitCode { +fn main() { let args = match Args::from_iter_safe(env::args()) { Ok(args) => args, Err(err) => { println!("{}", err); - return ExitCode::FAILURE; + return; } }; let image = match render( args.init.0, + args.first.0, args.iter.0, args.width.into(), args.height.into(), @@ -161,14 +154,12 @@ fn main() -> ExitCode { Ok(image) => image, Err(err) => { println!("Error: {}", err); - return ExitCode::FAILURE; + return; } }; if let Err(err) = image.save(&args.output_path) { println!("Error saving image: {}", err); - return ExitCode::FAILURE; + return; } - - ExitCode::SUCCESS } diff --git a/src/parser.rs b/src/parser.rs index 8043a2b..72b58cd 100644 --- a/src/parser.rs +++ b/src/parser.rs @@ -52,7 +52,7 @@ impl<'a> Parser<'a> { } TokenKind::Real(num) => ExprKind::Real(num), TokenKind::Imag(num) => ExprKind::Imag(num), - TokenKind::Ident(ref ident) => ExprKind::Var(ident.clone()), + TokenKind::Ident(ident) => ExprKind::Var(ident), _ => return Err(self.error("Unexpected token")), }; From d5749051e81e0df2bb516114eb3a8cfed83c3e68 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Maro=C5=A1=20Grego?= Date: Sun, 30 Jan 2022 18:17:21 +0100 Subject: [PATCH 2/2] Implement the exponentiation expression --- README.md | 2 +- src/ast.rs | 4 +++- src/eval.rs | 20 ++++++++++++++++++++ src/lex.rs | 2 ++ src/main.rs | 6 ++---- 5 files changed, 28 insertions(+), 6 deletions(-) diff --git a/README.md b/README.md index 668ee37..1bf2168 100644 --- a/README.md +++ b/README.md @@ -32,7 +32,7 @@ y The current y coordinate c The initial complex value of the current pixel z The value of the previous iteration ``` -They can be combined using arithmetic operations. +They can be combined using arithmetic operations and exponentiation (using the symbol `^`). ## Examples ``` diff --git a/src/ast.rs b/src/ast.rs index e0c8b5a..bffb19a 100644 --- a/src/ast.rs +++ b/src/ast.rs @@ -27,6 +27,7 @@ pub enum BinOp { Sub, Mul, Div, + Pow, } impl BinOp { @@ -36,6 +37,7 @@ impl BinOp { TokenKind::Sub => BinOp::Sub, TokenKind::Mul => BinOp::Mul, TokenKind::Div => BinOp::Div, + TokenKind::Pow => BinOp::Pow, _ => return None, }; @@ -45,7 +47,7 @@ impl BinOp { pub fn precedence(&self) -> u32 { match self { BinOp::Add | BinOp::Sub => 1, - BinOp::Mul | BinOp::Div => 2, + BinOp::Mul | BinOp::Div | BinOp::Pow => 2, } } } diff --git a/src/eval.rs b/src/eval.rs index 68475e9..5cb72b7 100644 --- a/src/eval.rs +++ b/src/eval.rs @@ -51,6 +51,16 @@ impl Context { Ok(left / right) } + BinOp::Pow => { + if right.v == 0.0.into() { + return Err(Error { + message: "Power by zero", + position: expr.position, + }); + } + + Ok(left.pow(right)) + } } } ExprKind::Var(var) => self.get(var).ok_or_else(|| Error { @@ -71,6 +81,16 @@ pub struct Value { pub d: Complex, } +impl Value { + fn pow(self, other: Value) -> Self { + let v = self.v.powc(other.v); + Value { + v, + d: (other.v * self.d / self.v + other.d * self.v.ln()) * v, + } + } +} + impl From for Value { fn from(value: f64) -> Value { Value { diff --git a/src/lex.rs b/src/lex.rs index c16e260..41ced32 100644 --- a/src/lex.rs +++ b/src/lex.rs @@ -14,6 +14,7 @@ pub enum TokenKind { Sub, Mul, Div, + Pow, Ident(u8), Real(f64), Imag(f64), @@ -32,6 +33,7 @@ pub fn tokenize(input: &str) -> Result, Error> { b'-' => TokenKind::Sub, b'*' => TokenKind::Mul, b'/' => TokenKind::Div, + b'^' => TokenKind::Pow, b'w' | b'h' | b'x' | b'y' | b'c' | b'z' => TokenKind::Ident(*c), b'i' => TokenKind::Imag(1.0), b'0'..=b'9' => { diff --git a/src/main.rs b/src/main.rs index 50e1212..b72d399 100644 --- a/src/main.rs +++ b/src/main.rs @@ -17,14 +17,12 @@ use std::sync::Arc; use std::thread; use structopt::StructOpt; -const ITERATIONS: u32 = 200; +const ITERATIONS: u32 = 201; #[derive(StructOpt)] struct Args { #[structopt(help = "Initialization expression (the value of the pixel)")] init: Expr, - #[structopt(help = "Start of the iteration")] - first: Expr, #[structopt(help = "Iteration expression")] iter: Expr, #[structopt(help = "Width of the image")] @@ -85,7 +83,7 @@ fn work( } let (r, dr) = (abs(z.v), abs(z.d)); - let distance = width as f64 * 0.7 * f64::ln(r) * r / dr; + let distance = width as f64 * 0.8 * f64::ln(r) * r / dr; let pv = std::cmp::min(f64::floor(255.0 * distance) as u8, 255); pixels.push(Rgb([pv, pv, pv])); }

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