#[path = "common/print.rs"]
mod print;

use nalgebra::{DMatrix, DVector};

use dyna3::engine::{ConfigNeighborhood, examples::realize_kaleidocycle};

fn main() {
    const SCALED_TOL: f64 = 1.0e-12;
    let realization = realize_kaleidocycle(SCALED_TOL);
    print::title("Kaleidocycle");
    print::realization_diagnostics(&realization);
    if let Ok(ConfigNeighborhood { config, nbhd: tangent }) = realization.result {
        // print the completed Gram matrix and the realized configuration
        print::gram_matrix(&config);
        print::config(&config);
        
        // find the kaleidocycle's twist motion by projecting onto the tangent
        // space
        const N_POINTS: usize = 12;
        let up = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
        let down = -&up;
        let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
            |n| [
                tangent.proj(&up.as_view(), n),
                tangent.proj(&down.as_view(), n+1)
            ]
        ).sum();
        let normalization = 5.0 / twist_motion[(2, 0)];
        println!("\nTwist motion:{}", (normalization * twist_motion).to_string().trim_end());
    }
}