Add Decomp3

Yes this is code duplication. But glam is not dimension-generic.

src/mathx.rs

@@ -1,4 +1,4 @@
-use glam::{FloatExt, Mat2, Mat3, Vec2};
+use glam::{FloatExt, Mat2, Mat3, Vec2, Vec3};
 
 mod bounds {
 	pub trait Pair<T> {}
@@ -93,6 +93,55 @@ where
 	}
 }
 
+/// Represents a 3×3 matrix decomposed as O^T D O, where O is orthogonal and D is diagonal.
+///
+/// Not every matrix can be decomposed like this, only that of a symmetric bilinear function.
+#[derive(Copy, Clone, Debug, PartialEq)]
+pub struct Decomp3 {
+	/// The orthogonal part.
+	///
+	/// Using a non-orthogonal matrix will yield to incorrect results (but no UB).
+	pub ortho: Mat3,
+
+	/// The diagonal part.
+	pub diag: Vec3,
+}
+
+impl Decomp3 {
+	/// Computes the square of this, more efficiently than doing that with a matrix.
+	pub fn square(&self) -> Self {
+		Self {
+			ortho: self.ortho,
+			diag: self.diag * self.diag,
+		}
+	}
+
+	/// Computes the inverse of this, more efficiently than doing that with a matrix.
+	pub fn inverse(&self) -> Self {
+		Self {
+			ortho: self.ortho,
+			diag: Vec3::splat(1.0) / self.diag,
+		}
+	}
+}
+
+impl From<Decomp3> for Mat3 {
+	fn from(value: Decomp3) -> Self {
+		value.ortho.transpose() * Mat3::from_diagonal(value.diag) * value.ortho
+	}
+}
+
+impl<T> std::ops::Mul<T> for Decomp3
+where
+	Mat3: std::ops::Mul<T>,
+{
+	type Output = <Mat3 as std::ops::Mul<T>>::Output;
+
+	fn mul(self, rhs: T) -> Self::Output {
+		Mat3::from(self) * rhs
+	}
+}
+
 #[cfg(test)]
 mod tests {
 	use super::*;