From e3eb04422eaeb5e7b777f0377448956a70537549 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:41:37 +0100
Subject: [PATCH 01/21] Ease requirements on `Arc`'s start/end angles

Don't require `start < end`. The rest of the system doesn't need this,
and it makes `Arc` itself simpler.
---
 crates/fj-kernel/src/builder/edge.rs |  8 ++---
 crates/fj-math/src/arc.rs            | 48 +++++++---------------------
 2 files changed, 13 insertions(+), 43 deletions(-)

diff --git a/crates/fj-kernel/src/builder/edge.rs b/crates/fj-kernel/src/builder/edge.rs
index 6ad4a737f..87c4fb2fb 100644
--- a/crates/fj-kernel/src/builder/edge.rs
+++ b/crates/fj-kernel/src/builder/edge.rs
@@ -119,12 +119,8 @@ impl HalfEdgeBuilder for PartialHalfEdge {
             .write()
             .update_as_circle_from_center_and_radius(arc.center, arc.radius);
 
-        let [a_curve, b_curve] = if arc.flipped_construction {
-            [arc.end_angle, arc.start_angle]
-        } else {
-            [arc.start_angle, arc.end_angle]
-        }
-        .map(|coord| Point::from([coord]));
+        let [a_curve, b_curve] =
+            [arc.start_angle, arc.end_angle].map(|coord| Point::from([coord]));
 
         for (vertex, point_curve) in
             self.vertices.each_mut_ext().zip_ext([a_curve, b_curve])
diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 0cd991056..b7baee920 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -19,9 +19,6 @@ pub struct Arc {
     ///
     /// Guaranteed to be greater than `end_angle`.
     pub end_angle: Scalar,
-
-    /// True if `start` and `end` were switched to ensure `end_angle` > `start_angle`
-    pub flipped_construction: bool,
 }
 
 impl Arc {
@@ -46,17 +43,15 @@ impl Arc {
         let flipped_construction = angle_rad <= Scalar::ZERO;
         let angle_rad = angle_rad.abs();
 
-        let [p0, p1] = if flipped_construction {
-            [p1, p0]
-        } else {
-            [p0, p1]
-        };
-
-        let (uv_factor, end_angle_offset) = if angle_rad > Scalar::PI {
+        let (mut uv_factor, end_angle_offset) = if angle_rad > Scalar::PI {
             (Scalar::from_f64(-1.), Scalar::TAU)
         } else {
             (Scalar::ONE, Scalar::ZERO)
         };
+        if flipped_construction {
+            uv_factor *= -1.;
+        }
+
         let unit_vector_p0_to_p1 =
             (p1 - p0) / distance_between_endpoints * uv_factor;
         let unit_vector_midpoint_to_center =
@@ -78,7 +73,6 @@ impl Arc {
             radius,
             start_angle,
             end_angle,
-            flipped_construction,
         }
     }
 }
@@ -143,7 +137,6 @@ mod tests {
 
         dbg!(arc.start_angle);
         dbg!(arc.end_angle);
-        dbg!(arc.flipped_construction);
         assert_abs_diff_eq!(arc.center, center, epsilon = epsilon);
         assert_abs_diff_eq!(
             arc.radius,
@@ -151,30 +144,11 @@ mod tests {
             epsilon = epsilon
         );
 
-        if a0 < a1 {
-            assert!(!arc.flipped_construction);
-            assert_abs_diff_eq!(
-                arc.start_angle,
-                Scalar::from(a0),
-                epsilon = epsilon
-            );
-            assert_abs_diff_eq!(
-                arc.end_angle,
-                Scalar::from(a1),
-                epsilon = epsilon
-            );
-        } else {
-            assert!(arc.flipped_construction);
-            assert_abs_diff_eq!(
-                arc.end_angle,
-                Scalar::from(a0),
-                epsilon = epsilon
-            );
-            assert_abs_diff_eq!(
-                arc.start_angle,
-                Scalar::from(a1),
-                epsilon = epsilon
-            );
-        }
+        assert_abs_diff_eq!(
+            arc.start_angle,
+            Scalar::from(a0),
+            epsilon = epsilon
+        );
+        assert_abs_diff_eq!(arc.end_angle, Scalar::from(a1), epsilon = epsilon);
     }
 }

