Overhaul interp1, interp2, interp3 functions. * NEWS: Announce change in 'cubic' interpolation method for interp2 to match Matlab. * bicubic.m: Use interp2 (..., "spline") in %!tests. * interp1.m: Improve docstring. Use switch statement instead of if/elseif tree for simpler code. Use more informative error message than 'table too short'. Add titles to demo plots. Add new demo block showing difference between 'pchip' and 'spline' methods. * interp2.m: Rewrite docstring. Use variable 'extrap' instead of 'extrapval' to match documentation. Use clearer messages in error() calls. Make 'cubic' use the same algorithm as 'pchip' for Matlab compatibility. Use Octave coding conventions regarding spaces between variable and parenthesis. Added input validation tests. * interp3.m: Rewrite docstring. Use clearer messages in error() calls. Make 'cubic' use the same algorithm as 'pchip' for Matlab compatibility. Simplify input processing. Rewrite some %!tests for clarity. Added input validation tests.

--- a/NEWS
+++ b/NEWS
@@ -1,6 +1,14 @@
 Summary of important user-visible changes for version 4.2:
 ---------------------------------------------------------
 
+ ** Interpolation function changes for Matlab compatibility
+
+    The interpolation method 'cubic' is now equivalent to 'pchip'
+    for interp1, interp2, and interp3.  Previously, 'cubic' was equivalent
+    to 'spline' for interp2.  This may produce different results as 'spline'
+    has continuous 1st and 2nd derivatives while 'pchip' only has a continuous
+    1st derivative.
+
  ** Other new functions added in 4.2:
 
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