From d6b5c8775988d5fb1017ab045309155263b0e814 Mon Sep 17 00:00:00 2001
From: Matthew Gordon <matthew.scott.gordon@gmail.com>
Date: Mon, 10 Feb 2020 16:52:09 -0500
Subject: [PATCH] Create Real trait to replace nalgebra::RealField

Real inherits RealField, but I want to add more to it.
---
 src/camera.rs                               | 12 ++---
 src/colour.rs                               | 16 ++++---
 src/image.rs                                | 14 +++---
 src/integrators.rs                          | 12 ++---
 src/lib.rs                                  |  3 ++
 src/materials.rs                            | 19 ++++----
 src/mesh.rs                                 |  9 ++--
 src/raycasting/axis_aligned_bounding_box.rs |  4 +-
 src/raycasting/mod.rs                       | 24 +++++-----
 src/raycasting/plane.rs                     | 13 +++---
 src/raycasting/sphere.rs                    | 13 +++---
 src/raycasting/triangle.rs                  | 25 ++++++-----
 src/realtype.rs                             |  6 +++
 src/sampler.rs                              |  6 +--
 src/scene.rs                                |  5 ++-
 src/util/algebra_utils.rs                   |  6 ++-
 src/util/axis_aligned_bounding_box.rs       |  7 +--
 src/util/interval.rs                        |  8 ++--
 src/util/normalizer.rs                      | 50 +++++++++++----------
 19 files changed, 141 insertions(+), 111 deletions(-)
 create mode 100644 src/realtype.rs

diff --git a/src/camera.rs b/src/camera.rs
index 043bc2f..477db28 100644
--- a/src/camera.rs
+++ b/src/camera.rs
@@ -1,4 +1,4 @@
-use nalgebra::{convert, Point3, RealField, Vector3};
+use nalgebra::{convert, Point3, Vector3};
 
 use super::colour::{ColourRgbF, NamedColour};
 use super::image::ImageRgbF;
@@ -7,9 +7,11 @@ use super::raycasting::Ray;
 use super::sampler::Sampler;
 use super::scene::Scene;
 
+use crate::Real;
+
 use std::sync::{Arc, Mutex};
 
-struct ImageSampler<T: RealField> {
+struct ImageSampler<T: Real> {
     image_height_pixels: u32,
     image_width_pixels: u32,
 
@@ -20,7 +22,7 @@ struct ImageSampler<T: RealField> {
     film_distance: T,
 }
 
-impl<T: RealField> ImageSampler<T> {
+impl<T: Real> ImageSampler<T> {
     pub fn new(width: u32, height: u32, camera_location: Point3<T>) -> ImageSampler<T> {
         let (film_width, film_height) = {
             let width: T = convert(width as f64);
@@ -64,13 +66,13 @@ impl<T: RealField> ImageSampler<T> {
     }
 }
 
-pub fn render_scene<T: RealField>(output_image: Arc<Mutex<ImageRgbF<T>>>, scene: Arc<Scene<T>>) {
+pub fn render_scene<T: Real>(output_image: Arc<Mutex<ImageRgbF<T>>>, scene: Arc<Scene<T>>) {
     let height = output_image.lock().unwrap().get_height();
     let width = output_image.lock().unwrap().get_width();
     partial_render_scene(output_image, scene, 0, height, 0, width, height, width)
 }
 
-pub fn partial_render_scene<T: RealField>(
+pub fn partial_render_scene<T: Real>(
     output_image: Arc<Mutex<ImageRgbF<T>>>,
     scene: Arc<Scene<T>>,
     row_start: u32,
diff --git a/src/colour.rs b/src/colour.rs
index 9aad6db..43dfa05 100644
--- a/src/colour.rs
+++ b/src/colour.rs
@@ -1,13 +1,15 @@
-use nalgebra::{convert, RealField, Vector3};
+use nalgebra::{convert, Vector3};
+
+use crate::Real;
 
 use std::ops::{Add, Mul};
 
 #[derive(Copy, Clone, Debug)]
-pub struct ColourRgbF<T: RealField> {
+pub struct ColourRgbF<T: Real> {
     values: Vector3<T>,
 }
 
-impl<T: RealField> ColourRgbF<T> {
+impl<T: Real> ColourRgbF<T> {
     pub fn new(red: T, green: T, blue: T) -> ColourRgbF<T> {
         ColourRgbF {
             values: Vector3::new(red, green, blue),
@@ -80,7 +82,7 @@ pub enum NamedColour {
     Navy,
 }
 
-impl<T: RealField> Add<ColourRgbF<T>> for ColourRgbF<T> {
+impl<T: Real> Add<ColourRgbF<T>> for ColourRgbF<T> {
     type Output = ColourRgbF<T>;
     fn add(self, rhs: ColourRgbF<T>) -> ColourRgbF<T> {
         ColourRgbF {
@@ -89,7 +91,7 @@ impl<T: RealField> Add<ColourRgbF<T>> for ColourRgbF<T> {
     }
 }
 
