X of Mixed Degrees
Degree 2 series
Degree 2 series
Blue Curve: degree 2, control points, P0(509.00, 275.00), P1(149.00, 328.00), P2(678.00, 583.00);
Red Curve: degree 3, control points, P0(294.00, 394.00), P1(795.00, 427.00), P2(321.00, 81.00), P3(403.00, 456.00);
Self Intersection point at: S0(393.864688662358390, 395.342701670712245); t1 = 0.077720883842140, t2 = 0.939193251426250;
The Intersection point(s) of these two curves: X00(383.051355468467932, 395.824278753572287), X01(472.224974857988059, 281.413094092112715), X02(417.454303050844146, 296.782487844015463); X03(395.138357158809470, 409.388198361759578); Blue Curve's t value(s): t00 = 0.554312983499651, t01 = 0.054781894267117, t02 = 0.157951477744365; t03 = 0.594437278126513; Red Curve's t value(s): t00 = 0.067903398555457, t01 = 0.603589375519780, t02 = 0.764936241487279; t03 = 0.954715262667968;
Red Curve: degree 3, control points, P0(294.00, 394.00), P1(795.00, 427.00), P2(321.00, 81.00), P3(403.00, 456.00);
Self Intersection point at: S0(393.864688662358390, 395.342701670712245); t1 = 0.077720883842140, t2 = 0.939193251426250;
The Intersection point(s) of these two curves: X00(383.051355468467932, 395.824278753572287), X01(472.224974857988059, 281.413094092112715), X02(417.454303050844146, 296.782487844015463); X03(395.138357158809470, 409.388198361759578); Blue Curve's t value(s): t00 = 0.554312983499651, t01 = 0.054781894267117, t02 = 0.157951477744365; t03 = 0.594437278126513; Red Curve's t value(s): t00 = 0.067903398555457, t01 = 0.603589375519780, t02 = 0.764936241487279; t03 = 0.954715262667968;
Quadratic X Cubic Bezier curves - data 1
Blue Curve: degree 2, control points, P0(279.00, 284.00), P1(832.00, 337.00), P2(262.00, 233.00);
Red Curve: degree 4, control points, P0(298.00, 313.00), P1(725.00, 92.00), P2(325.00, 584.00), P3(255.00, 84.00), P4(507.00, 306.00);
Self Intersection point at: S0(435.925804709087345, 258.083251203894918); t0 = 0.115395476113407, t1 = 0.916006780523880; S1(475.514970489608345, 280.941404448482217); t2 = 0.321844589031943, t3 = 0.966630903247506; S2(371.916404771919474, 278.521875087941964); t4 = 0.050281336678881, t5 = 0.671593518420310;
The Intersection point(s) of these two curves: X00(344.959802610897782, 290.120892880735653), X01(417.379274004097908, 262.610372464894908), X02(479.701192713976639, 275.836547999800928); X03(444.351700343480957, 298.179415303423525), X04(386.939517451345182, 293.749301493071584), X05(377.215471270257922, 254.642404149843458); X06(461.945303547669937, 271.916208831198787), X07(501.708302013433581, 301.411220145058451); Blue Curve's t value(s): t00 = 0.063766872479048, t01 = 0.837779242190420, t02 = 0.744957216546720; t03 = 0.183809493227345, t04 = 0.109846140633535, t05 = 0.886169678578682; t06 = 0.774531355566295, t07 = 0.282257768541911; Red Curve's t value(s): t00 = 0.030043298635356, t01 = 0.092796262784459, t02 = 0.297449310503973; t03 = 0.426526669543943, t04 = 0.593107549725979, t05 = 0.784081227467510; t06 = 0.950635238922812, t07 = 0.994696383120645;
Red Curve: degree 4, control points, P0(298.00, 313.00), P1(725.00, 92.00), P2(325.00, 584.00), P3(255.00, 84.00), P4(507.00, 306.00);
Self Intersection point at: S0(435.925804709087345, 258.083251203894918); t0 = 0.115395476113407, t1 = 0.916006780523880; S1(475.514970489608345, 280.941404448482217); t2 = 0.321844589031943, t3 = 0.966630903247506; S2(371.916404771919474, 278.521875087941964); t4 = 0.050281336678881, t5 = 0.671593518420310;
