Merge pull request #221 from hannobraun/coords

Make math code more convenient to use

src/camera.rs

@@ -45,19 +45,15 @@ impl Camera {
             //
             // To do that, first compute the model's highest point, as well as
             // the furthest point from the origin, in x and y.
-            let highest_point = aabb.max.z();
-            let furthest_point = [
-                aabb.min.x().abs(),
-                aabb.max.x(),
-                aabb.min.y().abs(),
-                aabb.max.y(),
-            ]
-            .into_iter()
-            .reduce(Scalar::max)
-            // `reduce` can only return `None`, if there are no items in
-            // the iterator. And since we're creating an array full of
-            // items above, we know this can't panic.
-            .unwrap();
+            let highest_point = aabb.max.z;
+            let furthest_point =
+                [aabb.min.x.abs(), aabb.max.x, aabb.min.y.abs(), aabb.max.y]
+                    .into_iter()
+                    .reduce(Scalar::max)
+                    // `reduce` can only return `None`, if there are no items in
+                    // the iterator. And since we're creating an array full of
+                    // items above, we know this can't panic.
+                    .unwrap();
 
             // The actual furthest point is not far enough. We don't want the
             // model to fill the whole screen.
@@ -74,7 +70,7 @@ impl Camera {
 
         let initial_offset = {
             let mut offset = aabb.center();
-            *offset.z_mut() = Scalar::ZERO;
+            offset.z = Scalar::ZERO;
             -offset
         };
 
@@ -84,8 +80,8 @@ impl Camera {
 
             rotation: Transform::identity(),
             translation: Translation::from([
-                initial_offset.x().into_f64(),
-                initial_offset.y().into_f64(),
+                initial_offset.x.into_f64(),
+                initial_offset.y.into_f64(),
                 -initial_distance.into_f64(),
             ]),
         }

src/kernel/approximation.rs

@@ -90,22 +90,22 @@ impl Approximation {
         // As this is a cycle, neighboring edges are going to share vertices.
         // Let's remove all those duplicates.
         points.sort_by(|a, b| {
-            if a.x() < b.x() {
+            if a.x < b.x {
                 return Ordering::Less;
             }
-            if a.x() > b.x() {
+            if a.x > b.x {
                 return Ordering::Greater;
             }
-            if a.y() < b.y() {
+            if a.y < b.y {
                 return Ordering::Less;
             }
-            if a.y() > b.y() {
+            if a.y > b.y {
                 return Ordering::Greater;
             }
-            if a.z() < b.z() {
+            if a.z < b.z {
                 return Ordering::Less;
             }
-            if a.z() > b.z() {
+            if a.z > b.z {
                 return Ordering::Greater;
             }
 

src/kernel/geometry/curves/circle.rs

@@ -48,7 +48,7 @@ impl Circle {
     /// error.
     pub fn point_model_to_curve(&self, point: &Point<3>) -> Point<1> {
         let v = point - self.center;
-        let atan = Scalar::atan2(v.y(), v.x());
+        let atan = Scalar::atan2(v.y, v.x);
         let coord = if atan >= Scalar::ZERO {
             atan
         } else {
@@ -59,13 +59,13 @@ impl Circle {
 
     /// Convert a point on the curve into model coordinates
     pub fn point_curve_to_model(&self, point: &Point<1>) -> Point<3> {
-        self.center + self.vector_curve_to_model(&point.coords())
+        self.center + self.vector_curve_to_model(&point.coords)
     }
 
     /// Convert a vector on the curve into model coordinates
-    pub fn vector_curve_to_model(&self, point: &Vector<1>) -> Vector<3> {
+    pub fn vector_curve_to_model(&self, vector: &Vector<1>) -> Vector<3> {
         let radius = self.radius.magnitude();
-        let angle = point.t();
+        let angle = vector.t;
 
         let (sin, cos) = angle.sin_cos();
 

src/kernel/geometry/curves/line.rs

@@ -1,5 +1,3 @@
-use approx::AbsDiffEq;
-
 use crate::math::{Point, Transform, Vector};
 
 /// A line, defined by a point and a vector
@@ -50,17 +48,17 @@ impl Line {
 
     /// Convert a point on the curve into model coordinates
     pub fn point_curve_to_model(&self, point: &Point<1>) -> Point<3> {
-        self.origin + self.vector_curve_to_model(&point.coords())
+        self.origin + self.vector_curve_to_model(&point.coords)
     }
 
     /// Convert a vector on the curve into model coordinates
-    pub fn vector_curve_to_model(&self, point: &Vector<1>) -> Vector<3> {
-        self.direction * point.t()
+    pub fn vector_curve_to_model(&self, vector: &Vector<1>) -> Vector<3> {
+        self.direction * vector.t
     }
 }
 
