wallswitch 0.60.5

//! Newton-Raphson Basin fractal generator overlay.
//!
//! This module implements the Relaxed Newton-Raphson fractal for solving complex polynomial
//! equations of the form z^p - 1 = 0. By introducing a complex relaxation parameter (lambda),
//! the standard basins of attraction warp into intricate, symmetric, mandala-like
//! structures featuring nested circular bands, spiral arms, and crystalline structures.

use crate::effects::{
    MAX_ITERATIONS, MIN_ITERATIONS, Viewport, ViewportSpecs, blend_and_vignette_pixel,
    get_rotation_steps, partition_rows, rotate_point,
};
use crate::{
    Complex, ImageEffect, NEON_PALETTES, NeonColor, WallSwitchError, WallSwitchResult,
    get_random_integer,
};
use image::RgbImage;
use std::{io::Error, path::Path, thread};

/// Valid operational range for randomized zoom viewport allocation.
const ZOOM_RANGE: [f64; 2] = [1.5, 3.8];

/// Structural parameters for polynomial evaluation and deformation.
///
/// Holds the power p of the equation z^p - 1 = 0, the relaxation parameter lambda,
/// and a user-friendly preset name.
#[derive(Debug, Clone, Copy, PartialEq)]
pub struct NewtonPreset {
    /// Power of the polynomial.
    pub power: u32,
    /// Complex relaxation scale parameter.
    pub lambda: Complex,
    /// Human-readable name of the specific layout.
    pub name: &'static str,
}

impl ImageEffect for NewtonGenerator {
    /// Applies the Newton-Raphson fractal overlay directly onto an in-memory image buffer.
    fn apply(&self, rgb_img: &mut RgbImage) {
        self.apply_effect_in_memory(rgb_img);
    }

    /// Returns a formatted string containing specific diagnostic details of the active effect.
    fn info(&self) -> String {
        format!(
            "fractal [{}]\n\
            f(z) = z^{} - 1 = 0, where lambda = {:5.2} {} {:4.2}i (iter = {:4}, zoom = {:.2}), color: {}",
            self.preset.name,
            self.preset.power,
            self.preset.lambda.re,
            if self.preset.lambda.im >= 0.0 {
                "+"
            } else {
                "-"
            },
            self.preset.lambda.im.abs(),
            self.scan_iterations,
            self.zoom,
            self.color_palette
        )
    }
}

/// A procedural generator for rendering Newton-Raphson Basin fractals onto backgrounds.
pub struct NewtonGenerator {
    /// Active parameters governing formula geometry.
    pub preset: NewtonPreset,
    /// Maximum scan operations limits.
    pub scan_iterations: u32,
    /// Neon visual coloring profiles.
    pub color_palette: NeonColor,
    /// Viewport translation zoom index.
    pub zoom: f64,
    /// Cosine of active viewport rotation angle.
    pub cos_angle: f64,
    /// Sine of active viewport rotation angle.
    pub sin_angle: f64,
}

impl Default for NewtonGenerator {
    fn default() -> Self {
        Self {
            preset: NewtonPreset {
                power: 3,
                lambda: Complex::new(1.0, 0.3),
                name: "Gothic Rose Mandala",
            },
            scan_iterations: get_random_integer::<_, u32>(MIN_ITERATIONS / 10, MAX_ITERATIONS / 10)
                .max(60),
            color_palette: NEON_PALETTES[0],
            zoom: 2.0,
            cos_angle: 1.0,
            sin_angle: 0.0,
        }
    }
}

impl NewtonGenerator {
    /// Generates a randomized Newton Basin configuration fitted to the aspect ratio.
    pub fn random(monitor: &crate::Monitor) -> Self {
        let width = monitor.resolution.width as u32;
        let height = monitor.resolution.height as u32;

