Tangents to Splines

Discussion in 'AutoCAD' started by ......... :-\)\), Sep 6, 2005.

  1. 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 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

    Remove the HATESPAM to email direct ...

    PS: I can send the ACAD file to anyone who needs it to visualise the
    problem.
     
    ......... :-\)\), Sep 6, 2005
    #1
  2. I have had a number of suggestions my direct email to draw a line from the
    point of tangency on the first curve as a perpendicular to the second curve.

    This produces a tangent which is close but not exact. 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.

    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.

    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
     
    ......... :-\)\), Sep 7, 2005
    #2
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