diff -r 000000000000 -r 55b4c97d44c5 geometry.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/geometry.py	Sun Dec 10 15:37:26 2017 +0200
@@ -0,0 +1,66 @@
+class Vertex:
+    def __init__(self, x, y, z):
+        self.x, self.y, self.z = x, y, z
+    def __repr__(self):
+        return str.format('Vertex({!r}, {!r}, {!r})', self.x, self.y, self.z)
+    def distance_to(self, other):
+        # can't use hypot because of 3 arguments
+        from math import sqrt
+        return sqrt(
+            (self.x - other.x) ** 2 +
+            (self.y - other.y) ** 2 +
+            (self.z - other.z) ** 2
+        )
+
+class LineSegment:
+    def __init__(self, v1, v2):
+        self.v1, self.v2 = v1, v2
+    def __repr__(self):
+        return str.format('LineSegment({!r}, {!r})', self.v1, self.v2)
+
+def is_real(number):
+    return isinstance(number, int) or isinstance(number, float)
+
+class TransformationMatrix:
+    '''
+        A 3×3 matrix forming the top-left portion of a full 4×4 transformation
+        matrix.
+    '''
+    def __init__(self, values):
+        assert(all(is_real(x) for x in values))
+        assert len(values) == 9
+        self.values = values
+    def __repr__(self):
+        return str.format('TransformationMatrix({!r})', self.values)
+    def __getitem__(self, index):
+        return self.values[index]
+
+def complete_matrix(matrix, anchor):
+    '''
+        Combines a 3×3 matrix and an anchor vertex into a full 4×4
+        transformation matrix.
+    '''
+    return [
+        matrix[0], matrix[1], matrix[2], anchor.x,
+        matrix[3], matrix[4], matrix[5], anchor.y,
+        matrix[6], matrix[7], matrix[8], anchor.z,
+        0, 0, 0, 1,
+    ]
+
+def transform(vertex, transformation_matrix):
+    '''
+        Transforms a vertex by a 4×4 transformation matrix.
+    '''
+    u = transformation_matrix[0] * vertex.x \
+        + transformation_matrix[1] * vertex.y \
+        + transformation_matrix[2] * vertex.z \
+        + transformation_matrix[3]
+    v = transformation_matrix[4] * vertex.x \
+        + transformation_matrix[5] * vertex.y \
+        + transformation_matrix[6] * vertex.z \
+        + transformation_matrix[7]
+    w = transformation_matrix[8] * vertex.x \
+        + transformation_matrix[9] * vertex.y \
+        + transformation_matrix[10] * vertex.z \
+        + transformation_matrix[11]
+    return Vertex(u, v, w)