From 4464a9fae62226c0b9406af2c89ed9e35c198fc8 Mon Sep 17 00:00:00 2001
From: Matthew Gordon <matthew.scott.gordon@gmail.com>
Date: Sat, 20 Jun 2020 09:13:20 -0400
Subject: [PATCH] Add utility function to generate dodecahedron

---
 src/util/mod.rs       |   1 +
 src/util/polyhedra.rs | 132 ++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 133 insertions(+)
 create mode 100644 src/util/polyhedra.rs

diff --git a/src/util/mod.rs b/src/util/mod.rs
index 1914db3..5936783 100644
--- a/src/util/mod.rs
+++ b/src/util/mod.rs
@@ -7,3 +7,4 @@ pub mod morton;
 pub mod normalizer;
 mod tile_iterator;
 pub use tile_iterator::{Tile, TileIterator};
+pub mod polyhedra;
diff --git a/src/util/polyhedra.rs b/src/util/polyhedra.rs
new file mode 100644
index 0000000..bf88e59
--- /dev/null
+++ b/src/util/polyhedra.rs
@@ -0,0 +1,132 @@
+use itertools::izip;
+use nalgebra::{convert, Point3, Vector3};
+
+use crate::materials::Material;
+use crate::raycasting::Triangle;
+use crate::Real;
+
+use std::sync::Arc;
+
+pub fn triangulate_polygon<T: Real>(
+    vertices: &Vec<Point3<T>>,
+    normal: &Vector3<T>,
+    material: Arc<dyn Material<T>>,
+) -> Vec<Triangle<T>> {
+    assert!(vertices.len() >= 3);
+    let hinge = vertices[0];
+    izip!(vertices.iter().skip(1), vertices.iter().skip(2))
+        .map(|(a, b)| Triangle {
+            vertices: [hinge, *a, *b],
+            normals: [*normal, *normal, *normal],
+            material: Arc::clone(&material),
+        })
+        .collect()
+}
+
+pub fn generate_dodecahedron<T: Real>(
+    centre: Point3<T>,
+    size: T,
+    material: Arc<dyn Material<T>>,
+) -> Vec<Triangle<T>> {
+    let phi = convert((1.0 + (5.0_f64).sqrt()) / 2.0);
+    let phi_inv = T::one() / phi;
+    let one = T::one();
+    let zero = T::zero();
+
+    let faces = vec![
+        vec![
+            Vector3::new(phi_inv, zero, phi),
+            Vector3::new(-phi_inv, zero, phi),
+            Vector3::new(-one, -one, one),
+            Vector3::new(zero, -phi, phi_inv),
+            Vector3::new(one, -one, one),
+        ],
+        vec![
+            Vector3::new(phi_inv, zero, phi),
+            Vector3::new(-phi_inv, zero, phi),
+            Vector3::new(-one, one, one),
+            Vector3::new(zero, phi, phi_inv),
+            Vector3::new(one, one, one),
+        ],
+        vec![
+            Vector3::new(phi_inv, zero, phi),
+            Vector3::new(one, -one, one),
+            Vector3::new(phi, -phi_inv, zero),
+            Vector3::new(phi, phi_inv, zero),
+            Vector3::new(one, one, one),
+        ],
+        vec![
+            Vector3::new(-phi_inv, zero, phi),
+            Vector3::new(-one, -one, one),
+            Vector3::new(-phi, -phi_inv, zero),
+            Vector3::new(-phi, phi_inv, zero),
+            Vector3::new(-one, one, one),
+        ],
+        vec![
+            Vector3::new(-one, -one, one),
+            Vector3::new(-phi, -phi_inv, zero),
+            Vector3::new(-one, -one, -one),
+            Vector3::new(zero, -phi, -phi_inv),
+            Vector3::new(zero, -phi, phi_inv),
+        ],
+        vec![
+            Vector3::new(zero, -phi, phi_inv),
+            Vector3::new(zero, -phi, -phi_inv),
+            Vector3::new(one, -one, -one),
+            Vector3::new(phi, -phi_inv, zero),
+            Vector3::new(one, -one, one),
+        ],
+        vec![
+            Vector3::new(zero, phi, phi_inv),
+            Vector3::new(zero, phi, -phi_inv),
+            Vector3::new(-one, one, -one),
+            Vector3::new(-phi, phi_inv, zero),
+            Vector3::new(-one, one, one),
+        ],
+        vec![
+            Vector3::new(one, one, one),
+            Vector3::new(phi, phi_inv, zero),
+            Vector3::new(one, one, -one),
+            Vector3::new(zero, phi, -phi_inv),
+            Vector3::new(zero, phi, phi_inv),
+        ],
+        vec![
+            Vector3::new(one, -one, -one),
+            Vector3::new(zero, -phi, -phi_inv),
+            Vector3::new(-one, -one, -one),
+            Vector3::new(-phi_inv, zero, -phi),
+            Vector3::new(phi_inv, zero, -phi),
+        ],
+        vec![
+            Vector3::new(one, one, -one),
+            Vector3::new(zero, phi, -phi_inv),
+            Vector3::new(-one, one, -one),
+            Vector3::new(-phi_inv, zero, -phi),
+            Vector3::new(phi_inv, zero, -phi),
+        ],
+        vec![
+            Vector3::new(one, one, -one),
+            Vector3::new(phi, phi_inv, zero),
+            Vector3::new(phi, -phi_inv, zero),
+            Vector3::new(one, -one, -one),
+            Vector3::new(phi_inv, zero, -phi),
+        ],
+        vec![
+            Vector3::new(-one, one, -one),
+            Vector3::new(-phi, phi_inv, zero),
+            Vector3::new(-phi, -phi_inv, zero),
+            Vector3::new(-one, -one, -one),
+            Vector3::new(-phi_inv, zero, -phi),
+        ],
+    ];
+
+    let scale = size * convert(3f64.sqrt() / 2.0);
+    faces
+        .iter()
+        .flat_map(|face| {
+            let normal = (face[1] - face[0]).cross(&(face[2] - face[1]));
+            let transformed_face = face.iter().map(|v| centre + v * scale).collect();
+            triangulate_polygon(&transformed_face, &normal, Arc::clone(&material))
+        })
+        .collect()
+}