Category Archives: Visualization

ILNumerics for Scientists – Going 3D


Last time I started with one of the easiest problems in quantum mechanics: the particle in a box. This time I’ll add 1 dimension and we’ll see a particle in a 2D box. To visualize its wave function and density we need 3D surface plots.

2D Box

This time we have a particle that is confined in a 2D box. The potential within the box is zero and outside the box infinity. Again the solution is well-known and can be found on Wikipedia. This time the state of the wave function is determined by two numbers. These are typically called quantum numbers and refer to the X and the Y direction, respectively.

The absolute size of the box doesn’t really matter and we didn’t worry about it in the 1D case. However, the relative size of the length and the width make a difference. The solution to our problem reads

$\Psi_{n,k}(x,y) = \sqrt{\frac{4}{L_x L_y}} \cdot \sin(n \cdot \pi \cdot x / L_x) \cdot \sin(k \cdot \pi \cdot y / L_y)$

The Math

Very similar to the 1D case I quickly coded the wave function and the density for further plotting. I had to make sure that the arrays are fit for 3D plotting, so the code looks a little bit different compared to last post’s

     public static ILArray<double> CalcWF(int EVXID, int EVYID, double LX, double LY, int MeshSize)
        ILArray<double> X = linspace<double>(0, LX, MeshSize);
        ILArray<double> Y = linspace<double>(0, LY, MeshSize);

        ILArray<double> Y2d = 1;
        ILArray<double> X2d = meshgrid(X, Y, Y2d);

        ILArray<double> Z = sqrt(4.0 / LX / LY) * sin(EVXID * pi * X2d / LX) * sin(EVYID * pi * Y2d / LY);

        return Z.Concat(X2d,2).Concat(Y2d,2);

Again, this took me like 10 minutes and I was done.

The Visualization

This time the user can choose the quantum numbers for X and Y direction, the ratio between the length and the width of the box and also the number of mesh points along each axis for plotting. This makes the visualization panel a little bit more involved. Nevertheless, it’s still rather simple and easy to use. This time it took me only 45 minutes – I guess I learned a lot from last time.

The result

Here is the result of my little program. You can click and play with it. If you’re interested, you can download the Particle2DBox source code. Have fun!

Particle2DBoxThis is a screenshot of the application. I chose the second quantum number along the x axis and the fourth quantum number along the y axis. The box is twice as long in y direction as it is in x direction. The mesh size is 100 in each direction. On the left hand side you see the wave function and on the right hand side the probability density.

Getting to know your Scene Graph

Did you ever miss a certain feature in your ILNumerics scene graph? You probably did. But did you know, that most of the missing “features” mean nothing more than a missing “property”? Often enough, there is only a convenient access to a certain scene graph object needed in order to finalize a required configuration.

Recently, a user asked how to turn the background of a legend object in ILNumerics plots transparent. There doesn’t seem to be a straight forward way to that. One might expect code like the following to work:

var legend = new ILLegend("Line 1", "Line 2");
legend.Background.Color = Color.FromArgb(200, Color.White);

Continue reading Getting to know your Scene Graph

Fun with HDF5, ILNumerics and Excel

It is amazing how many complex business processes in major industries today are supported by a tool that shines by its simplicity: Microsoft Excel. ‘Recently’ (with Visual Studio 2010) Microsoft managed to polish the development tools for all Office applications significantly. The whole Office product line is now ready to serve as a convenient, flexible base framework for stunning custom business logic, custom computations and visualizations – with just a little help of tools like ILNumerics.

ExcelWorkbook1In this blog post I am going to show how easy it is to extend the common functionality of Excel. We will enable an Excel Workbook to load arbitrary HDF5 data files, inspect the content of such files and show the data as interactive 2D or 3D plots. Continue reading Fun with HDF5, ILNumerics and Excel

Plotting Fun with ILNumerics and IronPython

Since the early days of IronPython, I keep shifting one bullet point down on my ToDo list:

* Evaluate options to use ILNumerics from IronPython

Several years ago there has been some attempts from ILNumerics users who successfully utilized ILNumerics from within IronPython. But despite our fascination for these attempts, we were not able to catch up and deeply evaluate all options for joining both projects. Years went by and Microsoft has dropped support for IronPython in the meantime. Nevertheless, a considerably large community seems to be active on IronPython. Finally, today is the day I am going to give this a first quick shot.

Continue reading Plotting Fun with ILNumerics and IronPython

Dark color schemes with ILPanel

I recently got a request for help in building an application, where ILPanel was supposed to create some plots with a dark background area. Dark color schemes are very popular in some industrial domains and ILNumerics’ ILPanel gives the full flexibility for supporting dark colors. Here comes a simple example:

Continue reading Dark color schemes with ILPanel

C# for 3D visualizations and Plotting in .NET

2D and 3D Visualizations are an important feature for a wide range of domains: both software developers and scientists often need convenient visualization facilities to create interactive scenes and to make data visible. The ILNumerics math library brings powerful visualization features to C# and .NET: ILView, the ILNumerics Scene Graph API and its plotting engine. We’d like to give an overview over our latest achievements.

ILView: a simple way to create interactive 3d visualizations

We have created ILView as an extension to our interactive web component: It allows you to simply try out ILNumerics’ 2d and 3d visualization features by chosing the output format .exe in our visualization examples. But that’s not all: ILView is also a general REPL for the evaluation of computational expressions using C# language. ILView is Open Source – find it on GitHub!

Screenshot of ILView
Using ILView for interactive 3D Visualization

ILNumerics Scene Graph: realize complex visualizations in .NET

The ILNumeric’s scene graph is the core of ILNumerics’ visualization engine. No matter if you want to create complex interactive 3D visualizations, or if you aim at enhancing and re-configuring existing scenes in .NET: The ILNumerics scene graph offers a convenient way to realize stunning graphics with C#. It uses OpenGL, GDI, and it’s possible to export scenes into vector and pixel graphics.

Screenshot of an interactive 3D scene
Using C# for 3D visualizations: the ILNumerics Scene Graph

Scientific Plotting: visualize your data using C#

With ILNumerics’ visualization capabilities, C# becomes the language of choice for scientists, engineers and developers who need to visualize data: Our plotting API and different kinds of plotting types (contour plots, surface plots etc.) make easy work of creating beautiful scientific visualizations.

Screenshot of a Surface Plot in ILNumerics
Scientific Plotting in .NET: A Surface Plot created with ILNumerics