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r.e.s.
science forum beginner

Joined: 29 Apr 2005
Posts: 27

Posted: Mon Jul 04, 2005 1:27 pm    Post subject: Re: need help with formula

"r.e.s." <r.s@ZZmindspring.com> wrote ...
 Quote: "Art" wrote ... This requires that the points be converted to xy coordinates, but I am not sure how to go about doing this. Each triangle would then consist of Distance between A and B <-- c Distance between A and Point-n <-- a Distance between B and Point-n <-- b x = (c^2 + a^2 - b^2) / (2c) y = sqrt(a^2 - x^2).

For whatever reason, the earlier replies by Lynn Kurtz
have only now appeared on my server -- sorry for the
repetition. Anyway, this makes for easy Excel plots.

--r.e.s.
r.e.s.
science forum beginner

Joined: 29 Apr 2005
Posts: 27

Posted: Mon Jul 04, 2005 12:47 am    Post subject: Re: need help with formula

"Art" <ajryan@adelphia.net> wrote ...

 Quote: This requires that the points be converted to xy coordinates, but I am not sure how to go about doing this. Each triangle would then consist of Distance between A and B <-- c Distance between A and Point-n <-- a Distance between B and Point-n <-- b

Take A at (0,0) and B at (c,0), and say the data point
is at distance a from A and distance b from B, with
the angle at A in the range from 0 to pi (inclusive).

By the law of cosines, b^2 = c^2 + a^2 - 2 c a cosA,
and (a cosA) is just the x-coordinate of point P. So
the x- and y-coordinates of P are

x = (c^2 + a^2 - b^2) / (2c)
and y = sqrt(a^2 - x^2).

--r.e.s.
Lynn Kurtz
science forum Guru

Joined: 02 May 2005
Posts: 603

Posted: Sun Jul 03, 2005 3:10 pm    Post subject: Re: need help with formula

On Sun, 03 Jul 2005 01:04:15 -0400, Art <ajryan@adelphia.net> wrote:

 Quote: Hi again Lynn. Will any of this be a problem with -x coordinates? Probably half the points will be on the -x axis. Thanks again. Art

No, that wouldn't matter. The only place where care must be taken is
if some points are on opposite sides of your baseline, which I presume
you can easily prevent by positioning your baseline appropriately.

Tell you what, I have a little time on my hands currently, and if you
want to send me a set of data points and baseline length, I will try
it out in Maple and show you what the results look like. If you want
to do that, just email me a text file with your data points. Remove
the anti-spam portion of my email address if you email me.

--Lynn
Lynn Kurtz
science forum Guru

Joined: 02 May 2005
Posts: 603

Posted: Sun Jul 03, 2005 3:03 pm    Post subject: Re: need help with formula

On Sun, 03 Jul 2005 00:57:54 -0400, Art <ajryan@adelphia.net> wrote:

 Quote: Hi Lynn: BTW, what is maple?

Maple is a comprehensive symbolic mathematics program that can
simplify expressions, solve equations, plot curves and surfaces etc.
See:

http://www.maplesoft.com/

There is a less powerful student edition which would likely be more

 Quote: Would maple by any chance do all this calculating for me?

Yes. You could input your set of measurements and receive a plot as
output. I am sure there are also other, possibly less expensive,
programs that will do it too but I have no experience with them.

 Quote: I would ultimately like to have a program that I can import my customers data into and have it calculated automatically.

That is no problem.

--Lynn
Art
science forum beginner

Joined: 02 Jul 2005
Posts: 9

Posted: Sun Jul 03, 2005 3:04 am    Post subject: Re: need help with formula

Hi again Lynn.

Will any of this be a problem with
-x coordinates? Probably half the points
will be on the -x axis.

Thanks again.

Art

Lynn Kurtz wrote:

 Quote: On Sat, 02 Jul 2005 18:03:57 -0400, Art wrote: What they are giving me are the measurements to each point around the circumference, which typically are anywhere from 1-2' apart, from points A and B, (the base). The base itself is a line we establish which is a reference point and is parallel to the longest side of the free form object. It is typically anywhere from 8-15' long, meaning A and B are 8-15' apart. The data is supplied in ft and inches and converted to inches. I basically am trying to find the formulas by which I can triangulate the measurements supplied by my customers and convert them directly into xy coordinates so as to create a graphical representation of the area of the free form via a plotting program, or even a spreasheet. Each point around the circumference should have an equivalent xy coordinate, which can only be obtained by triangulation, correct? Does this help any? Yes. Say your baseline is b units long, put your origin at A so that the xy coordinates of A are (0, 0) and B are (b, 0). Let's say the distance from A to a point P is m and from B to P is n. Then the point P lies on the intersection of a circle of radius m about A and of radius n about B. The equations of these two circles are: x^2 + y^2 = m^2 and (x - b)^2 + y^2 = n^2 You can eliminate y by subtracting them and solve for x which gives: x = (b^2 + m^2 - n^2) / (2b) Put this in the first equation to get y^2 = m^2 - {(b^2 + m^2 - n^2) / (2b)}^2 and y will be the positive square root of this presuming all the points are on the y side of the baseline. This would be very easy to automate and plot with something like Maple. --Lynn
Art
science forum beginner

Joined: 02 Jul 2005
Posts: 9

Posted: Sun Jul 03, 2005 2:57 am    Post subject: Re: need help with formula

Hi Lynn:

Thank you very much.
You have no idea how many
people have responded to
this request in the past
that didn't seem to have
any clue what I was asking
for, even after several
clarifications.