From 92e85e408dd166539f1ecc20be6b142293925777 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:42:42 +0100
Subject: [PATCH 02/21] Update doc comments

---
 crates/fj-math/src/arc.rs | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index b7baee920..2fa759129 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -11,13 +11,9 @@ pub struct Arc {
     pub radius: Scalar,
 
     /// Angle of `start` relative to `center`, in radians
-    ///
-    /// Guaranteed to be less than `end_angle`.
     pub start_angle: Scalar,
 
     /// Angle of `end` relative to `center`, in radians
-    ///
-    /// Guaranteed to be greater than `end_angle`.
     pub end_angle: Scalar,
 }
 

From bc71fc79cc25c84629807e66f8934dd5e9845cb4 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:44:57 +0100
Subject: [PATCH 03/21] Inline variable

---
 crates/fj-math/src/arc.rs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 2fa759129..412a11788 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -37,9 +37,9 @@ impl Arc {
             (radius.powi(2) - (distance_between_endpoints.powi(2) / 4.)).sqrt();
 
         let flipped_construction = angle_rad <= Scalar::ZERO;
-        let angle_rad = angle_rad.abs();
 
-        let (mut uv_factor, end_angle_offset) = if angle_rad > Scalar::PI {
+        let (mut uv_factor, end_angle_offset) = if angle_rad.abs() > Scalar::PI
+        {
             (Scalar::from_f64(-1.), Scalar::TAU)
         } else {
             (Scalar::ONE, Scalar::ZERO)

From 9d9a5ea6762a5de854d5c12e4d87852eae3add62 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:45:46 +0100
Subject: [PATCH 04/21] Inline variable

---
 crates/fj-math/src/arc.rs | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 412a11788..8758cb236 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -36,15 +36,13 @@ impl Arc {
         let distance_center_to_midpoint =
             (radius.powi(2) - (distance_between_endpoints.powi(2) / 4.)).sqrt();
 
-        let flipped_construction = angle_rad <= Scalar::ZERO;
-
         let (mut uv_factor, end_angle_offset) = if angle_rad.abs() > Scalar::PI
         {
             (Scalar::from_f64(-1.), Scalar::TAU)
         } else {
             (Scalar::ONE, Scalar::ZERO)
         };
-        if flipped_construction {
+        if angle_rad <= Scalar::ZERO {
             uv_factor *= -1.;
         }
 

From ebbab66f64ed053a1c059ceae755b6fcd8302ed0 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:50:45 +0100
Subject: [PATCH 05/21] Refactor

---
 crates/fj-math/src/arc.rs | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 8758cb236..42f0809d4 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -36,8 +36,9 @@ impl Arc {
         let distance_center_to_midpoint =
             (radius.powi(2) - (distance_between_endpoints.powi(2) / 4.)).sqrt();
 
-        let (mut uv_factor, end_angle_offset) = if angle_rad.abs() > Scalar::PI
-        {
+        let angle_more_than_half_turn = angle_rad.abs() > Scalar::PI;
+
+        let (mut uv_factor, end_angle_offset) = if angle_more_than_half_turn {
             (Scalar::from_f64(-1.), Scalar::TAU)
         } else {
             (Scalar::ONE, Scalar::ZERO)

From 51947428a8f5df1d0436f1d49e39825bf48a71b1 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:51:33 +0100
Subject: [PATCH 06/21] Refactor

---
 crates/fj-math/src/arc.rs | 17 +++++++++++------
 1 file changed, 11 insertions(+), 6 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 42f0809d4..d32c586f3 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -38,14 +38,19 @@ impl Arc {
 
         let angle_more_than_half_turn = angle_rad.abs() > Scalar::PI;
 