The Intersection point(s) of these two curves: X00(344.959802610897782, 290.120892880735653), X01(417.379274004097908, 262.610372464894908), X02(479.701192713976639, 275.836547999800928); X03(444.351700343480957, 298.179415303423525), X04(386.939517451345182, 293.749301493071584), X05(377.215471270257922, 254.642404149843458); X06(461.945303547669937, 271.916208831198787), X07(501.708302013433581, 301.411220145058451); Blue Curve's t value(s): t00 = 0.063766872479048, t01 = 0.837779242190420, t02 = 0.744957216546720; t03 = 0.183809493227345, t04 = 0.109846140633535, t05 = 0.886169678578682; t06 = 0.774531355566295, t07 = 0.282257768541911; Red Curve's t value(s): t00 = 0.030043298635356, t01 = 0.092796262784459, t02 = 0.297449310503973; t03 = 0.426526669543943, t04 = 0.593107549725979, t05 = 0.784081227467510; t06 = 0.950635238922812, t07 = 0.994696383120645;
Quadratic X Quartic Bezier curves - data 2
Blue Curve: degree 2, control points, P0(447.00, 447.00), P1(356.00, 96.00), P2(438.00, 511.00);
Red Curve: degree 5, control points, P0(499.00, 380.00), P1( 52.00, 324.00), P2(925.00, 224.00), P3( 21.00, 623.00), P4(599.00, 235.00), P5(366.00, 363.00);
The Intersection point(s) of these two curves: X00(426.020538660066393, 367.793454211513506), X01(409.990738044331920, 363.775294406705825), X02(405.614106041237733, 338.480514058438757); X03(420.237057644340439, 346.855126344472865), X04(426.659319199715242, 370.138340087518827), X05(413.771185592348047, 384.705734050363219); X06(411.100056652550222, 369.983798783859697), X07(420.919916957273585, 349.296511942611346), X08(417.927182320540282, 338.670078674838010); X09(406.292604890635744, 342.510694884464556); Blue Curve's t value(s): t00 = 0.131778635477117, t01 = 0.776534598152124, t02 = 0.719566052794853; t03 = 0.176742218749511, t04 = 0.127123139721016, t05 = 0.816896572793047; t06 = 0.789021139583281, t07 = 0.171136601194386, t08 = 0.196409994040924; t09 = 0.729445333896453; Red Curve's t value(s): t00 = 0.042154050926579, t01 = 0.056108863035518, t02 = 0.288684948495805; t03 = 0.349835075711569, t04 = 0.470528517002744, t05 = 0.594477124179707; t06 = 0.741534557822281, t07 = 0.830888446101009, t08 = 0.920043205545427; t09 = 0.950733953675731;
Red Curve: degree 5, control points, P0(499.00, 380.00), P1( 52.00, 324.00), P2(925.00, 224.00), P3( 21.00, 623.00), P4(599.00, 235.00), P5(366.00, 363.00);
The Intersection point(s) of these two curves: X00(426.020538660066393, 367.793454211513506), X01(409.990738044331920, 363.775294406705825), X02(405.614106041237733, 338.480514058438757); X03(420.237057644340439, 346.855126344472865), X04(426.659319199715242, 370.138340087518827), X05(413.771185592348047, 384.705734050363219); X06(411.100056652550222, 369.983798783859697), X07(420.919916957273585, 349.296511942611346), X08(417.927182320540282, 338.670078674838010); X09(406.292604890635744, 342.510694884464556); Blue Curve's t value(s): t00 = 0.131778635477117, t01 = 0.776534598152124, t02 = 0.719566052794853; t03 = 0.176742218749511, t04 = 0.127123139721016, t05 = 0.816896572793047; t06 = 0.789021139583281, t07 = 0.171136601194386, t08 = 0.196409994040924; t09 = 0.729445333896453; Red Curve's t value(s): t00 = 0.042154050926579, t01 = 0.056108863035518, t02 = 0.288684948495805; t03 = 0.349835075711569, t04 = 0.470528517002744, t05 = 0.594477124179707; t06 = 0.741534557822281, t07 = 0.830888446101009, t08 = 0.920043205545427; t09 = 0.950733953675731;
Quadratic X Quintic Bezier curves - data 3
Degree 3 series
Degree 3 series
Blue Curve: degree 4, control points, P0(532.00, 355.00), P1(170.00, 88.00), P2(451.00, 627.00), P3(777.00, 60.00), P4(340.00, 357.00);
Self Intersection point at: S0(440.203598320524009, 297.043553202191845); t0 = 0.079333866999058, t1 = 0.930715354966790; S1(412.540274136393350, 311.725096385354220); t2 = 0.402109608005885, t3 = 0.952878561723736; S2(473.368427247624538, 315.406151019601396); t4 = 0.045957899750563, t5 = 0.525577315676522;
Red Curve: degree 3, control points, P0(545.00, 354.00), P1( 20.00, 171.00), P2(882.00, 392.00), P3(359.00, 300.00);
