bevy_mesh/primitives/dim3/
sphere.rs

1use crate::{Indices, Mesh, MeshBuilder, Meshable, PrimitiveTopology};
2use bevy_asset::RenderAssetUsages;
3use bevy_math::{ops, primitives::Sphere};
4use bevy_reflect::prelude::*;
5use core::f32::consts::PI;
6use hexasphere::shapes::IcoSphere;
7use thiserror::Error;
8
9/// An error when creating an icosphere [`Mesh`] from a [`SphereMeshBuilder`].
10#[derive(Clone, Copy, Debug, Error)]
11pub enum IcosphereError {
12    /// The icosphere has too many vertices.
13    #[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)")]
14    TooManyVertices {
15        /// The number of subdivisions used. 79 is the largest allowed value for a mesh to be generated.
16        subdivisions: u32,
17        /// The number of vertices generated. 65535 is the largest allowed value for a mesh to be generated.
18        number_of_resulting_points: u32,
19    },
20}
21
22/// A type of sphere mesh.
23#[derive(Clone, Copy, Debug, Reflect)]
24#[reflect(Default, Debug, Clone)]
25pub enum SphereKind {
26    /// An icosphere, a spherical mesh that consists of similar sized triangles.
27    Ico {
28        /// The number of subdivisions applied.
29        /// The number of faces quadruples with each subdivision.
30        subdivisions: u32,
31    },
32    /// A UV sphere, a spherical mesh that consists of quadrilaterals
33    /// apart from triangles at the top and bottom.
34    Uv {
35        /// The number of longitudinal sectors, aka the horizontal resolution.
36        #[doc(alias = "horizontal_resolution")]
37        sectors: u32,
38        /// The number of latitudinal stacks, aka the vertical resolution.
39        #[doc(alias = "vertical_resolution")]
40        stacks: u32,
41    },
42}
43
44impl Default for SphereKind {
45    fn default() -> Self {
46        Self::Ico { subdivisions: 5 }
47    }
48}
49
50/// A builder used for creating a [`Mesh`] with an [`Sphere`] shape.
51#[derive(Clone, Copy, Debug, Default, Reflect)]
52#[reflect(Default, Debug, Clone)]
53pub struct SphereMeshBuilder {
54    /// The [`Sphere`] shape.
55    pub sphere: Sphere,
56    /// The type of sphere mesh that will be built.
57    pub kind: SphereKind,
58}
59
60impl SphereMeshBuilder {
61    /// Creates a new [`SphereMeshBuilder`] from a radius and [`SphereKind`].
62    #[inline]
63    pub const fn new(radius: f32, kind: SphereKind) -> Self {
64        Self {
65            sphere: Sphere { radius },
66            kind,
67        }
68    }
69
70    /// Sets the [`SphereKind`] that will be used for building the mesh.
71    #[inline]
72    pub const fn kind(mut self, kind: SphereKind) -> Self {
73        self.kind = kind;
74        self
75    }
76
77    /// Creates an icosphere mesh with the given number of subdivisions.
78    ///
79    /// The number of faces quadruples with each subdivision.
80    /// If there are `80` or more subdivisions, the vertex count will be too large,
81    /// and an [`IcosphereError`] is returned.
82    ///
83    /// A good default is `5` subdivisions.
84    pub fn ico(&self, subdivisions: u32) -> Result<Mesh, IcosphereError> {
85        if subdivisions >= 80 {
86            /*
87            Number of triangles:
88            N = 20
89
90            Number of edges:
91            E = 30
92
93            Number of vertices:
94            V = 12
95
96            Number of points within a triangle (triangular numbers):
97            inner(s) = (s^2 + s) / 2
98
99            Number of points on an edge:
100            edges(s) = s
101
102            Add up all vertices on the surface:
103            vertices(s) = edges(s) * E + inner(s - 1) * N + V
104
105            Expand and simplify. Notice that the triangular number formula has roots at -1, and 0, so translating it one to the right fixes it.
