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+extern crate cgmath;
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+
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+use std::collections::HashMap;
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+use std::fs::File;
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+use std::io::Write;
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+use std::path::Path;
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+
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+use cgmath::prelude::*;
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+use cgmath::Vector3;
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+use serde::ser::{SerializeSeq, Serializer};
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+use serde::Serialize;
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+
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+#[derive(Debug)]
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+struct Triangle {
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+ a: usize,
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+ b: usize,
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+ c: usize,
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+}
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+
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+impl Triangle {
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+ fn new(a: usize, b: usize, c: usize) -> Triangle {
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+ Triangle { a, b, c }
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+ }
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+}
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+
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+impl Serialize for Triangle {
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+ fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
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+ where
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+ S: Serializer,
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+ {
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+ let vec_indices = vec![self.a, self.b, self.c];
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+ let mut seq = serializer.serialize_seq(Some(vec_indices.len()))?;
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+ for index in vec_indices {
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+ seq.serialize_element(&index)?;
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+ }
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+ seq.end()
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+ }
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+}
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+
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+#[derive(Debug)]
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+struct ArraySerializedVector(Vector3<f32>);
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+
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+#[derive(Serialize, Debug)]
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+struct Polyhedron {
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+ positions: Vec<ArraySerializedVector>,
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+ cells: Vec<Triangle>,
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+}
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+
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+impl Serialize for ArraySerializedVector {
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+ fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
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+ where
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+ S: Serializer,
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+ {
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+ let values = vec![self.0.x, self.0.y, self.0.z];
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+ let mut seq = serializer.serialize_seq(Some(values.len()))?;
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+ for value in values {
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+ seq.serialize_element(&value)?;
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+ }
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+ seq.end()
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+ }
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+}
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+
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+impl Polyhedron {
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+ fn new() -> Polyhedron {
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+ Polyhedron {
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+ positions: vec![],
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+ cells: vec![],
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+ }
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+ }
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+
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+ fn new_isocahedron(radius: f32, detail: usize) -> Polyhedron {
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+ let t = (1.0 + (5.0 as f32).sqrt()) / 2.0;
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+ let base_isocahedron = Polyhedron {
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+ positions: vec![
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+ ArraySerializedVector(Vector3::new(-1.0, t, 0.0)),
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+ ArraySerializedVector(Vector3::new(1.0, t, 0.0)),
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+ ArraySerializedVector(Vector3::new(-1.0, -t, 0.0)),
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+ ArraySerializedVector(Vector3::new(1.0, -t, 0.0)),
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+ ArraySerializedVector(Vector3::new(0.0, -1.0, t)),