-        let (mut uv_factor, end_angle_offset) = if angle_more_than_half_turn {
-            (Scalar::from_f64(-1.), Scalar::TAU)
+        let uv_factor =
+            match (angle_rad <= Scalar::ZERO, angle_more_than_half_turn) {
+                (false, false) => Scalar::ONE,
+                (false, true) => -Scalar::ONE,
+                (true, false) => -Scalar::ONE,
+                (true, true) => Scalar::ONE,
+            };
+
+        let end_angle_offset = if angle_more_than_half_turn {
+            Scalar::TAU
         } else {
-            (Scalar::ONE, Scalar::ZERO)
+            Scalar::ZERO
         };
-        if angle_rad <= Scalar::ZERO {
-            uv_factor *= -1.;
-        }
 
         let unit_vector_p0_to_p1 =
             (p1 - p0) / distance_between_endpoints * uv_factor;

From 522156f592672fbfdf0688de6f0ca0ead4462428 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:54:05 +0100
Subject: [PATCH 07/21] Refactor

---
 crates/fj-math/src/arc.rs | 41 +++++++++++++++++++++++----------------
 1 file changed, 24 insertions(+), 17 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index d32c586f3..234733362 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -33,18 +33,33 @@ impl Arc {
         let distance_between_endpoints = (p1 - p0).magnitude();
         let radius = distance_between_endpoints
             / (2. * (angle_rad.abs().into_f64() / 2.).sin());
-        let distance_center_to_midpoint =
-            (radius.powi(2) - (distance_between_endpoints.powi(2) / 4.)).sqrt();
 
         let angle_more_than_half_turn = angle_rad.abs() > Scalar::PI;
 
-        let uv_factor =
-            match (angle_rad <= Scalar::ZERO, angle_more_than_half_turn) {
-                (false, false) => Scalar::ONE,
-                (false, true) => -Scalar::ONE,
-                (true, false) => -Scalar::ONE,
-                (true, true) => Scalar::ONE,
-            };
+        let center = {
+            let uv_factor =
+                match (angle_rad <= Scalar::ZERO, angle_more_than_half_turn) {
+                    (false, false) => Scalar::ONE,
+                    (false, true) => -Scalar::ONE,
+                    (true, false) => -Scalar::ONE,
+                    (true, true) => Scalar::ONE,
+                };
+
+            let unit_vector_p0_to_p1 =
+                (p1 - p0) / distance_between_endpoints * uv_factor;
+
+            let unit_vector_midpoint_to_center =
+                Vector::from([-unit_vector_p0_to_p1.v, unit_vector_p0_to_p1.u]);
+            let distance_center_to_midpoint = (radius.powi(2)
+                - (distance_between_endpoints.powi(2) / 4.))
+                .sqrt();
+
+            Point {
+                coords: (p0.coords + p1.coords) / 2.
+                    + unit_vector_midpoint_to_center
+                        * distance_center_to_midpoint,
+            }
+        };
 
         let end_angle_offset = if angle_more_than_half_turn {
             Scalar::TAU
@@ -52,14 +67,6 @@ impl Arc {
             Scalar::ZERO
         };
 
-        let unit_vector_p0_to_p1 =
-            (p1 - p0) / distance_between_endpoints * uv_factor;
-        let unit_vector_midpoint_to_center =
-            Vector::from([-unit_vector_p0_to_p1.v, unit_vector_p0_to_p1.u]);
-        let center = Point {
-            coords: (p0.coords + p1.coords) / 2.
-                + unit_vector_midpoint_to_center * distance_center_to_midpoint,
-        };
         let start_angle = {
             let center_to_start = p0 - center;
             center_to_start.v.atan2(center_to_start.u)

From 8c96af536c31480f6ca7f7ebf319b12aebb3aac4 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:54:23 +0100
Subject: [PATCH 08/21] Simplify variable name

---
 crates/fj-math/src/arc.rs | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 234733362..681b1215b 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -37,16 +37,16 @@ impl Arc {
         let angle_more_than_half_turn = angle_rad.abs() > Scalar::PI;
 
         let center = {
-            let uv_factor =
-                match (angle_rad <= Scalar::ZERO, angle_more_than_half_turn) {
-                    (false, false) => Scalar::ONE,
-                    (false, true) => -Scalar::ONE,
-                    (true, false) => -Scalar::ONE,
-                    (true, true) => Scalar::ONE,
-                };
+            let f = match (angle_rad <= Scalar::ZERO, angle_more_than_half_turn)
+            {
+                (false, false) => Scalar::ONE,
+                (false, true) => -Scalar::ONE,
+                (true, false) => -Scalar::ONE,
+                (true, true) => Scalar::ONE,
+            };
 
             let unit_vector_p0_to_p1 =
-                (p1 - p0) / distance_between_endpoints * uv_factor;
+                (p1 - p0) / distance_between_endpoints * f;
 
             let unit_vector_midpoint_to_center =
                 Vector::from([-unit_vector_p0_to_p1.v, unit_vector_p0_to_p1.u]);

