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Offline ianlh  
#1 Posted : 18 July 2020 15:08:11(UTC)
ianlh


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Hi All,

Trying to work out a universal way of getting the length of intersecting lines, easy when lines are level, but not so (for me) others.

The image below shows a lifting lug, the angle of action can be 0 deg to 150 deg for example. I need to know the length of the lines from the red circle to the outline, individually, then I can see the shortest length, this must be for all angles, effectively tracing the intersection point through the angles. I know I can use Pythagoras, but was hoping to use something like GPC, but this works only for polygons?



Lug Horizontal.sm (27kb) downloaded 8 time(s).
Offline Ber7  
#2 Posted : 18 July 2020 19:42:58(UTC)
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Try a short circle code.
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Offline Jean Giraud  
#3 Posted : 19 July 2020 01:09:52(UTC)
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Anything helpful in there ?

Solve Circle Ellipse Strophoid NASA.sm (239kb) downloaded 13 time(s).
Offline ianlh  
#4 Posted : 19 July 2020 12:39:06(UTC)
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Hi Jean,

I will have a look, I'm sure I can use something.
Thanks
Offline Ber7  
#5 Posted : 20 July 2020 11:24:38(UTC)
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ianlh, in your example it’s convenient to use the rotation matrix

Lug Horizontal1.sm (19kb) downloaded 12 time(s).
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Offline Jean Giraud  
#6 Posted : 20 July 2020 14:34:13(UTC)
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Whereas the system is built scalar wrt θ
make it more convenient local at graph display.

Lug Horizontal_2.sm (23kb) downloaded 7 time(s).
Offline mkraska  
#7 Posted : 20 July 2020 19:46:20(UTC)
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This provides the shortest distance from the segments of the polygon to the circle. However, the distance isn't really to the segment but to a line through the endpoints of the segment. There is no test if the normal to the line through c is between the vertices of the segment.

For the given geometry this works. For proof of strength this is only useful if a given force may act under any angle but the force doesn't depend on that angle.

Lug Horizontal_Kr.sm (32kb) downloaded 7 time(s).
2020-07-20 18_32_25-Window.png
Martin Kraska

Pre-configured portable distribution of SMath Studio: https://en.smath.info/wi...th%20with%20Plugins.ashx
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Offline Razonar  
#8 Posted : 21 July 2020 08:25:44(UTC)
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Originally Posted by: ianlh Go to Quoted Post
Hi All,

Trying to work out a universal way of getting the length of intersecting lines, easy when lines are level, but not so (for me) others.
...


Hi. Your request it's about a complex computer graphic problem. This is a page for an undergraduated course: https://www.fing.edu.uy/inco/cursos/compgraf/

This paper have a pseudo code for solve partially your problem:

http://www.itseng.org/re...roblems/1979-Bentley.pdf

Hope that's helps.
Alvaro.
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Offline Razonar  
#9 Posted : 21 July 2020 08:44:11(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
ianlh, in your example it’s convenient to use the rotation matrix

Lug Horizontal1.sm (19kb) downloaded 12 time(s).


Hi. This is what's actually do the Ber'f function:

Clipboard01.gif

But notice that for use matrix multiplication for translations you must to use homogeneous coords ( http://elopez.fime.uanl.mx/@materias/732/@Tema%203%20-%20Transformaciones%202D.pdf page 15)

Best regards.
Alvaro.
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Offline Ber7  
#10 Posted : 21 July 2020 13:37:50(UTC)
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Thank you, Razonar.Aapplying homogeneous coordinates helps automate the process.

Variant with homogeneous coordinates

Lug Horizontal3.sm (18kb) downloaded 7 time(s).

Edited by user 21 July 2020 14:37:24(UTC)  | Reason: Not specified

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Offline Razonar  
#11 Posted : 21 July 2020 20:15:57(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
...
Variant with homogeneous coordinates ...


Another variant.

Lug Horizontal4.sm (35kb) downloaded 6 time(s).

Clipboard01.gif

Clipboard02.gif

Homogeneous coordinates are helpful in projective geometry and conics and quadrics. For instance, preserve the duality, because you can use line coordinates ( https://en.wikipedia.org/wiki/Line_coordinates ).

I try to modify for use that in https://en.smath.com/for..._postst17357_Conics.aspx but can't found a close end. This is my atemp for the dual of a conic, it's envelope:

Clipboard04.gif

Best regards.
Alvaro
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Offline Ber7  
#12 Posted : 24 July 2020 15:27:21(UTC)
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Rotate around an arbitrary axis in space


3d rotate.sm (22kb) downloaded 11 time(s).
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Offline Razonar  
#13 Posted : 27 July 2020 06:37:33(UTC)
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Hi Ber. That's not science, that's art. Maybe you can find this book interesting: Modern Robotics.

At page 608 in the pdf, for example:

Clipboard01.gif

Clipboard02.gif

The notation isn't the best, but it can be converted to a general Rotations and translations for the forward kinematics of a robot.

Best regards.
Alvaro.
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Offline Ber7  
#14 Posted : 27 July 2020 11:31:15(UTC)
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Hello Razonar. "Modern Robotics" book
sparked my big interest. Thank you for the link.
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