Added Quaternions

2026-09-05 21:01:52 +00:00 · 2021-08-25 22:19:02 +02:00
parent e239de52d6
commit 9dbf9fd501
2 changed files with 251 additions and 0 deletions
@@ -0,0 +1,41 @@
+using System;
+using GlitchyEngine.Math;
+using GlitchyEngine;
+
+namespace DirectX.Math
+{
+	extension Matrix
+	{
+		public static Self RotationQuaternion(Quaternion quat)
+		{
+			float xSq = quat.X * quat.X;
+			float ySq = quat.Y * quat.Y;
+			float zSq = quat.Z * quat.Z;
+
+			float xy = quat.X * quat.Y;
+			float xz = quat.X * quat.Z;
+			float xw = quat.X * quat.W;
+			float yz = quat.Y * quat.Z;
+			float yw = quat.Y * quat.W;
+			float zw = quat.Z * quat.W;
+
+			Self result = .(
+				1 - 2 * ySq - 2 * zSq, 2 * xy + 2 * zw, 2 * xz - 2 * yw, 0,
+				2 * xy - 2 * zw, 1 - 2 * xSq - 2 * zSq, 2 * yz + 2 * xw, 0,
+				2 * xz + 2 * yw, 2 * yz - 2 * xw, 1 - 2 * xSq - 2 * ySq, 0,
+				0, 0, 0, 1);
+
+			return result;
+		}
+
+		/*[Test]
+		static void TestQuaternionToMatrix()
+		{
+			// Rotation around Z-Axis by 90°
+			Quaternion quat = .(0, 0, 0.707107f, 0.707107f);
+			quat.Normalize();
+
+
+		}*/
+	}
+}
@@ -0,0 +1,210 @@
+using System;
+
+namespace GlitchyEngine.Math
+{
+	public struct Quaternion
+	{
+		public const Quaternion Zero = .();
+		public const Quaternion One = .(1.0f, 1.0f, 1.0f, 1.0f);
+		public const Quaternion Identity = .(0.0f, 0.0f, 0.0f, 1.0f);
+
+		// qv: (X, Y, Z), sv: W
+		public float X, Y, Z, W;
+
+		public this() => this = default;
+		
+		public this(float x, float y, float z, float w)
+		{
+			X = x;
+			Y = y;
+			Z = z;
+			W = w;
+		}
+
+		public this(Vector3 xy, float z, float w)
+		{
+			X = xy.X;
+			Y = xy.Y;
+			Z = z;
+			W = w;
+		}
+
+		public this(Vector3 xyz, float w)
+		{
+			X = xyz.X;
+			Y = xyz.Y;
+			Z = xyz.Z;
+			W = w;
+		}
+		
+		public this(Vector4 vector)
+		{
+			X = vector.X;
+			Y = vector.Y;
+			Z = vector.Z;
+			W = vector.W;
+		}
+
+		public Vector3 Axis => .(X, Y, Z);
+		public float Scalar => W;
+
+		public void Normalize() mut
+		{
+			float invLength = 1.0f / Length();
+
+			X *= invLength;
+			Y *= invLength;
+			Z *= invLength;
+			W *= invLength;
+		}
+
+		public static Quaternion Normalize(Quaternion q)
+		{
+			float invLength = 1.0f / Length(q);
+
+			return Quaternion(q.X * invLength, q.Y * invLength, q.Z * invLength, q.W * invLength);
+		}
+
+		public float Length()
+		{
+			return Math.Sqrt([Inline]LengthSquared());
+		}
+
+		public static float Length(Quaternion q)
+		{
+			return Math.Sqrt([Inline]LengthSquared(q));
+		}
+		
+		public float LengthSquared()
+		{
+			return X * X + Y * Y + Z * Z + W * W;
+		}
+
+		public static float LengthSquared(Quaternion q)
+		{
+			return q.X * q.X + q.Y * q.Y + q.Z * q.Z + q.W * q.W;
+		}
+		
+		public static float Dot(Self l, Self r)
+		{
+			return l.X * r.X + l.Y * r.Y + l.Z * r.Z + l.W * r.W;
+		}
+		
+		public static Quaternion Lerp(Quaternion a, Quaternion b, float interpolationValue)
+		{
+			return a + interpolationValue * (b - a);
+		}
+
+		public static Quaternion Slerp(Quaternion previousQuaternion, Quaternion nextQuaternion, float interpolationValue)
+		{
+			// Based on https://github.com/KhronosGroup/glTF-Tutorials/blob/master/gltfTutorial/gltfTutorial_007_Animations.md
+
+			var nextQuaternion;
+
+			float dot = Dot(previousQuaternion, nextQuaternion);
+			
+			//make sure we take the shortest path in case dot Product is negative
+			if(dot < 0.0f)
+			{