106            subdivisions(s) = 30s + 20((s^2 - 2s + 1 + s - 1) / 2) + 12
107            subdivisions(s) = 30s + 10s^2 - 10s + 12
108            subdivisions(s) = 10(s^2 + 2s) + 12
109
110            Factor an (s + 1) term to simplify in terms of calculation
111            subdivisions(s) = 10(s + 1)^2 + 12 - 10
112            resulting_vertices(s) = 10(s + 1)^2 + 2
113            */
114            let temp = subdivisions + 1;
115            let number_of_resulting_points = temp * temp * 10 + 2;
116            return Err(IcosphereError::TooManyVertices {
117                subdivisions,
118                number_of_resulting_points,
119            });
120        }
121        let generated = IcoSphere::new(subdivisions as usize, |point| {
122            let inclination = ops::acos(point.y);
123            let azimuth = ops::atan2(point.z, point.x);
124
125            let norm_inclination = inclination / PI;
126            let norm_azimuth = 0.5 - (azimuth / core::f32::consts::TAU);
127
128            [norm_azimuth, norm_inclination]
129        });
130
131        let raw_points = generated.raw_points();
132
133        let points = raw_points
134            .iter()
135            .map(|&p| (p * self.sphere.radius).into())
136            .collect::<Vec<[f32; 3]>>();
137
138        let normals = raw_points
139            .iter()
140            .copied()
141            .map(Into::into)
142            .collect::<Vec<[f32; 3]>>();
143
144        let uvs = generated.raw_data().to_owned();
145
146        let mut indices = Vec::with_capacity(generated.indices_per_main_triangle() * 20);
147
148        for i in 0..20 {
149            generated.get_indices(i, &mut indices);
150        }
151
152        let indices = Indices::U32(indices);
153
154        Ok(Mesh::new(
155            PrimitiveTopology::TriangleList,
156            RenderAssetUsages::default(),
157        )
158        .with_inserted_indices(indices)
159        .with_inserted_attribute(Mesh::ATTRIBUTE_POSITION, points)
160        .with_inserted_attribute(Mesh::ATTRIBUTE_NORMAL, normals)
161        .with_inserted_attribute(Mesh::ATTRIBUTE_UV_0, uvs))
162    }
163
164    /// Creates a UV sphere [`Mesh`] with the given number of
165    /// longitudinal sectors and latitudinal stacks, aka horizontal and vertical resolution.
166    ///
167    /// A good default is `32` sectors and `18` stacks.
168    pub fn uv(&self, sectors: u32, stacks: u32) -> Mesh {
169        // Largely inspired from http://www.songho.ca/opengl/gl_sphere.html
170
171        let sectors_f32 = sectors as f32;
172        let stacks_f32 = stacks as f32;
173        let length_inv = 1. / self.sphere.radius;
174        let sector_step = 2. * PI / sectors_f32;
175        let stack_step = PI / stacks_f32;
176
177        let n_vertices = (stacks * sectors) as usize;
178        let mut vertices: Vec<[f32; 3]> = Vec::with_capacity(n_vertices);
179        let mut normals: Vec<[f32; 3]> = Vec::with_capacity(n_vertices);
180        let mut uvs: Vec<[f32; 2]> = Vec::with_capacity(n_vertices);
181        let mut indices: Vec<u32> = Vec::with_capacity(n_vertices * 2 * 3);
182
183        for i in 0..stacks + 1 {
184            let stack_angle = PI / 2. - (i as f32) * stack_step;
185            let xy = self.sphere.radius * ops::cos(stack_angle);
186            let z = self.sphere.radius * ops::sin(stack_angle);
187
188            for j in 0..sectors + 1 {
189                let sector_angle = (j as f32) * sector_step;
190                let x = xy * ops::cos(sector_angle);
191                let y = xy * ops::sin(sector_angle);
192
193                vertices.push([x, y, z]);
194                normals.push([x * length_inv, y * length_inv, z * length_inv]);
195                uvs.push([(j as f32) / sectors_f32, (i as f32) / stacks_f32]);
196            }
197        }
198
199        // indices
200        //  k1--k1+1
201        //  |  / |
202        //  | /  |
203        //  k2--k2+1
204        for i in 0..stacks {
205            let mut k1 = i * (sectors + 1);
206            let mut k2 = k1 + sectors + 1;
207            for _j in 0..sectors {
208                if i != 0 {
209                    indices.push(k1);
210                    indices.push(k2);
211                    indices.push(k1 + 1);
212                }
213                if i != stacks - 1 {
214                    indices.push(k1 + 1);
215                    indices.push(k2);
216                    indices.push(k2 + 1);
217                }
218                k1 += 1;
219                k2 += 1;
220            }
221        }
222
223        Mesh::new(
224            PrimitiveTopology::TriangleList,
225            RenderAssetUsages::default(),
226        )
227        .with_inserted_indices(Indices::U32(indices))
228        .with_inserted_attribute(Mesh::ATTRIBUTE_POSITION, vertices)
229        .with_inserted_attribute(Mesh::ATTRIBUTE_NORMAL, normals)
230        .with_inserted_attribute(Mesh::ATTRIBUTE_UV_0, uvs)
231    }
232}
233
234impl MeshBuilder for SphereMeshBuilder {
235    /// Builds a [`Mesh`] according to the configuration in `self`.
236    ///
237    /// # Panics
238    ///
239    /// Panics if the sphere is a [`SphereKind::Ico`] with a subdivision count
240    /// that is greater than or equal to `80` because there will be too many vertices.
241    fn build(&self) -> Mesh {
242        match self.kind {
243            SphereKind::Ico { subdivisions } => self.ico(subdivisions).unwrap(),
244            SphereKind::Uv { sectors, stacks } => self.uv(sectors, stacks),
245        }
246    }
247}
248
249impl Meshable for Sphere {
250    type Output = SphereMeshBuilder;
251
252    fn mesh(&self) -> Self::Output {
253        SphereMeshBuilder {
254            sphere: *self,
255            ..Default::default()
256        }
257    }
258}
259
260impl From<Sphere> for Mesh {
261    fn from(sphere: Sphere) -> Self {
262        sphere.mesh().build()
263    }
264}
bevy_mesh/primitives/dim3/sphere.rs

bevy_mesh/primitives/dim3/
sphere.rs
