Cubic splines in JavaScript (via CoffeeScript)
For a recent study two colleagues needed to elicit a cumulative probability distribution function (CDF) from survey respondents.
We decided it would be nice to allow respondents to interact with this CDF after providing some key values, and implemented this in the web browser with <canvas>
(falling back on FlashCanvas for IE).
In the process, we implemented three kinds of cubic spline calculation in the everwonderful CoffeeScript: natural, clamped and (what we actually needed) monotonic cubic splines.
You can play with some examples below: clickanddrag the round handles, or doubleclick to enter values directly. Feel free to borrow the code (ideally with attribution) if it’s of use to you.
Monotonic
Natural
Clamped (to a slope of 1 at both ends)
The spline code
class MonotonicCubicSpline # by George MacKerron, mackerron.com # adapted from: # http://sourceforge.net/mailarchive/forum.php?thread_name= # EC90C5C6C9824F498D46A64F270C5247%40gmail.com&forum_name=matplotlibusers # (easier to read at http://old.nabble.com/%22PiecewiseCubicHermiteInterpolating # Polynomial%22inpythontd25204843.html) # with help from: # F N Fritsch & R E Carlson (1980) 'Monotone Piecewise Cubic Interpolation', # SIAM Journal of Numerical Analysis 17(2), 238  246. # http://en.wikipedia.org/wiki/Monotone_cubic_interpolation # http://en.wikipedia.org/wiki/Cubic_Hermite_spline constructor: (x, y) > n = x.length delta = []; m = []; alpha = []; beta = []; dist = []; tau = [] for i in [0...(n  1)] delta[i] = (y[i + 1]  y[i]) / (x[i + 1]  x[i]) m[i] = (delta[i  1] + delta[i]) / 2 if i > 0 m[0] = delta[0] m[n  1] = delta[n  2] to_fix = [] for i in [0...(n  1)] to_fix.push(i) if delta[i] == 0 for i in to_fix m[i] = m[i + 1] = 0 for i in [0...(n  1)] alpha[i] = m[i] / delta[i] beta[i] = m[i + 1] / delta[i] dist[i] = Math.pow(alpha[i], 2) + Math.pow(beta[i], 2) tau[i] = 3 / Math.sqrt(dist[i]) to_fix = [] for i in [0...(n  1)] to_fix.push(i) if dist[i] > 9 for i in to_fix m[i] = tau[i] * alpha[i] * delta[i] m[i + 1] = tau[i] * beta[i] * delta[i] @x = x[0...n] # copy @y = y[0...n] # copy @m = m interpolate: (x) > for i in [(@x.length  2)..0] break if @x[i] <= x h = @x[i + 1]  @x[i] t = (x  @x[i]) / h t2 = Math.pow(t, 2) t3 = Math.pow(t, 3) h00 = 2 * t3  3 * t2 + 1 h10 = t3  2 * t2 + t h01 = 2 * t3 + 3 * t2 h11 = t3  t2 y = h00 * @y[i] + h10 * h * @m[i] + h01 * @y[i + 1] + h11 * h * @m[i + 1] y class CubicSpline # natural or clamped # by George MacKerron, mackerron.com # adapted from: # http://www.michonline.com/ryan/csc/m510/splinepresent.html constructor: (x, a, d0, dn) > return unless x? and a? clamped = d0? and dn? n = x.length  1 h = []; y = []; l = []; u = []; z = []; c = []; b = []; d = []; k = []; s = [] for i in [0...n] h[i] = x[i + 1]  x[i] k[i] = a[i + 1]  a[i] s[i] = k[i] / h[i] if clamped y[0] = 3 * (a[1]  a[0]) / h[0]  3 * d0 y[n] = 3 * dn  3 * (a[n]  a[n  1]) / h[n  1] for i in [1...n] y[i] = 3 / h[i] * (a[i + 1]  a[i])  3 / h[i  1] * (a[i]  a[i  1]) if clamped l[0] = 2 * h[0] u[0] = 0.5 z[0] = y[0] / l[0] else l[0] = 1 u[0] = 0 z[0] = 0 for i in [1...n] l[i] = 2 * (x[i + 1]  x[i  1])  h[i  1] * u[i  1] u[i] = h[i] / l[i] z[i] = (y[i]  h[i  1] * z[i  1]) / l[i] if clamped l[n] = h[n  1] * (2  u[n  1]) z[n] = (y[n]  h[n  1] * z[n  1]) / l[n] c[n] = z[n] else l[n] = 1 z[n] = 0 c[n] = 0 for i in [(n  1)..0] c[i] = z[i]  u[i] * c[i + 1] b[i] = (a[i + 1]  a[i]) / h[i]  h[i] * (c[i + 1] + 2 * c[i]) / 3 d[i] = (c[i + 1]  c[i]) / (3 * h[i]) @x = x[0..n] # copy @a = a[0...n] @b = b @c = c[0...n] @d = d derivative: > s = new this.constructor() s.x = @x[0...@x.length] # copy s.a = @b[0...@b.length] # copy s.b = 2 * c for c in @c s.c = 3 * d for d in @d s.d = 0 for x in [0...@d.length] s interpolate: (x) > for i in [(@x.length  1)..0] break if @x[i] <= x deltaX = x  @x[i] y = @a[i] + @b[i] * deltaX + @c[i] * Math.pow(deltaX, 2) + @d[i] * Math.pow(deltaX, 3) y 
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