Calculating points along a curve — OZONE Asylum, home of the Mad Scientists

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Calculating points along a curve

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Your Text: Insert Slimies » Insert UBB Code » Close Last Tag \| All Tags UBB Help	A curve described by a list of points is called a Spline. There are a lot of ways to create a spline from a list of points, the simplest being a straight line from each point to the next. More complicated spline representations can be smooth. My personal favorite is the "natural cubic spline." As with most splines, you represent the curve as a function on a variable t. As t goes from 0 to 1, the function f(t) goes from the first point to the second point. As t goes higher, it goes to each successive point. To make this work in 2 or 3 dimensions, we actually have a separate function for each dimension. In reality, we use a separate function for each segment. To enforce smoothness at each point, we require that the first and second derivatives of these functions match at their endpoints. The details are described here: http://mathworld.wolfram.com/CubicSpline.html Actually implementing this is pretty difficult, because once you create the matrix from the points you need to solve it. (Not impossible to implement, just time consuming.) It's best if you can find an external library that does all this for you. Once you have the function, you can get as many points from it as you want by plugging in different values of t. The POV-Ray scripting language can do what you want, and it's capable of outputting CSV files, if that's useful to you. Loading...
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