Quartic NURBS

Ex-01 degree 4 * degree 4

Blue NURBS -- Nonuniform, degree: 4, Ring-mode: ON;

Control points: 12;

P00(364.00, 322.00), P01( 93.00, 342.00), P02(308.00, 491.00), P03(567.00, 356.00), P04(272.00, 312.00), P05(425.00, 199.00),

P06(346.00, 44.00), P07(201.00, 166.00), P08(364.00, 322.00), P09( 93.00, 342.00), P10(308.00, 491.00), P11(567.00, 356.00),

Knots vector: 17;

{ 0.00, 2.00, 7.00, 13.00, 21.00, 23.00, 32.00, 36.00, 43.00, 51.00, 56.00, 62.00, 70.00, 72.00, 81.00, 85.00, }

{ 2.00 }

Control points of poly-Bezier: 33;

VALID (273.245581344665990, 429.572815734989720), (291.162929061784890, 433.273043478260890), (310.603661327231180, 435.231304347826100), (330.604576659038910, 434.699130434782660),

VALID (349.867704294872960, 432.316943346508590), (436.551778656126490, 421.597101449275390), (508.295652173913030, 373.414492753623220), (446.821739130434820, 346.127536231884050),

VALID (397.275782369804120, 319.562181477942370), (375.255357142857180, 307.755357142857180), (355.591071428571470, 296.091071428571470), (351.025487012987070, 282.798214285714270),

VALID (353.386918484227180, 267.727138869901980), (357.519423558897300, 241.352756892230560), (382.865914786967440, 209.532581453634070), (385.631265664160420, 171.464598997493740),

VALID (373.740531858492370, 142.813352371312900), (360.151121794871760, 110.069070512820520), (327.419070512820550, 89.624198717948701), (287.374198717948730, 104.861378205128200),

VALID (268.590985342630120, 136.072466824111560), (256.851476983055930, 155.579397210976140), (253.417303943619740, 181.326135852451640), (265.264657369920540, 208.501124606387800),

VALID (274.118561750140710, 233.569155990208660), (284.743247006404890, 263.650793650793670), (291.057365636312970, 290.698412698412710), (261.481759955444200, 308.603174603174580),

VALID (232.134475076580370, 326.112222222222160), (193.004761904761890, 349.457619047619000), (154.280952380952390, 372.099523809523820), (201.576190476190480, 414.771904761904810),

(273.245581344665990, 429.572815734989720)

Red NURBS -- Nonuniform, degree: 4, Ring-mode: ON;

Control points: 7;

P00(637.00, 307.00), P01(101.00, 425.00), P02(221.00, 114.00), P03(637.00, 307.00), P04(101.00, 425.00), P05(221.00, 114.00),

P06(637.00, 307.00)

Knots vector: 12;

{ 0.00, 2.00, 7.00, 13.00, 21.00, 26.00, 32.00, 40.00, 45.00, 51.00, 59.00, 64.00 }

Control points of poly-Bezier: 13;

VALID (218.319268256110350, 245.340034487929240), (242.330214424951240, 217.301130604288520), (288.661598440545790, 196.339337231968840), (348.950097465886980, 201.151423001949300),

VALID (394.279354953039160, 218.687370193159670), (448.674463937621790, 239.730506822612090), (481.528265107212460, 279.096003898635440), (442.873294346978580, 314.233430799220290),

VALID (385.389250905040400, 332.860682261208580), (308.743859649122780, 357.697017543859660), (198.624561403508780, 353.181929824561390), (179.901754385964920, 290.202280701754380),

(218.319268256110320, 245.340034487929220)

The intersection point(s) of above two NURBS: 4;

X00(406.752185284779780, 324.607410977503830), X01(373.427344630668700, 211.967466449268160), X02(267.102725994821470, 213.842982062529960),

X03(229.404634708218710, 327.741557677761990)

The t value(s) of X point(s) of Blue NURBS: 4;

t00 = 31.574196606445639, t01 = 39.259558219958301, t02 = 55.034700994293260,

t03 = 62.139658106233846

The t value(s) of X point(s) of Red NURBS: 4;

t00 = 31.408939300778538, t01 = 25.450709826306039, t02 = 22.764503662451464,

t03 = 36.194294896671636

Ex-02 degree 4 * degree 4

Blue NURBS -- Uniform, degree: 4, Ring-mode: ON;