-impl<T: RealField> Mul<T> for ColourRgbF<T> {
+impl<T: Real> Mul<T> for ColourRgbF<T> {
     type Output = ColourRgbF<T>;
     fn mul(self, rhs: T) -> ColourRgbF<T> {
         ColourRgbF {
@@ -98,7 +100,7 @@ impl<T: RealField> Mul<T> for ColourRgbF<T> {
     }
 }
 
-impl<T: RealField> Mul<ColourRgbF<T>> for ColourRgbF<T> {
+impl<T: Real> Mul<ColourRgbF<T>> for ColourRgbF<T> {
     type Output = ColourRgbF<T>;
     fn mul(self, rhs: ColourRgbF<T>) -> ColourRgbF<T> {
         ColourRgbF {
@@ -115,7 +117,7 @@ mod tests {
         use super::*;
         use quickcheck::{Arbitrary, Gen};
         use quickcheck_macros::quickcheck;
-        impl<T: Arbitrary + RealField> Arbitrary for ColourRgbF<T> {
+        impl<T: Arbitrary + Real> Arbitrary for ColourRgbF<T> {
             fn arbitrary<G: Gen>(g: &mut G) -> ColourRgbF<T> {
                 let values = <Vector3<T> as Arbitrary>::arbitrary(g);
                 ColourRgbF { values }
diff --git a/src/image.rs b/src/image.rs
index 77b8574..a26df56 100644
--- a/src/image.rs
+++ b/src/image.rs
@@ -1,9 +1,11 @@
 use std::convert::TryInto;
 
-use nalgebra::{clamp, convert, RealField, Vector3};
+use nalgebra::{clamp, convert, Vector3};
 
 use super::colour::{ColourRgbF, ColourRgbU8};
 
+use crate::Real;
+
 pub struct ImageRgbU8 {
     pixel_data: Vec<u8>,
     width: u32,
@@ -64,13 +66,13 @@ impl ImageRgbU8 {
     }
 }
 
-pub struct ImageRgbF<T: RealField> {
+pub struct ImageRgbF<T: Real> {
     pixel_data: Vec<T>,
     width: u32,
     height: u32,
 }
 
-impl<T: RealField> ImageRgbF<T> {
+impl<T: Real> ImageRgbF<T> {
     pub fn new(width: u32, height: u32) -> ImageRgbF<T> {
         ImageRgbF {
             width,
@@ -145,7 +147,7 @@ impl NormalizedAsByte for f64 {
     }
 }
 
-pub trait ToneMapper<T: RealField> {
+pub trait ToneMapper<T: Real> {
     fn apply_tone_mapping(&self, image_in: &ImageRgbF<T>, image_out: &mut ImageRgbU8);
 }
 
@@ -153,12 +155,12 @@ pub trait ToneMapper<T: RealField> {
 pub struct ClampingToneMapper {}
 
 impl ClampingToneMapper {
-    fn clamp<T: RealField + NormalizedAsByte>(v: &T) -> u8 {
+    fn clamp<T: Real + NormalizedAsByte>(v: &T) -> u8 {
         clamp(v, &T::zero(), &T::one()).normalized_to_byte()
     }
 }
 
-impl<T: RealField + NormalizedAsByte> ToneMapper<T> for ClampingToneMapper {
+impl<T: Real + NormalizedAsByte> ToneMapper<T> for ClampingToneMapper {
     fn apply_tone_mapping(&self, image_in: &ImageRgbF<T>, image_out: &mut ImageRgbU8) {
         assert!(image_in.get_width() == image_out.get_width());
         assert!(image_in.get_height() == image_out.get_height());
diff --git a/src/integrators.rs b/src/integrators.rs
index e3f2abe..255c4c8 100644
--- a/src/integrators.rs
+++ b/src/integrators.rs
@@ -1,27 +1,29 @@
-use nalgebra::{convert, RealField, Vector3};
+use nalgebra::{convert, Vector3};
 
 use super::colour::ColourRgbF;
 use super::raycasting::{IntersectionInfo, Ray};
 use super::sampler::Sampler;
 use super::util::algebra_utils::try_change_of_basis_matrix;
 
-pub trait Integrator<T: RealField> {
+use crate::Real;
+
+pub trait Integrator<T: Real> {
     fn integrate(&self, sampler: &Sampler<T>, info: &IntersectionInfo<T>) -> ColourRgbF<T>;
 }
 
-pub struct DirectionalLight<T: RealField> {
+pub struct DirectionalLight<T: Real> {
     pub direction: Vector3<T>,
     pub colour: ColourRgbF<T>,
 }
 
-pub struct WhittedIntegrator<T: RealField> {
+pub struct WhittedIntegrator<T: Real> {
     pub ambient_light: ColourRgbF<T>,
     pub lights: Vec<DirectionalLight<T>>,
 }
 
 // TODO: Get rid of the magic bias number, which should be calculated base on expected error
 // bounds and tangent direction
-impl<T: RealField> Integrator<T> for WhittedIntegrator<T> {
+impl<T: Real> Integrator<T> for WhittedIntegrator<T> {
     fn integrate(&self, sampler: &Sampler<T>, info: &IntersectionInfo<T>) -> ColourRgbF<T> {
         let world_to_bsdf_space =
             try_change_of_basis_matrix(&info.tangent, &info.cotangent, &info.normal)
diff --git a/src/lib.rs b/src/lib.rs
index e0111e9..5b9e733 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -5,10 +5,13 @@ pub mod integrators;
 pub mod materials;
 pub mod mesh;
 pub mod raycasting;
+pub mod realtype;
 pub mod sampler;
 pub mod scene;
 pub mod util;
 