-impl AbsDiffEq for Line {
-    type Epsilon = <f64 as AbsDiffEq>::Epsilon;
+impl approx::AbsDiffEq for Line {
+    type Epsilon = <f64 as approx::AbsDiffEq>::Epsilon;
 
     fn default_epsilon() -> Self::Epsilon {
         f64::default_epsilon()

src/kernel/geometry/surfaces/swept.rs

@@ -24,7 +24,7 @@ impl Swept {
 
     /// Convert a point in model coordinates to surface coordinates
     pub fn point_model_to_surface(&self, point: &Point<3>) -> Point<2> {
-        let u = self.curve.point_model_to_curve(point).t();
+        let u = self.curve.point_model_to_curve(point).t;
         let v = (point - self.curve.origin()).dot(&self.path.normalize())
             / self.path.magnitude();
 
@@ -33,13 +33,12 @@ impl Swept {
 
     /// Convert a point in surface coordinates to model coordinates
     pub fn point_surface_to_model(&self, point: &Point<2>) -> Point<3> {
-        self.curve.point_curve_to_model(&point.to_t()) + self.path * point.v()
+        self.curve.point_curve_to_model(&point.to_t()) + self.path * point.v
     }
 
     /// Convert a vector in surface coordinates to model coordinates
     pub fn vector_surface_to_model(&self, vector: &Vector<2>) -> Vector<3> {
-        self.curve.vector_curve_to_model(&vector.to_t())
-            + self.path * vector.v()
+        self.curve.vector_curve_to_model(&vector.to_t()) + self.path * vector.v
     }
 }
 

src/kernel/shapes/sweep.rs

@@ -20,7 +20,7 @@ use crate::{
 impl Shape for fj::Sweep {
     fn bounding_volume(&self) -> Aabb<3> {
         let mut aabb = self.shape.bounding_volume();
-        *aabb.max.z_mut() = self.length.into();
+        aabb.max.z = self.length.into();
         aabb
     }
 

src/kernel/triangulation.rs

@@ -40,8 +40,8 @@ impl HasPosition for SurfacePoint {
 
     fn position(&self) -> spade::Point2<Self::Scalar> {
         spade::Point2 {
-            x: self.value.u(),
-            y: self.value.v(),
+            x: self.value.u,
+            y: self.value.v,
         }
     }
 }

src/math/coordinates.rs

@@ -0,0 +1,22 @@
+use super::Scalar;
+
+/// 1-dimensional curve coordinates
+#[repr(C)]
+pub struct T {
+    pub t: Scalar,
+}
+
+/// 2-dimensional surface coordinates
+#[repr(C)]
+pub struct Uv {
+    pub u: Scalar,
+    pub v: Scalar,
+}
+
+/// 3-dimensional model coordinates
+#[repr(C)]
+pub struct Xyz {
+    pub x: Scalar,
+    pub y: Scalar,
+    pub z: Scalar,
+}

src/math/mod.rs

@@ -1,4 +1,5 @@
 pub mod aabb;
+pub mod coordinates;
 pub mod point;
 pub mod scalar;
 pub mod segment;

src/math/point.rs

@@ -1,8 +1,9 @@
 use std::ops;
 
-use approx::AbsDiffEq;
-
-use super::{Scalar, Vector};
+use super::{
+    coordinates::{Uv, Xyz, T},
+    Scalar, Vector,
+};
 
 /// An n-dimensional point
 ///
@@ -13,7 +14,9 @@ use super::{Scalar, Vector};
 /// The goal of this type is to eventually implement `Eq` and `Hash`, making it
 /// easier to work with vectors. This is a work in progress.
 #[derive(Clone, Copy, Debug, Eq, Hash, PartialEq, Ord, PartialOrd)]
-pub struct Point<const D: usize>([Scalar; D]);
+pub struct Point<const D: usize> {
+    pub coords: Vector<D>,
+}
 
 impl<const D: usize> Point<D> {
     /// Construct a `Point` at the origin of the coordinate system
@@ -23,74 +26,80 @@ impl<const D: usize> Point<D> {
 
     /// Construct a `Point` from an array
     pub fn from_array(array: [f64; D]) -> Self {
-        Self(array.map(Scalar::from_f64))
+        Self {
+            coords: array.map(Scalar::from_f64).into(),
+        }
     }
 
     /// Construct a `Point` from an nalgebra vector
     pub fn from_na(point: nalgebra::Point<f64, D>) -> Self {
-        Self(point.coords.data.0[0].map(Scalar::from_f64))
+        Self {
+            coords: point.coords.into(),
+        }
     }
 
     /// Convert the point into an nalgebra point
     pub fn to_na(&self) -> nalgebra::Point<f64, D> {
-        self.0.map(Scalar::into_f64).into()
+        nalgebra::Point {
+            coords: self.coords.into(),
+        }
     }
 
