Wolfram mathematica 分段零件之间的平滑连接

分段函数示例：

f[x_]:=Piecewise[{{x^2, 0<x<1-epsilon},{x,1<x<2-epsilon},{2,x>2}}]

---

我不确定我是否理解你的问题，但从我这里收集到的是一个想法

ClearAll[f]
e = 0.1
f[x_] := Piecewise[{{x^2, 0 < x < 1 - e}, {whatEver, 
    1 - e <= x <= 1 + e}, {x, 1 + e < x < 2}, {2, x > 2}}, error]

ClearAll[f]
e=0.1
f[x_]：=分段[{x^2，01-e首先，给定一个函数，我们应该在整个
{x，0,2}范围内精确地定义它
，即其范围上的值
1-epsilon您可以在定义区间起点和终点的函数之间逐渐改变。下面我通过根据区间中的位置移动这些函数加权和中的权重来实现这一点：

ClearAll[f]
epsilon = 0.1;
f[x_] :=
 Piecewise[
  {
   {x^2, 0 < x < 1 - epsilon},
   {Rescale[x, {1 - epsilon, 1}, {1, 0}] x^2 + Rescale[x, {1 - epsilon, 1}, {0, 1}] x, 
      1 - epsilon <= x <= 1}, 
   {x, 1 < x < 2 - epsilon},
   {Rescale[x, {2 - epsilon, 2}, {1, 0}] x + Rescale[x, {2 - epsilon, 2}, {0, 1}] 2, 
      2 - epsilon <= x <= 2},
   {2, x > 2}
   }
  ]

Plot[f[x], {x, 0, 2.5}]

ClearAll[f]
ε=0.1；
f[x_u3;]：=
分段[
{
{x^2，01-epsilon@Sjoerd C.de Vries两个都是很好的答案，我会给你们两个解决的标志，不幸的是+1将不得不这样做。Artes Docendo我认为操纵是个好主意。@Verbeia不，我没有。我不确定如何给予支持，跟随主题是否足够？
W[x_, eps_]:= P[x]//. Flatten@Solve[{#^2 == P[#],
                                     1   == P[1], 
                                     2#  == 3a#^2 +2b# +c, 
                                     1   == 3a +2b +c},   {a, b, c, d}]&@(1-eps)

Z[x_, eps_]:= P[x]//. Flatten@Solve[{#  == P[#],
                                     2  == P[2], 
                                     1  == 3a#^2 +2b# +c, 
                                     0  == 12a +4b +c},  {a, b, c, d}]&@(2-eps)  

f1[x_, eps_]:=  Piecewise[{{x^2, 0 <  x < 1 -eps}, {W[x, eps], 1 -eps <= x < 1},
                           { x , 1 <= x < 2 -eps}, {Z[x, eps], 2 -eps <= x < 2},
                                                   {    2    ,           x >=2}}]; 
Manipulate[ Plot[f1[x, eps],  {x, 0, 2.3}, 
                 PlotRange ->    {0, 2.3}, ImageSize->{650,650}]
                                                        //Quiet, {eps, 0, 1}]

Plot[f1[x, eps]/. eps -> .4, {x, 0, 2.3}, PlotRange -> {0, 2.3}, 
                             ImageSize -> {500, 500}, PlotStyle -> {Blue, Thick}]

ClearAll[f]
epsilon = 0.1;
f[x_] :=
 Piecewise[
  {
   {x^2, 0 < x < 1 - epsilon},
   {Rescale[x, {1 - epsilon, 1}, {1, 0}] x^2 + Rescale[x, {1 - epsilon, 1}, {0, 1}] x, 
      1 - epsilon <= x <= 1}, 
   {x, 1 < x < 2 - epsilon},
   {Rescale[x, {2 - epsilon, 2}, {1, 0}] x + Rescale[x, {2 - epsilon, 2}, {0, 1}] 2, 
      2 - epsilon <= x <= 2},
   {2, x > 2}
   }
  ]

Plot[f[x], {x, 0, 2.5}]