From a6683aa19fd69e40c7d7fcd286be08b3f3bee032 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:54:38 +0100
Subject: [PATCH 09/21] Simplify variable name

---
 crates/fj-math/src/arc.rs | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 681b1215b..aa95a4cab 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -34,11 +34,10 @@ impl Arc {
         let radius = distance_between_endpoints
             / (2. * (angle_rad.abs().into_f64() / 2.).sin());
 
-        let angle_more_than_half_turn = angle_rad.abs() > Scalar::PI;
+        let more_than_half_turn = angle_rad.abs() > Scalar::PI;
 
         let center = {
-            let f = match (angle_rad <= Scalar::ZERO, angle_more_than_half_turn)
-            {
+            let f = match (angle_rad <= Scalar::ZERO, more_than_half_turn) {
                 (false, false) => Scalar::ONE,
                 (false, true) => -Scalar::ONE,
                 (true, false) => -Scalar::ONE,
@@ -61,7 +60,7 @@ impl Arc {
             }
         };
 
-        let end_angle_offset = if angle_more_than_half_turn {
+        let end_angle_offset = if more_than_half_turn {
             Scalar::TAU
         } else {
             Scalar::ZERO

From dc2bfaa0bd105a84ae071d0eb542f243617c2097 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:55:09 +0100
Subject: [PATCH 10/21] Refactor

---
 crates/fj-math/src/arc.rs | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index aa95a4cab..75173f9cf 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -34,10 +34,11 @@ impl Arc {
         let radius = distance_between_endpoints
             / (2. * (angle_rad.abs().into_f64() / 2.).sin());
 
+        let clockwise_turn = angle_rad <= Scalar::ZERO;
         let more_than_half_turn = angle_rad.abs() > Scalar::PI;
 
         let center = {
-            let f = match (angle_rad <= Scalar::ZERO, more_than_half_turn) {
+            let f = match (clockwise_turn, more_than_half_turn) {
                 (false, false) => Scalar::ONE,
                 (false, true) => -Scalar::ONE,
                 (true, false) => -Scalar::ONE,

From db4a0d5ffa2cbaf92c2d4c4ce0476a9317e86fb3 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:55:39 +0100
Subject: [PATCH 11/21] Simplify match

---
 crates/fj-math/src/arc.rs | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 75173f9cf..8b90c0a43 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -39,10 +39,8 @@ impl Arc {
 
         let center = {
             let f = match (clockwise_turn, more_than_half_turn) {
-                (false, false) => Scalar::ONE,
-                (false, true) => -Scalar::ONE,
-                (true, false) => -Scalar::ONE,
-                (true, true) => Scalar::ONE,
+                (false, false) | (true, true) => Scalar::ONE,
+                (false, true) | (true, false) => -Scalar::ONE,
             };
 
             let unit_vector_p0_to_p1 =

From 616a2b01e0854a892f098589d0f2279a2dd65c5a Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:56:27 +0100
Subject: [PATCH 12/21] Refactor

---
 crates/fj-math/src/arc.rs | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 8b90c0a43..add8c1d7a 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -59,18 +59,18 @@ impl Arc {
             }
         };
 
-        let end_angle_offset = if more_than_half_turn {
-            Scalar::TAU
-        } else {
-            Scalar::ZERO
-        };
-
         let start_angle = {
             let center_to_start = p0 - center;
             center_to_start.v.atan2(center_to_start.u)
         };
         let end_angle = {
             let center_to_end = p1 - center;
+            let end_angle_offset = if more_than_half_turn {
+                Scalar::TAU
+            } else {
+                Scalar::ZERO
+            };
+
             center_to_end.v.atan2(center_to_end.u) + end_angle_offset
         };
         Self {

