working on adding 3D baker. also starting to massage together a good baker method test (2D), and added a stub file for 3D testing

lib/baker.py

@@ -16,11 +16,14 @@ def get_phis(X, r):
 
   # baker: eq 7
   A = np.array([
-                [1,   1,   1  ],
+                [      1,       1,       1],
                 [r[0][0], r[1][0], r[2][0]],
                 [r[0][1], r[1][1], r[2][1]],
                 ])
-  b = np.array([1, X[0], X[1]])
+  b = np.array([    1,
+                  X[0],
+                  X[1]
+              ])
   try:
     phi = np.linalg.solve(A,b)
   except:
@@ -29,6 +32,39 @@ def get_phis(X, r):
 
   return phi
 
+def get_phis_3D(X, r):
+  """
+    The get_phis function is used to get barycentric coordonites for a point on a triangle.
+
+    X -- the destination point (3D)
+         X = [0,0,0]
+    r -- the four points that make up the tetrahedron (3D)
+         r = [[-1, -1], [0, 2], [1, -1]]
+
+    this will return [0.333, 0.333, 0.333]
+  """
+
+  # baker: eq 7
+  A = np.array([
+                [      1,       1,       1,       1 ],
+                [r[0][0], r[1][0], r[2][0], r[3][0]],
+                [r[0][1], r[1][1], r[2][1], r[3][1]],
+                [r[0][2], r[1][2], r[2][2], r[3][2]],
+                ])
+  b = np.array([    1,
+                  X[0],
+                  X[1],
+                  X[2]
+              ])
+  try:
+    phi = np.linalg.solve(A,b)
+  except:
+    print >> sys.stderr, "warning: calculation of phis yielded a linearly dependant system"
+    phi = np.dot(np.linalg.pinv(A), b)
+
+  return phi
+
+
 def qlinear(X, r, q):
   """
     this calculates the linear portion of q from X to r
@@ -42,6 +78,19 @@ def qlinear(X, r, q):
   qlin = sum([q_i * phi_i for q_i, phi_i in zip(q[:len(phis)], phis)])
   return qlin
 
+def qlinear_3D(X, r, q):
+  """
+    this calculates the linear portion of q from X to r
+
+    X = destination point
+    r = simplex points
+    q = CFD quantities of interest at the simplex points(r)
+  """
+
+  phis = get_phis_3D(X, r)
+  qlin = sum([q_i * phi_i for q_i, phi_i in zip(q[:len(phis)], phis)])
+  return qlin
+
 def run_baker(X, g, tree, extra_points = 3, verbose = False):
   """
     This is the main function to call to get an interpolation to X from the tree
@@ -52,6 +101,7 @@ def run_baker(X, g, tree, extra_points = 3, verbose = False):
     g -- the grid object
 
     tree -- the kdtree search object (built from the g mesh)
+
   """
 
   (dist, indicies) = tree.query(X, 3 + extra_points)
@@ -59,8 +109,9 @@ def run_baker(X, g, tree, extra_points = 3, verbose = False):
   nn = [g.points[i] for i in indicies]
   nq = [g.q[i]      for i in indicies]
 
-  phi = get_phis(X, nn[:3])
-  qlin =  nq[0] * phi[0] + nq[1] * phi[1] + nq[2] * phi[2]
+  # calculate values only for the triangle
+  phi  = get_phis(X, nn[:3])
+  qlin = qlinear(X, nn[:3], nq[:3])# nq[0] * phi[0] + nq[1] * phi[1] + nq[2] * phi[2]
 
   error_term = 0.0
 
@@ -91,16 +142,6 @@ def run_baker(X, g, tree, extra_points = 3, verbose = False):
                 + b * phi[1] * phi[2]\
                 + c * phi[2] * phi[0]
 
-  exact = exact_func(X[0], X[1])
   q_final = qlin + error_term
 
-  if verbose:
-    print "current point : %s" % X
-    print "exact         : %0.4f" % exact
-    print "qlin          : %0.4f" % qlin
-    print "qlinerr       : %0.4f" % np.abs(exact - qlin)
-    print "q_final       : %0.4f" % q_final
-    print "q_final_err   : %0.4f" % np.abs(exact - q_final)
-    print
-
-  return (q_final, exact)
+  return qlin, error_term, q_final