How to graph acceleration from an equation given a sample period?

Question

I am unfamiliar with Mathematica and the necessary syntax to approach visualize acceleration over time. I would appreciate some assistance or reference to a starting point on how to go about solving this problem. Please note that I have never used Mathematica before.

I am writing some game code that handles a third-person camera rotation that increases in speed over time (acceleration) as the left or right directional buttons are held down.

I am currently polling the directional button once every t milliseconds where sampling begins at the base and increases linearly every 100ms by a delta towards a maximum sampling rate.

So, for example (in microseconds):

TurnAccelMin = 10000.0
TurnAccelMax = 2000.0
TurnDelta = 1000.0

Note that acceleration is based on the sample rate so a lower maximum results in more samples over time. Even though sampling is in milliseconds, acceleration is stored as microseconds to account for a finer delta.

I would like to graph this so that I can visually see how the delta affects the acceleration over time. While I can picture in my mind the linear acceleration, I want to graph this so that I can visualize how different kinds of acceleration (exponential, quadratic, etc.) affect acceleration over a sample period.

How can I graph this as a line given these values as an equation?

Currently (as linear), where x = Time between 0 and 5 seconds and y = Acceleration in milliseconds.

Ideally I would like to see a graph of points, each connected by a straight line, as well as a table of values for each point when it is polled.

MikeY · Answer

You wrote...

"where sampling begins at the base and increases linearly every 100ms by a delta towards a maximum sampling rate."

Are polling and sampling the same thing here? Do you mean...

where polling begins at the base and decreases linearly every 100ms by a delta towards a maximum polling rate."

In this case and with renamed variables to match what you are doing...

pollIntervalMax = 10000
pollIntervalMin = 2000
pollDelta = 1000

Assuming that is true, you can create a table of data. Breaking it up into its pieces...

numSteps = 12;
pollingPeriods = Table[Max[pollIntervalMax - pollDelta idx, pollIntervalMin], {idx, 1, numSteps}];

{9000, 8000, 7000, 6000, 5000, 4000, 3000, 2000, 2000, 2000, 2000, 2000}

Get polling times

pollingTimes = Accumulate[pollingPeriods]

{9000, 17000, 24000, 30000, 35000, 39000, 42000, 44000, 46000, 48000, 50000, 52000}

You can now plot the rotation rate as a function of time. Your rotation rate list is

rotRate = Range[numSteps]

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

ListLinePlot[Transpose[{pollingTimes, rotRate}]]

How to graph acceleration from an equation given a sample period?

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