I will test this out and
see what happens - it looks
to be exactly what I was
looking for.

BTW, what is maple?

Would maple by any chance
do all this calculating for
me? I would ultimately
like to have a program that I can
import my customers data into
and have it calculated automatically.

Thanks again.

Art

Lynn Kurtz wrote:

 Quote: On Sat, 02 Jul 2005 18:03:57 -0400, Art wrote: What they are giving me are the measurements to each point around the circumference, which typically are anywhere from 1-2' apart, from points A and B, (the base). The base itself is a line we establish which is a reference point and is parallel to the longest side of the free form object. It is typically anywhere from 8-15' long, meaning A and B are 8-15' apart. The data is supplied in ft and inches and converted to inches. I basically am trying to find the formulas by which I can triangulate the measurements supplied by my customers and convert them directly into xy coordinates so as to create a graphical representation of the area of the free form via a plotting program, or even a spreasheet. Each point around the circumference should have an equivalent xy coordinate, which can only be obtained by triangulation, correct? Does this help any? Yes. Say your baseline is b units long, put your origin at A so that the xy coordinates of A are (0, 0) and B are (b, 0). Let's say the distance from A to a point P is m and from B to P is n. Then the point P lies on the intersection of a circle of radius m about A and of radius n about B. The equations of these two circles are: x^2 + y^2 = m^2 and (x - b)^2 + y^2 = n^2 You can eliminate y by subtracting them and solve for x which gives: x = (b^2 + m^2 - n^2) / (2b) Put this in the first equation to get y^2 = m^2 - {(b^2 + m^2 - n^2) / (2b)}^2 and y will be the positive square root of this presuming all the points are on the y side of the baseline. This would be very easy to automate and plot with something like Maple. --Lynn
Lynn Kurtz
science forum Guru

Joined: 02 May 2005
Posts: 603

Posted: Sat Jul 02, 2005 9:14 pm    Post subject: Re: need help with formula

On Sat, 02 Jul 2005 18:03:57 -0400, Art <ajryan@adelphia.net> wrote:

 Quote: What they are giving me are the measurements to each point around the circumference, which typically are anywhere from 1-2' apart, from points A and B, (the base). The base itself is a line we establish which is a reference point and is parallel to the longest side of the free form object. It is typically anywhere from 8-15' long, meaning A and B are 8-15' apart. The data is supplied in ft and inches and converted to inches. I basically am trying to find the formulas by which I can triangulate the measurements supplied by my customers and convert them directly into xy coordinates so as to create a graphical representation of the area of the free form via a plotting program, or even a spreasheet. Each point around the circumference should have an equivalent xy coordinate, which can only be obtained by triangulation, correct? Does this help any?

Yes. Say your baseline is b units long, put your origin at A so that
the xy coordinates of A are (0, 0) and B are (b, 0). Let's say the
distance from A to a point P is m and from B to P is n. Then the point
P lies on the intersection of a circle of radius m about A and of
radius n about B. The equations of these two circles are:

x^2 + y^2 = m^2 and (x - b)^2 + y^2 = n^2

You can eliminate y by subtracting them and solve for x which gives:

x = (b^2 + m^2 - n^2) / (2b)

Put this in the first equation to get

y^2 = m^2 - {(b^2 + m^2 - n^2) / (2b)}^2

and y will be the positive square root of this presuming all the
points are on the y side of the baseline.

This would be very easy to automate and plot with something like
Maple.

--Lynn
Art
science forum beginner

Joined: 02 Jul 2005
Posts: 9

Posted: Sat Jul 02, 2005 8:03 pm    Post subject: Re: need help with formula

William Elliot wrote:

 Quote: On Sat, 2 Jul 2005, Art wrote: I sell custom made free-form covers. What's a free form cover? In order to help my customers visualize the result of the datasets they provide in order to spot possible problems before submitting their plot points for production, I would like to be able to take their input and create a scatterplot using excel. What are they giving you? In what form is in given and what does it represent?

Thanks for the response.

This is commonly used for land surveying.

What they are giving me are the measurements to each
point around the circumference, which typically
are anywhere from 1-2' apart, from points A and B, (the base).

The base itself is a line we establish which is a reference point
and is parallel to the longest side of the free form object.
It is typically anywhere from 8-15' long, meaning A and B are 8-15' apart.

The data is supplied in ft and inches and converted to inches.

I basically am trying to find the formulas by which I can triangulate
the measurements supplied by my customers and convert them directly into
xy coordinates so as to create a graphical representation of the area of
the free form via a plotting program, or even a spreasheet.

Each point around the circumference should have an equivalent xy
coordinate, which can only be obtained by triangulation, correct?

