diff --git a/Shared/Line.cs b/Shared/Line.cs
index 2dcf8de..bd6bca6 100644
--- a/Shared/Line.cs
+++ b/Shared/Line.cs
@@ -1,10 +1,11 @@
 using Microsoft.Xna.Framework;
 using System;
+using System.Collections.Generic;
 
 namespace SemiColinGames {
   public static class Line {
-    public static Point[] Rasterize(Point p1, Point p2) {
-      return Line.Rasterize(p1.X, p1.Y, p2.X, p2.Y);
+    public static void Rasterize(Point p1, Point p2, List<Point> result) {
+      Line.Rasterize(p1.X, p1.Y, p2.X, p2.Y, result);
     }
 
     // Rasterizes a line using Bresenham's line-drawing algorithm.
@@ -13,20 +14,17 @@ namespace SemiColinGames {
     // https://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm
     // http://members.chello.at/~easyfilter/bresenham.html
     // http://members.chello.at/~easyfilter/Bresenham.pdf (section 1.6)
-    public static Point[] Rasterize(int x1, int y1, int x2, int y2) {
+    public static void Rasterize(int x1, int y1, int x2, int y2, List<Point> result) {
       int dx = Math.Abs(x2 - x1);
       int stepX = x1 < x2 ? 1 : -1;
       int dy = -Math.Abs(y2 - y1);
       int stepY = y1 < y2 ? 1 : -1;
       int error = dx + dy;
       int errorXY;  // Error value e_xy from the PDF.
-      // The size of the output is the size of the longer dimension, plus one.
-      int resultSize = Math.Max(dx, -dy) + 1;
-      // TODO: an array or list should be passed in by the caller.
-      var result = new Point[resultSize];
 
       int i = 0;
-      result[0] = new Point(x1, y1);
+      result.Clear();
+      result.Add(new Point(x1, y1));
       while (x1 != x2 || y1 != y2) {
         i++;
         errorXY = 2 * error;
@@ -38,9 +36,8 @@ namespace SemiColinGames {
           error += dx;
           y1 += stepY;
         }
-        result[i] = new Point(x1, y1);
+        result.Add(new Point(x1, y1));
       }
-      return result;
     }
   }
 }
diff --git a/Shared/Player.cs b/Shared/Player.cs
index 379c926..d0c21bb 100644
--- a/Shared/Player.cs
+++ b/Shared/Player.cs
@@ -35,6 +35,9 @@ namespace SemiColinGames {
     private float ySpeed = 0;
     private float invincibilityTime = 0;
 
+    // For passing into Line.Rasterize() during movement updates.
+    private List<Point> movePoints = new List<Point>(100);
+
     public Player(Vector2 position, int facing) {
       this.position = position;
       Facing = facing;
@@ -83,10 +86,8 @@ namespace SemiColinGames {
       }
 
       bool harmedByCollision = false;
-      // TODO: pass in movePoints to Line.Rasterize instead of having that function allocate a
-      // new array.
-      Point[] movePoints = Line.Rasterize(0, 0, (int) movement.X, (int) movement.Y);
-      for (int i = 1; i < movePoints.Length; i++) {
+      Line.Rasterize(0, 0, (int) movement.X, (int) movement.Y, movePoints);
+      for (int i = 1; i < movePoints.Count; i++) {
         int dx = movePoints[i].X - movePoints[i - 1].X;
         int dy = movePoints[i].Y - movePoints[i - 1].Y;
         if (dy != 0) {
diff --git a/SharedTests/LineTests.cs b/SharedTests/LineTests.cs
index 5036aa7..e9e14c6 100644
--- a/SharedTests/LineTests.cs
+++ b/SharedTests/LineTests.cs
@@ -10,7 +10,8 @@ namespace SemiColinGames.Tests {
     public void TestRasterizeSinglePoint() {
       var p1 = new Point(10, 10);
       var expected = new Point[] { p1 };
-      var result = Line.Rasterize(p1, p1);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p1, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -26,7 +27,8 @@ namespace SemiColinGames.Tests {
         new Point(14, 10),
         new Point(15, 10)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -42,7 +44,8 @@ namespace SemiColinGames.Tests {
         new Point(11, 10),
         new Point(10, 10)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -58,7 +61,8 @@ namespace SemiColinGames.Tests {
         new Point(10, 14),
         new Point(10, 15)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -74,7 +78,8 @@ namespace SemiColinGames.Tests {
         new Point(10, 11),
         new Point(10, 10)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -90,7 +95,8 @@ namespace SemiColinGames.Tests {
         new Point(4, 4),
         new Point(5, 5)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -106,7 +112,8 @@ namespace SemiColinGames.Tests {
         new Point(4, 1),
         new Point(5, 0)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -122,7 +129,8 @@ namespace SemiColinGames.Tests {
         new Point(1, 4),
         new Point(0, 5)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -138,7 +146,8 @@ namespace SemiColinGames.Tests {
         new Point(1, 1),
         new Point(0, 0)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -158,7 +167,8 @@ namespace SemiColinGames.Tests {
         new Point(4, 8),
         new Point(4, 9)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -179,7 +189,8 @@ namespace SemiColinGames.Tests {
         new Point(5, 9),
         new Point(5, 10)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -200,7 +211,8 @@ namespace SemiColinGames.Tests {
         new Point(0, 1),
         new Point(0, 0)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -220,7 +232,8 @@ namespace SemiColinGames.Tests {
         new Point(8, 4),
         new Point(9, 4)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -241,7 +254,8 @@ namespace SemiColinGames.Tests {
         new Point(9, 5),
         new Point(10, 5)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
 
@@ -262,7 +276,8 @@ namespace SemiColinGames.Tests {
         new Point(1, 0),
         new Point(0, 0)
       };
-      var result = Line.Rasterize(p1, p2);
+      var result = new List<Point>();
+      Line.Rasterize(p1, p2, result);
       CollectionAssert.AreEqual(expected, result);
     }
   }