+use realtype::Real;
+
 #[cfg(bench)]
 mod tests {
     extern crate test;
diff --git a/src/materials.rs b/src/materials.rs
index 1f103b6..8f6875e 100644
--- a/src/materials.rs
+++ b/src/materials.rs
@@ -1,12 +1,13 @@
-use nalgebra::{clamp, convert, RealField, Vector3};
+use nalgebra::{clamp, convert, Vector3};
 
 use super::colour::{ColourRgbF, NamedColour};
+use crate::Real;
 
 use std::fmt::Debug;
 
 type Bsdf<'a, T> = Box<dyn Fn(Vector3<T>, Vector3<T>, ColourRgbF<T>) -> ColourRgbF<T> + 'a>;
 
-pub trait Material<T: RealField>: Debug + Sync + Send {
+pub trait Material<T: Real>: Debug + Sync + Send {
     fn bsdf<'a>(&'a self) -> Bsdf<'a, T>;
 
     fn sample(&self, _w_o: &Vector3<T>) -> Vec<Vector3<T>> {
@@ -15,12 +16,12 @@ pub trait Material<T: RealField>: Debug + Sync + Send {
 }
 
 #[derive(Debug)]
-pub struct LambertianMaterial<T: RealField> {
+pub struct LambertianMaterial<T: Real> {
     pub colour: ColourRgbF<T>,
     pub diffuse_strength: T,
 }
 
-impl<T: RealField> LambertianMaterial<T> {
+impl<T: Real> LambertianMaterial<T> {
     pub fn new_dummy() -> LambertianMaterial<T> {
         LambertianMaterial {
             colour: ColourRgbF::new(T::one(), T::one(), T::one()),
@@ -29,7 +30,7 @@ impl<T: RealField> LambertianMaterial<T> {
     }
 }
 
-impl<T: RealField> Material<T> for LambertianMaterial<T> {
+impl<T: Real> Material<T> for LambertianMaterial<T> {
     fn bsdf<'a>(&'a self) -> Bsdf<'a, T> {
         Box::new(
             move |_w_o: Vector3<T>, _w_i: Vector3<T>, colour_in: ColourRgbF<T>| {
@@ -40,14 +41,14 @@ impl<T: RealField> Material<T> for LambertianMaterial<T> {
 }
 
 #[derive(Debug)]
-pub struct PhongMaterial<T: RealField> {
+pub struct PhongMaterial<T: Real> {
     pub colour: ColourRgbF<T>,
     pub diffuse_strength: T,
     pub specular_strength: T,
     pub smoothness: T,
 }
 
-impl<T: RealField> Material<T> for PhongMaterial<T> {
+impl<T: Real> Material<T> for PhongMaterial<T> {
     fn bsdf<'a>(&'a self) -> Bsdf<'a, T> {
         Box::new(
             move |w_o: Vector3<T>, w_i: Vector3<T>, colour_in: ColourRgbF<T>| {
@@ -66,13 +67,13 @@ impl<T: RealField> Material<T> for PhongMaterial<T> {
 }
 
 #[derive(Debug)]
-pub struct ReflectiveMaterial<T: RealField> {
+pub struct ReflectiveMaterial<T: Real> {
     pub colour: ColourRgbF<T>,
     pub diffuse_strength: T,
     pub reflection_strength: T,
 }
 
-impl<T: RealField> Material<T> for ReflectiveMaterial<T> {
+impl<T: Real> Material<T> for ReflectiveMaterial<T> {
     fn bsdf<'a>(&'a self) -> Bsdf<'a, T> {
         Box::new(
             move |w_o: Vector3<T>, w_i: Vector3<T>, colour_in: ColourRgbF<T>| {
diff --git a/src/mesh.rs b/src/mesh.rs
index 8477d8a..d6a89d1 100644
--- a/src/mesh.rs
+++ b/src/mesh.rs
@@ -1,17 +1,18 @@
 mod wavefront_obj {
     use crate::materials::Material;
+    use crate::Real;
 
     use crate::raycasting::Triangle;
 
     use alga::general::SupersetOf;
-    use nalgebra::{convert, Point3, RealField, Vector3};
+    use nalgebra::{convert, Point3, Vector3};
     use obj::{IndexTuple, Obj, SimplePolygon};
 
     use std::io::Result;
     use std::path::Path;
     use std::sync::Arc;
 
-    fn get_vertex_and_normal<T: RealField>(
+    fn get_vertex_and_normal<T: Real>(
         index_tuple: &IndexTuple,
         vertex_positions: &Vec<[f32; 3]>,
         normal_positions: &Vec<[f32; 3]>,
@@ -28,7 +29,7 @@ mod wavefront_obj {
         (vertex, normal)
     }
 
