用Octave求曲率圆的圆心坐标
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设\(L:f(x)\)，其中\(P(a,b) \in L\)，则\(P\)点对应的的曲率圆的圆心坐标为：
\(x_{0}=a-f'(a) \frac{1+f'^{2} (a)}{f''(a)}\)，\(y_{0}=b+ \frac{1+f'^{2} (a)}{f''(a)}\)
求\( y=sin(x)\)在\( x=1\)处的曲率圆的圆心坐标.
程序代码如下
function [text_result, numeric_result] = func52(x_value, y_value)
    pkg load symbolic;
    x = sym('x');
    question = sin(x);
    x0 = x_value - (diff(question, x) * (1 + power(diff(question, x), 2)) / diff(diff(question, x), x));
    y0 = y_value + ((1 + power(diff(question, x), 2)) / diff(diff(question, x), x));
    result_x0 = limit(x0, x, x_value);
    result_y0 = limit(y0, x, x_value);
    text_result = ["\nx0=", disp(result_x0), "\ny0=", disp(result_y0)];
    numeric_result = [eval(result_x0), eval(result_y0)];
endfunction
结果如下
>> [text_result, numeric_result] = func52(1, sin(1))
warning: passing floating-point values to sym is dangerous, see "help sym"
warning: called from
    double_to_sym_heuristic at line 50 column 7
    sym at line 384 column 13
    plus at line 53 column 5
    func52 at line 6 column 8

text_result =
x0=    3
    cos (1)   cos(1)
    ─────── + ────── + 1
    sin(1)    sin(1)

y0=               2
        1      cos (1)   1327
    - ────── - ─────── + ────
      sin(1)   sin(1)    1577

numeric_result =

    1.8295  -0.6938
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