Finally generating correct normals

Have to detect and correct inverted normals during calculation since the winding
order of the generated truncated icosahedrons is inconsistent.

output/icosahedron_r1_d0.json

@@ -1 +1 @@
-{"positions":[[-0.8506508,0.0,0.5257311],[0.0,0.5257311,0.8506508],[-0.5257311,0.8506508,0.0],[0.5257311,0.8506508,0.0],[0.0,0.5257311,-0.8506508],[-0.8506508,0.0,-0.5257311],[0.8506508,0.0,0.5257311],[0.0,-0.5257311,0.8506508],[-0.5257311,-0.8506508,0.0],[0.0,-0.5257311,-0.8506508],[0.8506508,0.0,-0.5257311],[0.5257311,-0.8506508,0.0]],"cells":[[0,1,2],[1,3,2],[3,4,2],[4,5,2],[5,0,2],[1,6,3],[0,7,1],[5,8,0],[4,9,5],[3,10,4],[6,7,11],[7,8,11],[8,9,11],[9,10,11],[10,6,11],[6,1,7],[7,0,8],[8,5,9],[9,4,10],[10,3,6]]}
+{"positions":[[-0.8506508,0.0,0.5257311],[0.0,0.5257311,0.8506508],[-0.5257311,0.8506508,0.0],[0.5257311,0.8506508,0.0],[0.0,0.5257311,-0.8506508],[-0.8506508,0.0,-0.5257311],[0.8506508,0.0,0.5257311],[0.0,-0.5257311,0.8506508],[-0.5257311,-0.8506508,0.0],[0.0,-0.5257311,-0.8506508],[0.8506508,0.0,-0.5257311],[0.5257311,-0.8506508,0.0]],"cells":[[0,1,2],[1,3,2],[3,4,2],[4,5,2],[5,0,2],[1,6,3],[0,7,1],[5,8,0],[4,9,5],[3,10,4],[6,7,11],[7,8,11],[8,9,11],[9,10,11],[10,6,11],[6,1,7],[7,0,8],[8,5,9],[9,4,10],[10,3,6]],"normals":[[-0.85065085,0.0,0.52573115],[0.0,0.52573115,0.85065085],[-0.52573115,0.85065085,0.0],[0.52573115,0.85065085,0.0],[0.0,0.52573115,-0.85065085],[-0.85065085,0.0,-0.52573115],[0.85065085,0.0,0.52573115],[0.0,-0.52573115,0.85065085],[-0.5257311,-0.8506508,0.0],[0.0,-0.52573115,-0.85065085],[0.85065085,0.0,-0.52573115],[0.52573115,-0.85065085,0.0]],"faces":[]}

