Added IcoSphere for testing. Replaced Vector3D<T> with Vector3 since it is more performant

Nebulix/Rendering/Mesh.cs

@@ -1,20 +1,20 @@
-using Silk.NET.Maths;
+using System.Numerics;
 using Silk.NET.OpenGL;
 
 namespace Nebulix.Rendering
 {
 	public sealed class Mesh
 	{
-		public Vector3D<float>[] Vertices { get => vertices; 
-			set { vertices = value; regenerate = true; normals = new Vector3D<float>[vertices.Length];} }
+		public Vector3[] Vertices { get => vertices; 
+			set { vertices = value; regenerate = true; normals = new Vector3[vertices.Length];} }
 		public uint[] Indices { get => indices; set { indices = value; regenerate = true; } }
 		
-		private uint vao = 0, vbo = 0, ebo = 0;
+		private uint vao, vbo, ebo;
 		private bool regenerate = true;
 
-		private Vector3D<float>[] vertices = [];
+		private Vector3[] vertices = [];
 		private uint[] indices = [];
-		private Vector3D<float>[] normals = [];
+		private Vector3[] normals = [];
 
 		public void Clear()
 		{
@@ -29,13 +29,13 @@ namespace Nebulix.Rendering
 				uint i0 = indices[i];
 				uint i1 = indices[i+1];
 				uint i2 = indices[i+2];
-				Vector3D<float> v0 = vertices[i0];
-				Vector3D<float> v1 = vertices[i1];
-				Vector3D<float> v2 = vertices[i2];
+				Vector3 v0 = vertices[i0];
+				Vector3 v1 = vertices[i1];
+				Vector3 v2 = vertices[i2];
 
-				Vector3D<float> normal = Vector3D.Cross(v1-v0, v2-v0);
+				Vector3 normal = Vector3.Cross(v1-v0, v2-v0);
 				// Commenting this out, will result in the normals being weighted based on the triangle area
-				normal = Vector3D.Normalize(normal);
+				normal = Vector3.Normalize(normal);
 				normals[i0] += normal;
 				normals[i1] += normal;
 				normals[i2] += normal;
@@ -43,7 +43,7 @@ namespace Nebulix.Rendering
 
 			for (int i = 0; i < normals.Length; i++)
 			{
-				normals[i] = Vector3D.Normalize(normals[i]); // smoothing for shared vertices
+				normals[i] = Vector3.Normalize(normals[i]); // smoothing for shared vertices
 			}
 		}
 		

Nebulix/Rendering/Shaders/Shader.cs

@@ -1,6 +1,6 @@
-using Silk.NET.Maths;
-using Silk.NET.OpenGL;
+using Silk.NET.OpenGL;
 using System.Numerics;
+using Silk.NET.Maths;
 
 namespace Nebulix.Rendering;
 
@@ -35,6 +35,10 @@ public class Shader
         _glContext.Uniform1(_glContext.GetUniformLocation(_shaderProgramId, name), value);
     }
 
+    public void SetVector(string name, Vector3 value)
+    {
+	    _glContext.Uniform3(_glContext.GetUniformLocation(_shaderProgramId, name), value.X, value.Y, value.Z);
+    }
     public void SetVector(string name, Vector3D<float> value)
     {
 	    _glContext.Uniform3(_glContext.GetUniformLocation(_shaderProgramId, name), value.X, value.Y, value.Z);

Nebulix/Vector.cs

@@ -0,0 +1,35 @@
+using System.Numerics;
+
+namespace Nebulix;
+
+
+public static class VectorExtensions 
+{
+    public static Vector3 Up(this Vector3 _) => Vector3.UnitY;
+    public static Vector3 Down(this Vector3 _) => -Vector3.UnitY;
+    public static Vector3 Left(this Vector3 _) => Vector3.UnitX;
+    public static Vector3 Right(this Vector3 _) => -Vector3.UnitX;
+    public static Vector3 Front(this Vector3 _) => -Vector3.UnitZ;
+    public static Vector3 Back(this Vector3 _) => -Vector3.UnitZ;
+
+    // Thanks to: https://stackoverflow.com/a/67920029
+    public static Vector3 Slerp(this Vector3 start, Vector3 end, float percent)
+    {
+        // the cosine of the angle between 2 vectors.
+        float dot = Vector3.Dot(start, end);
+
+        // Clamp it to be in the range of Acos()
+        // This may be unnecessary, but floating point precision can be a fickle mistress.
+        Math.Clamp(dot, -1.0f, 1.0f);
+
+        // Acos(dot) returns the angle between start and end,
+        // And multiplying that by percent returns the angle between start and the final result.
+        float theta = (float)Math.Acos(dot) * percent;
+        Vector3 relativeVec = end - start * dot;
+        relativeVec = Vector3.Normalize(relativeVec);
+
+        // Orthonormal basis
+        // The final result.
+        return ((start * (float)Math.Cos(theta)) + (relativeVec * (float)Math.Sin(theta)));
+    }
+}

src/Camera/Camera.cs

@@ -1,4 +1,4 @@
-using Silk.NET.Maths;
+using System.Numerics;
 
 namespace Engine_silk.NET;
 
