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README.md
tp6.py

README.md

TP6 : Bezier surfaces

UPDATE : using matplotlib

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')
ax.axis('equal')
ax.axis('off')

...

for p in range(numpatch) :
    ...
    ax.plot_wireframe(X, Y, Z)
    ...

plt.show()

Today, we start working with surfaces, which means transition from 2D to 3D. We will use OpenGL for rendering, but don’t worry if you have little or no experience with OpenGL; a wrapper class Viewer is provided. Adding a surface patch is as easy as calling

viewer.add_patch(X,Y,Z)

First, we need to setup the required python packages PyOpenGL and PyGLFW. Do

cd GeoNum2017/
git pull

or, if you don't have the local repo

git clone https://github.com/GeoNumTP/GeoNum2017.git

You should now have the TP6/ and viewer/ folders, plus two new bash scripts: setupPackages.sh and exportPath.sh. Execute the following commands:

# download and extract packages
./setupPackages.sh
# export python path
# the extra dot in the beginning makes this change global
. ./exportPath.sh

Afterwards, you can test the viewer with

python viewer/viewer.py

For the TP6, you can pass datanames and density directly as command line args:

python tp6.py  [simple,wave,sphere,heart,teapot,teacup,teaspoon]  [density=10]

Representation

On the implementation level, the biggest difference between curves and surfaces is the representation we'll use. Before, we used a single matrix to represent the whole curve -- each coordinate was stored in a separate column. For surfaces, we could do something similar using three-dimensional arrays; instead, to facilitate understanding of the code, we'll represent the three coordinates in separate matrices Mx, My and Mz (or Sx, Sy, Sz for surface points).

Functions to modify

  • DeCasteljau : implement the De Casteljau algorithm for surfaces.
  • BezierSurf : compute Bezier surface points.

ToDo

  1. Implement the evaluation of Bézier surfaces for (u,v) in [0,1]². Use simple and wave for first tests (these contain only one patch).
  2. When you're sure the implementation works for the simple cases, test your algorithm on datasets with multiple patches: heart (2), sphere (8), teapot (32), teacup (26), teaspoon (16). Don't set the density parameter too high, always start with smaller values (5 or 10) as the number of computed points is density².
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