add bilinear weight generation (#112)

* The bilinear and generalized barycentric coordinate schemes that work for meshes with holes.  Updated from a previous version in order to fix a merge conflict.

* Minor updates to remove warnings when configuring with autotools 2.7+

* Disable exceptions for non-monotone bilinear maps

* Reduce requirement to autoconf-2.69

* Uncomment the exception

* Reduce tolerance for bilinear weight identification

* simplify gnomonic projection

use a simpler formula for projection on tangent plane
(gnommonic projection)
restore tolerance to 1.e-12 for points coincident to
polygon vertices for bilinear maps

* Revisions for the bilinear, non-integrated weight generation.

* Quick bug fix in method to compute bilinear weights.

---------

Co-authored-by: Vijay Mahadevan <[email protected]>
Co-authored-by: Iulian Grindeanu <[email protected]>

config/ax_blas.m4

@@ -68,11 +68,11 @@
 #   special exception to the GPL to apply to your modified version as well.
 
 AC_DEFUN([AX_BLAS], [
-AC_PREREQ(2.50)
+AC_PREREQ([2.69])
 ax_blas_ok=no
 
 AC_ARG_WITH(blas,
-  [AC_HELP_STRING([--with-blas=<lib>], [use BLAS library <lib>])])
+  [AS_HELP_STRING([--with-blas=<lib>],[use BLAS library <lib>])])
 case $with_blas in
   yes | "") ;;
   no) acx_blas_ok=disable ;;
@@ -115,7 +115,7 @@ fi
 # ax_blas_ok to yes, and execute ACTION-IF-FOUND.  On failure, set ax_blas_ok
 # to no and execute ACTION-IF-NOT-FOUND.
 AC_DEFUN([_AX_BLAS], [
-AC_PREREQ(2.50)
+AC_PREREQ([2.69])
 ax_blas_ok=no
 
 # Get fortran linker names of BLAS functions to check for.

configure.ac

@@ -2,15 +2,15 @@
 # Process this file with autoconf to produce a configure script.
 # Usage: autoreconf -fi
 #
-AC_PREREQ([2.68])
-AC_INIT([TempestRemap], [2.1.2], [[email protected]])
+AC_PREREQ([2.69])
+AC_INIT([TempestRemap],[2.1.2],[[email protected]])
 AC_CONFIG_AUX_DIR([config])
 AC_CONFIG_MACRO_DIR([config])
 #AC_CONFIG_SRCDIR([test/optimtest.m])
 AC_CONFIG_HEADERS([src/TempestConfig.h])
 
 AM_INIT_AUTOMAKE([foreign subdir-objects])
-AM_PROG_LIBTOOL
+LT_INIT
 AM_SILENT_RULES([yes])
 
 LT_INIT([disable-shared])

src/CoordTransforms.h

@@ -356,6 +356,26 @@ inline void GnomonicProjection(
 
 }
 
+// assume Tx, Tx, Tz is on unit sphere
+inline void SimpleGnomonicProjection(
+    double x,
+    double y,
+    double z,
+    double Tx,
+    double Ty,
+    double Tz,
+    double & Gx,
+    double & Gy,
+    double & Gz
+)
+{
+    double dotProduct = x*Tx + y*Ty + z*Tz;
+    _ASSERT(dotProduct!=0);
+    Gx = x/dotProduct;
+    Gy = y/dotProduct;
+    Gz = z/dotProduct;
+}
+
 ///////////////////////////////////////////////////////////////////////////////