From 0585a7e2499ae94b1927aac3d5d97e85a911fa86 Mon Sep 17 00:00:00 2001
From: Tristam MacDonald <tristam@trist.am>
Date: Mon, 18 Jan 2021 08:23:19 +0100
Subject: [PATCH 1/3] Make nested source public on CentralDifference

---
 src/source.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/source.rs b/src/source.rs
index 509484f..655bd89 100644
--- a/src/source.rs
+++ b/src/source.rs
@@ -33,7 +33,7 @@ pub trait HermiteSource: Source {
 
 /// Adapts a `Source` to a `HermiteSource` by deriving normals from the surface via central differencing
 pub struct CentralDifference<S: Source> {
-    source: S,
+    pub source: S,
     epsilon: f32,
 }
 

From 6ca10556a0e62e67928a9ce6da697b03e12ccd8b Mon Sep 17 00:00:00 2001
From: Tristam MacDonald <tristam@trist.am>
Date: Mon, 18 Jan 2021 08:25:01 +0100
Subject: [PATCH 2/3] Add some useful functions to the Vec type

---
 src/math.rs | 47 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)

diff --git a/src/math.rs b/src/math.rs
index 47e840d..42b4ead 100644
--- a/src/math.rs
+++ b/src/math.rs
@@ -48,6 +48,30 @@ impl Vec3 {
             z: 1.0,
         }
     }
+
+    /// Create a vector by taking the absolute value of each component in this vector
+    pub fn abs(&self) -> Self {
+        Self {
+            x: self.x.abs(),
+            y: self.y.abs(),
+            z: self.z.abs(),
+        }
+    }
+
+    /// Sum all of the components in this vector
+    pub fn component_sum(&self) -> f32 {
+        self.x + self.y + self.z
+    }
+
+    /// Find the maximum value out of all components in this vector
+    pub fn component_max(&self) -> f32 {
+        self.x.max(self.y.max(self.z))
+    }
+
+    /// Find the minimum value out of all components in this vector
+    pub fn component_min(&self) -> f32 {
+        self.x.min(self.y.min(self.z))
+    }
 }
 
 impl std::ops::Add for Vec3 {
@@ -81,6 +105,13 @@ impl std::ops::Mul<f32> for Vec3 {
         Vec3::new(self.x * other, self.y * other, self.z * other)
     }
 }
+impl std::ops::Mul<Vec3> for f32 {
+    type Output = Vec3;
+
+    fn mul(self, other: Vec3) -> Vec3 {
+        Vec3::new(self * other.x, self * other.y, self * other.z)
+    }
+}
 
 impl std::ops::Div for Vec3 {
     type Output = Vec3;
@@ -89,3 +120,19 @@ impl std::ops::Div for Vec3 {
         Vec3::new(self.x / other.x, self.y / other.y, self.z / other.z)
     }
 }
+
+impl std::ops::Div<f32> for Vec3 {
+    type Output = Vec3;
+
+    fn div(self, other: f32) -> Vec3 {
+        Vec3::new(self.x / other, self.y / other, self.z / other)
+    }
+}
+
+impl std::ops::Div<Vec3> for f32 {
+    type Output = Vec3;
+
+    fn div(self, other: Vec3) -> Vec3 {
+        Vec3::new(self / other.x, self / other.y, self / other.z)
+    }
+}

From 82fed2e1bfb6ac83dbccf970eaae1718067480f1 Mon Sep 17 00:00:00 2001
From: Tristam MacDonald <tristam@trist.am>
Date: Mon, 18 Jan 2021 09:03:30 +0100
Subject: [PATCH 3/3] Add support for evaluating max-norm distance fields