@@ -14,19 +14,19 @@ public enum MovementDirection
 
 public class Camera
 {
-	public Vector3D<float> Position => _position;
-	private readonly Vector3D<float> _worldUp;
-	private Vector3D<float> _position;
-	private Vector3D<float> _front;
-	private Vector3D<float> _right;
-	private Vector3D<float> _up;
+	public Vector3 Position => _position;
+	private readonly Vector3 _worldUp;
+	private Vector3 _position;
+	private Vector3 _front;
+	private Vector3 _right;
+	private Vector3 _up;
 	private float _yaw;
 	private float _pitch;
 
 	/// <summary>
 	/// The view matrix according to the current camera position and rotation
 	/// </summary>
-	public Matrix4X4<float> ViewMatrix { get => Matrix4X4.CreateLookAt(_position, _position + _front, _worldUp); }
+	public Matrix4x4 ViewMatrix { get => Matrix4x4.CreateLookAt(_position, _position + _front, _worldUp); }
 	public float MouseSensitivity { get; set; } = 0.1f;
 	/// <summary>
 	/// Controlls how fast the camera moves if a key is pressed
@@ -34,14 +34,14 @@ public class Camera
 	public float MovementSpeed { get; set; }
 	public float Fov { get; set; }
 
-	public Camera(Vector3D<float> position, float yaw = -90.0f, float pitch = 0, float movementSpeed = 2.5f, float fov = 45.0f)
+	public Camera(Vector3 position, float yaw = -90.0f, float pitch = 0, float movementSpeed = 2.5f, float fov = 45.0f)
 	{
 		_position = position;
 		_yaw = yaw;
 		_pitch = pitch;
 		MovementSpeed = movementSpeed;
 		Fov = fov;
-		_worldUp = Vector3D<float>.UnitY;
+		_worldUp = Vector3.UnitY;
 
 		UpdateCameraVectors();
 	}
@@ -99,15 +99,15 @@ public class Camera
 
 	private void UpdateCameraVectors()
 	{
-		Vector3D<float> front = new(
+		Vector3 front = new(
 			MathF.Cos(Maths.Convert.ToRadians(_yaw)) * MathF.Cos(Maths.Convert.ToRadians(_pitch)),
 			MathF.Sin(Maths.Convert.ToRadians(_pitch)),
 			MathF.Sin(Maths.Convert.ToRadians(_yaw)) * MathF.Cos(Maths.Convert.ToRadians(_pitch))
 			);
-		_front = Vector3D.Normalize(front);
+		_front = Vector3.Normalize(front);
 
-		_right = Vector3D.Normalize(Vector3D.Cross(_front, _worldUp));
-		_up = Vector3D.Normalize(Vector3D.Cross(_right, _front));
+		_right = Vector3.Normalize(Vector3.Cross(_front, _worldUp));
+		_up = Vector3.Normalize(Vector3.Cross(_right, _front));
 	}
 