Self Intersection point at: S0(430.013286021418651, 311.956737154401083); t1 = 0.095627628381054, t2 = 0.947766386402574;
The Intersection point(s) of these two curves: X00(517.007884260179367, 344.161152600067226), X01(479.657095665570523, 319.262972563025698), X02(406.152561971099828, 282.946317139196594); X03(380.129176477078715, 279.145841746067106), X04(372.956821874022410, 286.112011974441430), X05(398.039004097951931, 306.722854533586428); X06(441.752876410644035, 316.525625624315978), X07(460.566522619168097, 316.614765860179432), X08(504.542820234857459, 307.724880296440006); X09(419.614816161170097, 307.809354326610105), X10(449.611378948184267, 292.471612140202524), X11(416.136167657741339, 309.721802434698589); Blue Curve's t value(s): t00 = 0.010654103270295, t01 = 0.040384575742778, t02 = 0.125681284670761; t03 = 0.187409391334342, t04 = 0.251242544729490, t05 = 0.366661937014942; t06 = 0.463406494551450, t07 = 0.500374812307301, t08 = 0.591400259736403; t09 = 0.947502439470445, t10 = 0.922371211334885, t11 = 0.950168452934283; Red Curve's t value(s): t00 = 0.018683512639650, t01 = 0.896873324536471, t02 = 0.406534584086723; t03 = 0.335001183715975, t04 = 0.205706279851827, t05 = 0.973258607569029; t06 = 0.082578229622222, t07 = 0.918720559100150, t08 = 0.612908420294313; t09 = 0.108423878638536, t10 = 0.496767759368672, t11 = 0.959321132437703;
Self Intersection point at: S0(440.203598320524009, 297.043553202191845); t0 = 0.079333866999058, t1 = 0.930715354966790; S1(412.540274136393350, 311.725096385354220); t2 = 0.402109608005885, t3 = 0.952878561723736; S2(473.368427247624538, 315.406151019601396); t4 = 0.045957899750563, t5 = 0.525577315676522;
Red Curve: degree 3, control points, P0(545.00, 354.00), P1( 20.00, 171.00), P2(882.00, 392.00), P3(359.00, 300.00);
Self Intersection point at: S0(430.013286021418651, 311.956737154401083); t1 = 0.095627628381054, t2 = 0.947766386402574;
The Intersection point(s) of these two curves: X00(517.007884260179367, 344.161152600067226), X01(479.657095665570523, 319.262972563025698), X02(406.152561971099828, 282.946317139196594); X03(380.129176477078715, 279.145841746067106), X04(372.956821874022410, 286.112011974441430), X05(398.039004097951931, 306.722854533586428); X06(441.752876410644035, 316.525625624315978), X07(460.566522619168097, 316.614765860179432), X08(504.542820234857459, 307.724880296440006); X09(419.614816161170097, 307.809354326610105), X10(449.611378948184267, 292.471612140202524), X11(416.136167657741339, 309.721802434698589); Blue Curve's t value(s): t00 = 0.010654103270295, t01 = 0.040384575742778, t02 = 0.125681284670761; t03 = 0.187409391334342, t04 = 0.251242544729490, t05 = 0.366661937014942; t06 = 0.463406494551450, t07 = 0.500374812307301, t08 = 0.591400259736403; t09 = 0.947502439470445, t10 = 0.922371211334885, t11 = 0.950168452934283; Red Curve's t value(s): t00 = 0.018683512639650, t01 = 0.896873324536471, t02 = 0.406534584086723; t03 = 0.335001183715975, t04 = 0.205706279851827, t05 = 0.973258607569029; t06 = 0.082578229622222, t07 = 0.918720559100150, t08 = 0.612908420294313; t09 = 0.108423878638536, t10 = 0.496767759368672, t11 = 0.959321132437703;
Cubic X Quartic Bezier curves - data 1
Blue Curve: degree 5, control points,
P0(436.00, 358.00), P1( 20.00, 403.00), P2(925.00, 349.00), P3(187.00, 459.00), P4(586.00, 549.00), P5(370.00, 328.00);
Red Curve: degree 3, control points,
P0(330.00, 368.00), P1(775.00, 609.00), P2( 37.00, 151.00), P3(476.00, 456.00);
Self Intersection point at:
S0(414.224205680919795, 412.619834239034162); t1 = 0.078688717236807, t2 = 0.945389574756285;
The Intersection point(s) of these two curves:
X00(368.919870726338274, 366.018825262506368), X01(353.766302414667734, 368.300933808368995), X02(336.914763483779723, 371.740048883869918);