+				nextQuaternion = -nextQuaternion;
+				dot = -dot;
+			}
+			    
+			//if the two quaternions are too close to each other, just linear interpolate between the 4D vector
+			if(dot > 0.9995f)
+			    return Normalize(previousQuaternion + interpolationValue * (nextQuaternion - previousQuaternion));
+
+			//perform the spherical linear interpolation
+			var theta_0 = Math.Acos(dot);
+			var theta = interpolationValue * theta_0;
+			var sin_theta = Math.Sin(theta);
+			var sin_theta_0 = Math.Sin(theta_0);
+
+			var scalePreviousQuat = Math.Cos(theta) - dot * sin_theta / sin_theta_0;
+			var scaleNextQuat = sin_theta / sin_theta_0;
+			return scalePreviousQuat * previousQuaternion + scaleNextQuat * nextQuaternion;
+		}
+
+		public static Quaternion FromMatrix(Matrix matrix)
+		{
+			// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
+
+			var m = matrix.V;
+
+			Quaternion result = ?;
+
+			float tr = m._11 + m._22 + m._33;
+
+			if (tr > 0) { 
+			  float S = Math.Sqrt(tr + 1.0f) * 2f; // S=4*result.W 
+			  result.W = 0.25f * S;
+			  result.X = (m._32 - m._23) / S;
+			  result.Y = (m._13 - m._31) / S; 
+			  result.Z = (m._21 - m._12) / S; 
+			} else if ((m._11 > m._22)&(m._11 > m._33)) { 
+			  float S = Math.Sqrt(1.0f + m._11 - m._22 - m._33) * 2f; // S=4*result.X 
+			  result.W = (m._32 - m._23) / S;
+			  result.X = 0.25f * S;
+			  result.Y = (m._12 + m._21) / S; 
+			  result.Z = (m._13 + m._31) / S; 
+			} else if (m._22 > m._33) { 
+			  float S = Math.Sqrt(1.0f + m._22 - m._11 - m._33) * 2f; // S=4*result.Y
+			  result.W = (m._13 - m._31) / S;
+			  result.X = (m._12 + m._21) / S; 
+			  result.Y = 0.25f * S;
+			  result.Z = (m._23 + m._32) / S; 
+			} else { 
+			  float S = Math.Sqrt(1.0f + m._33 - m._11 - m._22) * 2f; // S=4*result.Z
+			  result.W = (m._21 - m._12) / S;
+			  result.X = (m._13 + m._31) / S;
+			  result.Y = (m._23 + m._32) / S;
+			  result.Z = 0.25f * S;
+			}
+
+			return result;
+		}
+		
+		public static Self operator +(Self value) => value;
+
+		public static Self operator +(Self l, Self r) => Self(l.X + r.X, l.Y + r.Y, l.Z + r.Z, l.W + r.W);
+
+		public static Self operator -(Self value) => Self(-value.X, -value.Y, -value.Z, -value.W);
+		
+		public static Self operator -(Self l, Self r) => Self(l.X - r.X, l.Y - r.Y, l.Z - r.Z, l.W - r.W);
+
+		public static Self operator *(float l, Self r) => Self(l * r.X, l * r.Y, l * r.Z, l * r.W);
+
+
+		[Inline]
+		public static implicit operator Vector4(in Self value) => *(Vector4*)&value;
+
+		[Inline]
+		public static implicit operator Quaternion(in Vector4 value) => *(Quaternion*)&value;
+
+		//public static Quaternion operator +(Self left, Self right) => return .();
+
+		/*
+		public static Quaternion Conjugate(Quaternion q)
+		{
+			return Quaternion(-q.Axis, q.Scalar);
+		}
+
+		public static Quaternion Inverse(Quaternion q)
+		{
+			Quaternion conjugate = Conjugate(q);
+
+			float magSquared = LengthSquared(q);
+
+			return Quaternion(conjugate / magSquared);
+		}
+
+		public static Quaternion operator *(Quaternion left, Quaternion right)
+		{
+			return Quaternion(left.Scalar * right.Axis + right.Scalar * left.Axis + Vector3.Cross(left.Axis, right.Axis),
+				left.Scalar * right.Scalar - Vector3.Dot(left.Axis, right.Axis));
+		}
+		*/
+
+		//public static Quaternion operator /(Quaternion left, float right) => Quaternion(left.X / right, left.Y / right, left.Z / right, left.W / right);
+	}
+}