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use std::f32::consts::PI;
use crate::{
mesh::{Indices, Mesh, MeshBuilder, Meshable},
render_asset::RenderAssetUsages,
};
use bevy_math::primitives::Sphere;
use hexasphere::shapes::IcoSphere;
use thiserror::Error;
use wgpu::PrimitiveTopology;
/// An error when creating an icosphere [`Mesh`] from a [`SphereMeshBuilder`].
#[derive(Clone, Copy, Debug, Error)]
pub enum IcosphereError {
/// The icosphere has too many vertices.
#[error("Cannot create an icosphere of {subdivisions} subdivisions due to there being too many vertices being generated: {number_of_resulting_points}. (Limited to 65535 vertices or 79 subdivisions)")]
TooManyVertices {
/// The number of subdivisions used. 79 is the largest allowed value for a mesh to be generated.
subdivisions: usize,
/// The number of vertices generated. 65535 is the largest allowed value for a mesh to be generated.
number_of_resulting_points: usize,
},
}
/// A type of sphere mesh.
#[derive(Clone, Copy, Debug)]
pub enum SphereKind {
/// An icosphere, a spherical mesh that consists of similar sized triangles.
Ico {
/// The number of subdivisions applied.
/// The number of faces quadruples with each subdivision.
subdivisions: usize,
},
/// A UV sphere, a spherical mesh that consists of quadrilaterals
/// apart from triangles at the top and bottom.
Uv {
/// The number of longitudinal sectors, aka the horizontal resolution.
#[doc(alias = "horizontal_resolution")]
sectors: usize,
/// The number of latitudinal stacks, aka the vertical resolution.
#[doc(alias = "vertical_resolution")]
stacks: usize,
},
}
impl Default for SphereKind {
fn default() -> Self {
Self::Ico { subdivisions: 5 }
}
}
/// A builder used for creating a [`Mesh`] with an [`Sphere`] shape.
#[derive(Clone, Copy, Debug, Default)]
pub struct SphereMeshBuilder {
/// The [`Sphere`] shape.
pub sphere: Sphere,
/// The type of sphere mesh that will be built.
pub kind: SphereKind,
}
impl SphereMeshBuilder {
/// Creates a new [`SphereMeshBuilder`] from a radius and [`SphereKind`].
#[inline]
pub const fn new(radius: f32, kind: SphereKind) -> Self {
Self {
sphere: Sphere { radius },
kind,
}
}
/// Sets the [`SphereKind`] that will be used for building the mesh.
#[inline]
pub const fn kind(mut self, kind: SphereKind) -> Self {
self.kind = kind;
self
}
/// Creates an icosphere mesh with the given number of subdivisions.
///
/// The number of faces quadruples with each subdivision.
/// If there are `80` or more subdivisions, the vertex count will be too large,
/// and an [`IcosphereError`] is returned.
///
/// A good default is `5` subdivisions.
pub fn ico(&self, subdivisions: usize) -> Result<Mesh, IcosphereError> {
if subdivisions >= 80 {
/*
Number of triangles:
N = 20
Number of edges:
E = 30
Number of vertices:
V = 12
Number of points within a triangle (triangular numbers):
inner(s) = (s^2 + s) / 2
Number of points on an edge:
edges(s) = s
Add up all vertices on the surface:
vertices(s) = edges(s) * E + inner(s - 1) * N + V
Expand and simplify. Notice that the triangular number formula has roots at -1, and 0, so translating it one to the right fixes it.