Control points: 12;

P00(364.00, 322.00), P01( 93.00, 342.00), P02(308.00, 491.00), P03(567.00, 356.00), P04(272.00, 312.00), P05(425.00, 199.00),

P06(346.00, 44.00), P07(201.00, 166.00), P08(364.00, 322.00), P09( 93.00, 342.00), P10(308.00, 491.00), P11(567.00, 356.00),

Knots vector: 17;

{ 0.00, 1.00, 2.00, 3.00, 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, 10.00, 11.00, 12.00, 13.00, 14.00, 15.00, }

{ 1.00 }

Control points of poly-Bezier: 33;

VALID (222.583333333333340, 410.041666666666690), (257.916666666666690, 430.083333333333370), (315.333333333333370, 443.666666666666630), (376.416666666666630, 433.583333333333370),

VALID (416.250000000000000, 415.458333333333370), (456.083333333333370, 397.333333333333370), (474.666666666666690, 371.166666666666740), (447.083333333333310, 352.583333333333370),

VALID (415.083333333333370, 334.916666666666690), (383.083333333333370, 317.250000000000000), (346.666666666666630, 300.500000000000000), (347.583333333333310, 278.000000000000000),

VALID (357.500000000000000, 250.875000000000000), (367.416666666666690, 223.750000000000000), (386.333333333333370, 192.000000000000000), (385.916666666666690, 156.750000000000000),

VALID (373.083333333333370, 131.291666666666690), (360.250000000000060, 105.833333333333340), (335.000000000000000, 90.166666666666686), (304.250000000000000, 97.583333333333343),

VALID (283.583333333333370, 117.958333333333340), (262.916666666666690, 138.333333333333340), (252.333333333333340, 171.666666666666690), (267.416666666666630, 207.833333333333310),

VALID (277.250000000000000, 239.750000000000000), (287.083333333333370, 271.666666666666690), (291.666666666666690, 299.333333333333310), (260.083333333333310, 315.666666666666630),

VALID (230.666666666666660, 331.708333333333310), (201.250000000000000, 347.750000000000000), (174.000000000000000, 363.500000000000000), (187.250000000000000, 390.000000000000000),

(222.583333333333340, 410.041666666666690)

Red NURBS -- Nonuniform, degree: 4, Ring-mode: ON;

Control points: 7;

P00(637.00, 307.00), P01(101.00, 425.00), P02(221.00, 114.00), P03(637.00, 307.00), P04(101.00, 425.00), P05(221.00, 114.00),

P06(637.00, 307.00)

Knots vector: 12;

{ 0.00, 3.00, 5.00, 14.00, 19.00, 21.00, 30.00, 35.00, 37.00, 46.00, 51.00, 53.00 }

Control points of poly-Bezier: 13;

VALID (201.821541950113360, 236.304331065759640), (215.652380952380950, 222.437619047619050), (234.633333333333330, 211.076666666666650), (257.366666666666670, 205.123333333333330),

VALID (280.916161616161620, 203.474646464646470), (386.888888888888860, 196.055555555555570), (509.388888888888860, 275.805555555555540), (380.853174603174580, 342.216269841269820),

VALID (275.193990929705250, 342.042596371882040), (216.494444444444470, 341.946111111111120), (164.855555555555550, 321.298888888888880), (167.244444444444440, 270.971111111111100),

(201.821541950113360, 236.304331065759610)

The intersection point(s) of above two NURBS: 4;

X00(382.581150576597910, 316.452599085565050), X01(370.454828022552190, 218.792901423169330), X02(266.788971777987850, 205.081166234768660),

X03(224.835863323727860, 334.916956268164650)

The t value(s) of X point(s) of Blue NURBS: 4;

t00 = 6.260405204765903, t01 = 7.277538864536936, t02 = 9.738047084850559,

t03 = 11.049989431152198

The t value(s) of X point(s) of Red NURBS: 4;

t00 = 27.510565810290878, t01 = 23.023534530140154, t02 = 20.696812415327763,

t03 = 31.168291739526172

Ex-03 degree 4 * degree 4

Blue NURBS -- Nonuniform, degree: 4, Ring-mode: ON;

Control points: 10;

P00(334.00, 253.00), P01(535.00, 462.00), P02(469.00, 262.00), P03(342.00, 143.00), P04(221.00, 249.00), P05(153.00, 435.00),