output/icosahedron_r1_d1.json

@@ -1 +1 @@
-{"positions":[[-0.809017,0.5,0.309017],[-0.309017,0.809017,0.5],[-0.5257311,0.8506508,0.0],[-0.5,0.309017,0.809017],[-0.8506508,0.0,0.5257311],[0.0,0.5257311,0.8506508],[0.0,1.0,0.0],[0.309017,0.809017,0.5],[0.5257311,0.8506508,0.0],[-0.309017,0.809017,-0.5],[0.309017,0.809017,-0.5],[0.0,0.5257311,-0.8506508],[-0.809017,0.5,-0.309017],[-0.5,0.309017,-0.809017],[-0.8506508,0.0,-0.5257311],[-1.0,0.0,0.0],[0.809017,0.5,0.309017],[0.5,0.309017,0.809017],[0.8506508,0.0,0.5257311],[0.0,0.0,1.0],[-0.5,-0.309017,0.809017],[0.0,-0.5257311,0.8506508],[-0.809017,-0.5,0.309017],[-0.809017,-0.5,-0.309017],[-0.5257311,-0.8506508,0.0],[-0.5,-0.309017,-0.809017],[0.0,0.0,-1.0],[0.0,-0.5257311,-0.8506508],[0.5,0.309017,-0.809017],[0.809017,0.5,-0.309017],[0.8506508,0.0,-0.5257311],[0.809017,-0.5,0.309017],[0.309017,-0.809017,0.5],[0.5257311,-0.8506508,0.0],[0.5,-0.309017,0.809017],[0.0,-1.0,0.0],[-0.309017,-0.809017,0.5],[0.309017,-0.809017,-0.5],[-0.309017,-0.809017,-0.5],[0.809017,-0.5,-0.309017],[0.5,-0.309017,-0.809017],[1.0,0.0,0.0]],"cells":[[0,1,2],[0,3,1],[4,3,0],[3,5,1],[1,6,2],[1,7,6],[5,7,1],[7,8,6],[6,9,2],[6,10,9],[8,10,6],[10,11,9],[9,12,2],[9,13,12],[11,13,9],[13,14,12],[12,0,2],[12,15,0],[14,15,12],[15,4,0],[7,16,8],[7,17,16],[5,17,7],[17,18,16],[3,19,5],[3,20,19],[4,20,3],[20,21,19],[15,22,4],[15,23,22],[14,23,15],[23,24,22],[13,25,14],[13,26,25],[11,26,13],[26,27,25],[10,28,11],[10,29,28],[8,29,10],[29,30,28],[31,32,33],[31,34,32],[18,34,31],[34,21,32],[32,35,33],[32,36,35],[21,36,32],[36,24,35],[35,37,33],[35,38,37],[24,38,35],[38,27,37],[37,39,33],[37,40,39],[27,40,37],[40,30,39],[39,31,33],[39,41,31],[30,41,39],[41,18,31],[34,19,21],[34,17,19],[18,17,34],[17,5,19],[36,22,24],[36,20,22],[21,20,36],[20,4,22],[38,25,27],[38,23,25],[24,23,38],[23,14,25],[40,28,30],[40,26,28],[27,26,40],[26,11,28],[41,16,18],[41,29,16],[30,29,41],[29,8,16]]}
+{"positions":[[-0.809017,0.5,0.309017],[-0.309017,0.809017,0.5],[-0.5257311,0.8506508,0.0],[-0.5,0.309017,0.809017],[-0.8506508,0.0,0.5257311],[0.0,0.5257311,0.8506508],[0.0,1.0,0.0],[0.309017,0.809017,0.5],[0.5257311,0.8506508,0.0],[-0.309017,0.809017,-0.5],[0.309017,0.809017,-0.5],[0.0,0.5257311,-0.8506508],[-0.809017,0.5,-0.309017],[-0.5,0.309017,-0.809017],[-0.8506508,0.0,-0.5257311],[-1.0,0.0,0.0],[0.809017,0.5,0.309017],[0.5,0.309017,0.809017],[0.8506508,0.0,0.5257311],[0.0,0.0,1.0],[-0.5,-0.309017,0.809017],[0.0,-0.5257311,0.8506508],[-0.809017,-0.5,0.309017],[-