---
 src/linear_hashed_marching_cubes.rs | 29 +++++++++++++++++++++++++----
 src/source.rs                       | 10 +++++++++-
 2 files changed, 34 insertions(+), 5 deletions(-)

diff --git a/src/linear_hashed_marching_cubes.rs b/src/linear_hashed_marching_cubes.rs
index 84b04bb..88651f9 100644
--- a/src/linear_hashed_marching_cubes.rs
+++ b/src/linear_hashed_marching_cubes.rs
@@ -17,7 +17,7 @@ use crate::marching_cubes_impl::{get_offset, interpolate, march_cube};
 use crate::marching_cubes_tables::EDGE_CONNECTION;
 use crate::math::Vec3;
 use crate::morton::Morton;
-use crate::source::{HermiteSource, Source};
+use crate::source::{HermiteSource, Norm, Source};
 use std::collections::HashMap;
 
 // Morton cube corners are ordered differently to the marching cubes tables, so remap them to match.
@@ -43,15 +43,29 @@ impl Edge {
 /// Extracts meshes from distance fields using marching cubes over a linear hashed octree.
 pub struct LinearHashedMarchingCubes {
     max_depth: usize,
+    norm: Norm,
 }
 
 impl LinearHashedMarchingCubes {
     /// Create a new LinearHashedMarchingCubes.
     ///
     /// The depth of the internal octree will be at most `max_depth`, causing the tree to span the
-    /// equivalent of a cubic grid at most `2.pow(max_depth)` in either direction.
+    /// equivalent of a cubic grid at most `2.pow(max_depth)` in either direction. Distances
+    /// will be evaluated in Euclidean space.
     pub fn new(max_depth: usize) -> Self {
-        Self { max_depth }
+        Self {
+            max_depth,
+            norm: Norm::Euclidean,
+        }
+    }
+
+    /// Create a new LinearHashedMarchingCubes.
+    ///
+    /// The depth of the internal octree will be at most `max_depth`, causing the tree to span the
+    /// equivalent of a cubic grid at most `2.pow(max_depth)` in either direction. Distances will
+    /// be evaluated in accordance with the provided Norm.
+    pub fn with_norm(max_depth: usize, norm: Norm) -> Self {
+        Self { max_depth, norm }
     }
 
     /// Extracts a mesh from the given [`Source`](../source/trait.Source.html).
@@ -119,6 +133,13 @@ impl LinearHashedMarchingCubes {
         self.extract_surface(&octree, &primal_vertices, indices, &mut base_index, extract);
     }
 
+    fn diagonal(&self, distance: f32) -> f32 {
+        match self.norm {
+            Norm::Euclidean => distance * SQRT_OF_3,
+            Norm::Max => distance,
+        }
+    }
+
     fn build_octree<S>(&mut self, source: &S) -> LinearHashedOctree<f32>
     where
         S: Source,
@@ -130,7 +151,7 @@ impl LinearHashedMarchingCubes {
             |key: Morton, distance: &f32| {
                 let level = key.level();
                 let size = key.size();
-                level < 2 || (level < max_depth && distance.abs() <= size * SQRT_OF_3)
+                level < 2 || (level < max_depth && distance.abs() <= self.diagonal(size))
             },
             |key: Morton| {
                 let p = key.center();
diff --git a/src/source.rs b/src/source.rs
index 655bd89..1560a67 100644
--- a/src/source.rs
+++ b/src/source.rs
@@ -14,11 +14,19 @@
 
 use crate::math::Vec3;
 
+/// The context in which signed distance fields should be evaluated
+pub enum Norm {
+    /// The L^2 or Euclidean norm is the one you are used to, i.e. where l = sqrt(x^2 + y^2 + z^2).
+    Euclidean,
+    /// The L^∞ or Max norm represents Manhattan/Taxicab distance, i.e. l = max(|x|, |y|, |z|).
+    Max,
+}
+
 /// A source capable of sampling a signed distance field at discrete coordinates.
 pub trait Source {
     /// Samples the distance field at the given (x, y, z) coordinates.
     ///
-    /// Must return the signed distance (i.e. negative for coodinates inside the surface),
+    /// Must return the signed distance (i.e. negative for coordinates inside the surface),
     /// as our Marching Cubes implementation will evaluate the surface at the zero-crossing.
     fn sample(&self, x: f32, y: f32, z: f32) -> f32;
 }

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