feat: added a simple Polynomial struct

crates/comet_math/src/lib.rs

@@ -1,15 +1,17 @@
-pub(crate) use utilities::*;
 pub use point::*;
 pub use vector::*;
 pub use matrix::*;
 pub use bezier::*;
 pub use easings::*;
+pub use polynomial::*;
+pub use interpolation::*;
 
-mod utilities;
 pub mod point;
 pub mod vector;
 pub mod matrix;
 pub mod quaternion;
 pub mod bezier;
 pub mod easings;
-pub mod noise;
+pub mod noise;
+pub mod polynomial;
+pub mod interpolation;

crates/comet_math/src/polynomial.rs

@@ -0,0 +1,129 @@
+use std::ops::*;
+
+pub struct Polynomial {
+	coefficients: Vec<f32>,
+	degree: usize
+}
+
+impl Polynomial {
+	pub fn new(coefficients: Vec<f32>) -> Self {
+		let degree = coefficients.len() - 1;
+		Self {
+			coefficients,
+			degree
+		}
+	}
+
+	pub fn evaluate(&self, x: f32) -> f32 {
+		let mut result = 0.0;
+		for c in &self.coefficients {
+			result = result * x + c;
+		}
+		result
+	}
+
+	pub fn differentiate(&self) -> Self {
+		let mut new_coefficients = Vec::new();
+		for (i, &c) in self.coefficients.iter().enumerate() {
+			if i != 0 {
+				new_coefficients.push(c * i as f32);
+			}
+		}
+		Self::new(new_coefficients)
+	}
+
+	pub fn integrate(&self) -> Self {
+		let mut new_coefficients = Vec::new();
+		new_coefficients.push(0.0);
+		for (i, &c) in self.coefficients.iter().enumerate() {
+			new_coefficients.push(c / (i + 1) as f32);
+		}
+		Self::new(new_coefficients)
+	}
+}
+
+impl Add for Polynomial {
+	type Output = Self;
+
+	fn add(self, other: Self) -> Self {
+		let mut new_coefficients = Vec::new();
+		let mut i = 0;
+		while i < self.coefficients.len() || i < other.coefficients.len() {
+			let a = if i < self.coefficients.len() { self.coefficients[i] } else { 0.0 };
+			let b = if i < other.coefficients.len() { other.coefficients[i] } else { 0.0 };
+			new_coefficients.push(a + b);
+			i += 1;
+		}
+		Self::new(new_coefficients)
+	}
+}
+
+impl Sub for Polynomial {
+	type Output = Self;
+
+	fn sub(self, other: Self) -> Self {
+		let mut new_coefficients = Vec::new();
+		let mut i = 0;
+		while i < self.coefficients.len() || i < other.coefficients.len() {
+			let a = if i < self.coefficients.len() { self.coefficients[i] } else { 0.0 };
+			let b = if i < other.coefficients.len() { other.coefficients[i] } else { 0.0 };
+			new_coefficients.push(a - b);
+			i += 1;
+		}
+		Self::new(new_coefficients)
+	}
+}
+
+impl Mul for Polynomial {
+	type Output = Self;
+
+	fn mul(self, other: Self) -> Self {
+		let mut new_coefficients = vec![0.0; self.degree + other.degree + 1];
+		for (i, &a) in self.coefficients.iter().enumerate() {
+			for (j, &b) in other.coefficients.iter().enumerate() {
+				new_coefficients[i + j] += a * b;
+			}
+		}
+		Self::new(new_coefficients)
+	}
+}
+
+impl Div for Polynomial {
+	type Output = Self;
+
+	fn div(self, other: Self) -> Self {
+		let mut new_coefficients = vec![0.0; self.degree - other.degree + 1];
+		let mut dividend = self.coefficients.clone();
+		let divisor = other.coefficients.clone();
+		while dividend.len() >= divisor.len() {
+			let mut quotient = vec![0.0; dividend.len() - divisor.len() + 1];
+			let mut i = dividend.len() - divisor.len();
+			quotient[i] = dividend.last().unwrap() / divisor.last().unwrap();
+			for (j, &d) in divisor.iter().enumerate() {
+				dividend[i + j] -= quotient[i] * d;
+			}
+			new_coefficients[i] = quotient[i];
+			dividend.pop();
+		}
+		Self::new(new_coefficients)
+	}
+}
+
+impl std::fmt::Display for Polynomial {
+	fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
+		let terms: Vec<String> = self.coefficients.iter()
+			.enumerate()
+			.filter(|(_, &c)| c != 0.0)
+			.map(|(i, &c)| {
+				if i == 0 {
+					format!("{}", c)
+				} else if i == 1 {
+					format!("{}x", c)
+				} else {
+					format!("{}x^{}", c, i)
+				}
+			})
+			.collect();
+		write!(f, "{}", terms.join(" + "))
+	}
+}