-    fn get_triangles<T: RealField>(
+    fn get_triangles<T: Real>(
         polygon: &SimplePolygon,
         vertex_positions: &Vec<[f32; 3]>,
         normal_positions: &Vec<[f32; 3]>,
@@ -63,7 +64,7 @@ mod wavefront_obj {
         }
     }
 
-    pub fn load_obj<T: RealField>(
+    pub fn load_obj<T: Real>(
         filename: &Path,
         material: Arc<dyn Material<T>>,
     ) -> Result<Vec<Triangle<T>>>
diff --git a/src/raycasting/axis_aligned_bounding_box.rs b/src/raycasting/axis_aligned_bounding_box.rs
index 304929a..2275d6c 100644
--- a/src/raycasting/axis_aligned_bounding_box.rs
+++ b/src/raycasting/axis_aligned_bounding_box.rs
@@ -1,4 +1,4 @@
-use nalgebra::RealField;
+use crate::Real;
 
 use crate::util::Interval;
 
@@ -8,7 +8,7 @@ use itertools::izip;
 
 pub use crate::util::axis_aligned_bounding_box::BoundingBox;
 
-impl<T: RealField> IntersectP<T> for BoundingBox<T> {
+impl<T: Real> IntersectP<T> for BoundingBox<T> {
     fn intersect(&self, ray: &Ray<T>) -> bool {
         let mut t_interval_in_bounds = Interval::infinite();
         for (&ray_origin, &ray_direction, bounds) in
diff --git a/src/raycasting/mod.rs b/src/raycasting/mod.rs
index 8da192f..ec0056c 100644
--- a/src/raycasting/mod.rs
+++ b/src/raycasting/mod.rs
@@ -1,6 +1,7 @@
-use nalgebra::{Point3, RealField, Vector3};
+use nalgebra::{Point3, Vector3};
 
 use super::materials::Material;
+use crate::Real;
 
 use std::sync::Arc;
 
@@ -16,14 +17,13 @@ pub use triangle::Triangle;
 pub mod axis_aligned_bounding_box;
 pub use axis_aligned_bounding_box::BoundingBox;
 
-
 #[derive(Clone, Debug)]
-pub struct Ray<T: RealField> {
+pub struct Ray<T: Real> {
     pub origin: Point3<T>,
     pub direction: Vector3<T>,
 }
 
-impl<T: RealField> Ray<T> {
+impl<T: Real> Ray<T> {
     pub fn new(origin: Point3<T>, direction: Vector3<T>) -> Ray<T> {
         Ray {
             origin,
@@ -41,7 +41,7 @@ impl<T: RealField> Ray<T> {
 }
 
 #[derive(Debug)]
-pub struct IntersectionInfo<T: RealField> {
+pub struct IntersectionInfo<T: Real> {
     pub distance: T,
     pub location: Point3<T>,
     pub normal: Vector3<T>,
@@ -51,21 +51,21 @@ pub struct IntersectionInfo<T: RealField> {
     pub material: Arc<dyn Material<T>>,
 }
 
-pub trait Intersect<T: RealField>: Send + Sync {
+pub trait Intersect<T: Real>: Send + Sync {
     /// Test if the ray intersects the object, and return information about the object and intersection.
     fn intersect<'a>(&'a self, ray: &Ray<T>) -> Option<IntersectionInfo<T>>;
 }
 
-pub trait IntersectP<T: RealField>: Send + Sync {
+pub trait IntersectP<T: Real>: Send + Sync {
     /// Test if the ray intersects the object, without calculating any extra information.
     fn intersect(&self, ray: &Ray<T>) -> bool;
 }
 
-pub trait HasBoundingBox<T: RealField>: Send + Sync {
+pub trait HasBoundingBox<T: Real>: Send + Sync {
     fn bounding_box(&self) -> BoundingBox<T>;
 }
 
-pub trait Primitive<T: RealField>: Intersect<T> + HasBoundingBox<T> {}
+pub trait Primitive<T: Real>: Intersect<T> + HasBoundingBox<T> {}
 
 #[cfg(test)]
 mod tests {
@@ -73,7 +73,7 @@ mod tests {
 
     use super::*;
     use quickcheck::{Arbitrary, Gen};
-    impl<T: Arbitrary + RealField> Arbitrary for Ray<T> {
+    impl<T: Arbitrary + Real> Arbitrary for Ray<T> {
         fn arbitrary<G: Gen>(g: &mut G) -> Ray<T> {
             let origin = <Point3<T> as Arbitrary>::arbitrary(g);
             let direction = <Vector3<T> as Arbitrary>::arbitrary(g);
@@ -98,9 +98,9 @@ mod tests {
         let p3 = ray.point_at(t3);
         let epsilon = [t1, t2, t3, ray.origin[0], ray.origin[1], ray.origin[2]]
             .iter()
-            .fold(0.0, |a, &b| a.max(b.abs()))
+            .fold(0.0f64, |a, &b| a.max(b.abs()))
             * std::f64::EPSILON
-            * 256.0;
+            * 256.0f64;
         (p2 - p1).cross(&(p3 - p2)).norm() < epsilon
     }
 
diff --git a/src/raycasting/plane.rs b/src/raycasting/plane.rs
index fd8ebda..7babf05 100644
--- a/src/raycasting/plane.rs
+++ b/src/raycasting/plane.rs
@@ -1,12 +1,13 @@
-use nalgebra::{convert, Point3, RealField, Vector3};
+use nalgebra::{convert, Point3, Vector3};
 
 use crate::materials::Material;
+use crate::Real;
 
 use super::{BoundingBox, HasBoundingBox, Intersect, IntersectionInfo, Primitive, Ray};
 
 use std::sync::Arc;
 
