I have the following situation and am trying to find the deflection point of the data, which corresponds to the blue line crosses , which I highlighted and found via CAD plotting. It is worth mentioning that I have already identified the crossing point of the lines through the functions of the sp package, which has the values of x= 2009.805 and y = 509.7997 . If anyone has an idea how to find this point where the line tends to tilt, thank you immensely.
plot(Ego2$X[5100:5500],Ego2$Y[5100:5500],"l", col="red")
par(new=TRUE)
lines(Trecho$Xt[1872:2542],Trecho$Yt[1872:2542])
#abline(v= 1989.467, col="blue")
#abline(h= 488.3509, col="blue")
Thisisapartofthedput(Ego2[5100:5400,c(2:3)])datafortheredlineinthegraph.
structure(list(X=c(1955.583984375,1955.73522949219,1955.87768554688,1956.02941894531,1956.18127441406,1956.32458496094,1956.47705078125,1956.62963867188,1956.77368164062,1956.92687988281,1957.08032226562,1957.22509765625,1957.37902832031,1957.53332519531,1957.6787109375,1957.83349609375,1957.98852539062,1958.134765625,1958.29040527344,1958.44616699219,1958.59313964844,1958.74951171875,1958.90612792969,1959.05383300781,1959.21105957031,1959.36840820312,1959.51684570312,1959.67492675781,1959.83312988281,1959.98229980469,1960.14111328125,1960.30017089844,1960.45007324219,1960.60961914062,1960.76953125,1960.92028808594,1961.08056640625,1961.24133300781,1961.39270019531,1961.55395507812,1961.71545410156,1961.86767578125,1962.02978515625,1962.19201660156,1962.34509277344,1962.50793457031,1962.67114257812,1962.82495117188,1962.98864746094,1963.15258789062,1963.30712890625,1963.4716796875,1963.63647460938,1963.79187011719,1963.95727539062,1964.12292480469,1964.27905273438,1964.4453125,1964.61169433594,1964.76867675781,1964.93566894531,1965.10302734375,1965.2607421875,1965.42858886719,1965.59680175781,1965.75537109375,1965.92407226562,1966.09301757812,1966.25231933594,1966.421875,1966.59167480469,1966.75183105469,1966.92224121094,1967.09289550781,1967.25378417969,1967.42504882812,1967.59655761719,1967.75817871094,1967.93029785156,1968.10266113281,1968.26513671875,1968.43811035156,1968.611328125,1968.77465820312,1968.94848632812,1969.12255859375,1969.28674316406,1969.46142578125,1969.63635253906,1969.80139160156,1969.97692871094,1970.15270996094,1970.31848144531,1970.49499511719,1970.67175292969,1970.83837890625,1971.015625,1971.19323730469,1971.36071777344,1971.53894042969,1971.71740722656,1971.88562011719,1972.06469726562,1972.244140625,1972.41320800781,1972.59313964844,1972.7734375,1972.943359375,1973.12414550781,1973.30529785156,1973.47607421875,1973.65783691406,1973.83984375,1974.01147460938,1974.19396972656,1974.376953125,1974.54931640625,1974.73278808594,1974.91650390625,1975.08972167969,1975.27392578125,1975.45849609375,1975.63244628906,1975.81762695312,1976.0029296875,1976.177734375,1976.36364746094,1976.54992675781,1976.72546386719,1976.91223144531,1977.09924316406,1977.27563476562,1977.46325683594,1977.65112304688,1977.82824707031,1978.01672363281,1978.20544433594,1978.38330078125,1978.57263183594,1978.76232910156,1978.94104003906,1979.13159179688,1979.322265625,1979.50183105469,1979.69262695312,1979.88342285156,1980.06311035156,1980.25439453125,1980.44580078125,1980.62609863281,1980.81787109375,1981.009765625,1981.19055175781,1981.3828125,1981.57531738281,1981.75671386719,1981.94958496094,1982.142578125,1982.32446289062,1982.51794433594,1982.71166992188,1982.89404296875