From 753dfe359a1e067af4ea3c66038aae958d42a643 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:56:42 +0100
Subject: [PATCH 13/21] Simplify variable name

---
 crates/fj-math/src/arc.rs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index add8c1d7a..952e2b5d7 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -65,13 +65,13 @@ impl Arc {
         };
         let end_angle = {
             let center_to_end = p1 - center;
-            let end_angle_offset = if more_than_half_turn {
+            let offset = if more_than_half_turn {
                 Scalar::TAU
             } else {
                 Scalar::ZERO
             };
 
-            center_to_end.v.atan2(center_to_end.u) + end_angle_offset
+            center_to_end.v.atan2(center_to_end.u) + offset
         };
         Self {
             center,

From 4794b3d2517d78c3ba103dfc63a3bd88cf2c7b37 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:57:06 +0100
Subject: [PATCH 14/21] Simplify variable name

---
 crates/fj-math/src/arc.rs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 952e2b5d7..11eabe70a 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -64,14 +64,14 @@ impl Arc {
             center_to_start.v.atan2(center_to_start.u)
         };
         let end_angle = {
-            let center_to_end = p1 - center;
+            let from_center = p1 - center;
             let offset = if more_than_half_turn {
                 Scalar::TAU
             } else {
                 Scalar::ZERO
             };
 
-            center_to_end.v.atan2(center_to_end.u) + offset
+            from_center.v.atan2(from_center.u) + offset
         };
         Self {
             center,

From a02f31cb113cd0360507fb9022c40629a8206a12 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:57:17 +0100
Subject: [PATCH 15/21] Simplify variable name

---
 crates/fj-math/src/arc.rs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 11eabe70a..e5271df8b 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -60,8 +60,8 @@ impl Arc {
         };
 
         let start_angle = {
-            let center_to_start = p0 - center;
-            center_to_start.v.atan2(center_to_start.u)
+            let from_center = p0 - center;
+            from_center.v.atan2(from_center.u)
         };
         let end_angle = {
             let from_center = p1 - center;

From 521f1ab550f77618f973f612d1b5cba373c14f3a Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:57:54 +0100
Subject: [PATCH 16/21] Improve wording in comment

---
 crates/fj-math/src/arc.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index e5271df8b..1549b0717 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -27,7 +27,7 @@ impl Arc {
         let p0 = p0.into();
         let p1 = p1.into();
 
-        // This is an implementation of this solution:
+        // This is an adaptation of this:
         // https://math.stackexchange.com/a/87374
 
         let distance_between_endpoints = (p1 - p0).magnitude();

From e9060e7e2c981b92814879d5f08a1c16b6a01853 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:59:14 +0100
Subject: [PATCH 17/21] Move variable closer to where it's used

---
 crates/fj-math/src/arc.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 1549b0717..02a626185 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -34,10 +34,10 @@ impl Arc {
         let radius = distance_between_endpoints
             / (2. * (angle_rad.abs().into_f64() / 2.).sin());
 
-        let clockwise_turn = angle_rad <= Scalar::ZERO;
         let more_than_half_turn = angle_rad.abs() > Scalar::PI;
 
         let center = {
+            let clockwise_turn = angle_rad <= Scalar::ZERO;
             let f = match (clockwise_turn, more_than_half_turn) {
                 (false, false) | (true, true) => Scalar::ONE,
                 (false, true) | (true, false) => -Scalar::ONE,

From 67b51f22ec8b7605d2c83548b04498537efba1fb Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 12:59:42 +0100
Subject: [PATCH 18/21] Group calculations used multiple times

---
 crates/fj-math/src/arc.rs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 02a626185..16fa45a85 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -31,11 +31,11 @@ impl Arc {
         // https://math.stackexchange.com/a/87374
 
         let distance_between_endpoints = (p1 - p0).magnitude();
+        let more_than_half_turn = angle_rad.abs() > Scalar::PI;
+
         let radius = distance_between_endpoints
             / (2. * (angle_rad.abs().into_f64() / 2.).sin());
 
-        let more_than_half_turn = angle_rad.abs() > Scalar::PI;
-
         let center = {
             let clockwise_turn = angle_rad <= Scalar::ZERO;
             let f = match (clockwise_turn, more_than_half_turn) {