-pub struct Plane<T: RealField> {
+pub struct Plane<T: Real> {
     normal: Vector3<T>,
     tangent: Vector3<T>,
     cotangent: Vector3<T>,
@@ -14,7 +15,7 @@ pub struct Plane<T: RealField> {
     material: Arc<dyn Material<T>>,
 }
 
-impl<T: RealField> Plane<T> {
+impl<T: Real> Plane<T> {
     pub fn new(
         normal: Vector3<T>,
         distance_from_origin: T,
@@ -35,7 +36,7 @@ impl<T: RealField> Plane<T> {
     }
 }
 
-impl<T: RealField> Intersect<T> for Plane<T> {
+impl<T: Real> Intersect<T> for Plane<T> {
     fn intersect<'a>(&'a self, ray: &Ray<T>) -> Option<IntersectionInfo<T>> {
         let ray_direction_dot_plane_normal = ray.direction.dot(&self.normal);
         let point_on_plane = self.normal * self.distance_from_origin;
@@ -64,7 +65,7 @@ impl<T: RealField> Intersect<T> for Plane<T> {
     }
 }
 
-impl<T: RealField> HasBoundingBox<T> for Plane<T> {
+impl<T: Real> HasBoundingBox<T> for Plane<T> {
     fn bounding_box(&self) -> BoundingBox<T> {
         let p0 = Point3::from(self.normal * self.distance_from_origin);
         let f = |v: Vector3<T>| {
@@ -87,7 +88,7 @@ impl<T: RealField> HasBoundingBox<T> for Plane<T> {
     }
 }
 
-impl<T: RealField> Primitive<T> for Plane<T> {}
+impl<T: Real> Primitive<T> for Plane<T> {}
 
 #[cfg(test)]
 mod tests {
diff --git a/src/raycasting/sphere.rs b/src/raycasting/sphere.rs
index 7fd7e3e..85b9701 100644
--- a/src/raycasting/sphere.rs
+++ b/src/raycasting/sphere.rs
@@ -1,18 +1,19 @@
-use nalgebra::{convert, Point3, RealField, Vector3};
+use nalgebra::{convert, Point3, Vector3};
 
 use crate::materials::Material;
+use crate::Real;
 
 use super::{BoundingBox, HasBoundingBox, Intersect, IntersectionInfo, Primitive, Ray};
 
 use std::sync::Arc;
 
-pub struct Sphere<T: RealField> {
+pub struct Sphere<T: Real> {
     centre: Point3<T>,
     radius: T,
     material: Arc<dyn Material<T>>,
 }
 
-impl<T: RealField> Sphere<T> {
+impl<T: Real> Sphere<T> {
     pub fn new(centre: Point3<T>, radius: T, material: Arc<dyn Material<T>>) -> Sphere<T> {
         Sphere {
             centre,
@@ -22,7 +23,7 @@ impl<T: RealField> Sphere<T> {
     }
 }
 
-impl<T: RealField> Intersect<T> for Sphere<T> {
+impl<T: Real> Intersect<T> for Sphere<T> {
     fn intersect<'a>(&'a self, ray: &Ray<T>) -> Option<IntersectionInfo<T>> {
         let two: T = convert(2.0);
         let four: T = convert(4.0);
@@ -77,14 +78,14 @@ impl<T: RealField> Intersect<T> for Sphere<T> {
     }
 }
 
-impl<T: RealField> HasBoundingBox<T> for Sphere<T> {
+impl<T: Real> HasBoundingBox<T> for Sphere<T> {
     fn bounding_box(&self) -> BoundingBox<T> {
         let radius_xyz = Vector3::new(self.radius, self.radius, self.radius);
         BoundingBox::from_corners(self.centre + radius_xyz, self.centre - radius_xyz)
     }
 }
 
-impl<T: RealField> Primitive<T> for Sphere<T> {}
+impl<T: Real> Primitive<T> for Sphere<T> {}
 
 #[cfg(test)]
 mod tests {
diff --git a/src/raycasting/triangle.rs b/src/raycasting/triangle.rs
index d38f92a..509e21d 100644
--- a/src/raycasting/triangle.rs
+++ b/src/raycasting/triangle.rs
@@ -1,18 +1,19 @@
 use crate::materials::Material;
+use crate::Real;
 
 use super::{BoundingBox, HasBoundingBox, Intersect, IntersectionInfo, Primitive, Ray};
-use nalgebra::{Point3, RealField, Vector2, Vector3};
+use nalgebra::{Point3, Vector2, Vector3};
 
 use std::sync::Arc;
 
 #[derive(Debug)]
-pub struct Triangle<T: RealField> {
+pub struct Triangle<T: Real> {
     pub vertices: [Point3<T>; 3],
     pub normals: [Vector3<T>; 3],
     pub material: Arc<dyn Material<T>>,
 }
 