        let presets = [
            // --- Classical Geometric Patterns ---
            NewtonPreset {
                power: 3,
                lambda: Complex::new(1.0, 0.3),
                name: "Gothic Rose Mandala",
            },
            NewtonPreset {
                power: 5,
                lambda: Complex::new(0.9, 0.1),
                name: "Imperial Star Compass",
            },
            NewtonPreset {
                power: 4,
                lambda: Complex::new(1.0, 0.0),
                name: "Stained Glass Kaleidoscope",
            },
            NewtonPreset {
                power: 6,
                lambda: Complex::new(0.85, 0.2),
                name: "Cosmic Snowflake Grid",
            },
            NewtonPreset {
                power: 3,
                lambda: Complex::new(1.35, 0.0),
                name: "Spiked Crown of Thorns",
            },
            NewtonPreset {
                power: 8,
                lambda: Complex::new(0.7, 0.4),
                name: "Quantum Energy Shells",
            },
            NewtonPreset {
                power: 5,
                lambda: Complex::new(1.1, 0.25),
                name: "Solar Flare Compass",
            },
            NewtonPreset {
                power: 3,
                lambda: Complex::new(0.8, 0.5),
                name: "Celtic Knotwork Ribbon",
            },
            NewtonPreset {
                power: 4,
                lambda: Complex::new(0.6, 0.6),
                name: "Nautilus Spiral Chamber",
            },
            NewtonPreset {
                power: 7,
                lambda: Complex::new(1.0, 0.05),
                name: "Hyper-Dimensional Matrix",
            },
            // --- Twisted & High-Deformation Wave Mandalas ---
            NewtonPreset {
                power: 6,
                lambda: Complex::new(1.15, 0.15),
                name: "Aetheric Frost Flower",
            },
            NewtonPreset {
                power: 8,
                lambda: Complex::new(0.90, 0.30),
                name: "Celestial Gearwork",
            },
            NewtonPreset {
                power: 3,
                lambda: Complex::new(0.75, 0.60),
                name: "Byzantine Dome",
            },
            NewtonPreset {
                power: 5,
                lambda: Complex::new(1.25, -0.20),
                name: "Abyssal Starfish",
            },
            NewtonPreset {
                power: 4,
                lambda: Complex::new(0.80, 0.45),
                name: "Hyperborean Sigil",
            },
            NewtonPreset {
                power: 7,
                lambda: Complex::new(1.0, -0.30),
                name: "Prismatic Labyrinth",
            },
            NewtonPreset {
                power: 3,
                lambda: Complex::new(0.95, 0.80),
                name: "Nebula Core Spiral",
            },
            NewtonPreset {
                power: 5,
                lambda: Complex::new(0.60, 0.80),
                name: "Aura Borealis Compass",
            },
            NewtonPreset {
                power: 10,
                lambda: Complex::new(0.85, 0.0),
                name: "Obsidian Glass Lattices",
            },
            NewtonPreset {
                power: 4,
                lambda: Complex::new(1.40, -0.40),
                name: "Bio-Polymer Filament",
            },
        ];

        let p_idx: usize = get_random_integer(0, NEON_PALETTES.len() - 1);
        let color_palette = NEON_PALETTES[p_idx];

        let angle_degrees: f64 = get_random_integer(0, 359);
        let radians = angle_degrees.to_radians();

        let preset_idx: usize = get_random_integer(0, presets.len() - 1);
        let selected_preset = presets[preset_idx];

        let mut newton = Self {
            preset: selected_preset,
            scan_iterations: get_random_integer(40, 100),
            color_palette,
            zoom: 2.0,
            cos_angle: radians.cos(),
            sin_angle: radians.sin(),
        };

        newton.optimize_fit(width, height);
        newton
    }

    /// Automatically scales the viewport boundaries with randomized micro-deviations.
    pub fn optimize_fit(&mut self, width: u32, height: u32) {
        let w_f = width as f64;
        let h_f = height as f64;
        let min_dim = w_f.min(h_f);

        let search_limit = 1.8_f64;
        let steps = 64;
        let inv_steps_minus_1 = 1.0 / (steps - 1) as f64;
        let range = 2.0 * search_limit;

        let scan_iterations = self.scan_iterations;
        let mut active_points = Vec::with_capacity(steps * steps);

        for step_y in 0..steps {
            let ry = -search_limit + (step_y as f64 * inv_steps_minus_1) * range;
            for step_x in 0..steps {
                let rx = -search_limit + (step_x as f64 * inv_steps_minus_1) * range;

                let (i, _, _) = compute_newton_escape(
                    Complex::new(rx, ry),
                    self.preset.power,
                    self.preset.lambda,
                    scan_iterations,
                );

