# NURBS intersection solution

Dear All,

Yes, it is not a typo. I am here to present you my real-time NURBS-X solution, it is is a sequel to my Bezier-X solution and it is a common solution. I hope it can be combined into CAD/CAM software in the near future. Also if anyone likes to clarify the relationship in between KNOTS and Control-Points of NURBS, welcome to visit my site to check about my KNOTS-EQUATION.

I am not good in English, so I let the data and picture speak for me.

``````Blue NURBS -- Nonuniform, degree: 3,  Ring-mode: ON;
Control points:  7;
P00(233.00, 374.00),  P01(183.00, 206.00),  P02(543.00, 122.00),  P03(557.00, 360.00),  P04(233.00, 374.00),  P05(183.00, 206.00),
P06(543.00, 122.00)
Knots vector:  11;
{    0.00,    6.00,    7.00,   13.00,   17.00,   21.00,   22.00,   28.00,   32.00,   36.00,   37.00 }
Control points of poly-Bezier:  13;
VALID	  (282.844155844155860, 208.836363636363670),  (337.285714285714280, 170.000000000000000),  (440.142857142857170, 146.000000000000000),
VALID	  (494.682539682539640, 186.888888888888890),  (549.222222222222170, 227.777777777777770),  (555.444444444444460, 333.555555555555540),
VALID	  (462.434343434343420, 358.783838383838430),  (439.181818181818190, 365.090909090909120),  (409.727272727272750, 366.363636363636370),
VALID	  (383.831168831168840, 365.272727272727310),  (228.454545454545440, 358.727272727272750),  (201.181818181818190, 267.090909090909120),
(282.844155844155860, 208.836363636363670)

Red NURBS -- Nonuniform, degree: 3,  Ring-mode: ON;
Control points:  6;
P00(259.00, 473.00),  P01(686.00, 268.00),  P02(210.00, 124.00),  P03(259.00, 473.00),  P04(686.00, 268.00),  P05(210.00, 124.00),
Knots vector:  10;
{    0.00,    8.00,   14.00,   21.00,   24.00,   30.00,   37.00,   40.00,   46.00,   53.00 }
Control points of poly-Bezier:  10;
VALID	  (516.206249999999950, 235.431250000000030),  (477.750000000000000, 205.000000000000000),  (388.500000000000000, 178.000000000000000),
VALID	  (332.062500000000060, 181.812500000000000),  (219.187500000000000, 189.437500000000000),  (237.562500000000000, 320.312500000000000),
VALID	  (321.360576923076910, 355.302884615384640),  (419.125000000000000, 396.125000000000000),  (605.937500000000000, 306.437500000000000),
(516.206249999999950, 235.431250000000030)

The intersection point(s) of above two NURBS:  6;
X00(335.609328952513810, 181.615081973415360),  X01(525.811201136526280, 308.925397222716240),  X02(533.117487761081070, 253.530321279449480),
X03(386.590110642571970, 365.379430477432270),  X04(256.110027051257420, 233.543875038688180),  X05(332.238048740214940, 359.208087319808670),
The t value(s) of X point(s) of Blue NURBS:  6;
t00 =  14.079692090067327,  t01 =  19.599948262974532,  t02 =  18.518048653176436,
t03 =  21.964653175409410,  t04 =  27.202885722603959,  t05 =  22.738607811361728,
The t value(s) of X point(s) of Red NURBS:  6;
t00 =  23.937889226425405,  t01 =  34.604081981733401,  t02 =  36.415241050009513,
t03 =  31.376605713345651,  t04 =  26.327775708765714,  t05 =  30.251769416541645,
``````

Enjoy your surfing!

@GregArden, do you want to add anything here?