diff --git a/axi/device.py b/axi/device.py
index c3daf09..cc2a149 100644
--- a/axi/device.py
+++ b/axi/device.py
@@ -10,8 +10,8 @@ STEPS_PER_MM = 80
 PEN_UP_DELAY = 100
 PEN_DOWN_DELAY = 100
 
-ACCELERATION = 8
-MAX_VELOCITY = 4
+ACCELERATION = 6
+MAX_VELOCITY = 3
 CORNER_FACTOR = 0.001
 
 VID_PID = '04D8:FD92'
diff --git a/axi/spatial.py b/axi/spatial.py
new file mode 100644
index 0000000..33bf6be
--- /dev/null
+++ b/axi/spatial.py
@@ -0,0 +1,57 @@
+from collections import defaultdict
+from math import hypot
+
+class Index(object):
+    def __init__(self, points, n=100):
+        self.n = n
+        self.x1 = min(p[0] for p in points)
+        self.x2 = max(p[0] for p in points)
+        self.y1 = min(p[1] for p in points)
+        self.y2 = max(p[1] for p in points)
+        self.bins = defaultdict(list)
+        self.size = 0
+        for point in points:
+            self.insert(point)
+
+    def normalize(self, x, y):
+        px = (x - self.x1) / (self.x2 - self.x1)
+        py = (y - self.y1) / (self.y2 - self.y1)
+        i = int(px * self.n)
+        j = int(py * self.n)
+        return (i, j)
+
+    def insert(self, point):
+        x, y = point[:2]
+        i, j = self.normalize(x, y)
+        self.bins[(i, j)].append(point)
+        self.size += 1
+
+    def remove(self, point):
+        x, y = point[:2]
+        i, j = self.normalize(x, y)
+        self.bins[(i, j)].remove(point)
+        self.size -= 1
+
+    def nearest(self, point):
+        x, y = point[:2]
+        i, j = self.normalize(x, y)
+        points = []
+        r = 0
+        while not points:
+            points.extend(self.ring(i, j, r))
+            r += 1
+        points.extend(self.ring(i, j, r))
+        return min(points,
+            key=lambda p: (hypot(x - p[0], y - p[1]), p[1], p[0]))
+
+    def ring(self, i, j, r):
+        if r == 0:
+            return self.bins[(i, j)]
+        result = []
+        for p in range(i - r, i + r + 1):
+            result.extend(self.bins[(p, j - r)])
+            result.extend(self.bins[(p, j + r)])
+        for q in range(j - r + 1, j + r):
+            result.extend(self.bins[(i - r, q)])
+            result.extend(self.bins[(i + r, q)])
+        return result