diff --git a/editor/src/experimental.rs b/editor/src/experimental.rs
index 577b84205e..6fa7b93382 100644
--- a/editor/src/experimental.rs
+++ b/editor/src/experimental.rs
@@ -1,8 +1,7 @@
 use ezgui::canvas::Canvas;
 use ezgui::input::UserInput;
 use ezgui::GfxCtx;
-use geom;
-use geom::{PolyLine, Pt2D};
+use geom::{PolyLine, Polygon, Pt2D};
 use graphics;
 use graphics::types::Color;
 use gui;
@@ -307,7 +306,7 @@ impl UI {
             Pt2D::new(947.7612927256201, 765.1100512564725), // 5
         ];
         //draw_polyline(g, &PolyLine::new(pts.clone()), 0.25, RED);
-        for tri in geom::triangulate(&pts).iter() {
+        for tri in Polygon::new(&pts).for_drawing().iter() {
             g.draw_polygon(BLUE, tri);
         }
 
diff --git a/editor/src/plugins/geom_validation.rs b/editor/src/plugins/geom_validation.rs
index d43cf7fe7b..863d6ab096 100644
--- a/editor/src/plugins/geom_validation.rs
+++ b/editor/src/plugins/geom_validation.rs
@@ -3,7 +3,7 @@ use ezgui::input::UserInput;
 use generator;
 use geo;
 use geo::prelude::Intersects;
-use geom::Pt2D;
+use geom::{Polygon, Pt2D};
 use graphics::math::Vec2d;
 use map_model::{geometry, BuildingID, IntersectionID, LaneID, Map, ParcelID};
 use piston::input::Key;
@@ -42,13 +42,13 @@ impl Validator {
             ));
         }
         for i in &draw_map.intersections {
-            objects.push((ID::Intersection(i.id), vec![make_poly(&i.polygon)]));
+            objects.push((ID::Intersection(i.id), vec![make_new_poly(&i.polygon)]));
         }
         for b in &draw_map.buildings {
-            objects.push((ID::Building(b.id), vec![make_poly(&b.fill_polygon)]));
+            objects.push((ID::Building(b.id), vec![make_new_poly(&b.fill_polygon)]));
         }
         for p in &draw_map.parcels {
-            objects.push((ID::Parcel(p.id), vec![make_poly(&p.fill_polygon)]));
+            objects.push((ID::Parcel(p.id), vec![make_new_poly(&p.fill_polygon)]));
         }
 
         println!(
@@ -139,6 +139,14 @@ fn make_poly(points: &Vec<Vec2d>) -> geo::Polygon<f64> {
     geo::Polygon::new(exterior.into(), Vec::new())
 }
 
+fn make_new_poly(p: &Polygon) -> geo::Polygon<f64> {
+    let exterior: Vec<geo::Point<f64>> = p.pts
+        .iter()
+        .map(|pt| geo::Point::new(pt.x(), pt.y()))
+        .collect();
+    geo::Polygon::new(exterior.into(), Vec::new())
+}
+
 // TODO duplicated with warp. generic handling of object types?
 fn get_pt(map: &Map, id: ID) -> Pt2D {
     match id {
diff --git a/editor/src/render/building.rs b/editor/src/render/building.rs
index ec0835a1fc..0b107a4f49 100644
--- a/editor/src/render/building.rs
+++ b/editor/src/render/building.rs
@@ -2,15 +2,12 @@
 
 use aabb_quadtree::geom::Rect;
 use ezgui::GfxCtx;
-use geom;
-use geom::PolyLine;
+use geom::{PolyLine, Polygon, Pt2D};
 use graphics;
 use graphics::math::Vec2d;
 use graphics::types::Color;
-use map_model;
-use map_model::geometry;
-use map_model::{BuildingID, Map};
-use render::PARCEL_BOUNDARY_THICKNESS;
+use map_model::{Building, BuildingID, Map};
+use render::{get_bbox, PARCEL_BOUNDARY_THICKNESS};
 use std::f64;
 
