From c1570b74e1e6d1dc90b06edf92b8b6df446279ec Mon Sep 17 00:00:00 2001
From: That_One_Nerd <dev@that-one-nerd.net>
Date: Tue, 5 Sep 2023 13:54:33 -0400
Subject: [PATCH] Isometrics work now.

---
 .../Mathematics/Algebra/ProjectionMatrix.cs   | 22 +++++++++++++++----
 Nerd_STF/Mathematics/Samples/Constants.cs     |  4 ++++
 2 files changed, 22 insertions(+), 4 deletions(-)

diff --git a/Nerd_STF/Mathematics/Algebra/ProjectionMatrix.cs b/Nerd_STF/Mathematics/Algebra/ProjectionMatrix.cs
index b165cd1..a4a8c2c 100644
--- a/Nerd_STF/Mathematics/Algebra/ProjectionMatrix.cs
+++ b/Nerd_STF/Mathematics/Algebra/ProjectionMatrix.cs
@@ -40,13 +40,27 @@ public class ProjectionMatrix : Matrix3x3
     public ProjectionMatrix(Fill<int> r1, Fill<int> r2, Fill<int> r3)
         : this(r1(0), r1(1), r1(2), r2(0), r2(1), r2(2), r3(0), r3(1), r3(2)) { }
 
-    public static ProjectionMatrix SingleViewProjection(CrossSection2d section) => new(new[,]
+    public static ProjectionMatrix Orthographic(CrossSection2d section) => new(new[,]
     {
         { section == CrossSection2d.XY || section == CrossSection2d.ZX ? 1 : 0, 0, 0 },
         { 0, section == CrossSection2d.XY || section == CrossSection2d.YZ ? 1 : 0, 0 },
         { 0, 0, section == CrossSection2d.YZ || section == CrossSection2d.ZX ? 1 : 0 }
     });
-    public static ProjectionMatrix IsometricProjection(Angle alpha, Angle beta)
+
+    public static ProjectionMatrix Isometric()
+    {
+        const float invSqrt2   = 0.707106781187f,
+                    invSqrt3   = 0.57735026919f,
+                    invSqrt6   = 0.408248290464f,
+                    invSqrt6_2 = 0.816496580928f;
+        return new(new[,]
+        {
+            { invSqrt2,          0, -invSqrt2 },
+            { invSqrt6, invSqrt6_2,  invSqrt6 },
+            {        0,          0,         0 },
+        });
+    }
+    public static ProjectionMatrix Isometric(Angle alpha, Angle beta)
     {
         Matrix3x3 alphaMat = new(new[,]
         {
@@ -66,8 +80,8 @@ public class ProjectionMatrix : Matrix3x3
             { 0, 1, 0 },
             { 0, 0, 0 }
         });
-        Matrix3x3 result = alphaMat * betaMat * flatten;
-        return new(result.ToFill2D());
+        Matrix3x3 result = (alphaMat * betaMat).Transpose() * flatten;
+        return new(result.Transpose().ToFill2D());
     }
 
     public Fill<Float3> Project(Fill<Float3> toProject) => i => this * toProject(i);
diff --git a/Nerd_STF/Mathematics/Samples/Constants.cs b/Nerd_STF/Mathematics/Samples/Constants.cs
index 418a349..9c9f57e 100644
--- a/Nerd_STF/Mathematics/Samples/Constants.cs
+++ b/Nerd_STF/Mathematics/Samples/Constants.cs
@@ -67,6 +67,10 @@ public static class Constants
     public const float Tan60Deg = Sqrt3;
     public const float Tan90Deg = float.PositiveInfinity;
 
+    public static readonly Angle IsometricAngle = (35.2643896828f, Angle.Type.Degrees);
+    public const float IsometricCos = 0.816496580928f;
+    public const float IsometricSin = 0.57737026919f;
+
     public const float AperyConstant = 1.2020569031f;
     public const float ArtinConstant = 0.3739558136f;
     public const float AsymptoticLebesgueConstant = 0.9894312738f;