                if i > 2 && i < scan_iterations - 2 {
                    active_points.push((rx, ry));
                }
            }
        }

        if !active_points.is_empty() {
            let mut best_zoom = f64::MAX;
            let mut best_cos = self.cos_angle;
            let mut best_sin = self.sin_angle;

            for (_rad, cos_t, sin_t) in get_rotation_steps() {
                let mut max_cx_abs = 0.0_f64;
                let mut max_cy_abs = 0.0_f64;

                for &(rx, ry) in &active_points {
                    let (cx, cy) = rotate_point(rx, ry, cos_t, sin_t);
                    max_cx_abs = max_cx_abs.max(cx.abs());
                    max_cy_abs = max_cy_abs.max(cy.abs());
                }

                let zoom_x = 2.0 * max_cx_abs * min_dim / w_f;
                let zoom_y = 2.0 * max_cy_abs * min_dim / h_f;
                let required_zoom = zoom_x.max(zoom_y);

                if required_zoom < best_zoom {
                    best_zoom = required_zoom;
                    best_cos = cos_t;
                    best_sin = sin_t;
                }
            }

            // Introduce a randomized scaling multiplier between 95% and 125%
            let rand_factor = get_random_integer::<_, f64>(95, 125) / 100.0;
            self.zoom = (best_zoom * rand_factor).clamp(ZOOM_RANGE[0], ZOOM_RANGE[1]);
            self.cos_angle = best_cos;
            self.sin_angle = best_sin;
        } else {
            // Roll a flat random zoom within the bounded range if no points detected
            let flat_rand = get_random_integer::<_, f64>(150, 250) / 100.0;
            self.zoom = flat_rand.clamp(ZOOM_RANGE[0], ZOOM_RANGE[1]);
        }
    }

    /// Renders the Newton Fractal Basin in-place over the active background memory buffer.
    pub fn apply_effect_in_memory(&self, rgb_img: &mut RgbImage) {
        let (width, height) = rgb_img.dimensions();
        let w_f = width as f64;
        let h_f = height as f64;

        let specs = ViewportSpecs {
            center: Complex::new(0.0, 0.0),
            zoom: self.zoom,
            cos_angle: self.cos_angle,
            sin_angle: self.sin_angle,
            is_julia: true,
        };
        let viewport = Viewport::new(w_f, h_f, &specs);

        let scan_iterations = self.scan_iterations;
        let power = self.preset.power;
        let lambda = self.preset.lambda;

        let (mut rows, width_usize) = partition_rows(rgb_img);

        let cores = thread::available_parallelism()
            .map(|n| n.get())
            .unwrap_or(4);
        let chunk_size = (rows.len() / cores).max(1);

        thread::scope(|scope| {
            let viewport_ref = &viewport;
            let color_palette = self.color_palette.to_array();
            for chunk in rows.chunks_mut(chunk_size) {
                scope.spawn(move || {
                    for (y, row_data) in chunk.iter_mut() {
                        let y_f = *y as f64;
                        for x in 0..width_usize {
                            let x_f = x as f64;
                            let z_init = viewport_ref.map(x_f, y_f);

                            let (i, diff_norm, z_final) =
                                compute_newton_escape(z_init, power, lambda, scan_iterations);

                            let smooth_i = if i < scan_iterations {
                                i as f32
                                    + (diff_norm.ln() as f32 / (1e-6_f64).ln() as f32)
                                        .clamp(0.0, 1.0)
                            } else {
                                scan_iterations as f32
                            };

                            let (fractal_rgb, alpha, s_alpha) = if i < scan_iterations {
                                let ripple_frequency = 0.5_f32;
                                let norm_dist =
                                    (smooth_i * ripple_frequency * std::f32::consts::PI)
                                        .sin()
                                        .abs();

                                let core = if norm_dist > 0.95 {
                                    (norm_dist - 0.95) / 0.05
                                } else {
                                    0.0
                                };

                                let glow = norm_dist.powi(5) * 0.40;
                                let profile = core * 0.70 + glow * 0.30;

                                let shadow_profile = (1.0 - norm_dist).powi(2) * 0.35;

                                let angle = z_final.im.atan2(z_final.re) as f32;
                                let light = 0.70_f32 + 0.30_f32 * (angle * 3.0).cos().abs();