0.809017,-0.5,-0.309017],[-0.5257311,-0.8506508,0.0],[-0.5,-0.309017,-0.809017],[0.0,0.0,-1.0],[0.0,-0.5257311,-0.8506508],[0.5,0.309017,-0.809017],[0.809017,0.5,-0.309017],[0.8506508,0.0,-0.5257311],[0.809017,-0.5,0.309017],[0.309017,-0.809017,0.5],[0.5257311,-0.8506508,0.0],[0.5,-0.309017,0.809017],[0.0,-1.0,0.0],[-0.309017,-0.809017,0.5],[0.309017,-0.809017,-0.5],[-0.309017,-0.809017,-0.5],[0.809017,-0.5,-0.309017],[0.5,-0.309017,-0.809017],[1.0,0.0,0.0]],"cells":[[0,1,2],[0,3,1],[4,3,0],[3,5,1],[1,6,2],[1,7,6],[5,7,1],[7,8,6],[6,9,2],[6,10,9],[8,10,6],[10,11,9],[9,12,2],[9,13,12],[11,13,9],[13,14,12],[12,0,2],[12,15,0],[14,15,12],[15,4,0],[7,16,8],[7,17,16],[5,17,7],[17,18,16],[3,19,5],[3,20,19],[4,20,3],[20,21,19],[15,22,4],[15,23,22],[14,23,15],[23,24,22],[13,25,14],[13,26,25],[11,26,13],[26,27,25],[10,28,11],[10,29,28],[8,29,10],[29,30,28],[31,32,33],[31,34,32],[18,34,31],[34,21,32],[32,35,33],[32,36,35],[21,36,32],[36,24,35],[35,37,33],[35,38,37],[24,38,35],[38,27,37],[37,39,33],[37,40,39],[27,40,37],[40,30,39],[39,31,33],[39,41,31],[30,41,39],[41,18,31],[34,19,21],[34,17,19],[18,17,34],[17,5,19],[36,22,24],[36,20,22],[21,20,36],[20,4,22],[38,25,27],[38,23,25],[24,23,38],[23,14,25],[40,28,30],[40,26,28],[27,26,40],[26,11,28],[41,16,18],[41,29,16],[30,29,41],[29,8,16]],"normals":[[-0.809017,0.5,0.309017],[-0.309017,0.809017,0.50000006],[-0.52573115,0.8506508,0.0],[-0.50000006,0.309017,0.809017],[-0.8506508,0.0,0.52573115],[-2.8343692e-9,0.52573115,0.8506508],[0.0,1.0,-2.2313862e-9],[0.309017,0.809017,0.5],[0.52573115,0.8506508,0.0],[-0.309017,0.809017,-0.5],[0.309017,0.809017,-0.5],[2.8343692e-9,0.52573115,-0.8506508],[-0.809017,0.5,-0.309017],[-0.5,0.309017,-0.809017],[-0.8506508,0.0,-0.52573115],[-1.0,-2.2313862e-9,0.0],[0.809017,0.50000006,0.309017],[0.5,0.309017,0.809017],[0.8506508,0.0,0.52573115],[2.2313862e-9,0.0,1.0],[-0.5,-0.309017,0.809017],[0.0,-0.52573115,0.8506508],[-0.809017,-0.5,0.309017],[-0.809017,-0.5,-0.309017],[-0.52573115,-0.8506508,0.0],[-0.5,-0.309017,-0.809017],[6.694158e-9,0.0,-1.0],[2.8343692e-9,-0.52573115,-0.8506508],[0.5,0.309017,-0.809017],[0.809017,0.50000006,-0.309017],[0.8506508,-2.8343692e-9,-0.52573115],[0.809017,-0.5,0.309017],[0.309017,-0.809017,0.50000006],[0.52573115,-0.8506508,0.0],[0.50000006,-0.309017,0.809017],[0.0,-1.0,-2.2313862e-9],[-0.309017,-0.809017,0.5],[0.309017,-0.809017,-0.5],[-0.309017,-0.809017,-0.5],[0.809017,-0.5,-0.309017],[0.5,-0.309017,-0.809017],[1.0,2.2313862e-9,0.0]],"faces":[]}

