Embedded Files
Degree-4 X degree-4, Ex-01
Blue Curve: degree 4, control points,
P0(591.00, 326.00), P1(1050.00, 565.00), P2(31.00, 88.00), P3(1160.00, 547.00), P4(584.00, 289.00);
Red Curve: degree 4, control points,
P0(610.00, 420.00), P1(1013.00, 60.00), P2(59.00, 734.00), P3(1084.00, 109.00), P4(628.00, 438.00);
The Intersection point(s) of these two curves:
X00(662.681356562044130, 371.362429780598920), X01(667.515314968547160, 366.662726794086320), X02(678.795763242399180, 355.415657770194460);
X03(693.931364982574000, 339.324921094735490), X04(670.905151055647710, 328.509294448938420), X05(638.705992414901630, 351.107531897401150);
X06(636.468105902881460, 352.965599776353600), X07(641.416758285039690, 348.932534096693360), X08(661.841404365001610, 363.563180072967840);
X09(682.560849538695490, 356.316124787590520), X10(653.765979588590650, 366.201204057211950), X11(709.441779073585620, 346.792783015714580);
X12(722.345321153934490, 366.224032227535190), X13(695.477233661463520, 387.898694012683900), X14(731.623757752992790, 358.006592490366980);
X15(699.466700831348480, 384.791392982011190);
Blue Curve's t value(s):
t[00] = 0.332867596187779, t[01] = 0.055016563878660, t[02] = 0.635066009376268;
t[03] = 0.935605545964777, t[04] = 0.953241380756346, t[05] = 0.030165279362803; t[06] = 0.449236429260055, t[07] = 0.525833369250902, t[08] = 0.049475472750695; t[09] = 0.643179766508269, t[10] = 0.359939022660531, t[11] = 0.921037640961379; t[12] = 0.726435022812732, t[13] = 0.243189014223362, t[14] = 0.892472215988304; t[15] = 0.099554298624574; Red Curve's t value(s): t[00] = 0.040384096641806, t[01] = 0.045287417974866, t[02] = 0.058204585970165; t[03] = 0.080963101999886, t[04] = 0.288064106979679, t[05] = 0.375399907059774; t[06] = 0.383154232763626, t[07] = 0.366582161260985, t[08] = 0.633984916617625; t[09] = 0.677127148456833, t[10] = 0.615394053095645, t[11] = 0.730944225867951; t[12] = 0.922265809166934, t[13] = 0.953023511689027, t[14] = 0.906559659781782; t[15] = 0.949229316521569;
Degree-4 X degree-4, Ex-02
Blue Curve: degree 4, control points,
P0(485.00, 408.00), P1(511.00, 19.00), P2(329.00, 751.00), P3(622.00, 54.00), P4(470.00, 434.00);
Red Curve: degree 4, control points,
P0(526.00, 368.00), P1(183.00, 197.00), P2(980.00, 571.00), P3(211.00, 137.00), P4(529.00, 394.00);
The Intersection point(s) of these two curves:
X00(500.897278943405350, 355.427528304725460), X01(487.407350904426720, 348.603342249482690), X02(482.566145244332570, 346.136568032183790);
X03(460.745523325233420, 334.809519476483390), X04(461.353169412542910, 327.643942038050340), X05(491.657908289116620, 337.396278415719960);
X06(487.301889868266470, 336.034004332955190), X07(506.003571211651490, 341.644922759107200), X08(502.689470912261410, 325.087453942136450);
X09(486.386030574838340, 317.971723380496940), X10(510.362642295449400, 328.938006623270780), X11(464.860412978736920, 311.423329588914330);
X12(477.793649235788910, 349.743197518428590), X13(487.285726874126680, 358.589328328003260), X14(460.900877890715830, 332.017432337480270);
X15(496.538878064475510, 366.829147973909130); Blue Curve's t value(s): t[00] = 0.929309841594294, t[01] = 0.047089068629839, t[02] = 0.611951621933575; t[03] = 0.384603324937037, t[04] = 0.356553502245651, t[05] = 0.662032701234161; t[06] = 0.060801628745282, t[07] = 0.908409377071206, t[08] = 0.725273863453001; t[09] = 0.085587490717338, t[10] = 0.881500061673371, t[11] = 0.297526122850508; t[12] = 0.584027059285908, t[13] = 0.037491968418443, t[14] = 0.373337489870719; t[15] = 0.943315324603093; Red Curve's t value(s): t[00] = 0.020282104992578, t[01] = 0.033401735496896, t[02] = 0.038662153407950; t[03] = 0.068511056017371, t[04] = 0.247281152295649, t[05] = 0.327273089053835; t[06] = 0.315867309742375, t[07] = 0.367227815150388, t[08] = 0.666969154777500; t[09] = 0.713710264219305, t[10] = 0.642883635328573, t[11] = 0.778332157360707; t[12] = 0.946135215583663, t[13] = 0.959240973967119, t[14] = 0.912671579105631;
