From 03b3caef8bff7df6b5c794abadb54802b66b37ae Mon Sep 17 00:00:00 2001
From: ickk <git@ickk.io>
Date: Sat, 4 May 2024 15:13:01 +1000
Subject: [PATCH] implement 4x4 `Matrix` as `Outermorphism` wip

- impl for `Scalar`, `Vector`, `Bivector`
---
 ega/src/lib.rs                   |   9 +++
 ega/src/outermorphisms/matrix.rs | 101 +++++++++++++++++++++++++++++++
 ega/src/outermorphisms/mod.rs    |  19 ++++++
 3 files changed, 129 insertions(+)
 create mode 100644 ega/src/outermorphisms/matrix.rs
 create mode 100644 ega/src/outermorphisms/mod.rs

diff --git a/ega/src/lib.rs b/ega/src/lib.rs
index 5c91a72..c8b306d 100644
--- a/ega/src/lib.rs
+++ b/ega/src/lib.rs
@@ -5,9 +5,11 @@ use ::libm::Libm;
 
 mod operators;
 mod optional_features;
+mod outermorphisms;
 mod values;
 
 pub use operators::*;
+pub use outermorphisms::*;
 pub use values::*;
 
 #[rustfmt::skip]
@@ -83,4 +85,11 @@ mod test_values {
   pub const PSEUDOSCALAR_A: Pseudoscalar = Pseudoscalar { e0123: 397. };
   pub const PSEUDOSCALAR_B: Pseudoscalar = Pseudoscalar { e0123: 401. };
   pub const PSEUDOSCALAR_C: Pseudoscalar = Pseudoscalar { e0123: -409. };
+
+  pub const MATRIX_A: Matrix = Matrix {
+    m00:  1.0, m01:  2.0, m02:  3.0, m03:  4.0,
+    m10:  5.0, m11:  6.0, m12:  7.0, m13:  8.0,
+    m20:  9.0, m21: 10.0, m22: 11.0, m23: 12.0,
+    m30: 13.0, m31: 14.0, m32: 15.0, m33: 16.0,
+  };
 }
diff --git a/ega/src/outermorphisms/matrix.rs b/ega/src/outermorphisms/matrix.rs
new file mode 100644
index 0000000..0be48d8
--- /dev/null
+++ b/ega/src/outermorphisms/matrix.rs
@@ -0,0 +1,101 @@
+use super::impl_outermorphism;
+use crate::*;
+
+/// A matrix whose column vectors have basis [e0, e1, e2, e3]
+///
+/// Note: This is different to matrices from other libraries, which often have
+/// a basis ordered more like [e1, e2, e3, e0] (homogeneous coordinates)
+#[rustfmt::skip]
+#[derive(Debug, Copy, Clone)]
+pub struct Matrix {
+  pub m00: f32, pub m01: f32, pub m02: f32, pub m03: f32,
+  pub m10: f32, pub m11: f32, pub m12: f32, pub m13: f32,
+  pub m20: f32, pub m21: f32, pub m22: f32, pub m23: f32,
+  pub m30: f32, pub m31: f32, pub m32: f32, pub m33: f32,
+}
+
+impl_outermorphism! { matrix_morph_scalar: Matrix, Scalar => Scalar }
+impl_outermorphism! { matrix_morph_vector: Matrix, Vector => Vector }
+impl_outermorphism! { matrix_morph_bivector: Matrix, Bivector => Bivector }
+
+fn matrix_morph_scalar(_: Matrix, s: Scalar) -> Scalar {
+  s
+}
+
+#[rustfmt::skip]
+fn matrix_morph_vector(m: Matrix, v: Vector) -> Vector {
+  let Matrix {
+    m00, m01, m02, m03,
+    m10, m11, m12, m13,
+    m20, m21, m22, m23,
+    m30, m31, m32, m33,
