Machine Learning with a Multi Layer Perceptron

With all the hype about machine learning and artificial intelligence I thought it would be a good time to refresh my knowledge on the subject. Machine learning meets a lot of scepticism because it is mostly in the media for questionable tasks. Like all tools it can be used for evil things but it also has a lot of beneficial applications. I’m mostly interested in using it for computer graphics, games and tools.
I have implemented a multi layer perceptron in C++, using the Eigen template library for linear algebra. The code is quite simple, it allows to create a neural network with a variable number of layers and nodes per layer, to train the network, to query the network and to reverse query the network.

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WebGL Zen Doodle

 

WebGL Zen Doodle
WebGL Zen Doodle Screenshot. Click link below for live demo.

This new WebGL demo demonstrates the drawing of a triangular zen doodle. Zen doodles are usually small drawings of arbitrary patterns drawn to relax or think.

The demo uses a simple triangle pattern which is created by starting with a triangle. Then, for a certain amount of times, a new triangle is created. Each new triangle (child) is rotated and then scaled to fit within the previously generated triangle (parent). There are other ways to create this pattern but this one very simple. To make things pretty, colors get more saturated to the inside and are animated. The vertices move and change size using some sine waves and the amount of rotation is also animated, giving the image a slow breathing feeling.

From the technical side, figuring out the scaling amount after each rotation is a bit tricky. To make it a bit easier I simply used triangles where all sides have the same length, which allows me to use a uniform scale. To calculate the scaling amount, the intersection of the direction vector (=line from the origin to the rotated  first vertex of the parent triangle) with the right side (assuming clockwise rotation) of the parent triangle is calculated. Since everything is calculated relative to the origin, the new scale is given by the length of the intersection vector.

WebGL Zen Doodle

 

 

WebGL Hello World

Earth rendered with WebGL
WebGL Hello World

This small demo shows the rendering of the earth using HTML5 and WebGL.

The demo uses shaders for per pixel lighting, procedural clouds, atmosphere and a day and night cycle. The high resolution textures are taken from NASAs visible earth gallery.  You can move using the WASD keys and change the view by clicking and dragging.

You can try it by clicking on the following link (WebGL-compatible browser required, e.g. Firefox, Chrome, Opera):

WebGL Hello World

 

Stochastic Order Independent Transparency

The rendering of transparent objects is not an easy task when using z-buffering. The reason is that the way z-buffering works requires to draw all transparent objects from back to front. However, this is not always possible since, for example, two triangles (or objects) could intersect each other, making it impossible to tell which one is in front of the other. To solve this problem, you need an algorithm which is order independent, hence the name order independent transparency. There are already a few algorithms for this: Using an A-Buffer, Depth Peeling , Screen-Door-Transparency and Stochastic Transparency, which I implemented as a test for another demo.

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LIDAR Rendering

When I had a day off, I thought it would be fun to write a small viewer for LIDAR point cloud data.
Most of the LIDAR data which is freely available in a simple ASCII format or in the LAS file format. While it is quite easy to read the point data from both formats, the LAS format is more flexible and requires more implementation effort.
After writing the reader I tried to render aerial LIDAR point data directly, but it didn’t work as expected. The reason: The file format stores an x, y and z coordinate, but it doesn’t say in which coordinate system. Most of the time, cartographic coordinate systems are used. Fortunately, there is the PROJ4 which allows you to project the point data to a coordinate system which is more useful vor visualization. Since I’m more interested in terrestial LIDAR data, I decided to implement PROJ4 later.
There isn’t much terrestial LIDAR data available for free, however, the UC Santa Barbara provides terrestial LIDAR scans of their campus in the ASCII format. Some data sets are locally aligned, making them well suited for direct rendering.
The following screenshots show my first results, with three data sets which contain about 11.2 million points in real time:

BonzaiGL_2013_06_16_13_58_31_046 BonzaiGL_2013_06_16_13_58_05_016 BonzaiGL_2013_06_16_13_58_56_076 BonzaiGL_2013_06_16_13_59_55_176 BonzaiGL_2013_06_16_13_57_54_446 BonzaiGL_2013_06_16_13_57_25_366 BonzaiGL_2013_06_16_13_56_56_386 BonzaiGL_2013_06_16_13_56_38_636

I’m not sure if I continue this project, but the next steps would be to see how many more points can be rendered in real time, to implement a spatial hierarchy and to evaluate other rendering techniques.

BonzaiSoftware 2013

It has been almost three years since my last post. There are two reasons: First, I’m busy at my current job as a software developer with ask GmbH, where we offer innovative visualisation solutions, automated document generation, and broadcast computer graphics. Second, there weren’t many exciting new algorithms or techniques in the last years. Combined with my lack of time and a few other reasons which I may explain in their own posts, I wasn’t able to do anything new worth posting.

So what’s new for 2013? As you can see, I migrated the old page to WordPress, giving the site a modern layout and making it easier for me to post new stuff. Since making new computer graphics demos with state of the art graphics becomes more and more time consuming, I’ll post less of them and try to focus on new articles and tutorials in the future.