 }

src/IcoSphere.cs

@@ -0,0 +1,183 @@
+using System.Numerics;
+using Nebulix;
+using Nebulix.Rendering;
+using Silk.NET.OpenGL;
+
+namespace Engine_silk.NET;
+
+public class IcoSphere
+{
+    private readonly Mesh mesh = new();
+    private readonly int resolution;
+    private readonly IcoSphereGenerator generator = new();
+    
+    public IcoSphere(int resolution)
+    {
+        if (resolution < 2)
+            throw new ArgumentOutOfRangeException(nameof(resolution), resolution,
+                "Resolution must be greater than 1");
+        this.resolution = resolution;
+    }
+
+    public void CreateSphere()
+    {
+        generator.Generate(resolution);
+        
+        mesh.Clear();
+        mesh.Vertices = generator.Vertices;
+        mesh.Indices = Array.ConvertAll(generator.Triangles, x => (uint)x);
+        mesh.CalculateNormals();
+    }
+    
+    public void RenderSphere(GL gl) // Will not be needed  
+    {
+        mesh.Render(gl);
+    }
+}
+
+// Thank you Sebastian Lague
+class IcoSphereGenerator 
+{
+
+    // Output:
+    public Vector3[] Vertices => vertices?.Items ?? Array.Empty<Vector3>();
+    public int[] Triangles => triangles?.Items ?? Array.Empty<int>();
+
+    // Internal:
+    FixedSizeList<Vector3>? vertices;
+    FixedSizeList<int>? triangles;
+    int numDivisions;
+    int numVertsPerFace;
+
+    // Indices of the vertex pairs that make up each of the initial 12 edges
+    static readonly int[] VertexPairs = { 0, 1, 0, 2, 0, 3, 0, 4, 1, 2, 2, 3, 3, 4, 4, 1, 5, 1, 5, 2, 5, 3, 5, 4 };
+    // Indices of the edge triplets that make up the initial 8 faces
+    static readonly int[] EdgeTriplets = { 0, 1, 4, 1, 2, 5, 2, 3, 6, 3, 0, 7, 8, 9, 4, 9, 10, 5, 10, 11, 6, 11, 8, 7 };
+    // The six initial vertices                up             left           back            right           forward        down
+    static readonly Vector3[] BaseVertices = { Vector3.UnitY, -Vector3.UnitX, -Vector3.UnitZ, Vector3.UnitX, Vector3.UnitZ, -Vector3.UnitY };
+
+    public void Generate (int resolution) {
+        numDivisions = Math.Max (0, resolution);
+        numVertsPerFace = ((numDivisions + 3) * (numDivisions + 3) - (numDivisions + 3)) / 2;
+        int numVerts = numVertsPerFace * 8 - (numDivisions + 2) * 12 + 6;
+        int numTrisPerFace = (numDivisions + 1) * (numDivisions + 1);
+
+        vertices = new FixedSizeList<Vector3> (numVerts);
+        triangles = new FixedSizeList<int> (numTrisPerFace * 8 * 3);
+
+        vertices.AddRange (BaseVertices);
+
+        // Create 12 edges, with n vertices added along them (n = numDivisions)
+        Edge[] edges = new Edge[12];
+        for (int i = 0; i < VertexPairs.Length; i += 2) {
+            Vector3 startVertex = vertices.Items[VertexPairs[i]];
+            Vector3 endVertex = vertices.Items[VertexPairs[i + 1]];
+
+            int[] edgeVertexIndices = new int[numDivisions + 2];
+            edgeVertexIndices[0] = VertexPairs[i];
+
+            // Add vertices along edge
+            for (int divisionIndex = 0; divisionIndex < numDivisions; divisionIndex++) {
+                float t = (divisionIndex + 1f) / (numDivisions + 1f);
+                edgeVertexIndices[divisionIndex + 1] = vertices.NextIndex;
+                vertices.Add (startVertex.Slerp(endVertex, t));
+            }
+            edgeVertexIndices[numDivisions + 1] = VertexPairs[i + 1];
+            int edgeIndex = i / 2;
+            edges[edgeIndex] = new Edge (edgeVertexIndices);
+        }
+
+        // Create faces
+        for (int i = 0; i < EdgeTriplets.Length; i += 3) {
+            int faceIndex = i / 3;
+            bool reverse = faceIndex >= 4;
+            CreateFace (edges[EdgeTriplets[i]], edges[EdgeTriplets[i + 1]], edges[EdgeTriplets[i + 2]], reverse);
+        }
+    }
+
+    void CreateFace (Edge sideA, Edge sideB, Edge bottom, bool reverse)
+    {
+        if (vertices is null) throw new ArgumentException("Vertices cannot be null", nameof(vertices));
+        if (triangles is null) throw new ArgumentException("triangles cannot be null", nameof(triangles));
+        
+        int numPointsInEdge = sideA.VertexIndices.Length;
+        var vertexMap = new FixedSizeList<int> (numVertsPerFace);
+        vertexMap.Add (sideA.VertexIndices[0]); // top of triangle
+
+        for (int i = 1; i < numPointsInEdge - 1; i++) {
+            // Side A vertex
+            vertexMap.Add (sideA.VertexIndices[i]);
+
+            // Add vertices between sideA and sideB
+            Vector3 sideAVertex = vertices.Items[sideA.VertexIndices[i]];
+            Vector3 sideBVertex = vertices.Items[sideB.VertexIndices[i]];
+            int numInnerPoints = i - 1;
+            for (int j = 0; j < numInnerPoints; j++) {
+                float t = (j + 1f) / (numInnerPoints + 1f);
+                vertexMap.Add (vertices.NextIndex);
+                vertices.Add (sideAVertex.Slerp(sideBVertex, t));
+            }
+
+            // Side B vertex
+            vertexMap.Add (sideB.VertexIndices[i]);
+        }
+
+        // Add bottom edge vertices
+        for (int i = 0; i < numPointsInEdge; i++) {
+            vertexMap.Add (bottom.VertexIndices[i]);
+        }
+
+        // Triangulate
+        int numRows = numDivisions + 1;
+        for (int row = 0; row < numRows; row++) {
+            // vertices down left edge follow quadratic sequence: 0, 1, 3, 6, 10, 15...
+            // the nth term can be calculated with: (n^2 - n)/2
+            int topVertex = ((row + 1) * (row + 1) - row - 1) / 2;
+            int bottomVertex = ((row + 2) * (row + 2) - row - 2) / 2;
+
+            int numTrianglesInRow = 1 + 2 * row;
+            for (int column = 0; column < numTrianglesInRow; column++) {
+                int v0, v1, v2;
+
+                if (column % 2 == 0) {
+                    v0 = topVertex;
+                    v1 = bottomVertex + 1;
+                    v2 = bottomVertex;
+                    topVertex++;
+                    bottomVertex++;
+                } else {
+                    v0 = topVertex;
+                    v1 = bottomVertex;
+                    v2 = topVertex - 1;
+                }
+
+                triangles.Add (vertexMap.Items[v0]);
+                triangles.Add (vertexMap.Items[(reverse) ? v2 : v1]);
+                triangles.Add (vertexMap.Items[(reverse) ? v1 : v2]);
+            }
+        }
+
+    }
+
+    // Convenience classes:
+
+    private record Edge(int[] VertexIndices);
+
+    private class FixedSizeList<T>(int size)
+    {
+        public readonly T[] Items = new T[size];
+        public int NextIndex;
+
+        public void Add (T item) {
+            Items[NextIndex] = item;
+            NextIndex++;
+        }
+
+        public void AddRange (IEnumerable<T> items) {
+            foreach (var item in items) {
+                Add (item);
+            }
+        }
+    }
+
+}