t[15] = 0.970122340641440;
Degree-4 X degree-4, Ex-03
Blue Curve: degree 4, control points,
P0(323.00, 519.00), P1(331.00, 290.00), P2(723.00, 357.00), P3(508.00, 512.00), P4(615.00, 164.00); Red Curve: degree 4, control points, P0(654.00, 205.00), P1(438.00, 267.00), P2(878.00, 491.00), P3(228.00, 268.00), P4(345.00, 524.00); The Intersection point(s) of these two curves: X00(591.879792152855660, 254.306164049466790), X01(588.907603524406340, 270.086331947337500), X02(579.230944761861110, 348.962641038351930); X03(519.606556414639730, 374.748836175684230), X04(380.923543197884270, 407.392984170232920), X05(331.939195745018650, 471.448273926678950); Blue Curve's t value(s): t[00] = 0.923051506230886, t[01] = 0.906031845675952, t[02] = 0.778665131339038; t[03] = 0.445342442649335, t[04] = 0.177336673770994, t[05] = 0.058322384857333; Red Curve's t value(s): t[00] = 0.144133268416172, t[01] = 0.183903943485573, t[02] = 0.424628852054439; t[03] = 0.584482642451469, t[04] = 0.801507479741077, t[05] = 0.939052707994151;
For demo only
Note:
The intersections in between degree-4 and degree-5 curves needs to be solved by a polynomial of 20 degree, which may not be safely solved with an 8-byte-double data type. Due to this limitation, without changing a new compiler my current program can only show this function for demo purpose.
Degree-4 X degree-5, Ex-01
Blue Curve: degree 4, control points,
P0(561.00, 524.00), P1(79.00, 346.00), P2(810.00, 387.00), P3(702.00, 50.00), P4(460.00, 118.00);
Red Curve: degree 5, control points,
P0(921.00, 102.00), P1(149.00, 282.00), P2(997.00, 273.00), P3(181.00, 366.00), P4(297.00, 592.00), P5(596.00, 487.00);
The Intersection point(s) of these two curves:
X00(623.359765973149020, 195.952105618870770), X01(518.942374035617830, 318.388513817111230), X02(408.688751350373020, 438.385983829404610);
X03(517.454732425002700, 507.080503411501350);
Blue Curve's t value(s):
t[00] = 0.671432885771935, t[01] = 0.429415750438457, t[02] = 0.152216124175936;
t[03] = 0.024852461478373;
Red Curve's t value(s):
t[00] = 0.135336236002403, t[01] = 0.419330218421692, t[02] = 0.670575115654319;
t[03] = 0.942598060396183;
Degree-4 X degree-5, Ex-02
Blue Curve: degree 5, control points,
P0(566.00, 522.00), P1(170.00, 578.00), P2(258.00, 151.00), P3(988.00, 678.00), P4(628.00, 44.00), P5(488.00, 555.00);
Red Curve: degree 4, control points,
P0(364.00, 441.00), P1(890.00, 388.00), P2(444.00, 183.00), P3(446.00, 537.00), P4(558.00, 542.00);
The Intersection point(s) of these two curves:
X00(524.113265858813630, 526.004559452474500), X01(379.044591497145350, 439.405572141074570), X02(522.689858483744270, 394.420748208995120);
X03(597.774100078911030, 379.497978196360350), X04(609.651653445881490, 359.825713976277430), X05(563.091876681469220, 399.001487159138380);
X06(506.957038140619600, 497.208212593439950);
Blue Curve's t value(s):
t[00] = 0.022387883435403, t[01] = 0.286564077054343, t[02] = 0.472358896161059;
t[03] = 0.564264637321521, t[04] = 0.843855771929123, t[05] = 0.906512674529447;
t[06] = 0.974643084512883;
Red Curve's t value(s):
t[00] = 0.910718193843143, t[01] = 0.007297016575346, t[02] = 0.611903533801729;
t[03] = 0.209829496125128, t[04] = 0.295106274508916, t[05] = 0.145120958345298;
t[06] = 0.835907466912241;
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