Refactor the 'Centroid' node to use Kurbo

node-graph/gcore/src/math/mod.rs

@@ -1,4 +1,5 @@
 pub mod bbox;
 pub mod math_ext;
+pub mod polynomial;
 pub mod quad;
 pub mod rect;

node-graph/gcore/src/math/polynomial.rs

@@ -0,0 +1,293 @@
+use std::fmt::{self, Display, Formatter};
+use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
+
+use kurbo::PathSeg;
+
+/// A struct that represents a polynomial with a maximum degree of `N-1`.
+///
+/// It provides basic mathematical operations for polynomials like addition, multiplication, differentiation, integration, etc.
+#[derive(Copy, Clone, Debug, PartialEq)]
+pub struct Polynomial<const N: usize> {
+	coefficients: [f64; N],
+}
+
+impl<const N: usize> Polynomial<N> {
+	/// Create a new polynomial from the coefficients given in the array.
+	///
+	/// The coefficient for nth degree is at the nth index in array. Therefore the order of coefficients are reversed than the usual order for writing polynomials mathematically.
+	pub fn new(coefficients: [f64; N]) -> Polynomial<N> {
+		Polynomial { coefficients }
+	}
+
+	/// Create a polynomial where all its coefficients are zero.
+	pub fn zero() -> Polynomial<N> {
+		Polynomial { coefficients: [0.; N] }
+	}
+
+	/// Return an immutable reference to the coefficients.
+	///
+	/// The coefficient for nth degree is at the nth index in array. Therefore the order of coefficients are reversed than the usual order for writing polynomials mathematically.
+	pub fn coefficients(&self) -> &[f64; N] {
+		&self.coefficients
+	}
+
+	/// Return a mutable reference to the coefficients.
+	///
+	/// The coefficient for nth degree is at the nth index in array. Therefore the order of coefficients are reversed than the usual order for writing polynomials mathematically.
+	pub fn coefficients_mut(&mut self) -> &mut [f64; N] {
+		&mut self.coefficients
+	}
+
+	/// Evaluate the polynomial at `value`.
+	pub fn eval(&self, value: f64) -> f64 {
+		self.coefficients.iter().rev().copied().reduce(|acc, x| acc * value + x).unwrap()
+	}
+
+	/// Return the same polynomial but with a different maximum degree of `M-1`.\
+	///
+	/// Returns `None` if the polynomial cannot fit in the specified size.
+	pub fn as_size<const M: usize>(&self) -> Option<Polynomial<M>> {
+		let mut coefficients = [0.; M];
+
+		if M >= N {
+			coefficients[..N].copy_from_slice(&self.coefficients);
+		} else if self.coefficients.iter().rev().take(N - M).all(|&x| x == 0.) {
+			coefficients.copy_from_slice(&self.coefficients[..M])
+		} else {
+			return None;
+		}
+
+		Some(Polynomial { coefficients })
+	}
+
+	/// Computes the derivative in place.
+	pub fn derivative_mut(&mut self) {
+		self.coefficients.iter_mut().enumerate().for_each(|(index, x)| *x *= index as f64);
+		self.coefficients.rotate_left(1);
+	}
+
+	/// Computes the antiderivative at `C = 0` in place.
+	///
+	/// Returns `None` if the polynomial is not big enough to accommodate the extra degree.
+	pub fn antiderivative_mut(&mut self) -> Option<()> {
+		if self.coefficients[N - 1] != 0. {
+			return None;
+		}
+		self.coefficients.rotate_right(1);
+		self.coefficients.iter_mut().enumerate().skip(1).for_each(|(index, x)| *x /= index as f64);
+		Some(())
+	}
+
+	/// Computes the polynomial's derivative.
+	pub fn derivative(&self) -> Polynomial<N> {
+		let mut ans = *self;
+		ans.derivative_mut();
+		ans
+	}
+
+	/// Computes the antiderivative at `C = 0`.
+	///
+	/// Returns `None` if the polynomial is not big enough to accommodate the extra degree.
+	pub fn antiderivative(&self) -> Option<Polynomial<N>> {
+		let mut ans = *self;
+		ans.antiderivative_mut()?;
+		Some(ans)
+	}
+}
+
+impl<const N: usize> Default for Polynomial<N> {
+	fn default() -> Self {
+		Self::zero()
+	}
+}
+
+impl<const N: usize> Display for Polynomial<N> {
+	fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
+		let mut first = true;
+		for (index, coefficient) in self.coefficients.iter().enumerate().rev().filter(|&(_, &coefficient)| coefficient != 0.) {
+			if first {
+				first = false;
+			} else {
+				f.write_str(" + ")?
+			}
+
+			coefficient.fmt(f)?;
+			if index == 0 {
+				continue;
+			}
+			f.write_str("x")?;
+			if index == 1 {
+				continue;
+			}
+			f.write_str("^")?;
+			index.fmt(f)?;
+		}
+
+		Ok(())
+	}
+}
+
+impl<const N: usize> AddAssign<&Polynomial<N>> for Polynomial<N> {
+	fn add_assign(&mut self, rhs: &Polynomial<N>) {