src/Program.cs

@@ -1,4 +1,5 @@
 using Nebulix;
+using Silk.NET.Maths;
 
 namespace Engine_silk.NET;
 
@@ -6,7 +7,6 @@ using Engine_silk.NET.Textures;
 using Nebulix.InputSystem;
 using Nebulix.Rendering;
 using Silk.NET.Input;
-using Silk.NET.Maths;
 using Silk.NET.OpenGL;
 using Silk.NET.Windowing;
 using System;
@@ -19,7 +19,6 @@ using System.Numerics;
 // Next to do will be cleaning this up by creating a shader class and maybe even an engine class
 // IEngine -> IEngine.Create(WindowOptions) -> return OpenGLEngine/VulkanEngine maybe?
 
-using Vector3 = Silk.NET.Maths.Vector3D<float>;
 
 public static class Program
 {
@@ -33,7 +32,7 @@ public static class Program
 	private static Camera _cam;
 	private static Vector2 _lastMousePosition;
 	private static uint _vao, _vbo;
-	private static Sphere sphere;
+	private static IcoSphere sphere;
 
 	public static void Main(string[] args)
 	{
@@ -141,7 +140,7 @@ public static class Program
 		
 		
 		// Sphere
-		sphere = new Sphere(10);
+		sphere = new IcoSphere(10);
 		sphere.CreateSphere();
 		_sphereShader =
 			new Nebulix.Rendering.Shader(_gl, "./Shaders/Sphere/sphere.vert", "./Shaders/Sphere/sphere.frag");
@@ -180,7 +179,7 @@ public static class Program
 		var difference = (float)(_window.Time * 10);
 		var modelMatrix = Matrix4x4.CreateRotationY(Maths.Convert.ToRadians(difference)) * Matrix4x4.CreateRotationX(Maths.Convert.ToRadians(difference));
 		var viewMatrix = _cam.ViewMatrix;
-		var projectionMatrix = Matrix4X4.CreatePerspectiveFieldOfView(Maths.Convert.ToRadians(_cam.Fov), Width / (float)Height, 0.1f, 100.0f);
+		var projectionMatrix = Matrix4x4.CreatePerspectiveFieldOfView(Maths.Convert.ToRadians(_cam.Fov), Width / (float)Height, 0.1f, 100.0f);
 		
