From ea60034a001497c38389b76a7cb4aa5c1a4d6d4a Mon Sep 17 00:00:00 2001
From: Daniel <danwip@hotmail.com>
Date: Sun, 7 Jan 2024 22:04:39 +0100
Subject: [PATCH] Improved quality of mapping points from cube to sphere

---
 src/Sphere.cs | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/src/Sphere.cs b/src/Sphere.cs
index f4667cd..1c8ebc0 100644
--- a/src/Sphere.cs
+++ b/src/Sphere.cs
@@ -85,7 +85,7 @@ namespace Engine_silk.NET
 					Vector2D<float> percent = new Vector2D<float>(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;
-					vertices[i] = Vector3D.Normalize(vertexPosition); // normalise vertex position to get it to be "on the sphere" and not "on the plane"
+					vertices[i] = ConvertToPointOnSphere(vertexPosition);
 
 					if (x != _resolution - 1 && y != _resolution - 1) // we didn't reach the bottom right point yet
 					{
@@ -107,5 +107,18 @@ namespace Engine_silk.NET
 			_mesh.Indices = indices;
 			_mesh.CalculateNormals();
 		}
+
+		// 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> ConvertToPointOnSphere(Vector3D<float> point)
+		{
+			float x2 = point.X * point.X;
+			float y2 = point.Y * point.Y;
+			float z2 = point.Z * point.Z;
+			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);
+		}
 	}
 }