diff --git a/demo/server/src/main.rs b/demo/server/src/main.rs
index aa5271c3..7ab42868 100644
--- a/demo/server/src/main.rs
+++ b/demo/server/src/main.rs
@@ -26,8 +26,9 @@ use bincode::Infinite;
 use euclid::{Point2D, Size2D, Transform2D};
 use pathfinder_font_renderer::{FontContext, FontInstanceKey, FontKey, GlyphKey};
 use pathfinder_partitioner::partitioner::Partitioner;
+use pathfinder_path_utils::monotonic::MonotonicPathSegmentStream;
 use pathfinder_path_utils::stroke;
-use pathfinder_path_utils::{PathBuffer, PathSegment, Transform2DPathStream};
+use pathfinder_path_utils::{PathBuffer, PathBufferStream, PathSegment, Transform2DPathStream};
 use rocket::http::{ContentType, Status};
 use rocket::request::Request;
 use rocket::response::{NamedFile, Redirect, Responder, Response};
@@ -410,7 +411,9 @@ fn partition_font(request: Json<PartitionFontRequest>)
 
         // This might fail; if so, just leave it blank.
         if let Ok(glyph_outline) = font_context.glyph_outline(&font_instance_key, &glyph_key) {
-            path_buffer.add_stream(Transform2DPathStream::new(glyph_outline, &glyph.transform))
+            let stream = Transform2DPathStream::new(glyph_outline, &glyph.transform);
+            let stream = MonotonicPathSegmentStream::new(stream);
+            path_buffer.add_stream(stream)
         }
 
         let last_subpath_index = path_buffer.subpaths.len();
@@ -497,9 +500,15 @@ fn partition_svg_paths(request: Json<PartitionSvgPathsRequest>)
         }
 
         match path.kind {
-            PartitionSvgPathKind::Fill => path_buffer.add_stream(stream.into_iter()),
+            PartitionSvgPathKind::Fill => {
+                path_buffer.add_stream(MonotonicPathSegmentStream::new(stream.into_iter()))
+            }
             PartitionSvgPathKind::Stroke(stroke_width) => {
-                stroke::stroke(&mut path_buffer, stream.into_iter(), stroke_width)
+                let mut temp_path_buffer = PathBuffer::new();
+                stroke::stroke(&mut temp_path_buffer, stream.into_iter(), stroke_width);
+                let stream = PathBufferStream::new(&temp_path_buffer);
+                let stream = MonotonicPathSegmentStream::new(stream);
+                path_buffer.add_stream(stream)
             }
         }
 
diff --git a/partitioner/src/geometry.rs b/partitioner/src/geometry.rs
index 759937f1..472b4e3e 100644
--- a/partitioner/src/geometry.rs
+++ b/partitioner/src/geometry.rs
@@ -10,6 +10,7 @@
 
 use euclid::Point2D;
 use euclid::approxeq::ApproxEq;
+use pathfinder_path_utils::curve::Curve;
 use std::cmp::Ordering;
 
 pub(crate) trait ApproxOrdered {
@@ -85,11 +86,6 @@ pub fn quadratic_bezier_quadratic_bezier_crossing_point(_a_p0: &Point2D<f32>,
     None
 }
 
-pub fn sample_quadratic_bezier(t: f32, p0: &Point2D<f32>, p1: &Point2D<f32>, p2: &Point2D<f32>)
-                               -> Point2D<f32> {
-    p0.lerp(*p1, t).lerp(p1.lerp(*p2, t), t)
-}
-
 pub fn solve_line_t_for_x(x: f32, a: &Point2D<f32>, b: &Point2D<f32>) -> f32 {
     if b.x == a.x {
         0.0
@@ -121,7 +117,7 @@ pub fn solve_quadratic_bezier_y_for_x(x: f32,
                                       p1: &Point2D<f32>,
                                       p2: &Point2D<f32>)
                                       -> f32 {
-    sample_quadratic_bezier(solve_quadratic_bezier_t_for_x(x, p0, p1, p2), p0, p1, p2).y
+    Curve::new(p0, p1, p2).sample(solve_quadratic_bezier_t_for_x(x, p0, p1, p2)).y
 }
 
 fn quadratic_bezier_axis_inflection_point(p0: f32, p1: f32, p2: f32) -> Option<f32> {
diff --git a/partitioner/src/partitioner.rs b/partitioner/src/partitioner.rs
index 1e09a89e..299e29ac 100644
--- a/partitioner/src/partitioner.rs
+++ b/partitioner/src/partitioner.rs
@@ -13,6 +13,7 @@ use euclid::Point2D;
 use geometry::{self, SubdividedQuadraticBezier};
 use log::LogLevel;
 use pathfinder_path_utils::PathBuffer;
+use pathfinder_path_utils::curve::Curve;
 use std::collections::BinaryHeap;
 use std::cmp::Ordering;
 use std::f32;
@@ -712,10 +713,7 @@ impl<'a> Partitioner<'a> {
             }
             control_point_vertex_index => {
                 let control_point = &self.b_vertex_positions[control_point_vertex_index as usize];
-                geometry::sample_quadratic_bezier(t,
-                                                  left_vertex_position,
-                                                  control_point,
-                                                  right_endpoint_position)
+                Curve::new(left_vertex_position, control_point, right_endpoint_position).sample(t)
             }
         }
     }
diff --git a/path-utils/src/lib.rs b/path-utils/src/lib.rs
index a3c7d77e..d7a6d449 100644
--- a/path-utils/src/lib.rs
+++ b/path-utils/src/lib.rs
@@ -98,6 +98,53 @@ impl PathBuffer {
     }
 }
 
+pub struct PathBufferStream<'a> {
+    path_buffer: &'a PathBuffer,
+    endpoint_index: u32,
+    subpath_index: u32,
+}
+
+impl<'a> PathBufferStream<'a> {
+    pub fn new<'b>(path_buffer: &'b PathBuffer) -> PathBufferStream<'b> {
+        PathBufferStream {
+            path_buffer: path_buffer,
+            endpoint_index: 0,
+            subpath_index: 0,
+        }
+    }
+}
+
+impl<'a> Iterator for PathBufferStream<'a> {
+    type Item = PathSegment;
+
+    fn next(&mut self) -> Option<PathSegment> {
+        if self.subpath_index as usize == self.path_buffer.subpaths.len() {
+            return None
+        }
+
+        let subpath = &self.path_buffer.subpaths[self.subpath_index as usize];
+        if self.endpoint_index == subpath.last_endpoint_index {
+            self.subpath_index += 1;
+            return Some(PathSegment::ClosePath)
+        }
+
+        let endpoint = &self.path_buffer.endpoints[self.endpoint_index as usize];
+        self.endpoint_index += 1;
+
+        if self.endpoint_index == subpath.first_endpoint_index {
+            return Some(PathSegment::MoveTo(endpoint.position))
+        }
+
+        if endpoint.control_point_index == u32::MAX {
+            return Some(PathSegment::LineTo(endpoint.position))
+        }
+
+        let control_point = &self.path_buffer
+                                 .control_points[endpoint.control_point_index as usize];
+        Some(PathSegment::CurveTo(*control_point, endpoint.position))
+    }
+}
+
 #[repr(C)]
 #[derive(Debug, Clone, Copy, Serialize, Deserialize)]
 pub struct Endpoint {