-impl<T: RealField> Intersect<T> for Triangle<T> {
+impl<T: Real> Intersect<T> for Triangle<T> {
     fn intersect<'a>(&'a self, ray: &Ray<T>) -> Option<IntersectionInfo<T>> {
         let translation = -ray.origin.coords;
         let indices = indices_with_index_of_largest_element_last(&ray.direction);
@@ -77,15 +78,15 @@ impl<T: RealField> Intersect<T> for Triangle<T> {
     }
 }
 
-impl<T: RealField> HasBoundingBox<T> for Triangle<T> {
+impl<T: Real> HasBoundingBox<T> for Triangle<T> {
     fn bounding_box(&self) -> BoundingBox<T> {
         BoundingBox::from_points(&self.vertices)
     }
 }
 
-impl<T: RealField> Primitive<T> for Triangle<T> {}
+impl<T: Real> Primitive<T> for Triangle<T> {}
 
-fn indices_with_index_of_largest_element_last<T: RealField>(v: &Vector3<T>) -> [usize; 3] {
+fn indices_with_index_of_largest_element_last<T: Real>(v: &Vector3<T>) -> [usize; 3] {
     if v.x > v.y {
         if v.z > v.x {
             [0, 1, 2]
@@ -105,24 +106,24 @@ fn is_valid_permutation(indices: &[usize; 3]) -> bool {
     (0..2).all(|i: usize| indices.iter().any(|&j| j == i))
 }
 
-fn permute_vector_elements<T: RealField>(v: &Vector3<T>, indices: &[usize; 3]) -> Vector3<T> {
+fn permute_vector_elements<T: Real>(v: &Vector3<T>, indices: &[usize; 3]) -> Vector3<T> {
     debug_assert!(is_valid_permutation(&indices));
     Vector3::new(v[indices[0]], v[indices[1]], v[indices[2]])
 }
 
-fn calculate_shear_to_z_axis<T: RealField>(v: &Vector3<T>) -> Vector2<T> {
+fn calculate_shear_to_z_axis<T: Real>(v: &Vector3<T>) -> Vector2<T> {
     Vector2::new(-v.x / v.z, -v.y / v.z)
 }
 
-fn apply_shear_to_z_axis<T: RealField>(v: &Vector3<T>, s: &Vector2<T>) -> Vector3<T> {
+fn apply_shear_to_z_axis<T: Real>(v: &Vector3<T>, s: &Vector2<T>) -> Vector3<T> {
     Vector3::new(v.x + s.x * v.z, v.y + s.y * v.z, v.z)
 }
 
-fn signed_edge_function<T: RealField>(a: &Vector3<T>, b: &Vector3<T>) -> T {
+fn signed_edge_function<T: Real>(a: &Vector3<T>, b: &Vector3<T>) -> T {
     a.x * b.y - b.x * a.y
 }
 
-fn signed_edge_functions<T: RealField>(vertices: &Vec<Vector3<T>>) -> Vector3<T> {
+fn signed_edge_functions<T: Real>(vertices: &Vec<Vector3<T>>) -> Vector3<T> {
     // Iterate over the inputs in such a way that each output element is calculated
     // from the twoother elements of the input. ( (y,z) -> x, (z,x) -> y, (x,y) -> z )
     Vector3::from_iterator(
@@ -136,7 +137,7 @@ fn signed_edge_functions<T: RealField>(vertices: &Vec<Vector3<T>>) -> Vector3<T>
     )
 }
 
-fn barycentric_coordinates_from_signed_edge_functions<T: RealField>(e: Vector3<T>) -> Vector3<T> {
+fn barycentric_coordinates_from_signed_edge_functions<T: Real>(e: Vector3<T>) -> Vector3<T> {
     e * (T::one() / e.iter().fold(T::zero(), |a, &b| a + b))
 }
 
diff --git a/src/realtype.rs b/src/realtype.rs
new file mode 100644
index 0000000..1aa2f9d
--- /dev/null
+++ b/src/realtype.rs
@@ -0,0 +1,6 @@
+use nalgebra::RealField;
+
+pub trait Real: RealField {}
+
+impl Real for f32 {}
+impl Real for f64 {}
diff --git a/src/sampler.rs b/src/sampler.rs
index 172bcb6..06422a3 100644
--- a/src/sampler.rs
+++ b/src/sampler.rs
@@ -1,13 +1,13 @@
 use super::raycasting::{IntersectionInfo, Ray};
 use super::scene::Scene;
 
-use nalgebra::RealField;
+use crate::Real;
 
-pub struct Sampler<'a, T: RealField> {
+pub struct Sampler<'a, T: Real> {
     pub scene: &'a Scene<T>,
 }
 
-impl<'a, T: RealField> Sampler<'a, T> {
+impl<'a, T: Real> Sampler<'a, T> {
     pub fn sample(&self, ray: &Ray<T>) -> Option<IntersectionInfo<T>> {
         self.scene
             .objects
diff --git a/src/scene.rs b/src/scene.rs
index d11d826..18c1536 100644
--- a/src/scene.rs
+++ b/src/scene.rs
@@ -1,10 +1,11 @@
-use nalgebra::{Point3, RealField};
+use nalgebra::{Point3};
 
 use crate::raycasting::Primitive;
+use crate::Real;
 
 use std::sync::Arc;
 
