Self-X

Once I was told that the Self-X problem is impossible to be solved, but now I have solved both problems on CubicBez and QuarticBez based on purely math theory. (a reference of the research history)

Long long time ago, I had heard this from a leading engineer, he said that the self-x point is an annoy interference during his model design with curved form, because of the computer does not have a real vision to exclude it automatically. So if we wish to promote the AUTO level of our computer then we have to find a way to solve it in program and make the computer to see or locate it for us.

Watch my show below, please!

Self-X degree-4, Ex01

Blue Curve: degree 4, control points,

P0(403.00, 430.00), P1(56.00, 48.00), P2(242.00, 617.00), P3(557.00, 154.00), P4(260.00, 391.00);

Self Intersection point at:

S0(319.599156364233070, 347.195685840169460); t[0] = 0.071404125892844, t[1] = 0.938836118743848;

S1(341.128502139096900, 333.841355215843920); t[2] = 0.631174624569079, t[3] = 0.906922968373645;

S2(306.124914508903710, 335.859333083927590); t[4] = 0.086129466926752, t[5] = 0.547334993280381;

Red Curve: degree 4, control points,

P0(829.00, 326.00), P1(300.00, 139.00), P2(796.00, 580.00), P3(750.00, 31.00), P4(639.00, 357.00);

Self Intersection point at:

S0(671.196279219232340, 282.490727510632040); t[0] = 0.101548635031237, t[1] = 0.919812460036603;

S1(662.054903107128670, 299.719056731105350); t[2] = 0.526698403626966, t[3] = 0.944705433925121;

S2(686.699120883840690, 285.236727700509900); t[4] = 0.087633796192055, t[5] = 0.608994432106783;

Self-X degree-4, Ex02

Blue Curve: degree 4, control points,

P0(445.00, 181.00), P1(56.00, 50.00), P2(346.00, 125.00), P3(531.00, 49.00), P4(260.00, 209.00);

Self Intersection point at:

S0(353.930790468025980, 149.527698657841280); t[0] = 0.071018392160894, t[1] = 0.878496465560017;

Red Curve: degree 4, control points,

P0(155.00, 249.00), P1(639.00, 121.00), P2(623.00, 316.00), P3(80.00, 132.00), P4(252.00, 272.00);

Self Intersection point at:

S0(221.250552144015840, 232.851829462574590); t[0] = 0.036259132889393, t[1] = 0.900332872329697;

S1(319.099894336511850, 214.439602467853040); t[2] = 0.100359817691574, t[3] = 0.683662149481412;

Self-X degree-3, Ex01

Blue Curve: degree 3, control points,

P0(250.00, 129.00), P1(109.00, 219.00), P2(416.00, 315.00), P3(103.00, 109.00);

Self Intersection point at:

S0(210.648607643816060, 186.485774426872890); t[1] = 0.222122639648940, t[2] = 0.838465917534741;

Red Curve: degree 3, control points,

P0(759.00, 303.00), P1(316.00, 116.00), P2(650.00, 142.00), P3(730.00, 316.00);

Self Intersection point at:

S0(709.884606833717040, 281.747599039836870); t[1] = 0.039668184641393, t[2] = 0.930195444733289;