     /// Convert to a 1-dimensional point
     pub fn to_t(&self) -> Point<1> {
-        Point([self.0[0]])
-    }
-
-    /// Access a mutable reference to the point's z coordinate
-    pub fn z_mut(&mut self) -> &mut Scalar {
-        &mut self.0[2]
-    }
-
-    /// Access the point's coordinates as a vector
-    pub fn coords(&self) -> Vector<D> {
-        Vector::from(self.0)
+        Point {
+            coords: self.coords.to_t(),
+        }
     }
 }
 
-impl Point<1> {
-    /// Access the curve point's t coordinate
-    pub fn t(&self) -> Scalar {
-        self.0[0]
+impl ops::Deref for Point<1> {
+    type Target = T;
+
+    fn deref(&self) -> &Self::Target {
+        self.coords.deref()
     }
 }
 
-impl Point<2> {
-    /// Access the point's x coordinate
-    pub fn u(&self) -> Scalar {
-        self.0[0]
-    }
+impl ops::Deref for Point<2> {
+    type Target = Uv;
 
-    /// Access the point's y coordinate
-    pub fn v(&self) -> Scalar {
-        self.0[1]
+    fn deref(&self) -> &Self::Target {
+        self.coords.deref()
     }
 }
 
-impl Point<3> {
-    /// Access the point's x coordinate
-    pub fn x(&self) -> Scalar {
-        self.0[0]
-    }
+impl ops::Deref for Point<3> {
+    type Target = Xyz;
 
-    /// Access the point's y coordinate
-    pub fn y(&self) -> Scalar {
-        self.0[1]
+    fn deref(&self) -> &Self::Target {
+        self.coords.deref()
     }
+}
 
-    /// Access the point's z coordinate
-    pub fn z(&self) -> Scalar {
-        self.0[2]
+impl ops::DerefMut for Point<1> {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        self.coords.deref_mut()
+    }
+}
+
+impl ops::DerefMut for Point<2> {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        self.coords.deref_mut()
+    }
+}
+
+impl ops::DerefMut for Point<3> {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        self.coords.deref_mut()
     }
 }
 
 impl<const D: usize> From<[Scalar; D]> for Point<D> {
     fn from(array: [Scalar; D]) -> Self {
-        Self(array)
+        Self {
+            coords: array.into(),
+        }
     }
 }
 
@@ -108,13 +117,13 @@ impl<const D: usize> From<nalgebra::Point<f64, D>> for Point<D> {
 
 impl<const D: usize> From<Point<D>> for [f32; D] {
     fn from(point: Point<D>) -> Self {
-        point.0.map(|scalar| scalar.into_f32())
+        point.coords.into()
     }
 }
 
 impl<const D: usize> From<Point<D>> for [f64; D] {
     fn from(point: Point<D>) -> Self {
-        point.0.map(|scalar| scalar.into_f64())
+        point.coords.into()
     }
 }
 
@@ -158,14 +167,14 @@ impl<const D: usize> ops::Mul<f64> for Point<D> {
     }
 }
 
-impl<const D: usize> AbsDiffEq for Point<D> {
-    type Epsilon = <f64 as AbsDiffEq>::Epsilon;
+impl<const D: usize> approx::AbsDiffEq for Point<D> {
+    type Epsilon = <Vector<D> as approx::AbsDiffEq>::Epsilon;
 
     fn default_epsilon() -> Self::Epsilon {
         f64::default_epsilon()
     }
 
     fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
-        self.0.abs_diff_eq(&other.0, epsilon)
+        self.coords.abs_diff_eq(&other.coords, epsilon)
     }
 }

src/math/scalar.rs

@@ -1,7 +1,5 @@
 use std::{cmp, f64::consts::PI, hash::Hash, ops};
 
-use approx::AbsDiffEq;
-
 /// A rational, finite scalar value
 ///
 /// This is a wrapper around `f64`. On construction, it checks that the `f64`
@@ -272,8 +270,8 @@ impl num_traits::Signed for Scalar {
     }
 }
 
-impl AbsDiffEq for Scalar {
-    type Epsilon = <f64 as AbsDiffEq>::Epsilon;
+impl approx::AbsDiffEq for Scalar {
+    type Epsilon = <f64 as approx::AbsDiffEq>::Epsilon;
 
     fn default_epsilon() -> Self::Epsilon {
         f64::default_epsilon()

src/math/vector.rs

@@ -1,8 +1,9 @@
 use std::ops;
 
-use approx::AbsDiffEq;
-
-use super::Scalar;
+use super::{
+    coordinates::{Uv, Xyz, T},
+    Scalar,
+};
 
