conic constructions, exact equations, finding tangents

[Anonymous]

How to enter a exact dimensioned curve, and/or find the tangent at a specified angle to a general sketch curve

I am trying to make Oblate Spheroid geometry based loudspeaker horn/waveguide

the geometry is a surface of revolution of a 2D hyperbola

characterized by hyperbola asymptotic angle and the size constraint of matching a selection of specific compression driver exit angle and diameter numbers at the throat

I can guess at a couple of approaches that have a heavy math preprocessing burden, would require typing lots of high precision digits

the 3 point and Rho conic entry method needs considerable math to hit the curve starting from the parameters I have – and I can't find where you document the equations you use that would let me make the calculation

I believe a 2D spline could also be calculated to give an exact fit to a hyperbola – again clear documentation – cold hard equations documenting what your splines are made of, how to enter the parameters – would need to control slope and curvature awkwardly at the throat endpoint with tedious calculation in other math tools

obviously I'd much prefer a native geometry driven approach

I can literally make a cone by revolving a triangle with the asymptotic angle

slice the body in a plane offset from the cone axis, project the face to a sketch plane

and then I'm stuck – can't apply a tangent constraint to snap a line with the correct angle slope from the axis to the curve

I can't seem get a line to snap tangent to a 3point, Rho conic sketch either – constraint syntax, grammar needs clearer explanation – words please, actual written documentation?

Use of tangent handles to modify curves makes disambiguation difficult

So far I can only make the specified angled line snap tangent to a circle or ellipse (although 1st try warped the ellipse, “fix/unfix” made it do what I wanted)

even then the intersection point doesn't appear, I have to trim away the construction line to get the endpoint of the curve

[Anonymous]

maybe a pic helps

I have done the complete construction in PTC Creo stating cold with no 3D CAD experience in ½ the time I've spent so far not getting to step 2 with Fusion

I really want to get to the CAM part of Fusion, cutting the layers from .stl was painful when Cut3D insists on raster finishing pass

[innovatenate]

There is a script you can run to import points from an excel spreadsheet (CSV) file to generate a curve. You may need to set up the equations for a curve in the excel sheet first. Take a look at the below autodesk screecast for more details.

https://screencast.autodesk.com/Main/Details/35f7beac-de8a-47c8-9ef7-0f927ab15b3d

You raise a good point on the conic curve tool. The documentation is a little bit light. 

My best guess at the moment, since the values range from 0-1 for rho, is that:

• Values of rho less than 0.5 result in an ellipse.
• Values of rho greater than 0.5 result in a hyperbola.
• Values equal to 0.5 result in a parabola.

However, I will seek verification of this and report back to you to confirm this for sure.

As far as the point, you can create a point in the sketch and then add a coincident constraint between the line, curve and the point to locate the tangency point as well.

I hope this helps, I will return with confirmation. Please let us know if you have any other questions.

Thanks!

[ShirleyShi]

If you imagine the conic as a rounded corner, then Rho is the ratio of the distance of the peak of the rounded corner to the sharp corner (D1/D2) (see below picture).

About the tangent constraint issue, could you record a video to show the problem more clearly? We support auto-add tangent constraint when creation if you select the intersection point of the connecting curves while inferring as vertex point.

[Anonymous]

I want a fixed geometry hyperbola - with specific dimensions/geometry - you haven't begun to tell me what the controlling equations are

once I have the correct hyperbola I want to find the point at wihich a tangent to the curve has a given angle relative to the axis

I can snap a given line drawn with a angle input to be tangent at that angle to a circle or ellipse - but not to a general spline curve - is this not yet implemented for hyperbola or spline curves?

also with the spline - no refence of the actual equations from which I could derive the inputs to hit an exact curve - since you apparently  use a 5th order fit I can't gues the form of the end constraints where curvature, rate of curvature inaddition to tangent angle would seem to be needed