+		self.coefficients.iter_mut().zip(rhs.coefficients.iter()).for_each(|(a, b)| *a += b);
+	}
+}
+
+impl<const N: usize> Add for &Polynomial<N> {
+	type Output = Polynomial<N>;
+
+	fn add(self, other: &Polynomial<N>) -> Polynomial<N> {
+		let mut output = *self;
+		output += other;
+		output
+	}
+}
+
+impl<const N: usize> Neg for &Polynomial<N> {
+	type Output = Polynomial<N>;
+
+	fn neg(self) -> Polynomial<N> {
+		let mut output = *self;
+		output.coefficients.iter_mut().for_each(|x| *x = -*x);
+		output
+	}
+}
+
+impl<const N: usize> Neg for Polynomial<N> {
+	type Output = Polynomial<N>;
+
+	fn neg(mut self) -> Polynomial<N> {
+		self.coefficients.iter_mut().for_each(|x| *x = -*x);
+		self
+	}
+}
+
+impl<const N: usize> SubAssign<&Polynomial<N>> for Polynomial<N> {
+	fn sub_assign(&mut self, rhs: &Polynomial<N>) {
+		self.coefficients.iter_mut().zip(rhs.coefficients.iter()).for_each(|(a, b)| *a -= b);
+	}
+}
+
+impl<const N: usize> Sub for &Polynomial<N> {
+	type Output = Polynomial<N>;
+
+	fn sub(self, other: &Polynomial<N>) -> Polynomial<N> {
+		let mut output = *self;
+		output -= other;
+		output
+	}
+}
+
+impl<const N: usize> MulAssign<&Polynomial<N>> for Polynomial<N> {
+	fn mul_assign(&mut self, rhs: &Polynomial<N>) {
+		for i in (0..N).rev() {
+			self.coefficients[i] = self.coefficients[i] * rhs.coefficients[0];
+			for j in 0..i {
+				self.coefficients[i] += self.coefficients[j] * rhs.coefficients[i - j];
+			}
+		}
+	}
+}
+
+impl<const N: usize> Mul for &Polynomial<N> {
+	type Output = Polynomial<N>;
+
+	fn mul(self, other: &Polynomial<N>) -> Polynomial<N> {
+		let mut output = *self;
+		output *= other;
+		output
+	}
+}
+
+/// Returns two [`Polynomial`]s representing the parametric equations for x and y coordinates of the bezier curve respectively.
+/// The domain of both the equations are from t=0.0 representing the start and t=1.0 representing the end of the bezier curve.
+pub fn pathseg_to_parametric_polynomial(segment: PathSeg) -> (Polynomial<4>, Polynomial<4>) {
+	match segment {
+		PathSeg::Line(line) => {
+			let term1 = line.p0 - line.p1;
+			(Polynomial::new([line.p0.x, term1.x, 0., 0.]), Polynomial::new([line.p0.y, term1.y, 0., 0.]))
+		}
+		PathSeg::Quad(quad_bez) => {
+			let term1 = 2. * (quad_bez.p1 - quad_bez.p0);
+			let term2 = quad_bez.p0 - 2. * quad_bez.p1.to_vec2() + quad_bez.p2.to_vec2();
+
+			(Polynomial::new([quad_bez.p0.x, term1.x, term2.x, 0.]), Polynomial::new([quad_bez.p0.y, term1.y, term2.y, 0.]))
+		}
+		PathSeg::Cubic(cubic_bez) => {
+			let term1 = 3. * (cubic_bez.p1 - cubic_bez.p0);
+			let term2 = 3. * (cubic_bez.p2 - cubic_bez.p1) - term1;
+			let term3 = cubic_bez.p3 - cubic_bez.p0 - term2 - term1;
+
+			(
+				Polynomial::new([cubic_bez.p0.x, term1.x, term2.x, term3.x]),
+				Polynomial::new([cubic_bez.p0.y, term1.y, term2.y, term3.y]),
+			)
+		}
+	}
+}
+
+#[cfg(test)]
+mod test {
+	use super::*;
+
+	#[test]
+	fn evaluation() {
+		let p = Polynomial::new([1., 2., 3.]);
+
+		assert_eq!(p.eval(1.), 6.);
+		assert_eq!(p.eval(2.), 17.);
+	}
+
+	#[test]
+	fn size_change() {
+		let p1 = Polynomial::new([1., 2., 3.]);
+		let p2 = Polynomial::new([1., 2., 3., 0.]);
+
+		assert_eq!(p1.as_size(), Some(p2));
+		assert_eq!(p2.as_size(), Some(p1));
+
+		assert_eq!(p2.as_size::<2>(), None);
+	}
+
+	#[test]
+	fn addition_and_subtaction() {
+		let p1 = Polynomial::new([1., 2., 3.]);
+		let p2 = Polynomial::new([4., 5., 6.]);
+
+		let addition = Polynomial::new([5., 7., 9.]);
+		let subtraction = Polynomial::new([-3., -3., -3.]);
+
+		assert_eq!(&p1 + &p2, addition);
+		assert_eq!(&p1 - &p2, subtraction);
+	}
+
+	#[test]
+	fn multiplication() {
+		let p1 = Polynomial::new([1., 2., 3.]).as_size().unwrap();
+		let p2 = Polynomial::new([4., 5., 6.]).as_size().unwrap();
+
+		let multiplication = Polynomial::new([4., 13., 28., 27., 18.]);
+
+		assert_eq!(&p1 * &p2, multiplication);
+	}
+
+	#[test]
+	fn derivative_and_antiderivative() {
+		let mut p = Polynomial::new([1., 2., 3.]);
+		let p_deriv = Polynomial::new([2., 6., 0.]);
+
+		assert_eq!(p.derivative(), p_deriv);
+
+		p.coefficients_mut()[0] = 0.;
+		assert_eq!(p_deriv.antiderivative().unwrap(), p);
+
+		assert_eq!(p.antiderivative(), None);
+	}
+
+	#[test]
+	fn display() {
+		let p = Polynomial::new([1., 2., 0., 3.]);
+
+		assert_eq!(format!("{:.2}", p), "3.00x^3 + 2.00x + 1.00");
+	}
+}