Re: Re: including specific values in parametric plots

• To: mathgroup at smc.vnet.net
• Subject: [mg101489] Re: [mg101420] Re: [mg101417] including specific values in parametric plots
• From: "David Park" <djmpark at comcast.net>
• Date: Wed, 8 Jul 2009 07:13:38 -0400 (EDT)
• References: <200907070904.FAA21975@smc.vnet.net> <104184.1246964804093.JavaMail.root@n11>

```Very nice, Bob. And counterintuitive.

Still, it would be interesting to know why the original poster thought the detail of his curves or surfaces was not good enough to fit properly and whether plotting certain points would actually solve his problem.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: Bob Hanlon [mailto:hanlonr at cox.net]

To include specific points you can exclude them

ParametricPlot[{Sin[u], Sin[2 u]}, {u, 0, 2 Pi},
Exclusions -> {0.522, 0.824},
ExclusionsStyle -> {AbsolutePointSize[1], Red}]

ParametricPlot3D[{Sin[2 u], Cos[2 u], u/5}, {u, 0, 5},
Exclusions -> {0.522, 0.824},
ExclusionsStyle -> {AbsolutePointSize[1], Red}]

Bob Hanlon

---- David Park <djmpark at comcast.net> wrote:

=============
It would be nice if you could give a specific example that illustrated a
particular case of the problem.

You can use options such as MaxRecursion and PlotPoints to refine a plot. It
is possible to have the second iterator depend on the value of the first
iterator. (Version 6+)

RegionFunction can be used to tailor the boundary of a plotted region.

It's possible to piece together a larger region from subregions.

I don't think it is possible to specify that special points be hit, but I
might learn otherwise.

If members of this group saw a more specific example I think it is likely
there would be some solution.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: Michael Young [mailto:michaelcharlesyoung at earthlink.net]

Hello,

I am modeling mechanical components in Mathematica and there are
places, (particularly where these must fit together), where the
geometry of a piece must change.

Can I, (or how would I), instruct Mathematica's ParametricPlot and
ParametricPlot3D symbols to include specific values within the
parameter set, (to be located at the geometric boundaries)?

(e.g.) If X is a parameter being swept between -1 and 1, how would i
instruct Mathematica to include the fixed values 0.522 and 0.824?

Further, if the precise location of a boundary is only known after
parameter X is given; is there a way (based on that information) to
instruct ParametricPlot3D to include a specific value within the range
of the second parameter, Y?

Michael Young

```

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