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I have triangle wave function such as

data={{100, 0.897875}, {200, 0.0502655}, {300, 0.871329}, {400, 1.51753}, {500, 1.93758}, {510, 2.03256}, {520, 2.05932}, {530, 2.11685}, {540, 2.05206}, {550, 2.16417}, {560, 2.1402}, {570, 2.37827}, {580, 2.26119}, {590, 2.34834}, {600, 2.61764}, {610, 2.38708}, {620, 2.5807}, {630, 2.60495}, {640, 2.71667}, {650, 2.62205}, {660, 2.72215}, {670, 2.93288}, {680, 2.86926}, {690, 2.89204}, {700, 2.96191}, {710, 2.95762}, {720, 3.06396}, {730, 3.11408}, {740, 3.12296}, {750, 3.13066}, {760, 3.06534}, {770, 3.01915}, {780, 2.96653}, {790, 2.85627}, {800, 2.94296}, {850, 2.72951}, {900, 2.39184}, {950, 2.15231}, {1000, 2.00896}, {1050, 1.76837}, {1100, 1.46249}, {1150, 1.25586}, {1200, 1.00514}, {1250, 0.791419}, {1300, 0.569458}, {1350, 0.295896}, {1400, 0.148705}, {1450, 0.0281875}, {1500, 0.0281875}, {1550, 0.486334}, {1600, 0.593384}, {1650, 0.768177}, {1700, 1.08933}, {1750, 1.17072}, {1800, 1.56239}, {1850, 1.93029}, {1900, 1.96159}, {1950, 2.13287}, {2000, 2.18754}, {2050, 2.42705}, {2100, 2.81983}, {2150, 3.02461}, {2200, 3.07996}, {2250, 2.9862}, {2300, 2.81268}, {2350, 2.6644}, {2400, 2.13366}, {2450, 2.15621}, {2500, 2.01812}, {2550, 1.77687}, {2600, 1.43318}, {2650, 1.38426}, {2700, 1.14923}, {2750, 0.829475}, {2800, 0.611538}, {2850, 0.489246}, {2900, 0.280524}, {2950, 0.197626}, {3000, 0.221858}}

enter image description here

I want to make code to unfold this equation, I did it manually by adding Pi with sign change. 

ListPlot[{{100, -0.897875`}, {200, 0.0502655`}, {300, 0.871329`}, {400, 1.51753`}, {500, 1.93758`}, {510, 2.03256`}, {520, 2.05932`}, {530, 2.11685`}, {540, 2.05206`}, {550, 2.16417`}, {560, 2.1402`}, {570, 2.37827`}, {580, 2.26119`}, {590, 2.34834`}, {600, 2.61764`}, {610, 2.38708`}, {620, 2.5807`}, {630, 2.60495`}, {640, 2.71667`}, {650, 2.62205`}, {660, 2.72215`}, {670, 2.93288`}, {680, 2.86926`}, {690, 2.89204`}, {700, 2.96191`}, {710, 2.95762`}, {720, 3.06396`}, {730, 3.11408`}, {740, 3.12296`}, {750, 3.13066`}, {760, 2 Pi - 3.06534`}, {770, 2 Pi - 3.01915`}, {780, 2 Pi - 2.96653`}, {790, 2 Pi - 2.85627`}, {800, 2 Pi - 2.94296`}, {850, 2 Pi - 2.72951`}, {900, 2 Pi - 2.39184`}, {950, 2 Pi - 2.15231`}, {1000, 2 Pi - 2.00896`}, {1050, 2 Pi - 1.76837`}, {1100, 2 Pi - 1.46249`}, {1150, 2 Pi - 1.25586`}, {1200, 2 Pi - 1.00514`}, {1250, 2 Pi - 0.791419`}, {1300, 2 Pi - 0.569458`}, {1350, 2 Pi - 0.295896`}, {1400, 2 Pi - 0.148705`}, {1450, 2 Pi - 0.0281875`}, {1500, 2 Pi + 0.0281875`}, {1550, 2 Pi + 0.486334`}, {1600, 2 Pi + 0.593384`}, {1650, 2 Pi + 0.768177`}, {1700, 2 Pi + 1.08933`}, {1750, 2 Pi + 1.17072`}, {1800, 2 Pi + 1.56239`}, {1850, 2 Pi + 1.93029`}, {1900, 2 Pi + 1.96159`}, {1950, 2 Pi + 2.13287`}, {2000, 2 Pi + 2.18754`}, {2050, 2 Pi + 2.42705`}, {2100, 2 Pi + 2.81983`}, {2150, 2 Pi + 3.02461`}, {2200, 4 Pi - 3.07996`}, {2250, 4 Pi - 2.9862`}, {2300, 4 Pi - 2.81268`}, {2350, 4 Pi - 2.6644`}, {2400, 4 Pi - 2.13366`}, {2450, 4 Pi - 2.15621`}, {2500, 4 Pi - 2.01812`}, {2550, 4 Pi - 1.77687`}, {2600, 4 Pi - 1.43318`}, {2650, 4 Pi - 1.38426`}, {2700, 4 Pi - 1.14923`}, {2750, 4 Pi - 0.829475`}, {2800, 4 Pi - 0.611538`}, {2850, 4 Pi - 0.489246`}, {2900, 4 Pi - 0.280524`}, {2950, 4 Pi - 0.197626`}, {3000, 4 Pi + 0.221858`}}]

enter image description here

Can anyone think of simpler way to do it automatically?

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3 Answers 3

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this is another approach by adding and substracting 2Pi,4Pi

S = {}; For[i = 1, i <= Length[data], i++, v = data[[i]][[2]]; AppendTo[S, {data[[i]][[1]], First@Nearest[{v, 2*Pi - v, 2*Pi + v, 4*Pi - v}, data[[i]][[1]]/230]}]] ListPlot[S]

enter image description here

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Define a function to transform data:

pw = Piecewise[{{{#, -#2}, # < 200}, {{##}, 200 <= # < 760}, {{#, 2 Pi - #2}, 760 <= # < 1500}, {{#, 2 Pi + #2}, 1500 <= # < 2200}, {{#, 4 Pi - #2}, 2200 <= # < 3000}, {{#, 4 Pi + #2}, 3000 <= #}}] &; data2= pw @@@ data; ListPlot[data2]

Mathematica graphics

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here is an attempt to apply the inversed sin function to your function..

enter image description here

This is the Sin function

enter image description here

and this is the result

the new data list is S

S = {}; For[i = 1, i <= Length[data], i++, AppendTo[S, {data[[i]][[1]], data[[i]][[2]] + (-Sin[data[[i]][[1]]/280] + 1)*1.5}]] ListPlot[S]

enter image description here

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  • $\begingroup$ This result doesn't look like what OP had in mind (his second image.) $\endgroup$ Commented Apr 25, 2017 at 0:47
  • $\begingroup$ yes, I was trying to be creative! I posted another answer (much simpler) that meets yours and OP's criteria $\endgroup$ Commented Apr 25, 2017 at 1:48

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