 /// An n-dimensional vector
 ///
@@ -13,7 +14,7 @@ use super::Scalar;
 /// The goal of this type is to eventually implement `Eq` and `Hash`, making it
 /// easier to work with vectors. This is a work in progress.
 #[derive(Clone, Copy, Debug, Eq, Hash, PartialEq, Ord, PartialOrd)]
-pub struct Vector<const D: usize>([Scalar; D]);
+pub struct Vector<const D: usize>(pub [Scalar; D]);
 
 impl<const D: usize> Vector<D> {
     /// Construct a `Vector` from an array
@@ -62,44 +63,83 @@ impl<const D: usize> Vector<D> {
     }
 }
 
-impl Vector<1> {
-    /// Access the curve vector's t coordinate
-    pub fn t(&self) -> Scalar {
-        self.0[0]
-    }
-}
-
 impl Vector<2> {
-    /// Access the surface vector's u coordinate
-    pub fn u(&self) -> Scalar {
-        self.0[0]
-    }
-
-    /// Access the surface vector's v coordinate
-    pub fn v(&self) -> Scalar {
-        self.0[1]
-    }
-
     /// Extend a 2-dimensional vector into a 3-dimensional one
     pub fn to_xyz(&self, z: Scalar) -> Vector<3> {
-        Vector::from([self.u(), self.v(), z])
+        Vector::from([self.u, self.v, z])
     }
 }
 
 impl Vector<3> {
-    /// Access the vector's x coordinate
-    pub fn x(&self) -> Scalar {
-        self.0[0]
-    }
-
-    /// Access the vector's y coordinate
-    pub fn y(&self) -> Scalar {
-        self.0[1]
-    }
-
     /// Construct a new vector from this vector's x and y components
     pub fn xy(&self) -> Vector<2> {
-        Vector::from([self.x(), self.y()])
+        Vector::from([self.x, self.y])
+    }
+}
+
+impl ops::Deref for Vector<1> {
+    type Target = T;
+
+    fn deref(&self) -> &Self::Target {
+        let ptr = self.0.as_ptr() as *const Self::Target;
+
+        // This is sound. We've created this pointer from a valid instance, that
+        // has the same size and layout as the target.
+        unsafe { &*ptr }
+    }
+}
+
+impl ops::Deref for Vector<2> {
+    type Target = Uv;
+
+    fn deref(&self) -> &Self::Target {
+        let ptr = self.0.as_ptr() as *const Self::Target;
+
+        // This is sound. We've created this pointer from a valid instance, that
+        // has the same size and layout as the target.
+        unsafe { &*ptr }
+    }
+}
+
+impl ops::Deref for Vector<3> {
+    type Target = Xyz;
+
+    fn deref(&self) -> &Self::Target {
+        let ptr = self.0.as_ptr() as *const Self::Target;
+
+        // This is sound. We've created this pointer from a valid instance, that
+        // has the same size and layout as the target.
+        unsafe { &*ptr }
+    }
+}
+
+impl ops::DerefMut for Vector<1> {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        let ptr = self.0.as_mut_ptr() as *mut Self::Target;
+
+        // This is sound. We've created this pointer from a valid instance, that
+        // has the same size and layout as the target.
+        unsafe { &mut *ptr }
+    }
+}
+
+impl ops::DerefMut for Vector<2> {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        let ptr = self.0.as_mut_ptr() as *mut Self::Target;
+
+        // This is sound. We've created this pointer from a valid instance, that
+        // has the same size and layout as the target.
+        unsafe { &mut *ptr }
+    }
+}
+
+impl ops::DerefMut for Vector<3> {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        let ptr = self.0.as_mut_ptr() as *mut Self::Target;
+
+        // This is sound. We've created this pointer from a valid instance, that
+        // has the same size and layout as the target.
+        unsafe { &mut *ptr }
     }
 }
 
@@ -127,6 +167,18 @@ impl<const D: usize> From<Vector<D>> for [f32; D] {
     }
 }
 
+impl<const D: usize> From<Vector<D>> for [f64; D] {
+    fn from(vector: Vector<D>) -> Self {
+        vector.0.map(|scalar| scalar.into_f64())
+    }
+}
+
+impl<const D: usize> From<Vector<D>> for nalgebra::SVector<f64, D> {
+    fn from(vector: Vector<D>) -> Self {
+        vector.to_na()
+    }
+}
+
 impl<const D: usize> ops::Add<Self> for Vector<D> {
     type Output = Self;
 
@@ -151,8 +203,8 @@ impl<const D: usize> ops::Div<Scalar> for Vector<D> {
     }
 }
 
-impl<const D: usize> AbsDiffEq for Vector<D> {
-    type Epsilon = <f64 as AbsDiffEq>::Epsilon;
+impl<const D: usize> approx::AbsDiffEq for Vector<D> {
+    type Epsilon = <Scalar as approx::AbsDiffEq>::Epsilon;
 
     fn default_epsilon() -> Self::Epsilon {
         f64::default_epsilon()