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+ ArraySerializedVector(Vector3::new(0.0, 1.0, t)),
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+ ArraySerializedVector(Vector3::new(0.0, -1.0, -t)),
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+ ArraySerializedVector(Vector3::new(0.0, 1.0, -t)),
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+ ArraySerializedVector(Vector3::new(t, 0.0, -1.0)),
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+ ArraySerializedVector(Vector3::new(t, 0.0, 1.0)),
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+ ArraySerializedVector(Vector3::new(-t, 0.0, -1.0)),
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+ ArraySerializedVector(Vector3::new(-t, 0.0, 1.0)),
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+ ],
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+ cells: vec![
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+ Triangle::new(0, 11, 5),
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+ Triangle::new(0, 5, 1),
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+ Triangle::new(0, 1, 7),
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+ Triangle::new(0, 7, 10),
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+ Triangle::new(0, 10, 11),
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+ Triangle::new(1, 5, 9),
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+ Triangle::new(5, 11, 4),
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+ Triangle::new(11, 10, 2),
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+ Triangle::new(10, 7, 6),
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+ Triangle::new(7, 1, 8),
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+ Triangle::new(3, 9, 4),
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+ Triangle::new(3, 4, 2),
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+ Triangle::new(3, 2, 6),
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+ Triangle::new(3, 6, 8),
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+ Triangle::new(3, 8, 9),
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+ Triangle::new(4, 9, 5),
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+ Triangle::new(2, 4, 11),
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+ Triangle::new(6, 2, 10),
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+ Triangle::new(8, 6, 7),
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+ Triangle::new(9, 8, 1),
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+ ],
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+ };
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+ let mut subdivided = Polyhedron::new();
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+ subdivided.subdivide(base_isocahedron, radius, detail);
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+ subdivided
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+ }
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+
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+ fn new_dual_isocahedron(radius: f32, detail: usize) -> Polyhedron {
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+ let isocahedron = Polyhedron::new_isocahedron(radius, detail);
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+ let mut dual_isocahedron = Polyhedron::new();
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+ dual_isocahedron.dual(isocahedron);
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+ dual_isocahedron
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+ }
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+
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+ fn subdivide(&mut self, other: Polyhedron, radius: f32, detail: usize) {
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+ // TODO: maybe make this part of the polygon stuct to avoid having to pass it around
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+ let mut added_vert_cache: HashMap<(i32, i32, i32), usize> = HashMap::new();
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+ let precision = 10_f32.powi(4);
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+ for triangle in other.cells {
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+ let a = other.positions[triangle.a].0;
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+ let b = other.positions[triangle.b].0;
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+ let c = other.positions[triangle.c].0;
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+ self.subdivide_triangle(a, b, c, radius, detail, precision, &mut added_vert_cache);
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+ }
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+ }
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+
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+ fn subdivide_triangle(
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+ &mut self,
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+ a: Vector3<f32>,
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+ b: Vector3<f32>,
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+ c: Vector3<f32>,
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+ radius: f32,
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+ detail: usize,
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+ precision: f32,
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+ added_vert_cache: &mut HashMap<(i32, i32, i32), usize>,
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+ ) {
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+ let cols = 2usize.pow(detail as u32);
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+ let mut new_vertices: Vec<Vec<Vector3<f32>>> = vec![];
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+
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+ for i in 0..=cols {
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+ new_vertices.push(vec![]);
