1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100

use crate::math::{Point, Real, Vector, DIM};
use crate::shape::Ball;
use crate::transformation::utils;
use na::{self, ComplexField, Point3, RealField};
use num_traits::One;

impl Ball {
    /// Discretize the boundary of this ball as a triangle-mesh.
    pub fn to_trimesh(
        &self,
        ntheta_subdiv: u32,
        nphi_subdiv: u32,
    ) -> (Vec<Point3<Real>>, Vec<[u32; 3]>) {
        let diameter = self.radius * 2.0;
        let (vtx, idx) = unit_sphere(ntheta_subdiv, nphi_subdiv);
        (utils::scaled(vtx, Vector::repeat(diameter)), idx)
    }
}

fn unit_sphere(ntheta_subdiv: u32, nphi_subdiv: u32) -> (Vec<Point3<Real>>, Vec<[u32; 3]>) {
    let pi = Real::pi();
    let two_pi = Real::two_pi();
    let pi_two = Real::frac_pi_2();
    let duvtheta = Real::one() / (ntheta_subdiv as Real); // step of uv.x coordinates.
    let duvphi = Real::one() / (nphi_subdiv as Real); // step of uv.y coordinates.
    let dtheta = two_pi * duvtheta;
    let dphi = pi * duvphi;

    let mut coords = Vec::new();
    let mut curr_phi = -pi_two;

    for _ in 0..nphi_subdiv + 1 {
        utils::push_circle(
            ComplexField::cos(curr_phi),
            ntheta_subdiv + 1,
            dtheta,
            ComplexField::sin(curr_phi),
            &mut coords,
        );
        curr_phi = curr_phi + dphi;
    }

    // index buffer
    let mut idx = Vec::new();

    for i in 0..nphi_subdiv {
        let bottom = i * (ntheta_subdiv + 1);
        let up = bottom + (ntheta_subdiv + 1);
        utils::push_open_ring_indices(bottom, up, ntheta_subdiv + 1, &mut idx);
    }

    (utils::scaled(coords, Vector::repeat(0.5)), idx)
}

/// Creates an hemisphere with a diameter of 1.
pub(crate) fn unit_hemisphere(
    ntheta_subdiv: u32,
    nphi_subdiv: u32,
) -> (Vec<Point<Real>>, Vec<[u32; DIM]>) {
    let two_pi = Real::two_pi();
    let pi_two = Real::frac_pi_2();
    let dtheta = two_pi / (ntheta_subdiv as Real);
    let dphi = pi_two / (nphi_subdiv as Real);

    let mut coords = Vec::new();
    let mut curr_phi: Real = 0.0;

    for _ in 0..nphi_subdiv - 1 {
        utils::push_circle(
            ComplexField::cos(curr_phi),
            ntheta_subdiv,
            dtheta,
            ComplexField::sin(curr_phi),
            &mut coords,
        );
        curr_phi = curr_phi + dphi;
    }

    coords.push(Point::new(na::zero(), na::one(), na::zero()));

    let mut idx = Vec::new();

    for i in 0..nphi_subdiv - 2 {
        utils::push_ring_indices(
            i * ntheta_subdiv,
            (i + 1) * ntheta_subdiv,
            ntheta_subdiv,
            &mut idx,
        );
    }

    utils::push_degenerate_top_ring_indices(
        (nphi_subdiv - 2) * ntheta_subdiv,
        coords.len() as u32 - 1,
        ntheta_subdiv,
        &mut idx,
    );

    (utils::scaled(coords, Vector::repeat(0.5)), idx)
}