del-geo 0.1.28

2D/3D geometry utility codes
Documentation 
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use num_traits::AsPrimitive;

pub struct ControlPoints<'a, Real, const N: usize> {
    pub p0: &'a nalgebra::SVector<Real, N>,
    pub p1: &'a nalgebra::SVector<Real, N>,
    pub p2: &'a nalgebra::SVector<Real, N>,
    pub p3: &'a nalgebra::SVector<Real, N>,
}

pub fn eval<Real, const N: usize>(
    p0: &nalgebra::SVector<Real, N>,
    p1: &nalgebra::SVector<Real, N>,
    p2: &nalgebra::SVector<Real, N>,
    p3: &nalgebra::SVector<Real, N>,
    t0: Real,
) -> nalgebra::SVector<Real, N>
where
    Real: nalgebra::RealField + Copy,
{
    let one = Real::one();
    let three = one + one + one;
    let t1 = one - t0;

    p0.scale(t1 * t1 * t1)
        + p1.scale(three * t0 * t1 * t1)
        + p2.scale(three * t0 * t0 * t1)
        + p3.scale(t0 * t0 * t0)
}

pub fn arclength_from_vtx2vecn<T, const N: usize>(vtxs: &[nalgebra::SVector<T, N>]) -> T
where
    T: nalgebra::RealField + Copy,
{
    if vtxs.len() < 2 {
        return T::zero();
    }
    let mut len: T = T::zero();
    for ip0 in 0..vtxs.len() - 1 {
        len += (vtxs[ip0] - vtxs[ip0 + 1]).norm();
    }
    len
}

pub fn sample_uniform_param<Real, const N: usize>(
    ndiv: usize,
    p0: &nalgebra::SVector<Real, N>,
    p1: &nalgebra::SVector<Real, N>,
    p2: &nalgebra::SVector<Real, N>,
    p3: &nalgebra::SVector<Real, N>,
    is_include_endpoint_start: bool,
    is_include_endpoint_end: bool,
) -> Vec<nalgebra::SVector<Real, N>>
where
    Real: Copy + 'static + nalgebra::RealField,
    usize: num_traits::AsPrimitive<Real>,
{
    let mut ret: Vec<nalgebra::SVector<Real, N>> = vec![];
    if is_include_endpoint_start {
        ret.push(*p0);
    }
    for idiv in 1..ndiv {
        let t0: Real = idiv.as_() / ndiv.as_();
        let p0 = eval(p0, p1, p2, p3, t0);
        ret.push(p0);
    }
    if is_include_endpoint_end {
        ret.push(*p3);
    }
    ret
}

pub fn sample_uniform_length<Real, const N: usize>(
    cps: ControlPoints<Real, N>,
    target_edge_length: Real,
    is_include_endpoint_start: bool,
    is_include_endpoint_end: bool,
    ndiv_sample: usize,
) -> Vec<nalgebra::SVector<Real, N>>
where
    Real: Copy + 'static + nalgebra::RealField + AsPrimitive<usize>,
    usize: num_traits::AsPrimitive<Real>,
    f64: num_traits::AsPrimitive<Real>,
{
    let mut ret: Vec<nalgebra::SVector<Real, N>> = vec![];
    if is_include_endpoint_start {
        ret.push(*cps.p0);
    }
    let ps = sample_uniform_param(ndiv_sample, cps.p0, cps.p1, cps.p2, cps.p3, true, true);
    assert_eq!(ps.len(), ndiv_sample + 1);
    let len = arclength_from_vtx2vecn(&ps);
    let ndiv_out: usize = (len / target_edge_length).ceil().as_();
    let elen: Real = len / ndiv_out.as_();
    // dbg!(len, ndiv_out, elen, target_edge_length);
    let mut len_to_go = elen;
    let mut traveled_len_in_edge = Real::zero();
    let mut i_div = 0;
    loop {
        if is_include_endpoint_start {
            if ret.len() == ndiv_out {
                break;
            }
        } else if ret.len() == ndiv_out - 1 {
            break;
        }
        if i_div == ps.len() - 1 {
            break;
        }
        let len_edge = (ps[i_div + 1] - ps[i_div]).norm();
        // println!("{} {} {} {} {}", i_div, len_to_go, traveled_len_in_edge, elen, len_edge);
        assert!(len_edge > traveled_len_in_edge);
        if len_edge - traveled_len_in_edge >= len_to_go {
            // there is a sampled point in this edge
            (traveled_len_in_edge, len_to_go) = (traveled_len_in_edge + len_to_go, elen);
            {
                // output point
                let r0 = traveled_len_in_edge / len_edge;
                assert!(r0 >= Real::zero() && r0 <= Real::one(), "{}", r0);
                let t = (i_div.as_() + r0) / ndiv_sample.as_();
                assert!(
                    t < Real::one(),
                    "t={} idiv={} ndiv_sample={} r0={}",
                    t,
                    i_div,
                    ndiv_sample,
                    r0
                );
                assert!(t > Real::zero(), "t={}", t);
                let q = eval(cps.p0, cps.p1, cps.p2, cps.p3, t);
                ret.push(q);
            }
        } else {
            // move next edge
            len_to_go -= len_edge - traveled_len_in_edge;
            traveled_len_in_edge = Real::zero();
            i_div += 1;
        }
    }
    if is_include_endpoint_end {
        ret.push(*cps.p3);
    }
    ret
}

#[test]
fn test() {
    let p0 = nalgebra::Vector2::<f32>::new(0.1, 0.2);
    let p1 = nalgebra::Vector2::<f32>::new(0.4, 0.3);
    let p2 = nalgebra::Vector2::<f32>::new(1.1, 1.3);
    let p3 = nalgebra::Vector2::<f32>::new(1.3, 0.8);
    let elen_trg = 0.1;
    let ps = sample_uniform_length(
        ControlPoints {
            p0: &p0,
            p1: &p1,
            p2: &p2,
            p3: &p3,
        },
        elen_trg,
        true,
        true,
        30,
    );
    for ip in 0..ps.len() - 1 {
        let q0 = ps[ip];
        let q1 = ps[ip + 1];
        let elen = (q0 - q1).norm();
        let dev = (elen - elen_trg).abs();
        // println!("{} {}", ip, dev);
        assert!(dev < 0.007, "{}", dev);
    }
}