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 ianlh #1 Posted : 18 July 2020 15:08:11(UTC) Rank: MemberGroups: Registered Joined: 18/12/2014(UTC)Posts: 11 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).
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 Ber7 #2 Posted : 18 July 2020 19:42:58(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 348Location: Beer-ShevaWas thanked: 453 time(s) in 244 post(s) Try a short circle code. 1 user thanked Ber7 for this useful post. on 18/07/2020(UTC)
 Jean Giraud #3 Posted : 19 July 2020 01:09:52(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,676Was thanked: 792 time(s) in 628 post(s) Anything helpful in there ? Solve Circle Ellipse Strophoid NASA.sm (239kb) downloaded 13 time(s).
 ianlh #4 Posted : 19 July 2020 12:39:06(UTC) Rank: MemberGroups: Registered Joined: 18/12/2014(UTC)Posts: 11 Hi Jean,I will have a look, I'm sure I can use something.Thanks
 Ber7 #5 Posted : 20 July 2020 11:24:38(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 348Location: Beer-ShevaWas thanked: 453 time(s) in 244 post(s) ianlh, in your example it’s convenient to use the rotation matrix Lug Horizontal1.sm (19kb) downloaded 12 time(s). 1 user thanked Ber7 for this useful post. on 21/07/2020(UTC)
 Jean Giraud #6 Posted : 20 July 2020 14:34:13(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,676Was thanked: 792 time(s) in 628 post(s) Whereas the system is built scalar wrt θmake it more convenient local at graph display. Lug Horizontal_2.sm (23kb) downloaded 7 time(s).
 mkraska #7 Posted : 20 July 2020 19:46:20(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/04/2012(UTC)Posts: 1,592Was thanked: 869 time(s) in 552 post(s) 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). Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wi...th%20with%20Plugins.ashx 2 users thanked mkraska for this useful post. on 20/07/2020(UTC),  on 21/07/2020(UTC)
 Razonar #8 Posted : 21 July 2020 08:25:44(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 493Was thanked: 292 time(s) in 181 post(s) Originally Posted by: ianlh 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.pdfHope that's helps.Alvaro. 1 user thanked Razonar for this useful post. on 21/07/2020(UTC)
 Razonar #9 Posted : 21 July 2020 08:44:11(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 493Was thanked: 292 time(s) in 181 post(s) Originally Posted by: Ber7 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: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. 2 users thanked Razonar for this useful post. on 21/07/2020(UTC),  on 21/07/2020(UTC)
 Ber7 #10 Posted : 21 July 2020 13:37:50(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 348Location: Beer-ShevaWas thanked: 453 time(s) in 244 post(s) 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 2 users thanked Ber7 for this useful post. on 21/07/2020(UTC),  on 21/07/2020(UTC)
 Razonar #11 Posted : 21 July 2020 20:15:57(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 493Was thanked: 292 time(s) in 181 post(s) Originally Posted by: Ber7 ... Variant with homogeneous coordinates ...Another variant. Lug Horizontal4.sm (35kb) downloaded 6 time(s).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:Best regards.Alvaro 2 users thanked Razonar for this useful post. on 21/07/2020(UTC),  on 22/07/2020(UTC)
 Ber7 #12 Posted : 24 July 2020 15:27:21(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 348Location: Beer-ShevaWas thanked: 453 time(s) in 244 post(s) Rotate around an arbitrary axis in space 3d rotate.sm (22kb) downloaded 11 time(s). 2 users thanked Ber7 for this useful post. on 24/07/2020(UTC),  on 25/07/2020(UTC)
 Razonar #13 Posted : 27 July 2020 06:37:33(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 493Was thanked: 292 time(s) in 181 post(s) 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: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. 2 users thanked Razonar for this useful post. on 27/07/2020(UTC),  on 27/07/2020(UTC)
 Ber7 #14 Posted : 27 July 2020 11:31:15(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 348Location: Beer-ShevaWas thanked: 453 time(s) in 244 post(s) Hello Razonar. "Modern Robotics" booksparked my big interest. Thank you for the link.
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