 #[derive(Debug)]
@@ -18,22 +15,19 @@ pub struct DrawBuilding {
     pub id: BuildingID,
     // TODO should just have one. use graphics::Line for now.
     boundary_polygons: Vec<Vec<Vec2d>>,
-    // TODO rm the other one
-    pub fill_polygon: Vec<Vec2d>,
-    fill_triangles: Vec<Vec<Vec2d>>,
+    pub fill_polygon: Polygon,
     front_path: Option<[f64; 4]>,
 }
 
 impl DrawBuilding {
-    pub fn new(bldg: &map_model::Building) -> DrawBuilding {
+    pub fn new(bldg: &Building) -> DrawBuilding {
         DrawBuilding {
             id: bldg.id,
-            fill_polygon: bldg.points.iter().map(|pt| [pt.x(), pt.y()]).collect(),
             // TODO ideally start the path on a side of the building
             front_path: bldg.front_path
                 .as_ref()
                 .map(|l| [l.pt1().x(), l.pt1().y(), l.pt2().x(), l.pt2().y()]),
-            fill_triangles: geom::triangulate(&bldg.points),
+            fill_polygon: Polygon::new(&bldg.points),
             boundary_polygons: PolyLine::new(bldg.points.clone())
                 .make_polygons_blindly(PARCEL_BOUNDARY_THICKNESS),
         }
@@ -54,13 +48,13 @@ impl DrawBuilding {
         for p in &self.boundary_polygons {
             g.draw_polygon(boundary_color, p);
         }
-        for p in &self.fill_triangles {
+        for p in &self.fill_polygon.for_drawing() {
             g.draw_polygon(fill_color, p);
         }
     }
 
     pub fn contains_pt(&self, x: f64, y: f64) -> bool {
-        geometry::point_in_polygon(x, y, &self.fill_polygon)
+        self.fill_polygon.contains_pt(Pt2D::new(x, y))
     }
 
     pub fn tooltip_lines(&self, map: &Map) -> Vec<String> {
@@ -76,10 +70,11 @@ impl DrawBuilding {
     }
 
     pub fn get_bbox(&self) -> Rect {
-        let mut polygons = vec![self.fill_polygon.clone()];
+        let mut b = self.fill_polygon.get_bounds();
         if let Some(line) = self.front_path {
-            polygons.push(vec![[line[0], line[1]], [line[2], line[3]]]);
+            b.update(line[0], line[1]);
+            b.update(line[2], line[3]);
         }
-        geometry::get_bbox_for_polygons(&polygons)
+        get_bbox(&b)
     }
 }
diff --git a/editor/src/render/intersection.rs b/editor/src/render/intersection.rs
index 60fc7b3f1f..e0456e0b4c 100644
--- a/editor/src/render/intersection.rs
+++ b/editor/src/render/intersection.rs
@@ -4,19 +4,19 @@ use aabb_quadtree::geom::Rect;
 use colors::{ColorScheme, Colors};
 use dimensioned::si;
 use ezgui::GfxCtx;
-use geom::{Line, Pt2D};
+use geom::{Line, Polygon, Pt2D};
 use graphics;
 use graphics::math::Vec2d;
 use graphics::types::Color;
 use map_model;
 use map_model::geometry;
-use render::DrawLane;
+use render::{get_bbox, DrawLane};
 use std::f64;
 
 #[derive(Debug)]
 pub struct DrawIntersection {
     pub id: map_model::IntersectionID,
-    pub polygon: Vec<Vec2d>,
+    pub polygon: Polygon,
     crosswalks: Vec<Vec<(Vec2d, Vec2d)>>,
     center: Pt2D,
     has_traffic_signal: bool,
@@ -28,39 +28,37 @@ impl DrawIntersection {
         map: &map_model::Map,
         lanes: &Vec<DrawLane>,
     ) -> DrawIntersection {
-        let mut pts: Vec<Vec2d> = Vec::new();
+        let mut pts: Vec<Pt2D> = Vec::new();
         for l in &inter.incoming_lanes {
-            let (pt1, pt2) = lanes[l.0].get_end_crossing();
-            pts.push(pt1);
-            pts.push(pt2);
+            let line = lanes[l.0].get_end_crossing();
+            pts.push(line.pt1());
+            pts.push(line.pt2());
         }
         for l in &inter.outgoing_lanes {
-            let (pt1, pt2) = lanes[l.0].get_start_crossing();
-            pts.push(pt1);
-            pts.push(pt2);
+            let line = lanes[l.0].get_start_crossing();
+            pts.push(line.pt1());
+            pts.push(line.pt2());
         }
 
