diff -r 495448cca603 -r 6aa955ad8122 src/sets.rs
--- a/src/sets.rs	Thu May 01 08:40:33 2025 -0500
+++ b/src/sets.rs	Thu May 01 13:06:58 2025 -0500
@@ -2,42 +2,51 @@
 This module provides various sets and traits for them.
 */
 
-use std::ops::{RangeFull,RangeFrom,Range,RangeInclusive,RangeTo,RangeToInclusive};
-use crate::types::*;
+use crate::euclidean::Euclidean;
+use crate::instance::{Instance, Space};
 use crate::loc::Loc;
-use crate::euclidean::Euclidean;
-use crate::instance::{Space, Instance};
+use crate::types::*;
 use serde::Serialize;
+use std::ops::{Range, RangeFrom, RangeFull, RangeInclusive, RangeTo, RangeToInclusive};
 
 pub mod cube;
 pub use cube::Cube;
 
 /// Trait for arbitrary sets. The parameter `U` is the element type.
-pub trait Set<U> where U : Space {
+pub trait Set<U>
+where
+    U: Space,
+{
     /// Check for element containment
-    fn contains<I : Instance<U>>(&self, item : I) -> bool;
+    fn contains<I: Instance<U>>(&self, item: I) -> bool;
 }
 
 /// Additional ordering (besides [`PartialOrd`]) of a subfamily of sets:
 /// greatest lower bound and least upper bound.
-pub trait SetOrd : Sized {
-     /// Returns the smallest set of same class contain both parameters.
-     fn common(&self, other : &Self) -> Self;
+pub trait SetOrd: Sized {
+    /// Returns the smallest set of same class contain both parameters.
+    fn common(&self, other: &Self) -> Self;
 
-     /// Returns the greatest set of same class contaied by n both parameter sets.
-     fn intersect(&self, other : &Self) -> Option<Self>;
+    /// Returns the greatest set of same class contaied by n both parameter sets.
+    fn intersect(&self, other: &Self) -> Option<Self>;
 }
 
-impl<U, const N : usize> Set<Loc<U, N>>
-for Cube<U,N>
-where U : Num + PartialOrd + Sized {
-    fn contains<I : Instance<Loc<U, N>>>(&self, item : I) -> bool {
-        self.0.iter().zip(item.ref_instance().iter()).all(|(s, x)| s.contains(x))
+impl<U, const N: usize> Set<Loc<N, U>> for Cube<N, U>
+where
+    U: Num + PartialOrd + Sized,
+{
+    fn contains<I: Instance<Loc<N, U>>>(&self, item: I) -> bool {
+        self.0
+            .iter()
+            .zip(item.ref_instance().iter())
+            .all(|(s, x)| s.contains(x))
     }
 }
 
-impl<U : Space> Set<U> for RangeFull {
-    fn contains<I : Instance<U>>(&self, _item : I) -> bool { true }
+impl<U: Space> Set<U> for RangeFull {
+    fn contains<I: Instance<U>>(&self, _item: I) -> bool {
+        true
+    }
 }
 
 macro_rules! impl_ranges {
@@ -56,45 +65,59 @@
     )* }
 }
 
-impl_ranges!(RangeFrom,Range,RangeInclusive,RangeTo,RangeToInclusive);
+impl_ranges!(RangeFrom, Range, RangeInclusive, RangeTo, RangeToInclusive);
 
 /// Halfspaces described by an orthogonal vector and an offset.
 ///
 /// The halfspace is $H = \\{ t v + a \mid a^⊤ v = 0 \\}$, where $v$ is the orthogonal
 /// vector and $t$ the offset.
-#[derive(Clone,Copy,Debug,Serialize,Eq,PartialEq)]
-pub struct Halfspace<A, F> where A : Euclidean<F>, F : Float {
-    pub orthogonal : A,
-    pub offset : F,
+#[derive(Clone, Copy, Debug, Serialize, Eq, PartialEq)]
+pub struct Halfspace<A, F>
+where
+    A: Euclidean<F>,
+    F: Float,
+{
+    pub orthogonal: A,
+    pub offset: F,
 }
 