,1983.08813476562,1983.28234863281,1983.46533203125,1983.66003417969,1983.85485839844,1984.03833007812,1984.23352050781,1984.42895507812,1984.61291503906,1984.80871582031,1985.00463867188,1985.18920898438,1985.38549804688,1985.58190917969,1985.76708984375,1985.9638671875,1986.16088867188,1986.34643554688,1986.54382324219,1986.74133300781,1986.92749023438,1987.12536621094,1987.32348632812,1987.51000976562,1987.70849609375,1987.90710449219,1988.09411621094,1988.29309082031,1988.49230957031,1988.67980957031,1988.87939453125,1989.07897949219,1989.26708984375,1989.46704101562,1989.66711425781,1989.85559082031,1990.05603027344,1990.25646972656,1990.4453125,1990.64611816406,1990.84716796875,1991.03637695312,1991.23767089844,1991.43896484375,1991.62866210938,1991.83032226562,1992.03210449219,1992.22216796875,1992.42431640625,1992.62646484375,1992.81701660156,1993.01953125,1993.22216796875,1993.41296386719,1993.61596679688,1993.81896972656,1994.01025390625,1994.21362304688,1994.41711425781,1994.60876464844,1994.8125,1995.01635742188,1995.20849609375,1995.41271972656,1995.61706542969,1995.8095703125,1996.01416015625,1996.21899414062,1996.41186523438,1996.61706542969,1996.822265625,1997.015625,1997.22119140625,1997.42687988281,1997.62060546875,1997.82666015625,1998.03283691406,1998.22705078125,1998.43347167969,1998.64001464844,1998.83459472656,1999.04150390625,1999.24853515625,1999.44360351562,1999.65087890625,1999.8583984375,2000.05383300781,2000.26159667969,2000.46948242188,2000.66540527344,2000.87365722656,2001.08203125,2001.27819824219,2001.48693847656,2001.69567871094,2001.89245605469,2002.1015625,2002.31079101562,2002.50793457031,2002.71740722656,2002.92712402344,2003.12463378906,2003.33471679688,2003.54479980469,2003.74279785156,2003.95324707031,2004.16394042969,2004.3623046875,2004.57336425781,2004.78442382812,2004.98327636719,2005.19482421875,2005.40649414062,2005.60583496094,2005.81774902344,2006.02990722656,2006.22973632812,2006.44226074219,2006.65490722656,2006.85522460938,2007.06823730469,2007.28137207031,2007.48229980469,2007.69580078125,2007.90954589844,2008.11096191406,2008.32507324219,2008.53942871094,2008.74145507812,2008.95617675781,2009.17126464844,2009.37377929688,2009.58923339844,2009.80480957031,2010.00793457031,2010.22399902344,2010.44030761719,2010.64404296875,2010.86071777344),Y=c(454.448608398438,454.600189208984,454.743133544922,454.895233154297,455.047576904297,455.191192626953,455.344055175781,455.497131347656,455.641448974609,455.795013427734,455.948822021484,456.093811035156,456.248138427734,456.402679443359,456.548370361328,456.703430175781,456.858734130859,457.005157470703,457.160980224609,457.317077636719,457.464233398438,457.620819091797,457.777679443359,457.925537109375,458.082885742188,458.240539550781,458.389129638672,458.547271728516,458.705657958984,458.855010986328,459.013916015625,459.173095703125,459.323181152344,459.482879638672,459.642852783203,459.793640136719,459.954132080078,460.114868164062,460.266418457031,460.427642822266,460.589172363281,460.741424560547,460.903442382812,461.065704345703,461.218658447266,461.381439208984,461.544494628906,461.698181152344,461.861755371094,462.025573730469,462.179992675781,462.344329833984,462.508911132812,462.6640625,462.829162597656,462.994537353516,463.150421142578,463.316284179688,463.482421875,463.639038085938,463.805694580078,463.972625732422,464.129974365234,464.297424316406,464.465148925781,464