-        let center = geometry::center(&pts.iter().map(|pt| Pt2D::new(pt[0], pt[1])).collect());
+        let center = geometry::center(&pts);
         // Sort points by angle from the center
-        pts.sort_by_key(|pt| {
-            center
-                .angle_to(Pt2D::new(pt[0], pt[1]))
-                .normalized_degrees() as i64
-        });
+        pts.sort_by_key(|pt| center.angle_to(*pt).normalized_degrees() as i64);
         let first_pt = pts[0].clone();
         pts.push(first_pt);
 
         DrawIntersection {
             center,
             id: inter.id,
-            polygon: pts,
+            polygon: Polygon::new(&pts),
             crosswalks: calculate_crosswalks(inter, map),
             has_traffic_signal: inter.has_traffic_signal,
         }
     }
 
     pub fn draw(&self, g: &mut GfxCtx, color: Color, cs: &ColorScheme) {
-        g.draw_polygon(color, &self.polygon);
+        for p in &self.polygon.for_drawing() {
+            g.draw_polygon(color, p);
+        }
 
         let crosswalk_marking = graphics::Line::new(
             cs.get(Colors::Crosswalk),
@@ -84,11 +82,11 @@ impl DrawIntersection {
     }
 
     pub fn contains_pt(&self, x: f64, y: f64) -> bool {
-        geometry::point_in_polygon(x, y, &self.polygon)
+        self.polygon.contains_pt(Pt2D::new(x, y))
     }
 
     pub fn get_bbox(&self) -> Rect {
-        geometry::get_bbox_for_polygons(&[self.polygon.clone()])
+        get_bbox(&self.polygon.get_bounds())
     }
 
     fn draw_stop_sign(&self, g: &mut GfxCtx, cs: &ColorScheme) {
diff --git a/editor/src/render/lane.rs b/editor/src/render/lane.rs
index 334ce1a055..03be7fa4f7 100644
--- a/editor/src/render/lane.rs
+++ b/editor/src/render/lane.rs
@@ -25,8 +25,8 @@ struct Marking {
 pub struct DrawLane {
     pub id: LaneID,
     pub polygons: Vec<Vec<Vec2d>>,
-    start_crossing: (Vec2d, Vec2d),
-    end_crossing: (Vec2d, Vec2d),
+    start_crossing: Line,
+    end_crossing: Line,
     markings: Vec<Marking>,
 
     // TODO pretty temporary
@@ -36,9 +36,8 @@ pub struct DrawLane {
 impl DrawLane {
     pub fn new(lane: &map_model::Lane, map: &map_model::Map) -> DrawLane {
         let road = map.get_r(lane.parent);
-        let start = perp_line(lane.first_line(), geometry::LANE_THICKNESS);
-        let end = perp_line(lane.last_line().reverse(), geometry::LANE_THICKNESS);
-
+        let start = new_perp_line(lane.first_line(), geometry::LANE_THICKNESS);
+        let end = new_perp_line(lane.last_line().reverse(), geometry::LANE_THICKNESS);
         let polygons = lane.lane_center_pts
             .make_polygons_blindly(geometry::LANE_THICKNESS);
 
@@ -76,8 +75,8 @@ impl DrawLane {
             id: lane.id,
             polygons,
             markings,
-            start_crossing: ([start[0], start[1]], [start[2], start[3]]),
-            end_crossing: ([end[0], end[1]], [end[2], end[3]]),
+            start_crossing: start,
+            end_crossing: end,
             draw_id_at: calculate_id_positions(lane).unwrap_or(Vec::new()),
         }
     }
@@ -161,12 +160,12 @@ impl DrawLane {
     }
 
     // Get the line marking the end of the lane, perpendicular to the direction of the lane
-    pub(crate) fn get_end_crossing(&self) -> (Vec2d, Vec2d) {
-        self.end_crossing
+    pub(crate) fn get_end_crossing(&self) -> &Line {
+        &self.end_crossing
     }
 
-    pub(crate) fn get_start_crossing(&self) -> (Vec2d, Vec2d) {
-        self.start_crossing
+    pub(crate) fn get_start_crossing(&self) -> &Line {
+        &self.start_crossing
     }
 }
 
@@ -178,6 +177,12 @@ fn perp_line(l: Line, length: f64) -> [f64; 4] {
     [pt1.x(), pt1.y(), pt2.x(), pt2.y()]
 }
 
