Graphite/node-graph/gcore/src/raster/curve.rs

use super::{Channel, Linear, LuminanceMut};
use crate::Node;
use dyn_any::{DynAny, StaticType, StaticTypeSized};
use std::ops::{Add, Mul, Sub};

#[derive(Debug, Clone, PartialEq, DynAny, specta::Type, serde::Serialize, serde::Deserialize)]
pub struct Curve {
	#[serde(rename = "manipulatorGroups")]
	pub manipulator_groups: Vec<CurveManipulatorGroup>,
	#[serde(rename = "firstHandle")]
	pub first_handle: [f32; 2],
	#[serde(rename = "lastHandle")]
	pub last_handle: [f32; 2],
}

impl Default for Curve {
	fn default() -> Self {
		Self {
			manipulator_groups: vec![],
			first_handle: [0.2; 2],
			last_handle: [0.8; 2],
		}
	}
}

impl std::hash::Hash for Curve {
	fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
		self.manipulator_groups.hash(state);
		[self.first_handle, self.last_handle].iter().flatten().for_each(|f| f.to_bits().hash(state));
	}
}

#[derive(Debug, Clone, Copy, PartialEq, DynAny, specta::Type, serde::Serialize, serde::Deserialize)]
pub struct CurveManipulatorGroup {
	pub anchor: [f32; 2],
	pub handles: [[f32; 2]; 2],
}

impl std::hash::Hash for CurveManipulatorGroup {
	fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
		for c in self.handles.iter().chain([&self.anchor]).flatten() {
			c.to_bits().hash(state);
		}
	}
}

#[derive(Debug)]
pub struct CubicSplines {
	pub x: [f32; 4],
	pub y: [f32; 4],
}

impl CubicSplines {
	pub fn solve(&self) -> [f32; 4] {
		let (x, y) = (&self.x, &self.y);

		// Build an augmented matrix to solve the system of equations using Gaussian elimination
		let mut augmented_matrix = [
			[
				2. / (x[1] - x[0]),
				1. / (x[1] - x[0]),
				0.,
				0.,
				// |
				3. * (y[1] - y[0]) / ((x[1] - x[0]) * (x[1] - x[0])),
			],
			[
				1. / (x[1] - x[0]),
				2. * (1. / (x[1] - x[0]) + 1. / (x[2] - x[1])),
				1. / (x[2] - x[1]),
				0.,
				// |
				3. * ((y[1] - y[0]) / ((x[1] - x[0]) * (x[1] - x[0])) + (y[2] - y[1]) / ((x[2] - x[1]) * (x[2] - x[1]))),
			],
			[
				0.,
				1. / (x[2] - x[1]),
				2. * (1. / (x[2] - x[1]) + 1. / (x[3] - x[2])),
				1. / (x[3] - x[2]),
				// |
				3. * ((y[2] - y[1]) / ((x[2] - x[1]) * (x[2] - x[1])) + (y[3] - y[2]) / ((x[3] - x[2]) * (x[3] - x[2]))),
			],
			[
				0.,
				0.,
				1. / (x[3] - x[2]),
				2. / (x[3] - x[2]),
				// |
				3. * (y[3] - y[2]) / ((x[3] - x[2]) * (x[3] - x[2])),
			],
		];

		// Gaussian elimination: forward elimination
		for row in 0..4 {
			let pivot_row_index = (row..4)
				.max_by(|&a_row, &b_row| augmented_matrix[a_row][row].abs().partial_cmp(&augmented_matrix[b_row][row].abs()).unwrap_or(std::cmp::Ordering::Equal))
				.unwrap();

			// Swap the current row with the row that has the largest pivot element
			augmented_matrix.swap(row, pivot_row_index);

			// Eliminate the current column in all rows below the current one
			for row_below_current in row + 1..4 {
				assert!(augmented_matrix[row][row].abs() > f32::EPSILON);

				let scale_factor = augmented_matrix[row_below_current][row] / augmented_matrix[row][row];
				for col in row..5 {
					augmented_matrix[row_below_current][col] -= augmented_matrix[row][col] * scale_factor
				}
			}
		}

		// Gaussian elimination: back substitution
		let mut solutions = [0.; 4];
		for col in (0..4).rev() {
			assert!(augmented_matrix[col][col].abs() > f32::EPSILON);

			solutions[col] = augmented_matrix[col][4] / augmented_matrix[col][col];

			for row in (0..col).rev() {
				augmented_matrix[row][4] -= augmented_matrix[row][col] * solutions[col];
				augmented_matrix[row][col] = 0.;
			}
		}

		solutions
	}

	pub fn interpolate(&self, input: f32, solutions: &[f32]) -> f32 {
		if input <= self.x[0] {
			return self.y[0];
		}
		if input >= self.x[self.x.len() - 1] {
			return self.y[self.x.len() - 1];
		}

		// Find the segment that the input falls between
		let mut segment = 1;
		while self.x[segment] < input {
			segment += 1;
		}
		let segment_start = segment - 1;
		let segment_end = segment;

		// Calculate the output value using quadratic interpolation
		let input_value = self.x[segment_start];
		let input_value_prev = self.x[segment_end];
		let output_value = self.y[segment_start];
		let output_value_prev = self.y[segment_end];
		let solutions_value = solutions[segment_start];
		let solutions_value_prev = solutions[segment_end];

		let output_delta = solutions_value_prev * (input_value - input_value_prev) - (output_value - output_value_prev);
		let solution_delta = (output_value - output_value_prev) - solutions_value * (input_value - input_value_prev);

		let input_ratio = (input - input_value_prev) / (input_value - input_value_prev);
		let prev_output_ratio = (1. - input_ratio) * output_value_prev;
		let output_ratio = input_ratio * output_value;
		let quadratic_ratio = input_ratio * (1. - input_ratio) * (output_delta * (1. - input_ratio) + solution_delta * input_ratio);

		let result = prev_output_ratio + output_ratio + quadratic_ratio;
		result.clamp(0., 1.)
	}
}

pub struct ValueMapperNode<C> {
	lut: Vec<C>,
}

unsafe impl<C: StaticTypeSized> StaticType for ValueMapperNode<C> {
	type Static = ValueMapperNode<C::Static>;
}

impl<C> ValueMapperNode<C> {
	pub const fn new(lut: Vec<C>) -> Self {
		Self { lut }
	}
}

impl<'i, L: LuminanceMut + 'i> Node<'i, L> for ValueMapperNode<L::LuminanceChannel>
where
	L::LuminanceChannel: Linear + Copy,
	L::LuminanceChannel: Add<Output = L::LuminanceChannel>,
	L::LuminanceChannel: Sub<Output = L::LuminanceChannel>,
	L::LuminanceChannel: Mul<Output = L::LuminanceChannel>,
{
	type Output = L;

	fn eval(&'i self, mut val: L) -> L {
		let luminance: f32 = val.luminance().to_linear();
		let floating_sample_index = luminance * (self.lut.len() - 1) as f32;
		let index_in_lut = floating_sample_index.floor() as usize;
		let a = self.lut[index_in_lut];
		let b = self.lut[(index_in_lut + 1).clamp(0, self.lut.len() - 1)];
		let result = a.lerp(b, L::LuminanceChannel::from_linear(floating_sample_index.fract()));
		val.set_luminance(result);
		val
	}
}