This code is a reproduction of the paper
"Poisson-Based Continuous Surface Generation
for Goal-Based Caustics" by Yue et al. 2014.
Dependecies:
1. numpy
2. scipy
3. matplotlib
4. open3d (for generating the Surface)
The code is provided in the file 'c.py'. The user
needs to provide the location of an input image
file, of size exactly 512x512, in either jpg or gif
format. This can be done by directly updating the
img_location parameter in the c.py file. The various
functions in the code have been explained in Appendix
A of the report already sent. Once it starts running,
it will write status updates to the command line, but
will not require any new inputs. Upon completion, the
user will see a support folder which create various
files, listed below:
1. h_{i}.txt: This is the height profile calculated
at the i-th iteration. Its an array of 512x512 and
gives the height of the surface at each point, in mm.
2. areas_dst.txt: This file gives the areas around
each point on the target screen. Its a single array
containing 512*512 entries.
3. D_{i}.txt: This files contains the difference
matrix calculated at the i-th iteration. Its an
array of size 512x512.
4. delT.txt: This file gives the values of delT
calculated during computation.
5. div_{i}.txt: This file gives the divergence
of the normals used during surface computation.
Its an array of size 512x512.
6. iter_{i}.jpg: This file shows the mesh at each
iteration. Its a picture file. Note: Pictures will
appear rotated by 90 deg. This is due to how numpy
handles rewrapping arrays in different sizes.
7. phi_{i}.txt: This if the pressure field phi at
each iteration. Its an array of 512x512.
8. source_{i}.txt: This file contains the location of
mesh points as a single array of length 512*512.
9. Other miscellaneous files generated by KeyShot during
rendering.
After the support files are generated, the user can
use the create_surface.py script to generate an stl
object of the 3d surface. The script requires the
open3d library to be installed which can be done with
pip(or pip3) install open3d
This file uses the h_15.txt and source_13.txt files
from the support folder to generate bpa_mesh.stl object
file which can then be imported in various 3d graphics
renderers to render the surface.
The directory also contains a samples folder which
includes 6 examples for which the script has already
been run and surfaces have been rendered.
Lastly, my futile attempts to implement the galerkin
method are captured in the file gallerkin.py. It requires
a difference matrix to work which can be provided directly
in the code. It also requires the scikits.umfpack in order
to solve the system of linear equations. It outputs three
files:
1. S.npz: contains the S matrix in sparse format.
2. g.txt: contains the g vector.
3. phi_galerkin.txt: contains the solution to the system
Su = g.