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Blender 2.5 and Blossoms

Using Blender 2.5 as Visualization Tool

For my PhD work I use Blender as visualization tool. It suits me because it uses python for scripting and is very flexible. I can also use it directly to navigate my results and render them for publication.

Blender has seen a major overhaul with version 2.5, nearly everything works differently: the GUI has changed, the internal python API has changed, the feature set has changed (grown mostly). Getting my stuff from Blender 2.4 to Blender 2.5 will be a major undertaking which I do not want to tackle now. However, I feel that it is about time to start learning it, because before I give my work to my successor, I should really port it to the current blender version.

Reviewing Interpolation

Also for my work, I am currently skimming through the book Curves and Surfaces for GACD by Gerald Farin. I need some inspiration for a better representation of my surfaces. It is a great book. If you are interested in programming 3D graphics or interpolation you should really get it.

The programming problem P1 in chapter 3 is the following:

Let three points be given by

$$$\vec{b}_0, \vec{b}_1, \vec{b}_2 = \begin{bmatrix}0 \\ 0\end{bmatrix}, \begin{bmatrix}40 \\ 20\end{bmatrix}, \begin{bmatrix}50 \\ 10\end{bmatrix}.$$$

For s = 0, 0.05, 0.1, ...1 and t = 0., 0.05, 0.1, ..., 1 plot the points b [s,t].

The function b is defined earlier in the book and is called a bivariate Blossom. It is defined by the following equation:

$$$\vec{b}[s,t] = (1-t)(1-s) \vec{b}_0 + [(1-t)s + t(1-s)]\vec{b}_1 + s t \vec{b}_2$$$

Using the brevity of Python, this results in this wonderful class definition:

import numpy as np

class Blossom(object):
    def __init__(self, p1, p2, p3):
        self._pts = np.asarray([p1, p2, p3])

    def __call__(self, t, s):

Putting it together

So I put together a python script that can be loaded and executed in Blender 2.5. It sets up a menu that is shown in the 3D View whenever a mesh with exactly 3 vertices is selected. It allows you to set the range for s and t and updates the Blossom mesh with the calculated points.

The final result looks something like this:

the menu is on the left, the Polygon and the Blossom is on the right

It took a while to put the script together: The documentation of the new python API is not very complete at the moment and googling for Blender 2.5 specific help is not trivial. I hope this script gets someone else jump started. You can find the python script here and the blender scene which also includes the python script here.

Update: The code is now also available on GitHub.

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