 		_shader.Use();
 		_shader.SetMatrix("modelMatrix", modelMatrix);

src/Sphere.cs

@@ -1,6 +1,6 @@
-using Nebulix;
+using System.Numerics;
+using Nebulix;
 using Nebulix.Rendering;
-using Silk.NET.Maths;
 using Silk.NET.OpenGL;
 
 namespace Engine_silk.NET
@@ -22,14 +22,14 @@ namespace Engine_silk.NET
 		public void CreateSphere()
 		{
 			// TODO: merge the individual meshes to one mesh
-			Vector3D<float>[] directions =
+			Vector3[] directions =
 			[
-				Vector3D<float>.UnitZ, -Vector3D<float>.UnitZ, 
-				Vector3D<float>.UnitY, -Vector3D<float>.UnitY,
-				Vector3D<float>.UnitX, -Vector3D<float>.UnitX
+				Vector3.UnitZ, -Vector3.UnitZ, 
+				Vector3.UnitY, -Vector3.UnitY,
+				Vector3.UnitX, -Vector3.UnitX
 			];
 
-			List<Vector3D<float>> vertices = new();
+			List<Vector3> vertices = new();
 			List<uint> indices = new();
 			for (int i = 0; i < directions.Length; i++)
 			{
@@ -64,24 +64,24 @@ namespace Engine_silk.NET
 		public Mesh Mesh => _mesh;
 
 		private readonly Mesh _mesh;
-		private readonly Vector3D<float> _localX;
-		private readonly Vector3D<float> _localY;
+		private readonly Vector3 _localX;
+		private readonly Vector3 _localY;
 
-		private readonly Vector3D<float> _localUp;
+		private readonly Vector3 _localUp;
 		private readonly uint _resolution;
 		
-		public Face(Vector3D<float> localUp, Mesh mesh, uint resolution)
+		public Face(Vector3 localUp, Mesh mesh, uint resolution)
 		{
 			_mesh = mesh;
 			_localX = new(localUp.Y, localUp.Z, localUp.X);
-			_localY = Vector3D.Cross(localUp, _localX);
+			_localY = Vector3.Cross(localUp, _localX);
 			_localUp = localUp;
 			_resolution = resolution;
 		}
 
 		internal void GenerateMesh()
 		{
-			var vertices = new Vector3D<float>[_resolution * _resolution];
+			var vertices = new Vector3[_resolution * _resolution];
 			// _resolution - 1 because the vertices index starts at 0 
 			// * 6 because each triangle needs 3 points and each small quad has 2 triangles 3*2 = 6
 			var indices = new uint[(_resolution - 1) * (_resolution - 1) * 6];
@@ -93,9 +93,9 @@ namespace Engine_silk.NET
 				for (uint x = 0; x < _resolution; x++)
 				{
 					i = x + y * _resolution;
-					Vector2D<float> percent = new Vector2D<float>(x, y) / (_resolution - 1);
+					Vector2 percent = new Vector2(x, y) / (_resolution - 1);
 					// place vertex on correct position of the plane to easily calculate indices
-					Vector3D<float> vertexPosition = _localUp + (percent.X - 0.5f) * 2 * _localX + (percent.Y - 0.5f) * 2 * _localY;
+					Vector3 vertexPosition = _localUp + (percent.X - 0.5f) * 2 * _localX + (percent.Y - 0.5f) * 2 * _localY;
 					vertices[i] = PointOnCubeToPointOnSphere(vertexPosition);
 
 					if (x != _resolution - 1 && y != _resolution - 1) // we didn't reach the bottom right point yet
@@ -121,7 +121,7 @@ namespace Engine_silk.NET
 
 		// Smooth mapping so that the points are not clumped on the former corners of the cube
 		// http://mathproofs.blogspot.com/2005/07/mapping-cube-to-sphere.html
-		private Vector3D<float> PointOnCubeToPointOnSphere(Vector3D<float> point)
+		private Vector3 PointOnCubeToPointOnSphere(Vector3 point)
 		{
 			float x2 = point.X * point.X;
 			float y2 = point.Y * point.Y;
@@ -129,7 +129,7 @@ namespace Engine_silk.NET
 			float newX = point.X * MathF.Sqrt(1 - y2 / 2 - z2 / 2 + (y2 * z2) / 3);
 			float newY = point.Y * MathF.Sqrt(1 - z2 / 2 - x2 / 2 + (z2 * x2) / 3);
 			float newZ = point.Z * MathF.Sqrt(1 - x2 / 2 - y2 / 2 + (x2 * y2) / 3);
-			return new Vector3D<float>(newX, newY, newZ);
+			return new Vector3(newX, newY, newZ);
 		}
 	}
 }