Drawing geodesic curves using the Bing maps Silverlight control

Posted on June 30, 2010 by Andrew

For an upcoming post I wanted to be able to plot the shortest routes between various positions on the Earth using the Bing Maps Silverlight control. Although since I started working on the problem Bing have provided a similar feature with their Distance Calculator App, the functions are not available for reuse via the public API. Interested developers may just want to skip the maths and just download the code.

Geodesic source code for Silverlight 4.0

Geodesics

The shortest path between two points on an arbitrary surface is called a Geodesic, and on a sphere, it is a Great Circle. Modelling the surface of the earth as a perfect sphere, the shortest distance between any two locations on the surface is then described by a section of a Great Circle, ie an arc that lies on the plane that is described by the vectors between its start and end points and the Earth’s centre ( see figure 1 ).

With this information, one way ( and the way I have adopted ) to plot such a curve is as follows:

Generate the points of the curve in two dimensions using the parametric equation of a circle.
Transform the plane of the 2d curve into 3D space such that it intersects the end points on the sphere, and the sphere’s centre.
Project the transformed points back into 2D space using the Mercator projection equations.

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Winter Camping

Posted on January 21, 2010 by Andrew

Last week myself and a group of friends took a winter camping trip up to the Lake District. An odd decision, it could be argued, seen as the region has recently seen both some of its worst flooding and coldest winters in recent years. Nonethless, equipped with ice axe, crampons and a generous supply of Kendal Mint Cake we set out to climb Scafell.

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Silverlight and CUDA interop

Posted on January 15, 2010 by Andrew

Update – source code now available

Microsoft have recently released a beta of Silverlight 4, which has limited support for native interoperation using COM. Potentially, this example could be applied to any number of native interop scenarios, however for this example I have chosen to use Nvidia’s CUDA technology.

Disclaimer : This is an example of what can be done, not necessarily, and in all likelihood, an example of how it should be done.

About CUDA

Up until around 2001 PC graphics cards, though powerful, implemented a fixed function pipeline that limited use to whatever was exposed by the APIs, usually Direct3D or OpenGL. The addition of a programmable pixel pipeline led to the use of graphics cards for more general computation tasks; at first using shaders directly, followed by higher level GPU specific programming languages, such as Brook, SH, and later NVidia’s CUDA. Most of this work was, and is, documented by the GPGPU group. NVIDIA’s website shows CUDA being used in a wide variety of applications but in practice it is best employed in so called “embarassingly parallel” problems.
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Using Merged ResourceDictionaries in Silverlight Themes

Posted on July 29, 2009 by Andrew

Silverlight 3.0 moved its featureset closer to that of WPF by adding support for merged Resource Dictionaries and Style Inheritance. Without these features, developing custom templates and styles for Silverlight controls can become a bit of a copy-and-paste nightmare. Since I have used the implicit theming feature built into the Silverlight Toolkit to make my Silverlight controls fit into the overall look and feel of this site, I was hoping that these features would enable me to refactor my themes developed for Silverlight 2.0 to be a bit less unwieldy.

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Implementation of the Reaction Diffusion Simulation

Posted on April 2, 2009 by Andrew

Update – This post was written before the release of Silverlight 3.0b, which provides a number of enhancements relevant to this implementation, such as a WriteableBitmap and Pixel Shaders

Rendering

The first obstacle to implementing the RD simulation is that Silverlight 2.0 does not by default provide a means of generating dynamic images. WPF has a WriteableBitmap, but no equivalent exists in Silverlight. However, it does support PNG streams so we can dynamically update a bitmap by encoding it to PNG on the fly. For this I have used Joe Stegman’s PNGEncoder class, which I have modified slightly to deal with RGB data and to reduce memory usage.
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Reaction-Diffusion Models

Posted on March 23, 2009 by Andrew

One of Alan Turing‘s many contributions to mathematics and science during the 20th century was his 1952 paper on “The Chemical Basis of Morphogenesis” in which he suggested that a simple model of coupled differential equations could account for pattern formation in natural processes such as those found on animal coats. Such models are known as Reaction-Diffusion models, and take the following general form
\[
\frac{\partial}{\partial t}\mathbf{q}=\mathbf{D}\nabla^2\mathbf{q}+\mathbf{R}(\mathbf{q})
\]

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URM Emulator

Posted on January 25, 2009 by Andrew

The Unlimited Register Machine (URM), designed by Nigel Cutland, is an abstraction of a computer similar to the Turing Machine – but somewhat easier to get to grips with and more in tune with the operation of a modern computer processor.

It also happens to be the model used by the Open University’s course on Mathematical Logic and Number Theory, and is the reason for this article since I studied the course in 2007.

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