Finding focus of an arc mathematically

[oldfox]

If it is not possible to generate a "tangent arc" using AlibreScript, then I need help with the formula to find the focus of the arc. I want to be able to use a script to generate the arc. Start and end points are known. The arc
must be tangent to the line on the left.
AddArc(Center,Start,End)

Thanks.

 

[idslk]

Hello Chris,

which points are given, which lines are given, are the lines under an certain angle, is the radius of the arc fixed...
Can you list some additional information refering to "your" sketch (see picture. I've added labels and the 2 blue lines 1+3)




Regards
Stefan

 

[oldfox]

Hi Stefan, thanks for the reply. My math just isn't up to this.

P5 is the Unknown and is needed.

Given: Points - Origin, P1, P2, and P8 is optional
Line 2 (Any length from P1)

Not needed but could be used:
Points - P3, P4, P8

Not needed:
Points - P6, P7
Lines - 1, 3, 4, 5

Lines 4 and 5 were only for "offset" construction and could be reference lines only.
I'm not sure if a Tangent Arc will work with a reference line or not.

Needed:
XY points - P1, P2, Origin
Line for Tangent Arc (line 2)

All lines are parallel with axes. No angles.

The arc radius will be determined by points 1 and 2 and tangent to line 2. Point 1 is the start point. Just like Alibre Design does it.
**********************************************
For a script I would only be using numbers for coordinates and the formula for POINT 5.

If I'm still not clear, just ask more.

Thanks again.

 

[Lew_Merrick]

Hi Stefan, thanks for the reply. My math just isn't up to this.

P5 is the Unknown and is needed.

Hi Chris -- OK, I assume that you know the Coordinate values for P1 and P2. I will define these as P1 = (X1,X2) and P2 = (X2,Y2) -- OK? Thus the3 Line from P1 to P2 has the Slope of (Y2-Y1)/(X2-X1), right? The Midpoint between P1 to P2 (PM1-2) has the value PM1-2 = ((X2+X1)/2,(T2+Y1)/2). Right? The Slope of the Counterpoint Defining Line is (-1/((Y2-Y1)(X2-X1)) -- Correct? Now you can define the Equation of the Counterpoint Defining Line merely by finding the "Y intercept value." Knowing the Equation of the Counterpoint Defining Line and the Coordinate Values for P1 or P2 calculating the Centerpoint Value should be nigh unto trivial. Right?

 

[oldfox]

Lew, Line 3 is not the chord.

 

[idslk]

Hello Chris,

can you draw what you want to get into a sketch including the contraint symbols and post a picture of that?

Regards
Stefan

 

[oldfox]

Hi Stefan,
Here's the part with, I hope, all of the information needed to see what I need. If you need more, ask for specific things and I'll get it to you.
Thanks,
Chris

 

[idslk]

Hello Chris,

a short picture with variable names and a formula:


in a spreadsheet...



Hope this helps

Regards
Stefan

 

[oldfox]

Hope this helps

Hi Stefan,
Completely understood. That's exactly what I needed. "The formula". Thank you so very much.
It calculates out to 6 places mm compared to AD's Measure tool.
Plenty good enough for me.
Are your letter variables German? (H, S, R) Radius I get but not H and S.

 

[Lew_Merrick]

Lew, Line 3 is not the chord.

Chris -- I thought that I had defined Line 1 as the Line connecting P1 to P2.

 

[idslk]

That's exactly what I needed.

I'm very pleased.

Are your letter variables German? (H, S, R) Radius I get but not H and S.

Variables are only variables...
R can stand for Radius, H for Höhe and S for Sehne which translates to radius, height and chord.
So Bolt on
Regards
Stefan

 

[oldfox]

Stefan, can you just confirm my rendition of the formula as a script would take it?

Chris -- I thought that I had defined Line 1 as the Line connecting P1 to P2.

Everyone makes a mistake every once in a while.

 

[oldfox]

I got it now. Formula works out.

So Bolt on

What would be Rivet on.

Thanks again.