-impl<A,F> Halfspace<A,F> where A : Euclidean<F>, F : Float {
+impl<A, F> Halfspace<A, F>
+where
+    A: Euclidean<F>,
+    F: Float,
+{
     #[inline]
-    pub fn new(orthogonal : A, offset : F) -> Self {
-        Halfspace{ orthogonal : orthogonal, offset : offset }
+    pub fn new(orthogonal: A, offset: F) -> Self {
+        Halfspace {
+            orthogonal: orthogonal,
+            offset: offset,
+        }
     }
 }
 
 /// Trait for generating a halfspace spanned by another set `Self` of elements of type `U`.
-pub trait SpannedHalfspace<F> where  F : Float {
+pub trait SpannedHalfspace<F>
+where
+    F: Float,
+{
     /// Type of the orthogonal vector describing the halfspace.
-    type A : Euclidean<F>;
+    type A: Euclidean<F>;
     /// Returns the halfspace spanned by this set.
     fn spanned_halfspace(&self) -> Halfspace<Self::A, F>;
 }
 
 // TODO: Gram-Schmidt for higher N.
-impl<F : Float> SpannedHalfspace<F> for [Loc<F, 1>; 2] {
-    type A = Loc<F, 1>;
+impl<F: Float> SpannedHalfspace<F> for [Loc<1, F>; 2] {
+    type A = Loc<1, F>;
     fn spanned_halfspace(&self) -> Halfspace<Self::A, F> {
         let (x0, x1) = (self[0], self[1]);
-        Halfspace::new(x1-x0, x0[0])
+        Halfspace::new(x1 - x0, x0[0])
     }
 }
 
 // TODO: Gram-Schmidt for higher N.
-impl<F : Float> SpannedHalfspace<F> for [Loc<F, 2>; 2] {
-    type A = Loc<F, 2>;
+impl<F: Float> SpannedHalfspace<F> for [Loc<2, F>; 2] {
+    type A = Loc<2, F>;
     fn spanned_halfspace(&self) -> Halfspace<Self::A, F> {
         let (x0, x1) = (&self[0], &self[1]);
         let d = x1 - x0;
@@ -104,28 +127,30 @@
     }
 }
 
-impl<A,F> Set<A> for Halfspace<A,F>
+impl<A, F> Set<A> for Halfspace<A, F>
 where
-    A : Euclidean<F>,
-    F : Float,
+    A: Euclidean<F>,
+    F: Float,
 {
     #[inline]
-    fn contains<I : Instance<A>>(&self, item : I) -> bool {
+    fn contains<I: Instance<A>>(&self, item: I) -> bool {
         self.orthogonal.dot(item) >= self.offset
     }
 }
 
 /// Polygons defined by `N` `Halfspace`s.
-#[derive(Clone,Copy,Debug,Eq,PartialEq)]
-pub struct NPolygon<A, F, const N : usize>(pub [Halfspace<A,F>; N])
-where A : Euclidean<F>, F : Float;
+#[derive(Clone, Copy, Debug, Eq, PartialEq)]
+pub struct NPolygon<A, const N: usize, F = f64>(pub [Halfspace<A, F>; N])
+where
+    A: Euclidean<F>,
+    F: Float;
 
-impl<A,F,const N : usize> Set<A> for NPolygon<A,F,N>
+impl<A, F, const N: usize> Set<A> for NPolygon<A, N, F>
 where
-    A : Euclidean<F>,
-    F : Float,
+    A: Euclidean<F>,
+    F: Float,
 {
-    fn contains<I : Instance<A>>(&self, item : I) -> bool {
+    fn contains<I: Instance<A>>(&self, item: I) -> bool {
         let r = item.ref_instance();
         self.0.iter().all(|halfspace| halfspace.contains(r))
     }