src/main.rs

@@ -3,6 +3,7 @@ extern crate cgmath;
 use std::collections::HashMap;
 use std::fs::File;
 use std::io::Write;
+use std::ops::AddAssign;
 use std::path::Path;
 
 use cgmath::prelude::*;
@@ -46,8 +47,10 @@ struct ArraySerializedVector(Vector3<f32>);
 struct Polyhedron {
     positions: Vec<ArraySerializedVector>,
     cells: Vec<Triangle>,
+    normals: Vec<ArraySerializedVector>,
     #[serde(skip)]
     added_vert_cache: HashMap<(i32, i32, i32), usize>,
+    faces: Vec<Vec<usize>>,
 }
 
 impl Serialize for ArraySerializedVector {
@@ -64,12 +67,20 @@ impl Serialize for ArraySerializedVector {
     }
 }
 
+impl AddAssign for ArraySerializedVector {
+    fn add_assign(&mut self, other: Self) {
+        *self = Self(self.0 + other.0);
+    }
+}
+
 impl Polyhedron {
     fn new() -> Polyhedron {
         Polyhedron {
             positions: vec![],
             cells: vec![],
+            normals: vec![],
             added_vert_cache: HashMap::new(),
+            faces: vec![],
         }
     }
 
@@ -99,7 +110,9 @@ impl Polyhedron {
                 Triangle::new(8, 6, 7),
                 Triangle::new(9, 8, 1),
             ],
+            normals: vec![],
             added_vert_cache: HashMap::new(),
+            faces: vec![],
         };
         base_isocahedron.add_position(Vector3::new(-1.0, t, 0.0));
         base_isocahedron.add_position(Vector3::new(1.0, t, 0.0));
@@ -119,11 +132,11 @@ impl Polyhedron {
         subdivided
     }
 
-    fn new_dual_isocahedron(radius: f32, detail: usize) -> Polyhedron {
+    fn new_truncated_isocahedron(radius: f32, detail: usize) -> Polyhedron {
         let isocahedron = Polyhedron::new_isocahedron(radius, detail);
-        let mut dual_isocahedron = Polyhedron::new();
+        let mut truncated_isocahedron = Polyhedron::new();
-        dual_isocahedron.dual(isocahedron);
+        truncated_isocahedron.truncated(isocahedron);
-        dual_isocahedron
+        truncated_isocahedron
     }
 
     fn subdivide(&mut self, other: Polyhedron, radius: f32, detail: usize) {
@@ -192,19 +205,22 @@ impl Polyhedron {
             return *added_vert_index;
         } else {
             self.positions.push(ArraySerializedVector(vertex));
+            self.normals
+                .push(ArraySerializedVector(Vector3::new(0.0, 0.0, 0.0)));
             let added_index = self.positions.len() - 1;
             self.added_vert_cache.insert(vertex_key, added_index);
             return added_index;
         }
     }
 
-    fn dual(&mut self, other: Polyhedron) {
+    fn truncated(&mut self, other: Polyhedron) {
         let vert_to_faces = other.vert_to_faces();
         let original_vert_count = other.positions.len();
         let triangle_centroids = other.triangle_centroids();
-        let mut mid_centroid_cache: HashMap<(usize, usize), Vector3<f32>> = HashMap::new();
+        let mut mid_centroid_cache: HashMap<(usize, usize, usize), Vector3<f32>> = HashMap::new();
         let mut hex_count = 0;
         let mut pent_count = 0;
+        let mut count = 0;
         for i in 0..original_vert_count {
             let faces = &vert_to_faces[&i];
             if faces.len() == 6 {
@@ -215,7 +231,9 @@ impl Polyhedron {
 
             let center_point = find_center_of_triangles(faces, &triangle_centroids);
 
-            for face_index in faces {
+            let mut new_face = Vec::new();
+
+            for face_index in faces.iter().rev() {
                 let triangle = &other.cells[*face_index];
                 let other_verts: Vec<usize> = vec![triangle.a, triangle.b, triangle.c]
                     .drain(..)
@@ -225,15 +243,19 @@ impl Polyhedron {
 
                 let centroid = triangle_centroids[face_index];
                 let mid_b_centroid = other.calculate_mid_centroid(
+                    sorted_triangle.a,
                     sorted_triangle.b,
                     faces,
+                    *face_index,
                     centroid,
                     &triangle_centroids,
                     &mut mid_centroid_cache,
                 );
                 let mid_c_centroid = other.calculate_mid_centroid(
+                    sorted_triangle.a,
                     sorted_triangle.c,
                     faces,
+                    *face_index,
                     centroid,
                     &triangle_centroids,
                     &mut mid_centroid_cache,
@@ -246,15 +268,18 @@ impl Polyhedron {
 
