title: Algorithm to construct curve bridging graph given points with location and velocity where time axis is constant
body: <p>I am recording the location and velocity of an object over time. I need to form a graph where the X axis is continuous (time) and the Y axis is one of the 3 dimensions of the object (X, Y, or Z). I will construct a graph for each of the 3 axes. When recording a point, I have its time and location/velocity. This is not a line of best fit; it needs to go through each point and most accurately as possible predict where the object was between samplings. I am trying to interpolate between the recorded points in a non-linear way.</p>
  
  <p>I am not sure what this data type would look like to store the curve. Later I need to reverse this graph so I can play back the recording. I know graphs are equations, and I do need a function where I can input a value (time) and return a result (location).</p>
  
  <p>So to restate my two-part question:</p>
  
  <ol>
  <li>What data type should this graph be stored as?</li>
  <li>What algorithm can I use provided time, location, and velocity?</li>
  </ol>
  
  <p>I am using C#.</p>