在分段二次贝塞尔曲线上找到控制点
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我需要编写一个程序来生成并显示一个分段的二次贝塞尔曲线，该曲线对每个数据点集进行插值（我有一个包含数据点的txt文件）。曲线应具有连续的切线方向，每个数据点的切线方向是两个相邻和弦方向的凸组合。
0.1 0,
0 0,
0 5,
0.25 5,
0.25 0,
5 0,
5 5,
10 5,
10 0,
9.5 0
没有找到相关结果
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耐钨徒
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class MonotonicCubicSpline # by George MacKerron, mackerron.com # adapted from: # http://sourceforge.net/mailarchive/forum.php?thread_name= # EC90C5C6-C982-4F49-8D46-A64F270C5247%40gmail.com&forum_name=matplotlib-users # (easier to read at http://old.nabble.com/%22Piecewise-Cubic-Hermite-Interpolating- # Polynomial%22-in-python-td25204843.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