                 self.cells.push(Triangle::new(
                     center_point_index,
+                    mid_c_centroid_index,
                     centroid_index,
-                    mid_b_centroid_index,
                 ));
+                new_face.push(self.cells.len() - 1);
                 self.cells.push(Triangle::new(
                     center_point_index,
                     centroid_index,
-                    mid_c_centroid_index,
+                    mid_b_centroid_index,
                 ));
+                new_face.push(self.cells.len() - 1);
             }
+            self.faces.push(new_face);
         }
         println!("hexagons: {}", hex_count);
         println!("pentagons: {}", pent_count);
@@ -299,35 +324,124 @@ impl Polyhedron {
 
     fn calculate_mid_centroid(
         &self,
+        spoke_vertex_index: usize,
         vertex_index: usize,
         faces: &Vec<usize>,
+        current_face_index: usize,
         centroid: Vector3<f32>,
         triangle_centroids: &HashMap<usize, Vector3<f32>>,
-        mid_centroid_cache: &mut HashMap<(usize, usize), Vector3<f32>>,
+        mid_centroid_cache: &mut HashMap<(usize, usize, usize), Vector3<f32>>,
     ) -> Vector3<f32> {
-        let adj_face_index = self.find_adjacent_face(vertex_index, faces).unwrap();
+        let adj_face_index = self
+            .find_adjacent_face(spoke_vertex_index, vertex_index, faces, current_face_index)
+            .unwrap();
         let adj_centroid = triangle_centroids[&adj_face_index];
-        if let Some(mid_centroid) = mid_centroid_cache.get(&(vertex_index, adj_face_index)) {
+        if let Some(mid_centroid) =
+            mid_centroid_cache.get(&(spoke_vertex_index, vertex_index, adj_face_index))
+        {
             return *mid_centroid;
         } else {
             let mid_centroid = centroid.clone().lerp(adj_centroid, 0.5);
-            mid_centroid_cache.insert((vertex_index, adj_face_index), mid_centroid);
+            mid_centroid_cache.insert(
+                (spoke_vertex_index, vertex_index, adj_face_index),
+                mid_centroid,
+            );
             return mid_centroid;
         }
     }
 