.623229980469,464.791442871094,464.9599609375,465.118774414062,465.287780761719,465.457061767578,465.616638183594,465.786437988281,465.956512451172,466.116821289062,466.287414550781,466.458282470703,466.619354248047,466.790740966797,466.96240234375,467.124206542969,467.29638671875,467.468872070312,467.631439208984,467.804443359375,467.977752685547,468.14111328125,468.31494140625,468.489105224609,468.653259277344,468.827972412109,469.002960205078,469.167938232422,469.343505859375,469.519348144531,469.685119628906,469.861511230469,470.038238525391,470.204803466797,470.382080078125,470.559631347656,470.72705078125,470.905181884766,471.083618164062,471.251831054688,471.430847167969,471.610137939453,471.779174804688,471.959045410156,472.139251708984,472.309112548828,472.489868164062,472.670959472656,472.841644287109,473.023315429688,473.205291748047,473.376831054688,473.559417724609,473.742340087891,473.914764404297,474.098297119141,474.282165527344,474.455505371094,474.640014648438,474.824829101562,474.999053955078,475.184509277344,475.370300292969,475.545440673828,475.731842041016,475.918609619141,476.094665527344,476.282012939453,476.4697265625,476.646697998047,476.835021972656,477.023712158203,477.201568603516,477.390869140625,477.580505371094,477.759368896484,477.949951171875,478.140838623047,478.320556640625,478.511474609375,478.702545166016,478.882598876953,479.074157714844,479.265930175781,479.446594238281,479.638763427734,479.831115722656,480.012390136719,480.205230712891,480.398315429688,480.580230712891,480.773773193359,480.967529296875,481.150115966797,481.344360351562,481.538818359375,481.722076416016,481.917022705078,482.112213134766,482.296142578125,482.491790771484,482.687683105469,482.872253417969,483.068603515625,483.265167236328,483.450378417969,483.647399902344,483.844635009766,484.030487060547,484.228179931641,484.426086425781,484.612579345703,484.810943603516,485.009552001953,485.196685791016,485.395721435547,485.595001220703,485.782806396484,485.982543945312,486.182556152344,486.371002197266,486.571472167969,486.772155761719,486.961273193359,487.162445068359,487.363830566406,487.553619384766,487.755523681641,487.957672119141,488.148193359375,488.350860595703,488.553833007812,488.745086669922,488.948608398438,489.152435302734,489.344512939453,489.548919677734,489.753601074219,489.946533203125,490.151824951172,490.357391357422,490.551177978516,490.757354736328,490.963836669922,491.158477783203,491.365539550781,491.572967529297,491.768463134766,491.976470947266,492.184783935547,492.381134033203,492.590057373047,492.79931640625,492.996551513672,493.206451416016,493.416656494141,493.614776611328,493.825622558594,494.036804199219,494.23583984375,494.447662353516,494.659790039062,494.859771728516,495.072570800781,495.285705566406,495.486602783203,495.700408935547,495.91455078125,496.116394042969,496.331207275391,496.546325683594,496.749145507812,496.964935302734,497.181060791016,497.384796142578,497.601623535156,497.818756103516,498.0234375,498.241271972656,498.459411621094,498.665069580078,498.883880615234,499.103057861328,499.309661865234,499.529479980469,499.749664306641,499.957214355469,500.178070068359,500.399291992188,500.607788085938,500.829650878906,501.051849365234,501.261322021484,501.484222412109,501.707427978516,501.917877197266,502.141784667969,502.366027832031,502.577423095703,502.802337646484,503.027618408203,503.239929199219,503.465881347656,503.692