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+ let aj = a.clone().lerp(c, i as f32 / cols as f32);
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+ let bj = b.clone().lerp(c, i as f32 / cols as f32);
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+ let rows = cols - i;
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+
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+ for j in 0..=rows {
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+ if j == 0 && i == cols {
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+ new_vertices[i].push(aj.normalize() * radius);
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+ } else {
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+ new_vertices[i]
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+ .push(aj.clone().lerp(bj, j as f32 / rows as f32).normalize() * radius);
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+ }
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+ }
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+ }
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+
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+ for i in 0..cols {
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+ for j in 0..2 * (cols - i) - 1 {
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+ let k = j / 2;
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+
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+ let mut triangle = Triangle { a: 0, b: 0, c: 0 };
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+ if j % 2 == 0 {
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+ triangle.a =
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+ self.add_position(new_vertices[i][k + 1], precision, added_vert_cache);
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+ triangle.b =
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+ self.add_position(new_vertices[i + 1][k], precision, added_vert_cache);
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+ triangle.c = self.add_position(new_vertices[i][k], precision, added_vert_cache);
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+ } else {
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+ triangle.a =
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+ self.add_position(new_vertices[i][k + 1], precision, added_vert_cache);
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+ triangle.b =
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+ self.add_position(new_vertices[i + 1][k + 1], precision, added_vert_cache);
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+ triangle.c =
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+ self.add_position(new_vertices[i + 1][k], precision, added_vert_cache);
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+ }
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+
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+ self.cells.push(triangle);
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+ }
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+ }
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+ }
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+
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+ fn add_position(
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+ &mut self,
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+ vertex: Vector3<f32>,
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+ precision: f32,
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+ added_vert_cache: &mut HashMap<(i32, i32, i32), usize>,
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+ ) -> usize {
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+ let vertex_key = (
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+ (vertex.x * precision).round() as i32,
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+ (vertex.y * precision).round() as i32,
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+ (vertex.z * precision).round() as i32,
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+ );
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+ if let Some(added_vert_index) = added_vert_cache.get(&vertex_key) {
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+ return *added_vert_index;
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+ } else {
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+ self.positions.push(ArraySerializedVector(vertex));
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+ let added_index = self.positions.len() - 1;
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+ added_vert_cache.insert(vertex_key, added_index);
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+ return added_index;
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+ }
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+ }
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+
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+ fn dual(&mut self, other: Polyhedron) {
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+ let vert_to_faces = other.vert_to_faces();
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+ let original_vert_count = other.positions.len();
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+ let triangle_centroids = other.triangle_centroids();
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+ let mut mid_centroid_cache: HashMap<(usize, usize), Vector3<f32>> = HashMap::new();
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+ let mut hex_count = 0;
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+ let mut pent_count = 0;
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+ for i in 0..original_vert_count {
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+ let faces = &vert_to_faces[&i];
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+ if faces.len() == 6 {
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+ hex_count += 1;
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+ } else {