X03(354.119093000801570, 381.000249627271387), X04(374.842850410479912, 384.155571625937910), X05(408.846473761144807, 390.254477761789815);
X06(466.121096128374859, 437.547979614816427), X07(467.894169687852013, 430.010117475628022), X08(461.714064690331213, 446.054416507233896);
X09(438.693220714947188, 424.909602104280225), X10(427.544189506863859, 402.199590710309849), X11(441.535866894229571, 431.928446880205115);
Blue Curve's t value(s):
t00 = 0.042823368092273, t01 = 0.058692670452746, t02 = 0.087496325946175;
t03 = 0.200361995447302, t04 = 0.239616414761425, t05 = 0.301070379685535;
t06 = 0.577476552388838, t07 = 0.537394207245549, t08 = 0.629630510525911;
t09 = 0.870928737921569, t10 = 0.913444358842828, t11 = 0.853731923064865;
Red Curve's t value(s):
t00 = 0.584935193387846, t01 = 0.858737928838793, t02 = 0.005252689914393;
t03 = 0.019015877374833, t04 = 0.896415322498589, t05 = 0.491895673213038;
t06 = 0.170429335963471, t07 = 0.334067024776204, t08 = 0.988820060072229;
t09 = 0.112599899265739, t10 = 0.449031424081166, t11 = 0.971728955199896;
Cubic X Quintic Bezier curves - data 2
Degree 4 series
Degree 4 series
Blue Curve: degree 4, control points, P0(592.00, 382.00), P1(148.00, 404.00), P2(701.00, 19.00), P3(616.00, 624.00), P4(435.00, 297.00);
Self Intersection point at: S0(442.389879004214549, 309.881008860802524); t0 = 0.312607684849139, t1 = 0.989705437607373; S1(498.983015714669591, 378.711161625212299); t2 = 0.066018387136773, t3 = 0.901275916607062; S2(553.845413186331029, 382.795044714334040); t4 = 0.023259728033477, t5 = 0.754558406367459;
Red Curve: degree 5, control points, P0(409.00, 306.00), P1(857.00, 422.00), P2(340.00, 264.00), P3( 71.00, 379.00), P4(820.00, 339.00), P5(491.00, 391.00);
The Intersection point(s) of these two curves: X00(437.691062778175024, 313.390060241929291), X01(445.765505525311312, 315.456279206362524), X02(555.387736836158410, 343.510255513408595); X03(557.268446616783876, 348.648465728988981), X04(463.880272508745918, 342.157379791228379), X05(427.201711550231778, 341.175186011862024); X06(429.629107933736179, 346.752430684579508), X07(472.270192656085442, 352.718808834125184), X08(556.748190696840652, 377.743981918972111); X09(538.689876871280944, 382.401618985355526), X10(559.509031681597207, 366.144318399381064), X11(512.886897851896720, 387.374543306063629); Blue Curve's t value(s): t00 = 0.296611189338292, t01 = 0.984940003445817, t02 = 0.632540948017646; t03 = 0.647290217528977, t04 = 0.958537879872135, t05 = 0.200426678585671; t06 = 0.183291999178712, t07 = 0.945725633191275, t08 = 0.735421532831628; t09 = 0.033703674355934, t10 = 0.697981408955413, t11 = 0.874818690380283; Red Curve's t value(s): t00 = 0.013590672441121, t01 = 0.017738604929422, t02 = 0.111821296302946; t03 = 0.220526861134753, t04 = 0.385363050170323, t05 = 0.465615438580333; t06 = 0.619010773833912, t07 = 0.703623716164567, t08 = 0.937226509972506; t09 = 0.962408159839362, t10 = 0.851798011676411, t11 = 0.985323152962331;
Self Intersection point at: S0(442.389879004214549, 309.881008860802524); t0 = 0.312607684849139, t1 = 0.989705437607373; S1(498.983015714669591, 378.711161625212299); t2 = 0.066018387136773, t3 = 0.901275916607062; S2(553.845413186331029, 382.795044714334040); t4 = 0.023259728033477, t5 = 0.754558406367459;
Red Curve: degree 5, control points, P0(409.00, 306.00), P1(857.00, 422.00), P2(340.00, 264.00), P3( 71.00, 379.00), P4(820.00, 339.00), P5(491.00, 391.00);
