I'm hitting a wall in some work I'm doing; I've searched on here for many, many threads regarding numerical interpolation and have found them either to contain too much math for me to interpret them, or that their coding solutions have been too specific to be generalized to the task I'm working on.
I have sets of coordinates (currently float x, y distances around an 0,0 origin point) which I am, via Javascript, transposing to latitude, longitude coordinates. (The transposition is easy, so don't worry about that — I'm just telling you that to make the application more clear.)
For the rest, refer to the below graphic:
The dots are the coordinates. (They are generated algorithmically.) The blue line shows a simple, linear interpolation between the points. What I want is something more like the red line. It's not quite an ellipse — you can see that around the first coordinates, it forms arcs that are almost like a perfect circle.
Note that some of the points are negative in various places. Note that the lines between them must be draw sequentially — an algorithm that generates the points out of sequence will make things much harder for this application.
What I'd like is to have a Javascript function that would let me do the following: specify two sequential points from this series (x1,y1; x2,y2), specify a number of interpolated steps in between (say, 5 to 10), and then output an array of coordinates that would, when linked linearly (that is, when a straight line is drawn between them), look something like the red line above (with the degree of curviness obviously constrained by the number of steps).
Of all of the many spline functions out there, which of these satisfies these requirements? The mathematical precision of the spline function is less important to me than the simplicity of adapting it to this purpose, and to its aesthetic output. I would be fine with manually setting the eccentricity/circle-ness of each individual set of coordinates, too (so the first ones really should be very circle-like, but the latter should not be).
Put another way, I am looking for a simple function for getting the interior coordinates of an arc between any two sets of coordinates. EDIT to clarify that I'm fine with there being a third variable that sets the inclination of the arc (positive or negative) and its eccentricity or whatever. The function doesn't necessarily have to know where it is on the diagram above, as I will know that. I'm just looking for something that can help me interpolate the arc points.
I think I understand the parameters of the problem; what I'm bad at is geometry and turning mathematical answers into usable Javascript. (Because I don't really understand the math.)
I have already looked at Midpoint circle algorithm and found it difficult to adapt to this purpose (because of the need for sequentiality and non-integer coordinates); I've also looked at a variety of spline interpolation methods and found them way too complicated for my dummy-self to make sense of.
Any pointers, help, and code would be appreciated!