+fn new_perp_line(l: Line, length: f64) -> Line {
+    let pt1 = l.shift(length / 2.0).pt1();
+    let pt2 = l.reverse().shift(length / 2.0).pt2();
+    Line::new(pt1, pt2)
+}
+
 fn calculate_sidewalk_lines(lane: &map_model::Lane) -> Marking {
     let tile_every = geometry::LANE_THICKNESS * si::M;
 
diff --git a/editor/src/render/mod.rs b/editor/src/render/mod.rs
index c4078c2342..98c2c76727 100644
--- a/editor/src/render/mod.rs
+++ b/editor/src/render/mod.rs
@@ -7,6 +7,8 @@ mod map;
 mod parcel;
 mod turn;
 
+use aabb_quadtree::geom::{Point, Rect};
+use geom::Bounds;
 use map_model::geometry;
 pub use render::lane::DrawLane;
 pub use render::map::DrawMap;
@@ -20,3 +22,16 @@ const TURN_ICON_ARROW_THICKNESS: f64 = geometry::BIG_ARROW_THICKNESS / 3.0;
 const BIG_ARROW_TIP_LENGTH: f64 = 1.0;
 const TURN_ICON_ARROW_TIP_LENGTH: f64 = BIG_ARROW_TIP_LENGTH * 0.8;
 const TURN_ICON_ARROW_LENGTH: f64 = 2.0;
+
+pub fn get_bbox(b: &Bounds) -> Rect {
+    Rect {
+        top_left: Point {
+            x: b.min_x as f32,
+            y: b.min_y as f32,
+        },
+        bottom_right: Point {
+            x: b.max_x as f32,
+            y: b.max_y as f32,
+        },
+    }
+}
diff --git a/editor/src/render/parcel.rs b/editor/src/render/parcel.rs
index 602750c59a..690c2958d8 100644
--- a/editor/src/render/parcel.rs
+++ b/editor/src/render/parcel.rs
@@ -2,22 +2,18 @@
 
 use aabb_quadtree::geom::Rect;
 use ezgui::GfxCtx;
-use geom;
-use geom::PolyLine;
+use geom::{PolyLine, Polygon};
 use graphics::math::Vec2d;
 use graphics::types::Color;
 use map_model;
-use map_model::geometry;
-use render::PARCEL_BOUNDARY_THICKNESS;
+use render::{get_bbox, PARCEL_BOUNDARY_THICKNESS};
 
 #[derive(Debug)]
 pub struct DrawParcel {
     pub id: map_model::ParcelID,
     // TODO should just have one. use graphics::Line for now.
     boundary_polygons: Vec<Vec<Vec2d>>,
-    // TODO clean this up
-    pub fill_polygon: Vec<Vec2d>,
-    fill_triangles: Vec<Vec<Vec2d>>,
+    pub fill_polygon: Polygon,
 }
 
 impl DrawParcel {
@@ -26,8 +22,7 @@ impl DrawParcel {
             id: p.id,
             boundary_polygons: PolyLine::new(p.points.clone())
                 .make_polygons_blindly(PARCEL_BOUNDARY_THICKNESS),
-            fill_polygon: p.points.iter().map(|pt| [pt.x(), pt.y()]).collect(),
-            fill_triangles: geom::triangulate(&p.points),
+            fill_polygon: Polygon::new(&p.points),
         }
     }
 
@@ -35,7 +30,7 @@ impl DrawParcel {
         for p in &self.boundary_polygons {
             g.draw_polygon(boundary_color, p);
         }
-        for p in &self.fill_triangles {
+        for p in &self.fill_polygon.for_drawing() {
             g.draw_polygon(fill_color, p);
         }
     }
@@ -43,6 +38,6 @@ impl DrawParcel {
     //pub fn contains_pt(&self, x: f64, y: f64) -> bool {}
 