-    fn find_adjacent_face(&self, vertex_index: usize, faces: &Vec<usize>) -> Option<usize> {
+    fn find_adjacent_face(
+        &self,
+        spoke_vertex_index: usize,
+        vertex_index: usize,
+        faces: &Vec<usize>,
+        current_face_index: usize,
+    ) -> Option<usize> {
         for face_index in faces {
+            if *face_index == current_face_index {
+                continue;
+            }
             let triangle = &self.cells[*face_index];
-            if triangle.a == vertex_index
+            if (triangle.a == spoke_vertex_index
-                || triangle.b == vertex_index
+                || triangle.b == spoke_vertex_index
-                || triangle.c == vertex_index
+                || triangle.c == spoke_vertex_index)
+                && (triangle.a == vertex_index
+                    || triangle.b == vertex_index
+                    || triangle.c == vertex_index)
             {
                 return Some(*face_index);
             }
         }
         None
     }
+
+    fn compute_triangle_normals(&mut self) {
+        let origin = Vector3::new(0.0, 0.0, 0.0);
+        for i in 0..self.cells.len() {
+            let vertex_a = &self.positions[self.cells[i].a].0;
+            let vertex_b = &self.positions[self.cells[i].b].0;
+            let vertex_c = &self.positions[self.cells[i].c].0;
+
+            let e1 = vertex_a - vertex_b;
+            let e2 = vertex_c - vertex_b;
+            let mut no = e1.cross(e2);
+
+            // detect and correct inverted normal
+            let dist = vertex_b - origin;
+            if no.dot(dist) < 0.0 {
+                no *= -1.0;
+            }
+
+            let normal_a = self.normals[self.cells[i].a].0 + no;
+            let normal_b = self.normals[self.cells[i].b].0 + no;
+            let normal_c = self.normals[self.cells[i].c].0 + no;
+
+            self.normals[self.cells[i].a] = ArraySerializedVector(normal_a);
+            self.normals[self.cells[i].b] = ArraySerializedVector(normal_b);
+            self.normals[self.cells[i].c] = ArraySerializedVector(normal_c);
+        }
+
+        for normal in self.normals.iter_mut() {
+            *normal = ArraySerializedVector(normal.0.normalize());
+        }
+    }
+
+    fn compute_face_normals(&mut self) {
+        let origin = Vector3::new(0.0, 0.0, 0.0);
+        for i in 0..self.faces.len() {
+            let first_cell = &self.cells[self.faces[i][0]];
+
+            let vertex_a = &self.positions[first_cell.a].0;
+            let vertex_b = &self.positions[first_cell.b].0;
+            let vertex_c = &self.positions[first_cell.c].0;
+
+            let e1 = vertex_a - vertex_b;
+            let e2 = vertex_c - vertex_b;
+            let mut normal = e1.cross(e2);
+
+            // detect and correct inverted normal
+            let dist = vertex_b - origin;
+            if normal.dot(dist) < 0.0 {
+                normal *= -1.0;
+            }
+
+            for c in 0..self.faces[i].len() {
+                let face_cell = &self.cells[self.faces[i][c]];
+
+                let normal_a = self.normals[face_cell.a].0 + normal;
+                let normal_b = self.normals[face_cell.b].0 + normal;
+                let normal_c = self.normals[face_cell.c].0 + normal;
+
+                self.normals[face_cell.a] = ArraySerializedVector(normal_a);
+                self.normals[face_cell.b] = ArraySerializedVector(normal_b);
+                self.normals[face_cell.c] = ArraySerializedVector(normal_c);
+            }
+        }
+
+        for normal in self.normals.iter_mut() {
+            *normal = ArraySerializedVector(normal.0.normalize());
+        }
+    }
 }
 
 fn calculate_centroid(pa: Vector3<f32>, pb: Vector3<f32>, pc: Vector3<f32>) -> Vector3<f32> {
@@ -356,7 +470,8 @@ fn generate_icosahedron_files(dir: &str, param_list: Vec<(f32, usize)>) {
         );
         let filename = Path::new(dir).join(format!("icosahedron_r{}_d{}.json", param.0, param.1));
         let mut file = File::create(filename).expect("Can't create file");
-        let icosahedron = Polyhedron::new_isocahedron(param.0, param.1);
+        let mut icosahedron = Polyhedron::new_isocahedron(param.0, param.1);
+        icosahedron.compute_triangle_normals();
         println!("triangles: {}", icosahedron.cells.len());
         println!("vertices: {}", icosahedron.positions.len());
         let icosahedron_json = serde_json::to_string(&icosahedron).expect("Problem serializing");
@@ -373,7 +488,9 @@ fn generate_hexsphere_files(dir: &str, param_list: Vec<(f32, usize)>) {
         );
         let filename = Path::new(dir).join(format!("hexsphere_r{}_d{}.json", param.0, param.1));
         let mut file = File::create(filename).expect("Can't create file");
-        let hexsphere = Polyhedron::new_dual_isocahedron(param.0, param.1);
+        let mut hexsphere = Polyhedron::new_truncated_isocahedron(param.0, param.1);
+        hexsphere.compute_triangle_normals();
+        // hexsphere.compute_face_normals();
         println!("triangles: {}", hexsphere.cells.len());
         println!("vertices: {}", hexsphere.positions.len());
         let hexsphere_json = serde_json::to_string(&hexsphere).expect("Problem serializing");
@@ -394,6 +511,8 @@ fn main() {
             (1.0, 5),
             (1.0, 6),
             (1.0, 7),
+            // (1.0, 8),
+            // (1.0, 9),
         ],
     );
     generate_icosahedron_files(