Spline example use cases

Prerequisites

• C++11 compatible compiler
• For a few examples ALGLIB is required

Building

Adjust the variables CC, CFLAGS and ALGLIB in the Makefile and execute as follows:

$ make 		# builds all self-contained examples
$ make more	# builds all examples which require ALGLIB
$ make tests	# builds and runs several tests

Example files (self contained)

• simple_demo.cpp: sets up a spline and evaluates it at a single point
• plot*.cpp: there are several examples to plot splines in different situations. They all produce numerical output which can be used with Gnuplot for visualisation. Shell scripts are provided to do this in one step: ./plot*.sh (or manually: ./plot > plot.csv, gnuplot plot.gp).
  • plot.cpp: plot splines, e.g.

    $ ./plot.sh -t hermite -x 0 0.5 1.5 2 -y 1.1 0.9 0.5 0.7
    
  • plot_avg_preserv.cpp: plots average preserving (area preserving/mass preserving) splines. These are splines which do not interpolate points but which have an average value in the interval [x_i, x_i+1] equal to y_i.

    $ ./plot_avg_preserv.sh -t cspline 
    
  • plot_parametric.cpp: plots a parametric spline, i.e. connects points in a 2D-plane, where the x-coordinates do no longer need to be strictly increasing. Add the -c flag to draw a closed curve.

    $ ./plot_parametric.sh -x 0 0 1 2 2 1 -y 0 1 0.5 0 1 0.5 -c
    
  • plot_bspline.cpp: plots a spline as a linear combination of cubic b-splines (basis splines) and compares it with splines implemented here. The -b flag specifies the coefficients for the b-splines (tk::spline::cspline with zero second derivative boundary conditions is identical to the results of b-splines).

    $ ./plot_bspline.sh -b 1 0 0 0 1.5 -t cspline
    

Example files (which require ALGLIB)

• bench.cpp: performs a benchmark of creating a spline and interpolating values. E.g. on a 2.4GHz CPU, spline size 50 and 1 million spline evaluations call:

   $ ./bench 2400 50 1000
                                   tk                      alglib
   random access:   loops=1e+06,   0.064s ( 153 cycl)      0.078s ( 188 cycl)
   spline creation: loops=2e+04,   0.200s (2.4e+04 cycl)   0.202s (2.4e+04 cycl)
   grid transform:  loops=2e+04,   0.250s (3.0e+04 cycl)   0.193s (2.3e+04 cycl)
  
• plot_alglib.cpp: plots ALGLIB spline against this spline implementation (does not have any command line options).

   $ ./plot_alglib.sh