-pub struct Scene<T: RealField> {
+pub struct Scene<T: Real> {
     pub camera_location: Point3<T>,
     pub objects: Vec<Arc<dyn Primitive<T>>>,
 }
diff --git a/src/util/algebra_utils.rs b/src/util/algebra_utils.rs
index a504ef4..d4dc9f3 100644
--- a/src/util/algebra_utils.rs
+++ b/src/util/algebra_utils.rs
@@ -1,6 +1,8 @@
-use nalgebra::{Matrix3, RealField, Vector3};
+use nalgebra::{Matrix3, Vector3};
 
-pub fn try_change_of_basis_matrix<T: RealField>(
+use crate::Real;
+
+pub fn try_change_of_basis_matrix<T: Real>(
     x: &Vector3<T>,
     y: &Vector3<T>,
     z: &Vector3<T>,
diff --git a/src/util/axis_aligned_bounding_box.rs b/src/util/axis_aligned_bounding_box.rs
index 02bce5f..0e55600 100644
--- a/src/util/axis_aligned_bounding_box.rs
+++ b/src/util/axis_aligned_bounding_box.rs
@@ -1,15 +1,16 @@
-use nalgebra::{Point3, RealField};
+use nalgebra::Point3;
 
 use crate::util::Interval;
+use crate::Real;
 
 use itertools::izip;
 
 #[derive(Debug, Clone, Copy)]
-pub struct BoundingBox<T: RealField> {
+pub struct BoundingBox<T: Real> {
     pub bounds: [Interval<T>; 3],
 }
 
-impl<T: RealField> BoundingBox<T> {
+impl<T: Real> BoundingBox<T> {
     pub fn from_corners(a: Point3<T>, b: Point3<T>) -> Self {
         let mut result = BoundingBox {
             bounds: [Interval::infinite(); 3],
diff --git a/src/util/interval.rs b/src/util/interval.rs
index 4389681..6f6b0bc 100644
--- a/src/util/interval.rs
+++ b/src/util/interval.rs
@@ -1,12 +1,14 @@
-use nalgebra::{convert, RealField};
+use nalgebra::convert;
+
+use crate::Real;
 
 #[derive(Debug, Clone, Copy)]
-pub struct Interval<T: RealField> {
+pub struct Interval<T: Real> {
     min: T,
     max: T,
 }
 
-impl<T: RealField> Interval<T> {
+impl<T: Real> Interval<T> {
     pub fn new(a: T, b: T) -> Self {
         if a > b {
             Interval { min: b, max: a }
diff --git a/src/util/normalizer.rs b/src/util/normalizer.rs
index 27e14cd..6c2dadf 100644
--- a/src/util/normalizer.rs
+++ b/src/util/normalizer.rs
@@ -1,17 +1,19 @@
 use super::axis_aligned_bounding_box::BoundingBox;
 use super::Interval;
 
-use nalgebra::{clamp, Point3, RealField};
+use crate::Real;
+
+use nalgebra::{clamp, Point3};
 
 use itertools::izip;
 
 #[derive(Debug, Copy, Clone)]
-pub struct RealFieldNormalizer<T: RealField> {
+pub struct RealNormalizer<T: Real> {
     min: T,
     range: T,
 }
 
-impl<T: RealField> RealFieldNormalizer<T> {
+impl<T: Real> RealNormalizer<T> {
     pub fn new(interval: Interval<T>) -> Self {
         let min = interval.get_min();
         let range = interval.get_max() - min;
@@ -28,21 +30,21 @@ impl<T: RealField> RealFieldNormalizer<T> {
 }
 
 #[derive(Debug)]
-pub struct Point3Normalizer<T: RealField> {
-    dimension_normalizers: [RealFieldNormalizer<T>; 3],
+pub struct Point3Normalizer<T: Real> {
+    dimension_normalizers: [RealNormalizer<T>; 3],
 }
 
-impl<T: RealField> Point3Normalizer<T> {
+impl<T: Real> Point3Normalizer<T> {
     pub fn new(bounds: BoundingBox<T>) -> Self {
         let mut normalizer = Point3Normalizer {
-            dimension_normalizers: [RealFieldNormalizer::new(Interval::empty()); 3],
+            dimension_normalizers: [RealNormalizer::new(Interval::empty()); 3],
         };
         for (normalizer, &bounds) in normalizer
             .dimension_normalizers
             .iter_mut()
             .zip(bounds.bounds.iter())
         {
-            *normalizer = RealFieldNormalizer::new(bounds);
+            *normalizer = RealNormalizer::new(bounds);
         }
         normalizer
     }
@@ -80,43 +82,43 @@ mod test {
 
     #[quickcheck]
     fn normalize_zero_to_one_yields_input(value: f64) -> bool {
-        let target = RealFieldNormalizer::new(Interval::new(0.0, 1.0));
+        let target = RealNormalizer::new(Interval::new(0.0, 1.0));
         target.normalize(value) == value
     }
 