+  } = m;
+  let Vector { e0: v0, e1: v1, e2: v2, e3: v3 } = v;
+
+  let e0 = m00*v0 + m01*v1 + m02*v2 + m03*v3;
+  let e1 = m10*v0 + m11*v1 + m12*v2 + m13*v3;
+  let e2 = m20*v0 + m21*v1 + m22*v2 + m23*v3;
+  let e3 = m30*v0 + m31*v1 + m32*v2 + m33*v3;
+
+  Vector { e0, e1, e2, e3 }
+}
+
+#[rustfmt::skip]
+fn matrix_morph_bivector(m: Matrix, b: Bivector) -> Bivector {
+  let Matrix {
+    m00, m01, m02, m03,
+    m10, m11, m12, m13,
+    m20, m21, m22, m23,
+    m30, m31, m32, m33,
+  } = m;
+  let Bivector {
+    e23: b23, e31: b31, e12: b12,
+    e01: b01, e02: b02, e03: b03,
+  } = b;
+
+  let w1 =  m11*b01 + m12*b02 + m13*b03;
+  let x1 = -m10*b01 + m12*b12 - m13*b31;
+  let y1 = -m10*b02 - m11*b12 + m13*b23;
+  let z1 = -m10*b03 + m11*b31 - m12*b23;
+
+  let w2 =  m21*b01 + m22*b02 + m23*b03;
+  let x2 = -m20*b01 + m22*b12 - m23*b31;
+  let y2 = -m20*b02 - m21*b12 + m23*b23;
+  let z2 = -m20*b03 + m21*b31 - m22*b23;
+
+  let w3 =  m31*b01 + m32*b02 + m33*b03;
+  let x3 = -m30*b01 + m32*b12 - m33*b31;
+  let y3 = -m30*b02 - m31*b12 + m33*b23;
+  let z3 = -m30*b03 + m31*b31 - m32*b23;
+
+  let e23 = m20*w3 + m21*x3 + m22*y3 + m23*z3;
+  let e31 = m30*w1 + m31*x1 + m32*y1 + m33*z1;
+  let e12 = m10*w2 + m11*x2 + m12*y2 + m13*z2;
+  let e01 = m00*w1 + m01*x1 + m02*y1 + m03*z1;
+  let e02 = m00*w2 + m01*x2 + m02*y2 + m03*z2;
+  let e03 = m00*w3 + m01*x3 + m02*y3 + m03*z3;
+
+  Bivector { e23, e31, e12, e01, e02, e03 }
+}
+
+#[rustfmt::skip]
+#[cfg(any(test, doctest))]
+mod tests {
+  use super::*;
+  use crate::test_values::*;
+
+  #[test]
+  fn matrix_morph_vector() {
+    let result = MATRIX_A.morph(VECTOR_A);
+    let expected = Vector { e0: 1622., e1: 4174., e2: 6726., e3: 9278. };
+    assert_eq!(dbg!(result), dbg!(expected));
+  }
+
+  #[test]
+  fn matrix_morph_bivector() {
+    let a = Meet::meet(MATRIX_A.morph(VECTOR_A), MATRIX_A.morph(VECTOR_B));
+    let b = MATRIX_A.morph(Meet::meet(VECTOR_A, VECTOR_B));
+
+    assert_eq!(dbg!(a), dbg!(b));
+  }
+}
diff --git a/ega/src/outermorphisms/mod.rs b/ega/src/outermorphisms/mod.rs
new file mode 100644
index 0000000..189e33b
--- /dev/null
+++ b/ega/src/outermorphisms/mod.rs
@@ -0,0 +1,19 @@
+mod matrix;
+pub use matrix::Matrix;
+
+/// A linear mapping extended to multivectors
+pub trait Outermorphism<Arg> {
+  fn morph(self, arg: Arg) -> Arg;
+}
+
+macro_rules! impl_outermorphism {
+  ($morph_fn:ident: $morph:ty, $arg:ty => $ret:ty) => {
+    impl crate::Outermorphism<$arg> for $morph {
+      #[inline]
+      fn morph(self, arg: $arg) -> $ret {
+        $morph_fn(self, arg)
+      }
+    }
+  };
+}
+pub(crate) use impl_outermorphism;