From d105d1500c4db7d6858a53fbb589da452ca1d020 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 13:01:03 +0100
Subject: [PATCH 19/21] Refactor

---
 crates/fj-math/src/arc.rs | 19 ++++++++++---------
 1 file changed, 10 insertions(+), 9 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 16fa45a85..2da7f6735 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -37,17 +37,18 @@ impl Arc {
             / (2. * (angle_rad.abs().into_f64() / 2.).sin());
 
         let center = {
-            let clockwise_turn = angle_rad <= Scalar::ZERO;
-            let f = match (clockwise_turn, more_than_half_turn) {
-                (false, false) | (true, true) => Scalar::ONE,
-                (false, true) | (true, false) => -Scalar::ONE,
-            };
+            let unit_vector_midpoint_to_center = {
+                let clockwise_turn = angle_rad <= Scalar::ZERO;
+                let f = match (clockwise_turn, more_than_half_turn) {
+                    (false, false) | (true, true) => Scalar::ONE,
+                    (false, true) | (true, false) => -Scalar::ONE,
+                };
 
-            let unit_vector_p0_to_p1 =
-                (p1 - p0) / distance_between_endpoints * f;
+                let unit_vector_p0_to_p1 =
+                    (p1 - p0) / distance_between_endpoints * f;
 
-            let unit_vector_midpoint_to_center =
-                Vector::from([-unit_vector_p0_to_p1.v, unit_vector_p0_to_p1.u]);
+                Vector::from([-unit_vector_p0_to_p1.v, unit_vector_p0_to_p1.u])
+            };
             let distance_center_to_midpoint = (radius.powi(2)
                 - (distance_between_endpoints.powi(2) / 4.))
                 .sqrt();

From fc4ae56f2328d3bb2b5478f6fd9b6eee032a9d48 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 13:01:56 +0100
Subject: [PATCH 20/21] Refactor

---
 crates/fj-math/src/arc.rs | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 2da7f6735..64dbac344 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -37,6 +37,7 @@ impl Arc {
             / (2. * (angle_rad.abs().into_f64() / 2.).sin());
 
         let center = {
+            let midpoint = (p0.coords + p1.coords) / 2.;
             let unit_vector_midpoint_to_center = {
                 let clockwise_turn = angle_rad <= Scalar::ZERO;
                 let f = match (clockwise_turn, more_than_half_turn) {
@@ -54,7 +55,7 @@ impl Arc {
                 .sqrt();
 
             Point {
-                coords: (p0.coords + p1.coords) / 2.
+                coords: midpoint
                     + unit_vector_midpoint_to_center
                         * distance_center_to_midpoint,
             }

From 3ca98bbfd49fd94dc3e5a529db37f8de1b477d16 Mon Sep 17 00:00:00 2001
From: Hanno Braun <hanno@braun-odw.eu>
Date: Thu, 16 Feb 2023 13:02:30 +0100
Subject: [PATCH 21/21] Refactor

---
 crates/fj-math/src/arc.rs | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/crates/fj-math/src/arc.rs b/crates/fj-math/src/arc.rs
index 64dbac344..5b4057244 100644
--- a/crates/fj-math/src/arc.rs
+++ b/crates/fj-math/src/arc.rs
@@ -37,7 +37,9 @@ impl Arc {
             / (2. * (angle_rad.abs().into_f64() / 2.).sin());
 
         let center = {
-            let midpoint = (p0.coords + p1.coords) / 2.;
+            let midpoint = Point {
+                coords: (p0.coords + p1.coords) / 2.,
+            };
             let unit_vector_midpoint_to_center = {
                 let clockwise_turn = angle_rad <= Scalar::ZERO;
                 let f = match (clockwise_turn, more_than_half_turn) {
@@ -54,11 +56,8 @@ impl Arc {
                 - (distance_between_endpoints.powi(2) / 4.))
                 .sqrt();
 
-            Point {
-                coords: midpoint
-                    + unit_vector_midpoint_to_center
-                        * distance_center_to_midpoint,
-            }
+            midpoint
+                + unit_vector_midpoint_to_center * distance_center_to_midpoint
         };
 
         let start_angle = {