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+ pent_count += 1;
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+ }
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+
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+ let center_point = find_center_of_triangles(faces, &triangle_centroids);
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+
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+ for face_index in faces {
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+ let triangle = &other.cells[*face_index];
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+ let other_verts: Vec<usize> = vec![triangle.a, triangle.b, triangle.c]
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+ .drain(..)
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+ .filter(|vert| *vert != i)
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+ .collect();
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+ let sorted_triangle = Triangle::new(i, other_verts[0], other_verts[1]);
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+
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+ let centroid = triangle_centroids[face_index];
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+ let mid_b_centroid = other.calculate_mid_centroid(
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+ sorted_triangle.b,
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+ faces,
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+ centroid,
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+ &triangle_centroids,
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+ &mut mid_centroid_cache,
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+ );
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+ let mid_c_centroid = other.calculate_mid_centroid(
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+ sorted_triangle.c,
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+ faces,
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+ centroid,
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+ &triangle_centroids,
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+ &mut mid_centroid_cache,
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+ );
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+
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+ let positions_start = self.positions.len();
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+ // TODO: remove duplication here:
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+ // push all triangle_centroids at beginning, same index as face_index
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+ // push center_point once in outer loop and save index
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+ // (is it okay if vertices show up in positions out of order like that?)
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+ // -- yes, I think it is okay
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+ self.positions.push(ArraySerializedVector(center_point));
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+ self.positions.push(ArraySerializedVector(centroid));
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+ self.positions.push(ArraySerializedVector(mid_b_centroid));
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+ self.positions.push(ArraySerializedVector(mid_c_centroid));
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+
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+ self.cells.push(Triangle::new(
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+ positions_start,
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+ positions_start + 1,
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+ positions_start + 2,
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+ ));
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+ self.cells.push(Triangle::new(
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+ positions_start,
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+ positions_start + 1,
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+ positions_start + 3,
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+ ));
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+ }
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+ }
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+ println!("hexagons: {}", hex_count);
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+ println!("pentagons: {}", pent_count);
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+ }
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+
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+ fn vert_to_faces(&self) -> HashMap<usize, Vec<usize>> {
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+ let mut vert_to_faces: HashMap<usize, Vec<usize>> = HashMap::new();
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+ for i in 0..self.cells.len() {
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+ let triangle = &self.cells[i];
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+
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+ if let Some(faces) = vert_to_faces.get_mut(&triangle.a) {
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+ faces.push(i);
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+ } else {
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+ vert_to_faces.insert(triangle.a, vec![i]);
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+ }
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+
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+ if let Some(faces) = vert_to_faces.get_mut(&triangle.b) {
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+ faces.push(i);
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+ } else {
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+ vert_to_faces.insert(triangle.b, vec![i]);
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+ }
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+
