5 关于隐函数作图的问题

在geogebra中用方程画出来,导出tikz代码,可以看到,二次曲线是用旋转标准曲线的方法画的,改成三次的话,提示tikz不支持隐函数画图

你可以试试「只有法语文档」的luadraw宏包:

想要优雅地绘制隐函数倾斜椭圆

% https://ask.latexstudio.net/ask/question/7513.html
\documentclass{standalone}
\usepackage{luadraw}
\begin{document}
\begin{luadraw}{name=implicit_function}
    local g = graph:new{window={-3,3,-3,3},size={10,10}}
    g:Linecap("round")
    local F = function(x,y) return x^2+y^2+x*y-1 end
    g:Dimplicit(F,{draw_options="thick"})
    g:Dgradbox(
        {Z(-2,-2),Z(2,2),1,1},{grid=true,title="\\textbf{Implicit Function Plot}"}
    )
    g:Show()
\end{luadraw}
\end{document}

想要随心所欲地绘制切线，参考nidarfp的回答

\documentclass{standalone}
\usepackage{luadraw}
\begin{document}
\begin{luadraw}{name=implicit_function_tangentline}
    local g = graph:new{window={-3,3,-3,3},size={10,10}}
    g:Linecap("round")
    % https://github.com/pfradin/luadraw/blob/a2759c0aeaf73e023362fac960ffdf704470925a/files/luadraw_lines.lua#L406-L421
    local DtangentI = function(f,x0,y0,len,draw_options) -- f:(x,y()) -> f(x,y)
        -- We assume that f(x0,y0)=0! 
        local h = 1e-6
        local A = Z(x0,y0) -- 定义复数点(x0,y0)
        local a,b = (f(x0+h,y0)-f(x0-h,y0))/(2*h), (f(x0,y0+h)-f(x0,y0-h))/(2*h)
        -- 定义 a,b 为f(x0)处的两个偏导数
        local v = Z(-b,a)
        if len == nil then -- 如果传入的参数为空，则绘制整条直线
            g:Dline({A,v},draw_options)
        else
            local u = len*v/cpx.abs(v)/2 -- 否则往两侧绘制长度为 len/2 的线段
            g:Dseg({A-u,A+u},draw_options) -- 绘制线段
        end
    end
    
    local F = function(x,y) return x^2+y^2+x*y-1 end
    g:Dimplicit(F,{draw_options="thick"})
    g:Dgradbox(
        {Z(-2,-2),Z(2,2),1,1},{grid=true,title="\\textbf{Implicit Function Plot}"}
    )
    local x0 = 1/2
    local L = solve(function(t) return F(x0,t) end,-2,2) -- 求解两个根获得直线的y_i坐标
    for _, y in ipairs(L) do -- 循环绘制多条切线
        DtangentI(F,x0,y,2,"thick,red") -- This work!
    end
    g:Show()
\end{luadraw}
\end{document}