分形 3D 动画
我将在 11 月份进行有关分形天线的演示（看看我之前的帖子），我想加入一些动画，使我的演示更容易可视化我所指的内容。这些动画大多数都相对较短，最多可能一分钟长。有一些动画会非常棒：
- 的迭代，描绘山脉的复杂特征
分形科赫曲线 - 动画以启动器（三角形）开始并添加新的迭代。要么我慢慢引入具有下一次迭代的新分形，要么我使用相同的模型，用户可以看到迭代向外分支。我更喜欢后一种技术。
显示分形。增加迭代，同时保持恒定长度，以证明分形尺寸缩小。
显示分形。增加迭代，同时保持恒定大小，以证明分形正在增加其总周长。
手机动画 - 显示有多个天线弹出的手机（可以是简单的线条草图）。
问题是，我以前从未制作过任何动画。在我已有的程序中，它们生成分形的坐标，这是否有用？
在尽可能短的时间内渲染这些动画的最佳方法是什么？距离演示会还有将近 6 周时间！搅拌机可能是一个选择，但我不知道如何去做。
此 NOVA 视频中有一些很棒的动画让你知道我在追求什么。
谢谢，
奥斯汀
I'm giving a presentation on Fractal Antennas (take a look at my previous threads) in November and I wanted to incorporate some animation to make my presentation easier to visualize the content I am referring to. Most of these animations would be relatively short, probably a minute long at the most. There are a few animations that would be fantastic to have:
Fractal Mountains - The animation continues to add new iterations that depict the complex features of a mountain range.
Fractal Koch Curve - The animation begins with an initiator (triangle) and adds new iterations. Either I slowly bring in the new fractal that has the next iteration, or I use the same model and users can see the iterations branching outward. I would prefer the latter technique.
Show a fractal. Increase the iteration, while keeping a constant length, to vindicate the fractal shrinking in size.
Show a fractal. Increase the iteration, while keeping a constant size, to vindicate the fractal is increasing it's total perimeter length.
Cell phone animation - show a cell phone that has multiple antennas popping out (they can be simple sketches of lines).
The trouble is, I've never done ANY animation before. In the programs I have already, they generate the coordinates of the fractals, if that can be of some use?
What is the best way to render those animations in the shortest time possible? The presentation is almost 6 weeks away! Blender might be an option, but I have no idea of how to go about this.
There are some great animations in this NOVA video that might give you an idea of what I'm after.
Thanks,
Austin
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就我个人而言，我使用 VPython 创建简单的 3D 图形和动画。这是一个易于学习的库，可以在 http://vpython.org/ 上免费获得。由于您已经有了坐标，因此将其合并到绘图中应该相当容易。
Blender 有点复杂，但如果你想花时间学习它，它也包含 python 脚本。
最后，引用一些 YouTube 评论：如果您使用该视频，只需引用它，或发送电子邮件并获得许可。如果您没有通过此演示文稿赚钱，那么您很可能会很好地使用这些视频。
Personally, I've used VPython to create simple 3D graphics and animations. It's an easy to learn library that's freely available at http://vpython.org/. Since you have the coordinates already, it should be fairly easy to for you to incorporate that into the drawing.
Blender is a bit more complicated, but also incorporates python scripting if you want to spend the time to learn it.
Lastly, referencing some of the YouTube comments: if you use the video just cite it, or email and get permission. If you're not making money on this presentation, then odds are you're going to just fine using the videos.
最简单的方法是使用 matplotlib.mplot3d。原理与 http://www.scipy.org/Cookbook 中描述的 2D 动画相同/Matplotlib/Animations 但您将使用 http://matplotlib.sourceforge.net/mpl_toolkits/mplot3d/tutorial.html。
我教授物理学中的计算机方法，其中一项活动是使用 Python 和 matplotlib 创建科赫雪花。我还让一群学生使用 Python 和 Chaco（用于交互）创建 3D 分形作为他们的项目，但使用 matplotlib 则非常简单。您还可以尝试 mayavi2，它是 Python 中的另一个 3D 绘图库。
如果您想创建电影，则需要将每个帧保存为图形文件，然后使用 Convert (ImageMagick)、mencoder、ffmpeg 或其他软件将文件转换为电影。
我也许可以提供一些伪代码/示例代码，但我现在太困了（距离我现在的位置是晚上 11:30）。
The easiest would be to use matplotlib.mplot3d. The principle is the same as in the 2D animation described at http://www.scipy.org/Cookbook/Matplotlib/Animations but you will be using the 3D methods described in http://matplotlib.sourceforge.net/mpl_toolkits/mplot3d/tutorial.html.
I teach computer methods in physics and one of the activities is to create a Koch snowflake using Python and matplotlib. I also had a group of students create 3D fractals as their project using Python and Chaco (for interactivity) but using matplotlib instead is pretty straightforward. You can also try mayavi2 which is another 3D plotting library in Python.
If you want to create a movie then you need to save each frame as a graphics file then convert the files into movie using convert (ImageMagick), mencoder, ffmpeg or some other software.
I can probably provide some pseudocode/sample code but I'm too sleepy at the moment (it's 11:30pm from where I am).