subdivisions(s) = 30s + 20((s^2 - 2s + 1 + s - 1) / 2) + 12
subdivisions(s) = 30s + 10s^2 - 10s + 12
subdivisions(s) = 10(s^2 + 2s) + 12
Factor an (s + 1) term to simplify in terms of calculation
subdivisions(s) = 10(s + 1)^2 + 12 - 10
resulting_vertices(s) = 10(s + 1)^2 + 2
*/
let temp = subdivisions + 1;
let number_of_resulting_points = temp * temp * 10 + 2;
return Err(IcosphereError::TooManyVertices {
subdivisions,
number_of_resulting_points,
});
}
let generated = IcoSphere::new(subdivisions, |point| {
let inclination = point.y.acos();
let azimuth = point.z.atan2(point.x);
let norm_inclination = inclination / std::f32::consts::PI;
let norm_azimuth = 0.5 - (azimuth / std::f32::consts::TAU);
[norm_azimuth, norm_inclination]
});
let raw_points = generated.raw_points();
let points = raw_points
.iter()
.map(|&p| (p * self.sphere.radius).into())
.collect::<Vec<[f32; 3]>>();
let normals = raw_points
.iter()
.copied()
.map(Into::into)
.collect::<Vec<[f32; 3]>>();
let uvs = generated.raw_data().to_owned();
let mut indices = Vec::with_capacity(generated.indices_per_main_triangle() * 20);
for i in 0..20 {
generated.get_indices(i, &mut indices);
}
let indices = Indices::U32(indices);
Ok(Mesh::new(
PrimitiveTopology::TriangleList,
RenderAssetUsages::default(),
)
.with_inserted_indices(indices)
.with_inserted_attribute(Mesh::ATTRIBUTE_POSITION, points)
.with_inserted_attribute(Mesh::ATTRIBUTE_NORMAL, normals)
.with_inserted_attribute(Mesh::ATTRIBUTE_UV_0, uvs))
}
/// Creates a UV sphere [`Mesh`] with the given number of
/// longitudinal sectors and latitudinal stacks, aka horizontal and vertical resolution.
///
/// A good default is `32` sectors and `18` stacks.
pub fn uv(&self, sectors: usize, stacks: usize) -> Mesh {
// Largely inspired from http://www.songho.ca/opengl/gl_sphere.html
let sectors_f32 = sectors as f32;
let stacks_f32 = stacks as f32;
let length_inv = 1. / self.sphere.radius;
let sector_step = 2. * PI / sectors_f32;
let stack_step = PI / stacks_f32;
let mut vertices: Vec<[f32; 3]> = Vec::with_capacity(stacks * sectors);
let mut normals: Vec<[f32; 3]> = Vec::with_capacity(stacks * sectors);
let mut uvs: Vec<[f32; 2]> = Vec::with_capacity(stacks * sectors);
let mut indices: Vec<u32> = Vec::with_capacity(stacks * sectors * 2 * 3);
for i in 0..stacks + 1 {
let stack_angle = PI / 2. - (i as f32) * stack_step;
let xy = self.sphere.radius * stack_angle.cos();
let z = self.sphere.radius * stack_angle.sin();
for j in 0..sectors + 1 {
let sector_angle = (j as f32) * sector_step;
let x = xy * sector_angle.cos();
let y = xy * sector_angle.sin();
vertices.push([x, y, z]);
normals.push([x * length_inv, y * length_inv, z * length_inv]);
uvs.push([(j as f32) / sectors_f32, (i as f32) / stacks_f32]);
}
}
// indices
// k1--k1+1
// | / |
// | / |
// k2--k2+1
for i in 0..stacks {
let mut k1 = i * (sectors + 1);
let mut k2 = k1 + sectors + 1;
for _j in 0..sectors {
if i != 0 {
indices.push(k1 as u32);
indices.push(k2 as u32);
indices.push((k1 + 1) as u32);
}
if i != stacks - 1 {
indices.push((k1 + 1) as u32);
indices.push(k2 as u32);
indices.push((k2 + 1) as u32);
}
k1 += 1;
k2 += 1;
}
}
Mesh::new(
PrimitiveTopology::TriangleList,
RenderAssetUsages::default(),
)
.with_inserted_indices(Indices::U32(indices))
.with_inserted_attribute(Mesh::ATTRIBUTE_POSITION, vertices)
.with_inserted_attribute(Mesh::ATTRIBUTE_NORMAL, normals)
.with_inserted_attribute(Mesh::ATTRIBUTE_UV_0, uvs)
}
}
impl MeshBuilder for SphereMeshBuilder {
/// Builds a [`Mesh`] according to the configuration in `self`.
///
/// # Panics
///
/// Panics if the sphere is a [`SphereKind::Ico`] with a subdivision count
/// that is greater than or equal to `80` because there will be too many vertices.
fn build(&self) -> Mesh {
match self.kind {
SphereKind::Ico { subdivisions } => self.ico(subdivisions).unwrap(),
SphereKind::Uv { sectors, stacks } => self.uv(sectors, stacks),
}
}
}
impl Meshable for Sphere {
type Output = SphereMeshBuilder;
fn mesh(&self) -> Self::Output {
SphereMeshBuilder {
sphere: *self,
..Default::default()
}
}
}
impl From<Sphere> for Mesh {
fn from(sphere: Sphere) -> Self {
sphere.mesh().build()
}
}