P06(334.00, 253.00), P07(535.00, 462.00), P08(469.00, 262.00), P09(342.00, 143.00)

Knots vector: 15;

{ 0.00, 4.00, 11.00, 18.00, 25.00, 29.00, 37.00, 43.00, 50.00, 57.00, 64.00, 68.00, 76.00, 82.00, 89.00 }

Control points of poly-Bezier: 25;

VALID (484.255811556864160, 330.854496380812180), (475.137813765182160, 308.023805668016170), (461.238542510121420, 281.575870445344150), (445.199028340080930, 257.597246963562780),

VALID (427.803796671165060, 237.931497975708510), (393.013333333333380, 198.599999999999990), (352.800000000000010, 176.520000000000010), (313.440000000000050, 186.440000000000000),

VALID (278.645208940719160, 214.258853255587950), (252.549115646258540, 235.122993197278900), (229.020952380952390, 266.055238095238110), (209.626666666666670, 301.106666666666680),

VALID (200.045128205128210, 327.257435897435930), (188.866666666666670, 357.766666666666650), (191.044444444444420, 376.161111111111150), (215.596296296296320, 361.765740740740800),

VALID (252.894197530864200, 348.592993827160510), (290.192098765432090, 335.420246913580290), (340.236049382716030, 323.470123456790130), (393.398024691358050, 346.755061728395050),

VALID (433.720550807217530, 365.808556505223180), (474.043076923077020, 384.862051282051310), (501.526153846153870, 399.684102564102550), (500.212307692307660, 370.808205128205150),

(484.255811556864160, 330.854496380812180)

Red NURBS -- Nonuniform, degree: 4, Ring-mode: ON;

Control points: 10;

P00(201.00, 181.00), P01(147.00, 322.00), P02(238.00, 434.00), P03(421.00, 433.00), P04(546.00, 342.00), P05(470.00, 167.00),

P06(201.00, 181.00), P07(147.00, 322.00), P08(238.00, 434.00), P09(421.00, 433.00)

Knots vector: 15;

{ 0.00, 0.00, 7.00, 14.00, 23.00, 29.00, 30.00, 31.00, 38.00, 45.00, 54.00, 60.00, 61.00, 62.00, 69.00 }

Control points of poly-Bezier: 25;

VALID (246.662304476104200, 399.556664949610760), (280.379475703324830, 418.789162404092050), (327.096227621483370, 431.373241687979540), (389.131393861892600, 432.868446291560130),

VALID (443.976753744976290, 409.606416697113670), (453.117647058823540, 405.729411764705900), (462.058823529411770, 401.164705882352910), (470.696078431372600, 395.849019607843100),

VALID (478.454520697167770, 389.887241285402980), (486.212962962962930, 383.925462962962910), (493.092592592592550, 377.317592592592520), (498.518518518518480, 370.168518518518570),

VALID (502.618634259259240, 362.641898148148190), (531.319444444444460, 309.955555555555580), (495.055555555555540, 238.769444444444470), (437.694444444444460, 205.218055555555570),

VALID (379.740525570548020, 195.041811385973690), (321.786606696651630, 184.865567216391810), (263.239880059970010, 198.064467766116930), (224.604760119940010, 220.378935532233900),

VALID (202.839738866362270, 247.828214443914420), (174.856140111762300, 283.120144473217980), (174.759847349052730, 326.900231702330640), (196.086547635273230, 370.707918767888830),

(246.662304476104200, 399.556664949610760)

The intersection point(s) of above two NURBS: 6;

X00(362.631818983902350, 192.777799053592330), X01(316.510246581429780, 193.416139995397000), X02(204.789889471353600, 363.659979426834980),

X03(194.621694396492900, 347.687267999276510), X04(485.983046411627020, 383.567860701479790), X05(493.492712337523700, 375.810818844341440),

The t value(s) of X point(s) of Blue NURBS: 6;

t00 = 32.503591721780275, t01 = 34.914702685099371, t02 = 46.936137878697863,

t03 = 44.359361725450768, t04 = 60.135180429120858, t05 = 61.392085821130763,

The t value(s) of X point(s) of Red NURBS: 6;

t00 = 38.517012232849588, t01 = 39.950267267347066, t02 = 51.609185515151367,

t03 = 50.681350929242832, t04 = 30.254747417188277, t05 = 30.545051130533103,

Ex-04 degree 4 * degree 4

Blue NURBS -- Nonuniform, degree: 4, Ring-mode: ON;

