Some History of Origin Of Sanjoy Nath's LOCKED_SET(C) in Sanjoy Nath's Geometrifying Trigonometry(C) - SanjoyNath/SanjoyNathGeometrifyingTrigonometry GitHub Wiki

In 2011 When there was a special requirement to convert Trigonometric expressions in terms of pictures for some CAD problems which had to some handshaking with ERP / SAP for polygons encoding decoding systems , and for Reverse Triangulation of Trigonometric Expression , it was very necessary to convert scalar nature of Trigonomaatric ratios (pure numerical values) into some geometric significance. This was not possible until we could think that as geometric significance . From pure Engineering Drawings standpoint it is known that length of line segments are scalars and these come from the trigonometric calculations and in the process the geometry vanish inside the trigonometric expressions . To re introduce these geometric orientations , scales and the picture formulations of line segments with proper orientations and geometric meanings , Sanjoy Nath considered some Autocads Blocks Triangles as Triangulated Face and the natural orientations of these whole bunch of Autocads blocks could guide the # recursive locus of the line segments and the # recursive locus of these whole locked sets (Autocads Blocks of Triangles and Polygons). For every different values of Theta , or multiple , sub multiple , compound angles there were different configurations of Dynamic blocks and which were configured with Some Eulerian Affine Transformations on CADs model space and Sanjoy Naths Engine of DXF programs could transform these Trigonometric expressions as folded plates for CNC operations . Then similarly different Kinds of Affine Transformations were defined iteratively on every incidence points of the Locked Sets(Autocad's BLOCKS of line segments) and these iterations ultimately bacame some Recursive conditions for power series problems which looked like creating fantastic picture proofs of Trigonometric Expressions . With time all of these + , - , x , ÷ were defined , then To the Power is consequetive multiplication or consecutive divisions were defined . Several Lisp , several VBA were written to render these Orientations . These Autocads blocks were done to find the pictures from the given Trigonometric expressions . Then Sanjoy Nath could understand that some of the pictures are coming perfect and some are looking very odd still the force transmissions(Verified with STAAD PRO space frames) that the moment distributions and Axial forces transfers are working same in the members even if the geometry is looking odd.These gave him the idea that there are 4 types of orientations like Klein's 4 Group and Frieze Group are present inside the Group Actions on these Trigonometric Objects(LOCKED SET better we call that PROPORTIONATELY AND CONFOMALLY LOCKED ARRANGEMENTS OF Geometric Objects as we do in case of BLOCKS of Autocad) then there are exhaustive set of pictures form for every Trigonometric expressions which we can think of as Simplical Complex in 2D . From 2013 these arrangements became more effective for shape encoding , cutting line optimizations , welding line planning and also for the Truss Structures optimizations ,Space frames planning problems and also for encoding and decoding of several class of irregular polygons(Encoding of plates , shapes , scraps in ERP/SAP) became more handy with these introduction of LOCKED_SET concepts into Trigonometric expressions. Autodesk also started taking interest into this since this was a big pain area for ERP/SAP implementations in case of PRE ENGINEERED STRUCTURES manufacturers to store and retrieve informations uniquely for odd shaped plates in warehouse and also for productions planning , Material Management modules inside ERP/SAP . Then Sanjoy Nath thought to extend this system to extend to make entire automated picture proof mechanism for Trigonometry expressions (Which are naturally scalar algebra in nature) but having large potential to reveal itself as geometric rendering (Reverse Trigonometry , Reverse Triangulations etc...) Ultimately it looked fine to name that Sanjoy Nath's Geometrifying Trigonometry. Even SAP implementation team to Material Management Teams started talking in these terminology of Sanjoy Nath's DADA's Geometrifying Trigonometry modukles . They were coming with new Trigonometric expressions to see the effect of lisp programs and the vba programs in Autocad.