     #[quickcheck]
     fn normalize_two_to_three_yields_input_minus_two(value: f64) -> bool {
-        let target = RealFieldNormalizer::new(Interval::new(2.0, 3.0));
+        let target = RealNormalizer::new(Interval::new(2.0, 3.0));
         target.normalize(value) == value - 2.0
     }
 
     #[quickcheck]
     fn normalize_negative_three_to_negative_two_yields_input_plus_three(value: f64) -> bool {
-        let target = RealFieldNormalizer::new(Interval::new(-3.0, -2.0));
+        let target = RealNormalizer::new(Interval::new(-3.0, -2.0));
         target.normalize(value) == value + 3.0
     }
 
     #[quickcheck]
     fn normalize_zero_to_two_yields_input_divided_by_two(value: f64) -> bool {
-        let target = RealFieldNormalizer::new(Interval::new(0.0, 2.0));
+        let target = RealNormalizer::new(Interval::new(0.0, 2.0));
         target.normalize(value) == value / 2.0
     }
 
     #[test]
     fn normalize_two_to_four_yields_zero_when_input_is_two() {
-        let target = RealFieldNormalizer::new(Interval::new(2.0, 4.0));
+        let target = RealNormalizer::new(Interval::new(2.0, 4.0));
         assert!(target.normalize(2.0) == 0.0)
     }
 
     #[test]
     fn normalize_two_to_four_yields_one_when_input_is_four() {
-        let target = RealFieldNormalizer::new(Interval::new(2.0, 4.0));
+        let target = RealNormalizer::new(Interval::new(2.0, 4.0));
         assert!(target.normalize(4.0) == 1.0)
     }
 
     #[quickcheck]
     fn normalize_two_to_four_yields_input_divided_by_two_minus_one(value: f64) -> bool {
-        let target = RealFieldNormalizer::new(Interval::new(2.0, 4.0));
+        let target = RealNormalizer::new(Interval::new(2.0, 4.0));
         target.normalize(value) == (value - 2.0) / 2.0
     }
 
@@ -124,7 +126,7 @@ mod test {
     fn normalize_and_clamp_two_to_four_yields_zero_when_input_less_than_or_equal_two(
         value: f64,
     ) -> bool {
-        let target = RealFieldNormalizer::new(Interval::new(2.0, 4.0));
+        let target = RealNormalizer::new(Interval::new(2.0, 4.0));
         target.normalize_and_clamp(value) == 0.0 || value > 2.0
     }
 
@@ -132,7 +134,7 @@ mod test {
     fn normalize_and_clamp_two_to_four_yields_one_when_input_greater_than_or_equal_four(
         value: f64,
     ) -> bool {
-        let target = RealFieldNormalizer::new(Interval::new(2.0, 4.0));
+        let target = RealNormalizer::new(Interval::new(2.0, 4.0));
         target.normalize_and_clamp(value) == 1.0 || value < 4.0
     }
 
@@ -140,7 +142,7 @@ mod test {
     fn normalize_and_clamp_two_to_four_yields_same_value_as_normalize_when_in_range(
         value: f64,
     ) -> bool {
-        let target = RealFieldNormalizer::new(Interval::new(2.0, 4.0));
+        let target = RealNormalizer::new(Interval::new(2.0, 4.0));
         target.normalize_and_clamp(value) == target.normalize(value) || value < 2.0 || value > 4.0
     }
 
@@ -150,9 +152,9 @@ mod test {
         b: Point3<f64>,
         c: Point3<f64>,
     ) -> bool {
-        let x_normalizer = RealFieldNormalizer::new(Interval::new(a.x.min(b.x), a.x.max(b.x)));
-        let y_normalizer = RealFieldNormalizer::new(Interval::new(a.y.min(b.y), a.y.max(b.y)));
-        let z_normalizer = dbg!(RealFieldNormalizer::new(Interval::new(
+        let x_normalizer = RealNormalizer::new(Interval::new(a.x.min(b.x), a.x.max(b.x)));
+        let y_normalizer = RealNormalizer::new(Interval::new(a.y.min(b.y), a.y.max(b.y)));
+        let z_normalizer = dbg!(RealNormalizer::new(Interval::new(
             a.z.min(b.z),
             a.z.max(b.z)
         )));
@@ -169,15 +171,15 @@ mod test {
         b: Point3<f64>,
         c: Point3<f64>,
     ) -> bool {
-        let x_normalizer = dbg!(RealFieldNormalizer::new(Interval::new(
+        let x_normalizer = dbg!(RealNormalizer::new(Interval::new(
             a.x.min(b.x),
             a.x.max(b.x)
         )));
-        let y_normalizer = dbg!(RealFieldNormalizer::new(Interval::new(
+        let y_normalizer = dbg!(RealNormalizer::new(Interval::new(
             a.y.min(b.y),
             a.y.max(b.y)
         )));
-        let z_normalizer = dbg!(RealFieldNormalizer::new(Interval::new(
+        let z_normalizer = dbg!(RealNormalizer::new(Interval::new(
             a.z.min(b.z),
             a.z.max(b.z)
         )));