Re: Cubic Bezier Curves Intersection

• To: mathgroup at smc.vnet.net
• Subject: [mg132070] Re: Cubic Bezier Curves Intersection
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 30 Nov 2013 02:25:25 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
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• References: <20131129084954.6B8E46A1D@smc.vnet.net>

```pts1 = {{0, 0}, {1, 1}, {2, 0}, {3, 2}};

pts2 = {{1, 1}, {0, 0}, {3, 2}, {2, 0}};

Clear[f1, f2]

f1[x_] :=
BezierFunction[pts1][x];

f2[x_] :=
BezierFunction[pts2][x];

xip = NMinimize[{
Norm[f1[x1] - f2[x2]],
0 <= x1 <= 1, 0 <= x2 <= 1},
{x1, x2}][[2]]

{x1 -> 0.700846, x2 -> 0.735816}

f1[x1] /. xip

{2.10254, 0.876654}

f2[x2] /. xip

{2.10254, 0.876654}

Show[
Graphics[
{Green, AbsolutePointSize[4], Point[pts1],
Darker[Red], Point[f1[x1] /. xip]},
Frame -> True],
ParametricPlot[
{f1[x], f2[x]}, {x, 0, 1}]]

Bob Hanlon

On Fri, Nov 29, 2013 at 3:49 AM, E. Martin-Serrano <
eMartinSerrano at telefonica.net> wrote:

> Hi,
>
> I would appreciate a  piece of Mathematica code implementing Cubic Bezier
> Curves Intersection.
>
> Any help either on the forum or  a notebook sent to the my  e-mail address
> will be welcome.
>
> Regards.
>
> E. Martin-Serrano
>
>
>
>

```

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