Does this help any?

 Quote: This requires that the points be converted to xy coordinates Not possible without any information about the points. What you written below makes little sense. Here's what I make of it. You have a closed simple curve with 60 points about the curve p1, p2,.. p60 which are use for a polygonal approximation of the curve. The coordinates of p1 are given (0,0) The coordinates of p2 are given (0,distance from p1 to p2) The coordinates of p3 require knowing the distance from p2 to p3 and the angle between, p1.p2 and p2.p3 or the distance from p1 to p3 and the angle between the base line p1.p2 and p1.p3 This later way may be easier. Points are made around the perimeter at certain intervals, say 1 - 60. A-B would represent the baseline Point A1 and B1 and AB would be used to calculate x1 and y1 Point A2 and B2 and AB would be used to calculate x2 and y2 and so on up to x60 and y60. Each triangle would then consist of Distance between A and B Distance between A and Point-n Distance between B and Point-n Make sense??? If anyone can help I would be most grateful. Please respond directly to this email. Thanks.
Lynn Kurtz
science forum Guru

Joined: 02 May 2005
Posts: 603

Posted: Sat Jul 02, 2005 6:20 pm    Post subject: Re: need help with formula

On Sat, 02 Jul 2005 15:19:08 -0400, Art <ajryan@adelphia.net> wrote:

 Quote: I sell custom made free-form covers. In order to help my customers visualize the result of the datasets they provide in order to spot possible problems before submitting their plot points for production, I would like to be able to take their input and create a scatterplot using excel. This requires that the points be converted to xy coordinates, but I am not sure how to go about doing this. I am aware that this entails the use of a few simple formulas, but, unfortunately, not simple enough for me. It's beem years since I have had any advanced math classes. Points are made around the perimeter at certain intervals, say 1 - 60. A-B would represent the baseline Point A1 and B1 and AB would be used to calculate x1 and y1 Point A2 and B2 and AB would be used to calculate x2 and y2 and so on up to x60 and y60. Each triangle would then consist of Distance between A and B Distance between A and Point-n Distance between B and Point-n Make sense???

No. You need to explain a bit more. For example, where you say:

 Quote: A-B would represent the baseline Point A1 and B1 and AB would be used to calculate x1 and y1

you need to explain what A1 and B1 are, what you are given about A1
and B1, how you use that to get x1 and y1, and for that matter, what
x1 and y1 represent. When you say A-B represents the baseline to you
mean A is the origin and B is on the positive x axis? You have a lot
of meaningless symbols until you explain what they represent.

--Lynn
William Elliot
science forum Guru

Joined: 24 Mar 2005
Posts: 1906

Posted: Sat Jul 02, 2005 6:10 pm    Post subject: Re: need help with formula

On Sat, 2 Jul 2005, Art wrote:

 Quote: I sell custom made free-form covers.

What's a free form cover?

 Quote: In order to help my customers visualize the result of the datasets they provide in order to spot possible problems before submitting their plot points for production, I would like to be able to take their input and create a scatterplot using excel. What are they giving you?

In what form is in given and what does it represent?

 Quote: This requires that the points be converted to xy coordinates

Not possible without any information about the points.
What you written below makes little sense. Here's what I make of it.

You have a closed simple curve with 60 points about the curve
p1, p2,.. p60 which are use for a polygonal approximation of
the curve. The coordinates of p1 are given (0,0)
The coordinates of p2 are given (0,distance from p1 to p2)

The coordinates of p3 require knowing the distance from
p2 to p3 and the angle between, p1.p2 and p2.p3
or the distance from p1 to p3 and the angle between
the base line p1.p2 and p1.p3 This later way may be easier.

 Quote: Points are made around the perimeter at certain intervals, say 1 - 60. A-B would represent the baseline Point A1 and B1 and AB would be used to calculate x1 and y1 Point A2 and B2 and AB would be used to calculate x2 and y2 and so on up to x60 and y60. Each triangle would then consist of Distance between A and B Distance between A and Point-n Distance between B and Point-n Make sense??? If anyone can help I would be most grateful. Please respond directly to this email. Thanks.
Art
science forum beginner

Joined: 02 Jul 2005
Posts: 9

 Posted: Sat Jul 02, 2005 5:19 pm    Post subject: need help with formula I sell custom made free-form covers. In order to help my customers visualize the result of the datasets they provide in order to spot possible problems before submitting their plot points for production, I would like to be able to take their input and create a scatterplot using excel. This requires that the points be converted to xy coordinates, but I am not sure how to go about doing this. I am aware that this entails the use of a few simple formulas, but, unfortunately, not simple enough for me. It's beem years since I have had any advanced math classes. Points are made around the perimeter at certain intervals, say 1 - 60. A-B would represent the baseline Point A1 and B1 and AB would be used to calculate x1 and y1 Point A2 and B2 and AB would be used to calculate x2 and y2 and so on up to x60 and y60. Each triangle would then consist of Distance between A and B Distance between A and Point-n Distance between B and Point-n Make sense??? If anyone can help I would be most grateful. Please respond directly to this email. Thanks.

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