This is my take on creating a Cartesian three space vector for use in physics applications as a full featured C++ object. It has only three doubles as the data members for x, y and z, but makes full use of namespace, Cartesian, const correct accessors and a variety of constructors, including copy and copy assign, that can build or modify the space object. All of the appropriate math operators, their commuted and in place variants are overloaded to support vector arithmetic. Additional functions including the dot and cross products, rotation operations as well as the output operator<<() are supported.

I have used this to investigate how far I can push C++ features like operator overloading by extending Python directly and using the boost and swig tools. I created similar unit tests for each using the skip decorator when there was a feature that was not supported or one I haven't yet figured out how to implement with that tool.

Each directory has its own Makefile with 'build', 'test', and 'clean' targets, e.g.

$ pwd
/Users/.../libSpace
$ make clean
$ make test

libSpace must be built first. There is a build.sh script that runs the Makefiles in all the directories in the necessary order and takes these targets as command line arguments.

$ pwd
/Users/.../CartesianSpace
$ ./build.sh clean
$ ./build.sh test

Each directory also has a suite of unit tests. libAngles uses gtest. The Python modules use Python native unittest.

To build the Boost wrappers you will, of course, need to install Boost.

The C++ library uses googletest to run the unit tests. I have downloaded and built it in /usr/local by following the instructions in the README

[root gtest-1.7.0]# export GTEST_DIR=/usr/local/gtest-1.7.0
[root gtest-1.7.0]# g++ -isystem ${GTEST_DIR}/include -I${GTEST_DIR} -pthread -c ${GTEST_DIR}/src/gtest-all.cc

[root@lrmz-iMac gtest-1.7.0]# ar -rv libgtest.a gtest-all.o
ar: creating archive libgtest.a
a - gtest-all.o

libSpace/Makefile sets its GTEST_DIR to /usr/local/gtest-1.7.0 and picks up libgtest.a from there.

I have been wanting to use homebrew to install boost, but some reason, I find it does not yet install libboost_python.a by default or even with the --with-python or --build-from-source options. So I built and installed it from source.

cd boost_1_56_0

./bootstrap.sh
./b2
sudo ./b2 install

The files are now in /usr/local/include and /usr/local/lib/libboost_* and python/Boost/setup.py sets BOOST_ROOT to point there. brew doctor will notice and complain about this.

I built this on my iMac using the g++ compiler that comes with Xcode, but there is nothing special that should cause a problem for other compilers.

TODO

See libSpace/example1.cpp.

// ============================================================
// Filename:    example1.cpp
//
// Description: Example of using libSpace
//
// Authors:     L.R. McFarland
// Created:     2014oct25
// ============================================================

#include <iostream>
#include <math.h>

#include <space.h>

int main () {

  Cartesian::space s1(10);
  Cartesian::space s2(0, 10);
  Cartesian::space s3;

  std::cout << "s1 = " << s1 << std::endl;
  std::cout << "s2 = " << s2 << std::endl;

  s3 = Cartesian::cross(s1, s2);

  std::cout << "s1 x s2 = " << s3 << std::endl;

  return 0;
}

This has its own make target "example1"

$ make example1
g++ -g -W -Wall -fPIC -I.   -c -o example1.o example1.cpp
g++ example1.o -o example1 -L. -lspace
$ ./example1.sh
# CARTESIAN_SPACE_ROOT not set. Using ..
s1 = <space><x>10</x><y>0</y><z>0</z></space>
s2 = <space><x>0</x><y>10</y><z>0</z></space>
s1 x s2 = <space><x>0</x><y>0</y><z>100</z></space>

Use the pylaunch.sh script to set the environment varialbes.

$ pwd
/Users/.../CartesianSpace/python/Boost
$ ./pylaunch.sh

>>> import space
>>> s1 = space.space(1)
>>> s2 = space.space(0, 1)
>>> s3 = space.cross(s1, s2)
>>> print s1, " x ", s2, " = ", s3
<space><x>1</x><y>0</y><z>0</z></space>  x  <space><x>0</x><y>1</y><z>0</z></space>  =  <space><x>0</x><y>0</y><z>1</z></space>

In python/Manual, repr() is different from str() as an alternative to the XML output.

$ pwd
/Users/.../CartesianSpace/python/Manual
$ ./pylaunch.sh

>>> import space
>>> s1 = space.space(1)
>>> s2 = space.space(0, 1)
>>> s3 = space.cross(s1, s2)
>>> print repr(s1), " x ", repr(s2), " = ", repr(s3)
(1, 0, 0)  x  (0, 1, 0)  =  (0, 0, 1)

• TBD

• rich comparison operators

This is a submodule of my space craft simulation program Orbits. The C++ model can either display the simulation in 3D with OpenGL or investigate derived properties like distance from another body, fuel, speed or angular momentum over time, by using the Python wrappers to extract the features of interest, with out having to re-code the simulation.

Demos are available on my web-site starbug.com