Control points: 10;

P00(150.00, 247.00), P01(385.00, 425.00), P02(371.00, 213.00), P03(545.00, 350.00), P04(521.00, 123.00), P05(300.00, 122.00),

P06(150.00, 247.00), P07(385.00, 425.00), P08(371.00, 213.00), P09(545.00, 350.00)

Knots vector: 15;

{ 0.00, 6.00, 8.00, 11.00, 14.00, 19.00, 23.00, 28.00, 30.00, 33.00, 36.00, 41.00, 45.00, 50.00, 52.00 }

Control points of poly-Bezier: 25;

VALID (357.404638009049730, 335.183152509255420), (384.976470588235260, 314.444117647058820), (394.270588235294100, 271.517647058823510), (426.832679738562090, 274.824836601307200),

VALID (458.093936092955690, 276.610554129059040), (483.102941176470550, 278.039128151260510), (507.279411764705860, 278.493960084033630), (518.044117647058780, 253.524422268907560),

VALID (512.122633902045660, 223.555775719378690), (504.720779220779260, 186.094967532467540), (471.246753246753200, 140.823051948051930), (405.305194805194840, 127.633116883116880),

VALID (337.671578421578430, 140.907342657342670), (310.618131868131850, 146.217032967032960), (283.293956043956090, 155.760989010989020), (257.668681318681370, 169.179670329670330),

VALID (238.985824175824210, 185.738571428571420), (210.961538461538450, 210.576923076923070), (198.557692307692320, 242.480769230769230), (219.471153846153870, 278.971153846153870),

VALID (249.266346153846140, 306.371590909090910), (279.061538461538420, 333.772027972027960), (317.738461538461540, 352.082517482517460), (340.861538461538430, 347.626573426573430),

(357.404638009049730, 335.183152509255480)

Red NURBS -- Nonuniform, degree: 4, Ring-mode: ON;

Control points: 7;

P00(197.00, 488.00), P01(115.00, 35.00), P02(733.00, 199.00), P03(197.00, 488.00), P04(115.00, 35.00), P05(733.00, 199.00),

P06(197.00, 488.00)

Knots vector: 12;

{ 0.00, 6.00, 8.00, 11.00, 14.00, 16.00, 19.00, 22.00, 24.00, 27.00, 30.00, 32.00 }

Control points of poly-Bezier: 13;

VALID (450.335454545454580, 159.075909090909080), (502.613636363636370, 181.965909090909090), (536.295454545454500, 220.306818181818190), (517.522727272727250, 264.329545454545500),

VALID (475.382727272727270, 297.446818181818230), (412.172727272727230, 347.122727272727270), (296.386363636363630, 372.261363636363630), (226.193181818181810, 316.880681818181810),

VALID (215.011363636363630, 255.107954545454560), (203.829545454545470, 193.335227272727280), (251.659090909090930, 125.170454545454530), (371.918181818181890, 124.740909090909070),

(450.335454545454580, 159.075909090909080)

The intersection point(s) of above two NURBS: 8;

X00(512.636308937296460, 247.779988333192360), X01(505.776691428742820, 263.818380680638940), X02(501.614965876270160, 195.948831070308870),

X03(346.869800547685600, 139.283828411105220), X04(215.534841745168190, 257.767900407018200), X05(218.285804554583080, 211.920672488999200),

X06(343.625790287411180, 342.409325691175920), X07(289.738507640627630, 334.234293835504790)

The t value(s) of X point(s) of Blue NURBS: 8;

t00 = 22.117171017197389, t01 = 21.328440798813705, t02 = 23.899984694636913,

t03 = 27.829692394132916, t04 = 31.817301824871439, t05 = 30.721780649721914,

t06 = 35.445085632774017, t07 = 33.953653177857746

The t value(s) of X point(s) of Red NURBS: 8;

t00 = 15.325418890637739, t01 = 15.533606058400647, t02 = 14.631764301962193,

t03 = 21.116240158646750, t04 = 18.967646199213455, t05 = 19.528318930488012,

t06 = 17.227621839269311, t07 = 17.738983980538176