                                let t_cycled = (smooth_i * 0.08) % 1.0;
                                let secondary_color =
                                    [color_palette[1], color_palette[2], color_palette[0]];

                                let r_grad = color_palette[0] * (1.0 - t_cycled)
                                    + secondary_color[0] * t_cycled;
                                let g_grad = color_palette[1] * (1.0 - t_cycled)
                                    + secondary_color[1] * t_cycled;
                                let b_grad = color_palette[2] * (1.0 - t_cycled)
                                    + secondary_color[2] * t_cycled;

                                let core_color = [r_grad, g_grad, b_grad];

                                let mut border_color = [1.0 - r_grad, 1.0 - g_grad, 1.0 - b_grad];
                                let max_val =
                                    border_color[0].max(border_color[1]).max(border_color[2]);
                                if max_val > 0.0 {
                                    border_color[0] /= max_val;
                                    border_color[1] /= max_val;
                                    border_color[2] /= max_val;
                                }

                                let r_blended =
                                    core_color[0] * norm_dist + border_color[0] * (1.0 - norm_dist);
                                let g_blended =
                                    core_color[1] * norm_dist + border_color[1] * (1.0 - norm_dist);
                                let b_blended =
                                    core_color[2] * norm_dist + border_color[2] * (1.0 - norm_dist);

                                let brightness_boost = 1.25_f32;

                                let rgb = [
                                    (r_blended * light * brightness_boost).clamp(0.0, 1.0),
                                    (g_blended * light * brightness_boost).clamp(0.0, 1.0),
                                    (b_blended * light * brightness_boost).clamp(0.0, 1.0),
                                ];

                                let iteration_fade = if i < 8 { i as f32 / 8.0 } else { 1.0 };

                                (
                                    rgb,
                                    profile * 0.95 * iteration_fade,
                                    shadow_profile * iteration_fade,
                                )
                            } else {
                                ([0.0, 0.0, 0.0], 0.0, 0.0)
                            };

                            let idx = x * 3;
                            blend_and_vignette_pixel(row_data, idx, fractal_rgb, alpha, s_alpha);
                        }
                    }
                });
            }
        });
    }

    /// Helper to process, render, and write output files directly to system storage.
    pub fn apply_effect<P: AsRef<Path>>(
        &self,
        input_path: P,
        output_path: P,
    ) -> WallSwitchResult<()> {
        let img = image::open(&input_path)
            .map_err(|e| WallSwitchError::UnableToFind(format!("Failed to open image: {e}")))?;

        let mut rgb_img = img.to_rgb8();
        self.apply_effect_in_memory(&mut rgb_img);

        rgb_img
            .save(&output_path)
            .map_err(|e| WallSwitchError::Io(Error::other(e)))?;

        Ok(())
    }
}

// ==============================================================================
// MATH ENGINE: RELAXED NEWTON-RAPHSON ROOT CONVERGENCE
// ==============================================================================

/// Evaluates polynomial convergence under a relaxed Newton-Raphson iteration loop.
///
/// This function uses the standard formula:
/// z_next = z - lambda * f(z) / f'(z)
///
/// where f(z) = z^p - 1 and f'(z) = p * z^(p-1).
#[inline(always)]
fn compute_newton_escape(
    z_init: Complex,
    power: u32,
    lambda: Complex,
    scan_iterations: u32,
) -> (u32, f64, Complex) {
    let mut z = z_init;
    let p_f = power as f64;

    let mut i = 0;
    let mut diff_norm = 1.0;

    while i < scan_iterations {
        if z.norm_sq() < 1e-8 {
            break;
        }

        let z_prev_p_minus_1 = z.pow(power - 1);
        let z_p = z_prev_p_minus_1 * z;

        // f(z) = z^p - 1
        let f_z = z_p - Complex::new(1.0, 0.0);

        // f'(z) = p * z^(p-1)
        let f_prime_z = z_prev_p_minus_1 * p_f;

        // step = lambda * f(z) / f'(z)
        let step = lambda * (f_z / f_prime_z);
        let z_next = z - step;

        diff_norm = step.norm_sq();

        if diff_norm < 1e-6 {
            z = z_next;
            break;
        }

        z = z_next;
        i += 1;
    }

    (i, diff_norm, z)
}