有沒有方法可以將圖片轉為函數？

If[First[pointList] === Last[pointList],

pointList, Append[pointList, First[pointList]]],
op === "Open", type = "Open"; pointList,
[CapitalDelta] == 0., type = "Closed";
pointList,
[CapitalDelta]/scale &< op, type = "Closed"; Append[pointList, First[pointList]], True, type = "Open"; Join[pointList, Rest[Reverse[pointList]]]]; (* re-parametrize curve by arclength *) [ScriptX][ScriptY]Function = BSplineFunction[L, SplineDegree -&> 4];
nds =
NDSolve[{s"[t] ==
Sqrt[[ScriptX][ScriptY]Function"[
t].[ScriptX][ScriptY]Function"[t]], s[0] == 0}, s,
{t, 0, 1}, MaxSteps -&> 10^5,
PrecisionGoal -&> 4];
(* total curve length *)
sMax = s[1] /. nds[[1]];
if =
Interpolation[
Table[{s[[Sigma]] /. nds[[1]], [Sigma]}, {[Sigma], 0, 1,
1/M}]];
X[t_Real] :=
BSplineFunction[L][Max[Min[1, if[(t + Pi)/(2 Pi) sMax]] , 0]][[
1]];
Y[t_Real] :=
BSplineFunction[L][Max[Min[1, if[(t + Pi)/(2 Pi) sMax]] , 0]][[
2]];
(* extract Fourier coefficients *)
{XFT, YFT} =
Fourier[Table[#[N @ t], {t, -Pi + [CurlyEpsilon],
Pi - [CurlyEpsilon], (2 Pi -
2 [CurlyEpsilon])/[Mu]}]] /@ {X, Y};
{type, 2 Pi/Sqrt[[Mu]] *
((Transpose[
Table[{Re[#], Im[#]} [Exp[I k Pi] #[[k + 1]]], {k, 0,
nMax}]] /@ {XFT, YFT}))} ];
pointListToLines[pointList_, neighborhoodSize_: 6] :=
Module[{L = DeleteDuplicates[pointList], NF, [Lambda], lineBag,
counter, seenQ, sLB, nearest,
nearest1, nextPoint,
couldReverseQ, [ScriptD], [ScriptN], [ScriptS]},
NF = Nearest[L] ;
[Lambda] = Length[L];
Monitor[
(* list of segments *)
lineBag = {};
counter = 0;
While[counter &< [Lambda], (* new segment *) sLB = {RandomChoice[DeleteCases[L, _?seenQ]]}; seenQ[sLB[[1]]] = True; counter++; couldReverseQ = True; (* complete segment *) While[(nearest = NF[Last[sLB], {Infinity, neighborhoodSize}]; nearest1 = SortBy[DeleteCases[nearest, _?seenQ], 1. EuclideanDistance[Last[sLB], #] ]; nearest1 =!= {} || couldReverseQ), If[nearest1 === {}, (* extend the other end; penalize sharp edges *) sLB = Reverse[sLB]; couldReverseQ = False, (* prefer straight continuation *) nextPoint = If[Length[sLB] &<= 3, nearest1[[1]], [ScriptD] = 1. Normalize[(sLB[[-1]] - sLB[[-2]]) + 1/2 (sLB[[-2]] - sLB[[-3]])]; [ScriptN] = {-1, 1} Reverse[[ScriptD]]; [ScriptS] = Sort[{Sqrt[([ScriptD].(# - sLB[[-1]]))^2 + (* perpendicular *) 2 ([ScriptN].(# - sLB[[-1]]))^2], # } /@ nearest1]; [ScriptS][[1, 2]]]; AppendTo[sLB, nextPoint]; seenQ[nextPoint] = True; counter++ ]]; AppendTo[lineBag, sLB]]; (* return segments sorted by length *) Reverse[SortBy[Select[lineBag , Length[#] &> 12 ], Length]],
(* monitor progress *)
Grid[{{Text[
Style["progress point joining", Darker[Green, 0.66]]],
ProgressIndicator[counter/[Lambda]]},
{Text[
Style["number of segments", Darker[Green, 0.66]]],
Length[lineBag] + 1}},
Alignment -&> Left, Dividers -&> Center]]];
Options[fourierComponents] = {"MaxOrder" -&> 500,
"OpenClose" -&> 0.025};(*MaxOrder是最多有多少個Sin項的意思，似乎越大越好。*)
fourierComponents[pointLists_, OptionsPattern[]] :=
Monitor[
Table[fourierComponentData[
pointLists[[k]],

If[Head[#] === List, #[[k]], #] [ OptionValue["MaxOrder"]],

If[Head[#] === List, #[[k]], #] [ OptionValue["OpenClose"]]],
{k, Length[pointLists]}],
Grid[{{Text[
Style["progress calculating Fourier coefficients",
Darker[Green, 0.66]]],
ProgressIndicator[k/Length[pointLists]]} },
Alignment -&> Left, Dividers -&> Center]] /;
Depth[pointLists] === 4;
makeFourierSeries[{"Closed" |
"Open", {{cax_, sax_}, {cay_, say_}}}, t_, n_] :=
{Sum[If[k == 0, 1/2, 1] cax[[k + 1]] Cos[k t] +
sax[[k + 1]] Sin[k t], {k, 0, Min[n, Length[cax]]}],
Sum[If[k == 0, 1/2, 1] cay[[k + 1]] Cos[k t] +
say[[k + 1]] Sin[k t], {k, 0, Min[n, Length[cay]]}]};
makeFourierSeriesApproximationManipulate[fCs_, maxOrder_: 60] :=
Manipulate[
With[{opts =
Sequence[PlotStyle -&> Black, Frame -&> True, Axes -&> False,
FrameTicks -&> None,
PlotRange -&> All, ImagePadding -&> 12]},
Show[{
ParametricPlot[
Evaluate[
makeFourierSeries[#, t, n] /@
Cases[fCs, {"Closed", _}]], {t, -Pi, Pi}, opts],
ParametricPlot[
Evaluate[
makeFourierSeries[#, t, n] /@
Cases[fCs, {"Open", _}]], {t, -Pi, 0}, opts]}] // Quiet],
{{n, 1, "max series order"}, 1, maxOrder, 1,
Appearance -&> "Labeled"},
TrackedSymbols :&> True, SaveDefinitions -&> True];
sinAmplitudeForm[kt_, {cF_, sF_}] :=
With[{[CurlyPhi] = phase[cF, sF]},
Sqrt[cF^2 + sF^2] Sin[kt + [CurlyPhi]]];

phase[cF_, sF_] := With[{T = Sqrt[cF^2 + sF^2]},
With[{g =
Total[
Abs[Table[
cF Cos[x] + sF Sin[x] -
T Sin[x + #1 ArcSin[cF/T] + #2], {x, 0, 1, 0.1}]]] },