| Author |
Message |
......... :-))
Guest
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 Posted:
Tue Sep 06, 2005 6:59 am Post subject:
Tangents to Splines |
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Hi All,
I have two splines that define cross sections of a body at different planes
(like the lines drawings of yacht or airplane). Each of the two splines
define a shape that are approximately elliptic (actually its a conic). The
two splines are approximately concentric (i.e. one is inside the other and
they don't overlap).
On the inner spline I have drawn a tangent to the spline at some arbitrary
point.
The problem I am trying to solve is how to find the point at which a
second tangent intersects the outer spline when the second tangent is
parallel to the first on the inner spline.
Anyone got any ideas ??
Thanks,
Steve
tdfsksHATESPAM@yahoo.com
Remove the HATESPAM to email direct ...
PS: I can send the ACAD file to anyone who needs it to visualise the
problem.
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Brian Salt
Guest
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| Posted:
Tue Sep 06, 2005 12:25 pm Post subject:
Re: Tangents to Splines |
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In article <431cf8b4$0$21677$afc38c87@news.optusnet.com.au>,
smjmitchellHATESPAM@yahoo.com (......... :-\)\)) wrote:
| Quote: | The problem I am trying to solve is how to find the point at which a
second tangent intersects the outer spline when the second tangent is
parallel to the first on the inner spline.
|
Perhaps draw a line from the intersection of the tangent/spline
perpendicular to the second spline?
whether it is sufficiently accurate for your purpose depends on the
accuracy of the 'concentricity' of the two splines, I suspect. |
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......... :-))
Guest
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| Posted:
Thu Sep 08, 2005 12:10 am Post subject:
Re: Tangents to Splines |
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This produces a tangent which is close but not exact (as you point out).
Unfortunately this is not good enough in this case.
The exact tangent could be found by a slight variation of this approach but
unfortunately I cannot figure out how to do this.
The line joining the two tangent points must be perpendicular to both
tangents (not just one as per your suggestion). In the general case the line
joining both points of tangency will have an angle to both tangents other
than 90 deg.
However if I could draw a line with a deferred perpendicular from the first
tangent to a point on the second tangent that is perpendicular with the
spline then this would give the right point on the second spline. However I
cannot make this work .... perhaps the maths cannot be solved hence ACAD
does not give the option.
The second possibility is to draw a tangent to the second spline with a
deferred tangency condition. I then need to find a way to force this second
tangent to be parallel to the first. I cannot see a way to do this either
.......
Further suggestions are welcome ...
Thanks,
Steve
"Brian Salt" <briansalt@NScix.co.uk> wrote in message
news:memo.20050906132507.21395A@briansalt.compulink.co.uk...
| Quote: | In article <431cf8b4$0$21677$afc38c87@news.optusnet.com.au>,
smjmitchellHATESPAM@yahoo.com (......... :-\)\)) wrote:
The problem I am trying to solve is how to find the point at which a
second tangent intersects the outer spline when the second tangent is
parallel to the first on the inner spline.
Perhaps draw a line from the intersection of the tangent/spline
perpendicular to the second spline?
whether it is sufficiently accurate for your purpose depends on the
accuracy of the 'concentricity' of the two splines, I suspect. |
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......... :-))
Guest
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| Posted:
Thu Sep 08, 2005 12:10 am Post subject:
Re: Tangents to Splines |
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Sorry let me rewrite one paragraph in my previous post to make it clear what
I meant:
A line passing through both tangents such that it is perpendicular to one
must also be perpendicular to the other (remember the tangents are
parallel). The suggested approach ends up with a line that is perpendicular
to only one tangent. In general such a line can only pass through one of the
points of tangency. A line joining both points of tangency will have an
angle to both tangents other than 90 deg.
"......... :-))" <smjmitchellHATESPAM@yahoo.com> wrote in message
news:431f64de$0$22808$afc38c87@news.optusnet.com.au...
| Quote: |
This produces a tangent which is close but not exact (as you point out).
Unfortunately this is not good enough in this case.
The exact tangent could be found by a slight variation of this approach
but
unfortunately I cannot figure out how to do this.
The line joining the two tangent points must be perpendicular to both
tangents (not just one as per your suggestion). In the general case the
line
joining both points of tangency will have an angle to both tangents other
than 90 deg.
However if I could draw a line with a deferred perpendicular from the
first
tangent to a point on the second tangent that is perpendicular with the
spline then this would give the right point on the second spline. However
I
cannot make this work .... perhaps the maths cannot be solved hence ACAD
does not give the option.
The second possibility is to draw a tangent to the second spline with a
deferred tangency condition. I then need to find a way to force this
second
tangent to be parallel to the first. I cannot see a way to do this either
......
Further suggestions are welcome ...
Thanks,
Steve
"Brian Salt" <briansalt@NScix.co.uk> wrote in message
news:memo.20050906132507.21395A@briansalt.compulink.co.uk...
In article <431cf8b4$0$21677$afc38c87@news.optusnet.com.au>,
smjmitchellHATESPAM@yahoo.com (......... :-\)\)) wrote:
The problem I am trying to solve is how to find the point at which a
second tangent intersects the outer spline when the second tangent is
parallel to the first on the inner spline.
Perhaps draw a line from the intersection of the tangent/spline
perpendicular to the second spline?
whether it is sufficiently accurate for your purpose depends on the
accuracy of the 'concentricity' of the two splines, I suspect.
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Brian Salt
Guest
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| Posted:
Thu Sep 08, 2005 1:40 pm Post subject:
Re: Tangents to Splines |
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In article <431f66bd$0$23738$afc38c87@news.optusnet.com.au>,
smjmitchellHATESPAM@yahoo.com (......... :-\)\)) wrote:
| Quote: | A line joining both points of tangency will have an
angle to both tangents other than 90 deg.
|
Yes indeed, when the two curves are not truly concentric or offsets of
each other.
I can't see how to do what you want, other than empirically, i.e. offset
the first tangent and move it to show a 'visible' intersection as a
tangent, and keep testing it until it is a tangent.
However, I have tried this with two offset half-ellipses, with the outer
one moved down so as to avoid the 'perpendicular' effect.
Draw the tangent to the first curve. Offset the tangent so that it is
outside the second curve. Draw a line joining the ends (upper in my
case) of the tangents. Draw a tangent to the second curve, perpendicular
to the tangent joining line. It requires careful selection of the tangent
point, since the curves are really made up of separate sections and it
easy to get a 'tangent' that actually cuts the curve at two points. |
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