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#### Finding intersection point between a line an a 3d surface

```How do i find the point of intersection between a line and a 3d surface?

I have the data to plot the line, although the line is not straight (has a bend), whilst the surface is a cone section
```
 0
Shenil
9/29/2010 2:08:21 PM
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```"Shenil " <shenilws@yahoo.com> wrote in message <i7vh8l\$4rf\$1@fred.mathworks.com>...
> How do i find the point of intersection between a line and a 3d surface?
>
> I have the data to plot the line, although the line is not straight (has a bend), whilst the surface is a cone section

You need to fit equations to these surfaces and to the line. With these equations, you can then solve for the intersection.

If your bent line consists of 2 straight-line pieces, it is only relevant to fit the piece that intersects the surface with a straight line (if it is not piece-wise straight, then we shouldn't really be calling it a line, but rather a curve).
```
 0
Matt
9/29/2010 2:21:05 PM
```"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i7vi0h\$sbh\$1@fred.mathworks.com>...
> "Shenil " <shenilws@yahoo.com> wrote in message <i7vh8l\$4rf\$1@fred.mathworks.com>...
> > How do i find the point of intersection between a line and a 3d surface?
> >
> > I have the data to plot the line, although the line is not straight (has a bend), whilst the surface is a cone section
>
> You need to fit equations to these surfaces and to the line. With these equations, you can then solve for the intersection.
>
> If your bent line consists of 2 straight-line pieces, it is only relevant to fit the piece that intersects the surface with a straight line (if it is not piece-wise straight, then we shouldn't really be calling it a line, but rather a curve).

Thanks for replying, i have the equation of the line and yes it is in 2 pieces, so need to consider both pieces.  However, how do fit equations to the surfaces?
Cheers
```
 0
Shenil
9/29/2010 2:42:04 PM
```"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <i7vi0h\$sbh\$1@fred.mathworks.com>...
> "Shenil " <shenilws@yahoo.com> wrote in message <i7vh8l\$4rf\$1@fred.mathworks.com>...
> > How do i find the point of intersection between a line and a 3d surface?
> >
> > I have the data to plot the line, although the line is not straight (has a bend), whilst the surface is a cone section
>
> You need to fit equations to these surfaces and to the line. With these equations, you can then solve for the intersection.
>
> If your bent line consists of 2 straight-line pieces, it is only relevant to fit the piece that intersects the surface with a straight line (if it is not piece-wise straight, then we shouldn't really be calling it a line, but rather a curve).

By the way, the surface is created using surf
```
 0
Shenil
9/29/2010 2:43:24 PM
```"Shenil " <shenilws@yahoo.com> wrote in message <i7vj7s\$lim\$1@fred.mathworks.com>...

> Thanks for replying, i have the equation of the line and yes it is in 2 pieces, so need to consider both pieces.
=======

No, as I said you don't need to consider both, assuming you know which piece intersects the surface. In that case only the equation for the intersecting piece is relevant.

>However, how do fit equations to the surfaces?
======

MATLAB has a Curve Fitting Toolbox

http://www.mathworks.com/products/curvefitting/

There are also a number of curve/surface fitting tools on the File Exchange.
```
 0
Matt
9/29/2010 3:19:05 PM

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