Posts Tagged ‘interpolation’

And Now, A Two-Point Cubic Spline

Friday, November 11th, 2011

The simple quadratic spline discussed my previous post seems to be sufficient for interpolating particle positions between two GADGET-2 snapshots for the purposes of making animations, but it's also possible to use a cubic spline for the task.  The advantages of using a cubic spline are (1) it can be more accurate—especially in cases where the acceleration changes sign once between snapshots, and (2) the derivatives at the end-points of the spline match the derivatives specified in the input data. In the case of the quadratic spline, if the acceleration (second derivative) changes sign even once during the interval, the interpolation is poor and the derivative of the spline at the end points is not guaranteed to match the specified value. Thus, in the case of the quadratic spline, the derivative is generally discontinuous when moving from one interval to another. This doesn't matter too much when making animations with reasonably small intervals, but it would be important for certain other situations. The disadvantage of the cubic spline is that it adds complexity. (more…)

Quadratic Spline Interpolation

Thursday, November 10th, 2011

While animating my first GADGET-2 galaxy mergers, I discovered that setting the frame rate to the common value of 25 frames per second resulted in movies that were too fast. The complexity of the merger process couldn't be appreciated--even though the snapshot interval was quite small (0.005 simulation time units). I had to interpolate the GADGET-2 snapshots in order to produce intermediate frames that could be used to slow the animation down. Linear interpolation didn't work well enough to meet my standards, so I looked for an efficient quadratic interpolation scheme. I wanted to perform a quadratic interpolation using only two snapshots at a time (a quadratic interpolation using two snapshots is possible in this case because each snapshot contains particle position and velocity information). The first thing that came to mind was simply using the familiar expression (more…)