diff --git a/cuburn/affine.py b/cuburn/affine.py
index e6b62cc..955186a 100644
--- a/cuburn/affine.py
+++ b/cuburn/affine.py
@@ -5,6 +5,9 @@ in row-major order, like C, instead of Fortran-style column-major storage.
 
 import numpy as np
 
+_ident = np.matrix([[1,0,0], [0,1,0], [0,0,1]], dtype=np.float64)
+_point = np.matrix([0,0,1], dtype=np.float64).T
+
 def from_flam3(a):
     """Convert from flam3-format [3][2] arrays to an affine matrix."""
     return np.matrix([ [a[0][0], a[1][0], a[2][0]]
@@ -12,15 +15,24 @@ def from_flam3(a):
                      , [0, 0, 1]])
 
 def scale(x, y):
-    return np.matrix([[x,0,0], [0,y,0], [0,0,1]])
+    r = _ident.copy()
+    r[0,0] = x
+    r[1,1] = y
+    return r
 
 def translate(x, y):
-    return np.matrix([[1,0,x], [0,1,y], [0,0,1]])
+    r = _ident.copy()
+    r[0,2] = x
+    r[1,2] = y
+    return r
 
 def rotOrigin(rad):
-    c = np.cos(rad)
+    r = _ident.copy()
+    r[0,0] = r[1,1] = np.cos(rad)
     s = np.sin(rad)
-    return np.matrix([[c, -s, 0], [s, c, 0], [0, 0, 1]])
+    r[0,1] = -s
+    r[1,0] = s
+    return r
 
 def rotate(rad, x, y):
     """Rotates around the given point (x, y)."""
@@ -29,6 +41,9 @@ def rotate(rad, x, y):
 def apply(m, x, y):
     """Apply matrix to point, returning new point as a tuple. Extends point
     to homogeneous coordinates before applying. Mostly here as an example."""
-    r = m * np.matrix([x, y, 1]).T
+    p = _point.copy()
+    p[0,0] = x
+    p[1,0] = y
+    r = m * p
     return r[0], r[1]