     pub fn get_bbox(&self) -> Rect {
-        geometry::get_bbox_for_polygons(&vec![self.fill_polygon.clone()])
+        get_bbox(&self.fill_polygon.get_bounds())
     }
 }
diff --git a/geom/src/lib.rs b/geom/src/lib.rs
index 341e0a8472..4dac9773ac 100644
--- a/geom/src/lib.rs
+++ b/geom/src/lib.rs
@@ -19,7 +19,7 @@ pub use bounds::Bounds;
 use dimensioned::si;
 pub use gps::LonLat;
 pub use line::Line;
-pub use polygon::triangulate;
+pub use polygon::Polygon;
 pub use polyline::PolyLine;
 pub use pt::{HashablePt2D, Pt2D};
 use std::marker;
diff --git a/geom/src/polygon.rs b/geom/src/polygon.rs
index 31babd0b00..304d4df20e 100644
--- a/geom/src/polygon.rs
+++ b/geom/src/polygon.rs
@@ -1,97 +1,144 @@
 use graphics::math::Vec2d;
-use Pt2D;
+use {Bounds, Pt2D};
 
-// Adapted from https://crates.io/crates/polygon2; couldn't use the crate directly because it
-// depends on nightly.
+#[derive(Debug)]
+pub struct Polygon {
+    // TODO urgh, just storing for geom validation. :P
+    pub pts: Vec<Pt2D>,
 
-pub fn triangulate(pts: &Vec<Pt2D>) -> Vec<Vec<Vec2d>> {
-    assert!(pts.len() >= 3);
+    // This could be stored more efficiently, but worry about it later when switching to gfx-rs.
+    triangles: Vec<Triangle>,
+}
 
-    let mut tgs = Vec::new();
-    let mut avl = Vec::with_capacity(pts.len());
-    for i in 0..pts.len() {
-        avl.push(i);
-    }
+impl Polygon {
+    // Adapted from https://crates.io/crates/polygon2; couldn't use the crate directly because it
+    // depends on nightly.
+    pub fn new(pts: &Vec<Pt2D>) -> Polygon {
+        assert!(pts.len() >= 3);
 
-    let mut i = 0;
-    let mut al = pts.len();
-    while al > 3 {
-        let i0 = avl[i % al];
-        let i1 = avl[(i + 1) % al];
-        let i2 = avl[(i + 2) % al];
+        let mut tgs = Vec::new();
+        let mut avl = Vec::with_capacity(pts.len());
+        for i in 0..pts.len() {
+            avl.push(i);
+        }
 
-        let a = pts[i0];
-        let b = pts[i1];
-        let c = pts[i2];
+        let mut i = 0;
+        let mut al = pts.len();
+        while al > 3 {
+            let i0 = avl[i % al];
+            let i1 = avl[(i + 1) % al];
+            let i2 = avl[(i + 2) % al];
 
-        let mut ear_found = false;
-        if is_triangle_convex(a, b, c) {
-            ear_found = true;
+            let a = pts[i0];
+            let b = pts[i1];
+            let c = pts[i2];
+            let tri = Triangle::new(a, b, c);
 
-            for j in 0..al {
-                let vi = avl[j];
+            let mut ear_found = false;
+            if tri.is_convex() {
+                ear_found = true;
 
-                if vi != i0 && vi != i1 && vi != i2 {
-                    if point_in_triangle(pts[vi], a, b, c) {
-                        ear_found = false;
-                        break;
+                for j in 0..al {
+                    let vi = avl[j];
+
+                    if vi != i0 && vi != i1 && vi != i2 {
+                        if tri.contains_pt(pts[vi]) {
+                            ear_found = false;
+                            break;
+                        }
                     }
                 }
             }
+
+            if ear_found {
+                tgs.push(i0);
+                tgs.push(i1);
+                tgs.push(i2);
+                avl.remove((i + 1) % al);
+                al -= 1;
+                i = 0;
+            } else if i > 3 * al {
+                break;
+            } else {
+                i += 1;
+            }
         }
 
-        if ear_found {
-            tgs.push(i0);
-            tgs.push(i1);
-            tgs.push(i2);
-            avl.remove((i + 1) % al);
-            al -= 1;
-            i = 0;
-        } else if i > 3 * al {
-            break;
-        } else {
-            i += 1;
+        tgs.push(avl[0]);
+        tgs.push(avl[1]);
+        tgs.push(avl[2]);
+
+        let mut triangles = Vec::new();
+        assert!(tgs.len() % 3 == 0);
+        for tri in tgs.chunks(3) {
+            triangles.push(Triangle::new(pts[tri[0]], pts[tri[1]], pts[tri[2]]));
+        }
+        Polygon {
+            pts: pts.clone(),
+            triangles,
         }
     }
 
