diff --git a/conftest.py b/conftest.py
new file mode 100644
index 0000000..2ca7a99
--- /dev/null
+++ b/conftest.py
@@ -0,0 +1,4 @@
+import os
+import sys
+
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
diff --git a/tests/support.py b/tests/support.py
new file mode 100644
index 0000000..719ad92
--- /dev/null
+++ b/tests/support.py
@@ -0,0 +1,28 @@
+from game.sim.level import parseAscii
+from game.sim.world import World
+from game.sim.inputCommand import InputCommand
+
+
+def makeLevel(lines, name="test"):
+    return parseAscii(name, lines)
+
+
+def makeWorld(lines, name="test"):
+    return World(parseAscii(name, lines))
+
+
+def command(**kwargs):
+    return InputCommand(**kwargs)
+
+
+def stepWorld(world, times=1, **kwargs):
+    cmd = InputCommand(**kwargs)
+    for _ in range(times):
+        world.step(cmd)
+    return world
+
+
+def settle(world, times=30):
+    for _ in range(times):
+        world.step(InputCommand())
+    return world
diff --git a/tests/test_geometry.py b/tests/test_geometry.py
new file mode 100644
index 0000000..67bb729
--- /dev/null
+++ b/tests/test_geometry.py
@@ -0,0 +1,71 @@
+import pytest
+
+from game.sim.geometry import Vec2, Aabb, clamp, sign, approach
+
+
+def test_aabbIntersectsOverlapping():
+    a = Aabb(0, 0, 10, 10)
+    b = Aabb(5, 5, 10, 10)
+    assert a.intersects(b)
+    assert b.intersects(a)
+
+
+def test_aabbDoesNotIntersectSeparated():
+    a = Aabb(0, 0, 10, 10)
+    b = Aabb(20, 0, 10, 10)
+    assert not a.intersects(b)
+
+
+def test_aabbTouchingEdgeIsNotOverlap():
+    a = Aabb(0, 0, 10, 10)
+    b = Aabb(10, 0, 10, 10)
+    assert not a.intersects(b)
+    assert a.touches(b)
+
+
+def test_aabbOverlapArea():
+    a = Aabb(0, 0, 10, 10)
+    b = Aabb(5, 5, 10, 10)
+    assert a.overlapArea(b) == pytest.approx(25.0)
+    assert a.overlapArea(Aabb(100, 100, 5, 5)) == 0.0
+
+
+def test_aabbContainsAndEdges():
+    box = Aabb(4, 6, 8, 10)
+    assert box.left == 4 and box.right == 12
+    assert box.top == 6 and box.bottom == 16
+    assert box.centerX == pytest.approx(8.0)
+    assert box.containsPoint(8, 10)
+    assert not box.containsPoint(100, 10)
+
+
+def test_aabbInflated():
+    box = Aabb(10, 10, 4, 4)
+    grown = box.inflated(2, 3)
+    assert grown.left == 8 and grown.right == 16
+    assert grown.top == 7 and grown.bottom == 17
+
+
+def test_vecArithmetic():
+    a = Vec2(3, 4)
+    assert a.length() == pytest.approx(5.0)
+    assert a.add(Vec2(1, 1)).asTuple() == (4.0, 5.0)
+    assert a.sub(Vec2(3, 4)).asTuple() == (0.0, 0.0)
+    assert a.scale(2).asTuple() == (6.0, 8.0)
+    normalized = a.normalized()
+    assert normalized.length() == pytest.approx(1.0)
+
+
+def test_vecDistanceAndZeroNormalize():
+    assert Vec2(0, 0).distanceTo(Vec2(3, 4)) == pytest.approx(5.0)
+    assert Vec2(0, 0).normalized().asTuple() == (0.0, 0.0)
+
+
+def test_helpers():
+    assert clamp(5, 0, 3) == 3
+    assert clamp(-1, 0, 3) == 0
+    assert clamp(2, 0, 3) == 2
+    assert sign(-4) == -1 and sign(4) == 1 and sign(0) == 0
+    assert approach(0, 10, 3) == 3
+    assert approach(10, 0, 3) == 7
+    assert approach(1, 2, 5) == 2
diff --git a/tests/test_slopes.py b/tests/test_slopes.py
new file mode 100644
index 0000000..24bb2db
--- /dev/null
+++ b/tests/test_slopes.py
@@ -0,0 +1,58 @@
+import pytest
+
+from game.sim import physics
+from game.sim.entity import Actor
+
+
+class FakeSlopeTerrain:
+    def __init__(self, slopes):
+        self.slopes = slopes
+
+    def slopeAt(self, col, row):
+        return self.slopes.get((col, row))
+
+
+def test_slopeSurfaceAscendRight():
+    assert physics.slopeSurfaceY(0, 0, 0, "ascendRight") == pytest.approx(16.0)
+    assert physics.slopeSurfaceY(0, 0, 16, "ascendRight") == pytest.approx(0.0)
+    assert physics.slopeSurfaceY(0, 0, 8, "ascendRight") == pytest.approx(8.0)
+
+
+def test_slopeSurfaceAscendLeft():
+    assert physics.slopeSurfaceY(0, 0, 0, "ascendLeft") == pytest.approx(0.0)
+    assert physics.slopeSurfaceY(0, 0, 16, "ascendLeft") == pytest.approx(16.0)
+
+
+def test_resolveSlopeSnapsPenetratingActor():
+    terrain = FakeSlopeTerrain({(0, 0): "ascendRight"})
+    actor = Actor(2, -6, 12, 16)
+    actor.vy = 1.0
+    snapped = physics.resolveSlope(actor, terrain, wasOnGround=False)
+    assert snapped
+    assert actor.onGround
+    assert actor.bottom == pytest.approx(physics.slopeSurfaceY(0, 0, actor.centerX, "ascendRight"))
+    assert actor.vy == 0.0
+
+
+def test_walkingUpSlopeGainsHeight():
+    terrain = FakeSlopeTerrain({(0, 0): "ascendRight"})
+    actor = Actor(0, 0, 12, 16)
+    actor.vy = 1.0
+    physics.resolveSlope(actor, terrain, wasOnGround=False)
+    lowBottom = actor.bottom
+    actor.x = 6
+    actor.vy = 1.0
+    physics.resolveSlope(actor, terrain, wasOnGround=True)
+    assert actor.bottom < lowBottom
+
+
+def test_resolveSlopeClingsWhenDescending():
+    terrain = FakeSlopeTerrain({(0, 0): "ascendLeft"})
+    actor = Actor(2, 0, 12, 16)
+    surface = physics.slopeSurfaceY(0, 0, actor.centerX, "ascendLeft")
+    actor.y = surface - actor.h - 3.0
+    actor.vy = 0.5
+    snapped = physics.resolveSlope(actor, terrain, wasOnGround=True)
+    assert snapped
+    assert actor.onGround
+    assert actor.bottom == pytest.approx(surface)