Changeset 1488

Timestamp:

Jun 1, 2005, 1:29:00 PM (19 years ago)

Author:

ole

Message:

Comments about gradient computation

Location:

inundation/ga/storm_surge/pyvolution

Files:

• util.py (modified) (1 diff)
• util_ext.h (modified) (1 diff)

inundation/ga/storm_surge/pyvolution/util.py

@@ -951 +951 @@
 
 
-#Redefine these to use separate_by_polygon which will put all inside indices
-#in the first part of the indices array and outside indices in the last
+#These have been redefined to use separate_by_polygon which will
+#put all inside indices in the first part of the indices array and
+#outside indices in the last
 
 def inside_polygon(points, polygon, closed = True, verbose = False):

inundation/ga/storm_surge/pyvolution/util_ext.h

@@ -36 +36 @@
               double q0, double q1, double q2, 
               double *a, double *b) {
+              
+  /*Compute gradient (a,b) based on three points (x0,y0), (x1,y1) and (x2,y2) 
+  with values q0, q1 and q2.
+  
+  Extrapolation formula (q0 is selected as an arbitrary origin)
+    q(x,y) = q0 + a*(x-x0) + b*(y-y0)                    (1)
+  
+  Substituting the known values for q1 and q2 into (1) yield the 
+  equations for a and b 
+  
+      q1-q0 = a*(x1-x0) + b*(y1-y0)                      (2)
+      q2-q0 = a*(x2-x0) + b*(y2-y0)                      (3)      
+      
+  or in matrix form
+  
+  /               \  /   \   /       \  
+  |  x1-x0  y1-y0 |  | a |   | q1-q0 |
+  |               |  |   | = |       | 
+  |  x2-x0  y2-y0 |  | b |   | q2-q0 |
+  \               /  \   /   \       /
+   
+  which is solved using the standard determinant technique    
+      
+  */
+              
 
   double det;