-    tgs.push(avl[0]);
-    tgs.push(avl[1]);
-    tgs.push(avl[2]);
-
-    let mut result = Vec::new();
-    assert!(tgs.len() % 3 == 0);
-    for tri in tgs.chunks(3) {
-        result.push(vec![
-            pts[tri[0]].to_vec(),
-            pts[tri[1]].to_vec(),
-            pts[tri[2]].to_vec(),
-        ]);
+    pub fn for_drawing(&self) -> Vec<Vec<Vec2d>> {
+        self.triangles
+            .iter()
+            .map(|tri| vec![tri.pt1.to_vec(), tri.pt2.to_vec(), tri.pt3.to_vec()])
+            .collect()
     }
 
-    result
+    pub fn contains_pt(&self, pt: Pt2D) -> bool {
+        self.triangles
+            .iter()
+            .find(|tri| tri.contains_pt(pt))
+            .is_some()
+    }
+
+    pub fn get_bounds(&self) -> Bounds {
+        let mut b = Bounds::new();
+        for tri in &self.triangles {
+            b.update_pt(&tri.pt1);
+            b.update_pt(&tri.pt2);
+            b.update_pt(&tri.pt3);
+        }
+        b
+    }
 }
 
-fn is_triangle_convex(a: Pt2D, b: Pt2D, c: Pt2D) -> bool {
-    ((a.y() - b.y()) * (c.x() - b.x()) + (b.x() - a.x()) * (c.y() - b.y())) >= 0.0
+#[derive(Debug)]
+struct Triangle {
+    pt1: Pt2D,
+    pt2: Pt2D,
+    pt3: Pt2D,
 }
 
-fn point_in_triangle(p: Pt2D, a: Pt2D, b: Pt2D, c: Pt2D) -> bool {
-    let v0x = c.x() - a.x();
-    let v0y = c.y() - a.y();
-    let v1x = b.x() - a.x();
-    let v1y = b.y() - a.y();
-    let v2x = p.x() - a.x();
-    let v2y = p.y() - a.y();
+impl Triangle {
+    fn new(pt1: Pt2D, pt2: Pt2D, pt3: Pt2D) -> Triangle {
+        Triangle { pt1, pt2, pt3 }
+    }
 
-    let dot00 = v0x * v0x + v0y * v0y;
-    let dot01 = v0x * v1x + v0y * v1y;
-    let dot02 = v0x * v2x + v0y * v2y;
-    let dot11 = v1x * v1x + v1y * v1y;
-    let dot12 = v1x * v2x + v1y * v2y;
+    fn is_convex(&self) -> bool {
+        ((self.pt1.y() - self.pt2.y()) * (self.pt3.x() - self.pt2.x())
+            + (self.pt2.x() - self.pt1.x()) * (self.pt3.y() - self.pt2.y())) >= 0.0
+    }
 
-    let denom = dot00 * dot11 - dot01 * dot01;
-    let u = (dot11 * dot02 - dot01 * dot12) / denom;
-    let v = (dot00 * dot12 - dot01 * dot02) / denom;
+    fn contains_pt(&self, pt: Pt2D) -> bool {
+        let v0x = self.pt3.x() - self.pt1.x();
+        let v0y = self.pt3.y() - self.pt1.y();
+        let v1x = self.pt2.x() - self.pt1.x();
+        let v1y = self.pt2.y() - self.pt1.y();
+        let v2x = pt.x() - self.pt1.x();
+        let v2y = pt.y() - self.pt1.y();
 
-    (u >= 0.0) && (v >= 0.0) && (u + v < 1.0)
+        let dot00 = v0x * v0x + v0y * v0y;
+        let dot01 = v0x * v1x + v0y * v1y;
+        let dot02 = v0x * v2x + v0y * v2y;
+        let dot11 = v1x * v1x + v1y * v1y;
+        let dot12 = v1x * v2x + v1y * v2y;
+
+        let denom = dot00 * dot11 - dot01 * dot01;
+        let u = (dot11 * dot02 - dot01 * dot12) / denom;
+        let v = (dot00 * dot12 - dot01 * dot02) / denom;
+
+        (u >= 0.0) && (v >= 0.0) && (u + v < 1.0)
+    }
 }