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+ if let Some(faces) = vert_to_faces.get_mut(&triangle.c) {
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+ faces.push(i);
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+ } else {
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+ vert_to_faces.insert(triangle.c, vec![i]);
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+ }
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+ }
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+ vert_to_faces
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+ }
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+
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304
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+ fn triangle_centroids(&self) -> HashMap<usize, Vector3<f32>> {
|
|
|
305
|
+ let mut triangle_centroids: HashMap<usize, Vector3<f32>> = HashMap::new();
|
|
|
306
|
+ for i in 0..self.cells.len() {
|
|
|
307
|
+ let a = self.positions[self.cells[i].a].0;
|
|
|
308
|
+ let b = self.positions[self.cells[i].b].0;
|
|
|
309
|
+ let c = self.positions[self.cells[i].c].0;
|
|
|
310
|
+ triangle_centroids.insert(i, calculate_centroid(a, b, c));
|
|
|
311
|
+ }
|
|
|
312
|
+ triangle_centroids
|
|
|
313
|
+ }
|
|
|
314
|
+
|
|
|
315
|
+ fn calculate_mid_centroid(
|
|
|
316
|
+ &self,
|
|
|
317
|
+ vertex_index: usize,
|
|
|
318
|
+ faces: &Vec<usize>,
|
|
|
319
|
+ centroid: Vector3<f32>,
|
|
|
320
|
+ triangle_centroids: &HashMap<usize, Vector3<f32>>,
|
|
|
321
|
+ mid_centroid_cache: &mut HashMap<(usize, usize), Vector3<f32>>,
|
|
|
322
|
+ ) -> Vector3<f32> {
|
|
|
323
|
+ let adj_face_index = self.find_adjacent_face(vertex_index, faces).unwrap();
|
|
|
324
|
+ let adj_centroid = triangle_centroids[&adj_face_index];
|
|
|
325
|
+ if let Some(mid_centroid) = mid_centroid_cache.get(&(vertex_index, adj_face_index)) {
|
|
|
326
|
+ return *mid_centroid;
|
|
|
327
|
+ } else {
|
|
|
328
|
+ let mid_centroid = centroid.clone().lerp(adj_centroid, 0.5);
|
|
|
329
|
+ mid_centroid_cache.insert((vertex_index, adj_face_index), mid_centroid);
|
|
|
330
|
+ return mid_centroid;
|
|
|
331
|
+ }
|
|
|
332
|
+ }
|
|
|
333
|
+
|
|
|
334
|
+ fn find_adjacent_face(&self, vertex_index: usize, faces: &Vec<usize>) -> Option<usize> {
|
|
|
335
|
+ for face_index in faces {
|
|
|
336
|
+ let triangle = &self.cells[*face_index];
|
|
|
337
|
+ if triangle.a == vertex_index
|
|
|
338
|
+ || triangle.b == vertex_index
|
|
|
339
|
+ || triangle.c == vertex_index
|
|
|
340
|
+ {
|
|
|
341
|
+ return Some(*face_index);
|
|
|
342
|
+ }
|
|
|
343
|
+ }
|
|
|
344
|
+ None
|
|
|
345
|
+ }
|
|
|
346
|
+}
|
|
|
347
|
+
|
|
|
348
|
+fn calculate_centroid(pa: Vector3<f32>, pb: Vector3<f32>, pc: Vector3<f32>) -> Vector3<f32> {
|
|
|
349
|
+ let vab_half = (pb.clone() - pa) / 2.0;
|
|
|
350
|
+ let pab_half = pa.clone() + vab_half;
|
|
|
351
|
+ ((pc.clone() - pab_half) * (1.0 / 3.0)) + pab_half
|
|
|
352
|
+}
|
|
|
353
|
+
|
|
|
354
|
+fn find_center_of_triangles(
|
|
|
355
|
+ triangle_indices: &Vec<usize>,
|
|
|
356
|
+ triangle_centroids: &HashMap<usize, Vector3<f32>>,
|
|
|
357
|
+) -> Vector3<f32> {
|
|
|
358
|
+ let mut center_point: Vector3<f32> = Vector3::new(0.0, 0.0, 0.0);
|
|
|
359
|
+ for triangle_index in triangle_indices.iter() {
|
|
|
360
|
+ center_point += triangle_centroids[triangle_index];
|
|
|
361
|
+ }
|
|
|
362
|
+ center_point /= triangle_indices.len() as f32;
|
|
|
363
|
+ center_point
|
|
|
364
|
+}
|
|
|
365
|
+
|
|
|
366
|
+fn generate_icosahedron_files(dir: &str, param_list: Vec<(f32, usize)>) {
|
|
|
367
|
+ for param in param_list {
|
|
|
368
|
+ println!(
|
|
|
369
|
+ "Generating icosahedron with radius {} and detail {}...",
|
|
|
370
|
+ param.0, param.1
|
|
|
371
|
+ );
|
|
|
372
|
+ let filename = Path::new(dir).join(format!("icosahedron_r{}_d{}.json", param.0, param.1));
|
|
|
373
|
+ let mut file = File::create(filename).expect("Can't create file");
|
|
|
374
|
+ let icosahedron = Polyhedron::new_isocahedron(param.0, param.1);
|
|
|
375
|
+ println!("triangles: {}", icosahedron.cells.len());
|
|
|
376
|
+ println!("vertices: {}", icosahedron.positions.len());
|
|
|
377
|
+ let icosahedron_json = serde_json::to_string(&icosahedron).expect("Problem serializing");
|
|
|
378
|
+ file.write_all(icosahedron_json.as_bytes())
|
|
|
379
|
+ .expect("Can't write to file");
|
|
|
380
|
+ }
|
|
|
381
|
+}
|
|
|
382
|
+
|
|
|
383
|
+fn generate_hexsphere_files(dir: &str, param_list: Vec<(f32, usize)>) {
|
|
|
384
|
+ for param in param_list {
|
|
|
385
|
+ println!(
|
|
|
386
|
+ "Generating hexsphere with radius {} and detail {}...",
|
|
|
387
|
+ param.0, param.1
|
|
|
388
|
+ );
|
|
|
389
|
+ let filename = Path::new(dir).join(format!("hexsphere_r{}_d{}.json", param.0, param.1));
|
|
|
390
|
+ let mut file = File::create(filename).expect("Can't create file");
|
|
|
391
|
+ let hexsphere = Polyhedron::new_dual_isocahedron(param.0, param.1);
|
|
|
392
|
+ println!("triangles: {}", hexsphere.cells.len());
|
|
|
393
|
+ println!("vertices: {}", hexsphere.positions.len());
|
|
|
394
|
+ let hexsphere_json = serde_json::to_string(&hexsphere).expect("Problem serializing");
|
|
|
395
|
+ file.write_all(hexsphere_json.as_bytes())
|
|
|
396
|
+ .expect("Can't write to file");
|
|
|
397
|
+ }
|
|
|
398
|
+}
|
|
|
399
|
+
|
|
|
400
|
+fn main() {
|
|
|
401
|
+ generate_hexsphere_files(
|
|
|
402
|
+ "output/",
|
|
|
403
|
+ vec![
|
|
|
404
|
+ (1.0, 0),
|
|
|
405
|
+ (1.0, 1),
|
|
|
406
|
+ (1.0, 2),
|
|
|
407
|
+ (1.0, 3),
|
|
|
408
|
+ (1.0, 4),
|
|
|
409
|
+ (1.0, 5),
|
|
|
410
|
+ (1.0, 6),
|
|
|
411
|
+ (1.0, 7),
|
|
|
412
|
+ ],
|
|
|
413
|
+ );
|
|
|
414
|
+ generate_icosahedron_files(
|
|
|
415
|
+ "output/",
|
|
|
416
|
+ vec![
|
|
|
417
|
+ (1.0, 0),
|
|
|
418
|
+ (1.0, 1),
|
|
|
419
|
+ (1.0, 2),
|
|
|
420
|
+ (1.0, 3),
|
|
|
421
|
+ (1.0, 4),
|
|
|
422
|
+ (1.0, 5),
|
|
|
423
|
+ (1.0, 6),
|
|
|
424
|
+ (1.0, 7),
|
|
|
425
|
+ ],
|
|
|
426
|
+ );
|
|
|
427
|
+}
|
