matlab分段拟合曲线断点连续

要实现分段拟合曲线断点连续，可以使用matlab中的Spline插值函数。具体步骤如下：

1. 将数据按照断点进行分段，得到每个段的数据。

2. 对每个段的数据使用Spline插值函数进行拟合，得到每个段的曲线函数。

3. 将各段曲线函数拼接起来，得到整个曲线的函数。

4. 对于断点处的连续性，可以通过要求相邻两个段的曲线在断点处函数值相等和导数相等来实现。

具体的matlab代码如下：

% 假设x、y为原始数据
% breakpoints为断点位置

% 分段
n = length(breakpoints);
for i = 1:n+1
    if i == 1
        x_seg{i} = x(x<=breakpoints(i));
        y_seg{i} = y(x<=breakpoints(i));
    elseif i == n+1
        x_seg{i} = x(x>breakpoints(i-1));
        y_seg{i} = y(x>breakpoints(i-1));
    else
        x_seg{i} = x(x>breakpoints(i-1) & x<=breakpoints(i));
        y_seg{i} = y(x>breakpoints(i-1) & x<=breakpoints(i));
    end
end

% 对每个段进行Spline插值
for i = 1:n+1
    p{i} = spline(x_seg{i}, y_seg{i});
end

% 拼接各段曲线函数
syms xx
f = piecewise(xx<=breakpoints(1), p{1}(xx), xx>breakpoints(n), p{n+1}(xx));
for i = 2:n
    f = piecewise(xx<=breakpoints(i), p{i}(xx), f);
end

% 确保断点处连续
for i = 1:n
    f_breakpoint = subs(f, xx, breakpoints(i));
    eq1 = subs(p{i}, xx, breakpoints(i)) == f_breakpoint;
    eq2 = subs(p{i+1}, xx, breakpoints(i)) == f_breakpoint;
    eq3 = subs(diff(p{i}), xx, breakpoints(i)) == subs(diff(p{i+1}), xx, breakpoints(i));
    [A,B] = equationsToMatrix([eq1, eq2, eq3], [p{i}.coefs(end,:), p{i+1}.coefs(1,:)]);
    coefs = linsolve(A,B);
    p{i}.coefs(end,:) = coefs(1,:);
    p{i+1}.coefs(1,:) = coefs(2,:);
end