# Tangents to Splines

• posted

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 snipped-for-privacy@yahoo.com Remove the HATESPAM to email direct ...

PS: I can send the ACAD file to anyone who needs it to visualise the problem.

• posted

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.

• posted

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

• posted

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.

• posted

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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