138671875,503.905395507812,504.132293701172,504.359558105469,504.57373046875,504.801635742188,505.029846191406,505.244934082031,505.473785400391,505.702972412109,505.918975830078,506.148803710938,506.378967285156,506.595886230469,506.826690673828,507.057800292969,507.275634765625,507.507354736328,507.739379882812,507.958038330078,508.190673828125,508.423583984375,508.64306640625,508.876556396484,509.1103515625,509.330657958984,509.565002441406,509.799652099609,510.020782470703,510.256011962891,510.491516113281,510.713470458984,510.949554443359)),.Names=c("X", "Y"), row.names = 5100:5400, class = "data.frame")
>
And the output of the data that comprises Excerpt is: dput(Trecho[2120:2220,c(1:2)]) referring to the black line
structure(list(Xt = c(1963.17542, 1963.882527, 1964.589634, 1965.296741,
1966.003848, 1966.710954, 1967.418061, 1968.125168, 1968.832275,
1969.539382, 1970.246488, 1970.953595, 1971.660702, 1972.367809,
1973.074915, 1973.782022, 1974.489129, 1975.196236, 1975.903343,
1976.610449, 1977.317556, 1978.024663, 1978.73177, 1979.438876,
1980.145983, 1980.85309, 1981.560197, 1982.267304, 1982.97441,
1983.681517, 1984.388624, 1985.095731, 1985.802837, 1986.509944,
1987.217051, 1987.924158, 1988.631265, 1989.338371, 1990.045478,
1990.752585, 1991.459692, 1992.166799, 1992.873905, 1993.581012,
1994.288119, 1994.995226, 1995.702332, 1996.409439, 1997.116546,
1997.823653, 1998.53076, 1999.237866, 1999.944973, 2000.65208,
2001.359187, 2002.066293, 2002.7734, 2003.480507, 2004.187614,
2004.894721, 2005.601827, 2006.308934, 2007.016041, 2007.723148,
2008.430254, 2009.137361, 2009.844468, 2010.551575, 2011.258682,
2011.965788, 2012.672895, 2013.380002, 2014.087109, 2014.794216,
2015.501322, 2016.208429, 2016.915536, 2017.622643, 2018.329749,
2019.036856, 2019.743963, 2020.45107, 2021.158177, 2021.865283,
2022.57239, 2023.279497, 2023.986604, 2024.69371, 2025.400817,
2026.107924, 2026.815031, 2027.522138, 2028.229244, 2028.936351,
2029.643458, 2030.350565, 2031.057671, 2031.764778, 2032.471885,
2033.178992, 2033.886099), Yt = c(463.1754204, 463.8825272, 464.589634,
465.2967408, 466.0038476, 466.7109543, 467.4180611, 468.1251679,
468.8322747, 469.5393815, 470.2464883, 470.953595, 471.6607018,
472.3678086, 473.0749154, 473.7820222, 474.4891289, 475.1962357,
475.9033425, 476.6104493, 477.3175561, 478.0246628, 478.7317696,
479.4388764, 480.1459832, 480.85309, 481.5601968, 482.2673035,
482.9744103, 483.6815171, 484.3886239, 485.0957307, 485.8028374,
486.5099442, 487.217051, 487.9241578, 488.6312646, 489.3383713,
490.0454781, 490.7525849, 491.4596917, 492.1667985, 492.8739053,
493.581012, 494.2881188, 494.9952256, 495.7023324, 496.4094392,
497.1165459, 497.8236527, 498.5307595, 499.2378663, 499.9449731,
500.6520798, 501.3591866, 502.0662934, 502.7734002, 503.480507,
504.1876138, 504.8947205, 505.6018273, 506.3089341, 507.0160409,
507.7231477, 508.4302544, 509.1373612, 509.844468, 510.5515748,
511.2586816, 511.9657883, 512.6728951, 513.3800019, 514.0871087,
514.7942155, 515.5013223, 516.208429, 516.9155358, 517.6226426,
518.3297494, 519.0368562, 519.7439629, 520.4510697, 521.1581765,
521.8652833, 522.5723901, 523.2794968, 523.9866036, 524.6937104,
525.4008172, 526.107924, 526.8150308, 527.5221375, 528.2292443,
528.9363511, 529.6434579, 530.3505647, 531.0576714, 531.7647782,
532.471885, 533.1789918, 533.8860986)), .Names = c("Xt", "Yt"
), row.names = 2120:2220, class = "data.frame")