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## NURBS intersection solution

Beginner
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Dear All,

Long time ago, I had released the information about my Bezier curves' intersection solution here, now I am happily to let you know that my NURBS intersection solution is finally completed. I hope that I will have the chance to combine my solution into the contemporary CAD/CAM and Game software in the near future.

If you'd like to know about what I have tried and what I have found about NURBS, welcome to visit my new NURBS-X site to review the detail.

Enclosed is a piece of NURBS-X sample data for your review, in which there are one quartic degree NURBS intersects with a cubic degree NURBS.

Blue NURBS -- Nonuniform, degree: 4,  Ring-mode: ON;
Control points:  8;
P00(225.00, 273.00),  P01(244.00, 352.00),  P02(516.00, 299.00),  P03(472.00, 205.00),  P04(225.00, 273.00),  P05(244.00, 352.00),
P06(516.00, 299.00),  P07(472.00, 205.00)
Knots vector:  13;
{    0.00,    0.00,    7.00,   16.00,   16.00,   17.00,   24.00,   33.00,   33.00,   34.00,   41.00,   50.00,   50.00 }
Control points of poly-Bezier:  17;
VALID   (373.488235294117660, 326.282352941176500),  (388.000000000000000, 323.941176470588230),  (404.000000000000000, 320.823529411764700),  (417.676470588235300, 317.404411764705860),
VALID   (429.232050173010410, 313.791576557093440),  (510.121107266435960, 288.501730103806270),  (487.086505190311410, 253.719723183391010),  (429.633217993079600, 246.404844290657420),
VALID   (373.784034385813130, 255.407182634083030),  (301.977941176470610, 266.981617647058780),  (232.823529411764700, 305.529411764705860),  (242.882352941176490, 347.352941176470610),
VALID   (373.488235294117660, 326.282352941176500),  (373.488235294117660, 326.282352941176500),  (373.488235294117660, 326.282352941176500),  (373.488235294117660, 326.282352941176500),
(373.488235294117660, 326.282352941176500)

Red NURBS -- Nonuniform, degree: 3,  Ring-mode: ON;
Control points:  7;
P00(373.00, 376.00),  P01(245.00, 298.00),  P02(352.00, 191.00),  P03(548.00, 284.00),  P04(373.00, 376.00),  P05(245.00, 298.00),
P06(352.00, 191.00)
Knots vector:  11;
{    0.00,    7.00,   16.00,   20.00,   26.00,   32.00,   41.00,   45.00,   51.00,   57.00,   66.00 }
Control points of poly-Bezier:  13;
VALID   (279.952631578947380, 302.078947368421040),  (271.750000000000000, 271.250000000000000),  (311.875000000000000, 231.125000000000000),
VALID   (359.937500000000000, 224.348214285714280),  (408.000000000000000, 217.571428571428580),  (464.000000000000000, 244.142857142857110),
VALID   (475.494736842105230, 271.706766917293240),  (492.736842105263180, 313.052631578947400),  (409.842105263157860, 356.631578947368440),
VALID   (342.360323886639660, 344.461538461538510),  (312.368421052631560, 339.052631578947400),  (285.421052631578960, 322.631578947368440),
(279.952631578947380, 302.078947368421040)

The intersection point(s) of above two NURBS:  4;
X00(477.661930373181010, 280.179763324569540),  X01(475.725826637142290, 272.276194239744770),  X02(278.882394153096360, 293.792684483944300),
X03(305.249610243883690, 331.006991172625930)
The t value(s) of X point(s) of Blue NURBS:  4;
t00 =  19.222165964276165,  t01 =  19.813464310758949,  t02 =  27.684827002549188,
t03 =  31.485753231881930
The t value(s) of X point(s) of Red NURBS:  4;
t00 =  32.613862742507173,  t01 =  32.041307043354557,  t02 =  20.525542414101757,
t03 =  42.808571378651095

Hunt Chang

2 Replies
Beginner
592 Views

Oops,

I did not noticed the picture link was not work. Please check the pictures at here and here.