The Intersection point(s) of these two curves: X00(437.691062778175024, 313.390060241929291), X01(445.765505525311312, 315.456279206362524), X02(555.387736836158410, 343.510255513408595); X03(557.268446616783876, 348.648465728988981), X04(463.880272508745918, 342.157379791228379), X05(427.201711550231778, 341.175186011862024); X06(429.629107933736179, 346.752430684579508), X07(472.270192656085442, 352.718808834125184), X08(556.748190696840652, 377.743981918972111); X09(538.689876871280944, 382.401618985355526), X10(559.509031681597207, 366.144318399381064), X11(512.886897851896720, 387.374543306063629); Blue Curve's t value(s): t00 = 0.296611189338292, t01 = 0.984940003445817, t02 = 0.632540948017646; t03 = 0.647290217528977, t04 = 0.958537879872135, t05 = 0.200426678585671; t06 = 0.183291999178712, t07 = 0.945725633191275, t08 = 0.735421532831628; t09 = 0.033703674355934, t10 = 0.697981408955413, t11 = 0.874818690380283; Red Curve's t value(s): t00 = 0.013590672441121, t01 = 0.017738604929422, t02 = 0.111821296302946; t03 = 0.220526861134753, t04 = 0.385363050170323, t05 = 0.465615438580333; t06 = 0.619010773833912, t07 = 0.703623716164567, t08 = 0.937226509972506; t09 = 0.962408159839362, t10 = 0.851798011676411, t11 = 0.985323152962331;
Quartic X Quintic Bezier curves - data 1
Blue Curve: degree 4, control points, P0(497.00, 277.00), P1(438.00, 635.00), P2( 19.00, 142.00), P3(799.00, 368.00), P4(363.00, 340.00);
Self Intersection point at: S0(372.721763935194076, 340.590530886707370); t0 = 0.508530995822251, t1 = 0.994290235145508; S1(479.746193531535482, 338.496301709553052); t2 = 0.051973175818381, t3 = 0.888015678571174; S2(484.860438659027750, 325.479167667490231); t4 = 0.039028967387033, t5 = 0.771059094349510;
Red Curve: degree 5, control points, P0(484.00, 366.00), P1(248.00, 498.00), P2(345.00, 214.00), P3(443.00, 449.00), P4(511.00, 160.00), P5(379.00, 431.00);
The Intersection point(s) of these two curves: X00(450.709408317414272, 382.650378428982435), X01(371.124814735140944, 398.192949230298950), X02(355.275945197235615, 363.625427460400829); X03(381.184407027073462, 341.046210567479534), X04(412.666591119019415, 324.299286479906073), X05(426.268960646840583, 342.299571682500016); X06(439.238270138466930, 320.887264513990260), X07(391.757596663819413, 405.379230521827196); Blue Curve's t value(s): t00 = 0.113769954287381, t01 = 0.289216267143051, t02 = 0.420899720224864; t03 = 0.989081620612969, t04 = 0.606134355151267, t05 = 0.956129561324464; t06 = 0.660254560575327, t07 = 0.233371502794553; Red Curve's t value(s): t00 = 0.030810060735740, t01 = 0.150842491630550, t02 = 0.339316473885755; t03 = 0.460715185576097, t04 = 0.576879904982592, t05 = 0.901179522932042; t06 = 0.844872965150839, t07 = 0.979407625463579;
Self Intersection point at: S0(372.721763935194076, 340.590530886707370); t0 = 0.508530995822251, t1 = 0.994290235145508; S1(479.746193531535482, 338.496301709553052); t2 = 0.051973175818381, t3 = 0.888015678571174; S2(484.860438659027750, 325.479167667490231); t4 = 0.039028967387033, t5 = 0.771059094349510;
Red Curve: degree 5, control points, P0(484.00, 366.00), P1(248.00, 498.00), P2(345.00, 214.00), P3(443.00, 449.00), P4(511.00, 160.00), P5(379.00, 431.00);
The Intersection point(s) of these two curves: X00(450.709408317414272, 382.650378428982435), X01(371.124814735140944, 398.192949230298950), X02(355.275945197235615, 363.625427460400829); X03(381.184407027073462, 341.046210567479534), X04(412.666591119019415, 324.299286479906073), X05(426.268960646840583, 342.299571682500016); X06(439.238270138466930, 320.887264513990260), X07(391.757596663819413, 405.379230521827196); Blue Curve's t value(s): t00 = 0.113769954287381, t01 = 0.289216267143051, t02 = 0.420899720224864; t03 = 0.989081620612969, t04 = 0.606134355151267, t05 = 0.956129561324464; t06 = 0.660254560575327, t07 = 0.233371502794553; Red Curve's t value(s): t00 = 0.030810060735740, t01 = 0.150842491630550, t02 = 0.339316473885755; t03 = 0.460715185576097, t04 = 0.576879904982592, t05 = 0.901179522932042; t06 = 0.844872965150839, t07 = 0.979407625463579;
Quartic X Quintic Bezier curves - data 2