How can i get all possible geometric shapes from given trigonometric equation?

[SanjoyNath]

Dear Experts,

Sometimes structural engineers (from client)have given us some cross checking tasks to fit and set with truss elements or shape elements (scraps from plates) to reuse these with proper places as and where these fits best.

Sometimes Architects come up with(Dream that computers can do everything and expects things very fast) and asks us to model truss elements (such that they can put loads on these to check) and outer surfaces in such a way that some given equation (3D surface equation) fulfills

We were trying to model this problem with some intuitive technic , but it is tedious to prepare the whole software single handedly.

Is there any ready made tool for form finding and do model on Autocad / or Autodesk systems(We have tried to do this in Revit , Dynamo , We have tried Rhino , Grasshopper , which dont generate all possible Shapes from the given equation)or any other plugin/lisp to generate (Geometric Shapes) model elements (Line segments or curve segments or Locked sets of arrangements of Geometric objects from given mathematical or algebraic equations) ?

refer Geometrifying Trigonometry (our inhouse struggle to model for attacking such problems)

refer Form Finding references that Structural engineers and these Architects talk about(To prepare plugins to automodel from mathematical equations)

We are struggling to prepare models to generate all possible geometric shapes from the given Trigonometric Equations or identities.We have shared these here to make it more understandable (upto which we have struggled yet to make some options.) I am working with @dbhunia to make some smarter solutions and he thinks this need to get addressed and come up with some more technicalities (theoretically) before we start developing these inhouse.

If some ready resolution is there , then we can straightforward use that to save our time and resources

https://geometrifyin...ng-Trigonometry

https://geometrifyin...uctable-Numbers

https://geometrifyin...a-CopyGADrawing

https://geometrifyin...Modeling-Issues

https://geometrifyin...egments-Jungles

https://geometrifyin...wingAPIServices

https://geometrifyin...ng-Trigonometry

https://geometrifyin...Representations

https://geometrifyin...Cos-Θ-2-0-5-for

https://geometrifyin...to-become-equal

https://geometrifyin...s-PH*PH-PB*PB-P

https://geometrifyin...he-initial-line

https://geometrifyin...t-it-is-BP-*-BP

https://geometrifyin...he-line-segment

https://geometrifyin...d-Θ-It-is-HP*HP

https://geometrifyin...nometry-≡-≈-Æ-æ

https://geometrifyin...is-a-Locked-Set

https://geometrifyin...he-initial-line

https://geometrifyin...k-of-the-System

https://geometrifyin...ple-and-Compoun

https://geometrifyin...ngement-has-two

https://geometrifyin...-not-mean-Recip

https://geometrifyin...on-in-String-Du

https://geometrifyin...peration-in-Str

https://geometrifyin...an-First-and-La

https://geometrifyin...n-is-Reverse-of

https://geometrifyin...rt-2-HEA-or-HEP

https://geometrifyin...-Formal-Systems

https://geometrifyin...-Dots-and-Stars

https://geometrifyin...ns-on-GT-String

https://geometrifyin...egment-H-Itself

https://geometrifyin...c-Formal-System

https://geometrifyin...ifying-Trigonom

https://geometrifyin...ng-Trigonometry

https://geometrifyin...of-Trigonometry

https://geometrifyin...ng-trigonometry

https://geometrifyin...rules-explained

https://geometrifyin...ng-trigonometry

https://geometrifyin...ng-Trigonometry

[SanjoyNath]

Dear Experts,

If any readymade product to focus this issue , then please let us know.

If we like to address this with Lisp on Autocad , then there is another thread for this

https://forums.autodesk.com/t5/visual-lisp-autolisp-and-general/is-there-any-lisp-to-generate-all-po...

[Pointdump]

Sanjoy,

"We are struggling to prepare models to generate all possible geometric shapes..."

That makes two of us. I am struggling to understand your question. Can you elaborate, in simple terms, what you are trying to do? Maybe a picture?

Dave

[leeminardi]

To answer your question "Is there any ready made tool for form finding and do model on Autocad..." the answer is I doubt it.  I looked through a few of your references and it appears that most of the tasks you seek are simple, but specialized translations/rotations/scaling of triangles.

I think a good place for you to start it to make a few declarative sentences of the form:

Given this I would like to get that. 

The more clear and concise your question the more likely you will get a satisfactory response.   Minimize extraneous discussion.  Focus!

[SanjoyNath]

Yes Dave,

___________________________________________________________________________

"We are struggling to prepare models to generate all possible geometric shapes..."

That makes two of us. I am struggling to understand your question. Can you elaborate, in simple terms, what you are trying to do? Maybe a picture?

___________________________________________________________________________

Surely , i should explain it more thoroughly here.

Suppose in a Trigonometric Equation only one           Sin(Θ) is written. This means we can think that only one Right Angled Triangle is present.But when there are more than one Trigonometric ratio present , we cannot visualize how many (Possible)Triangles are involved and where are these triangles located.

Suppose  Sin(Θ) x Sin (Θ) involves four different possible Triangles as in the picture here below

4 types of configuration due to single multiplication

If every such Trigonometric multiplication generates 4 types of configurations , then it is a large possible combination of such arrangements in chain reaction of multiplications and additions of Trigonometric terms.

If we consider trigonometric sum means putting one line segment at the end of other then first of all these output line segments need to become parallel to each other.

Toe-Tip -Toe-Tip is only possible for parallel line segments when we try to do additions in trigonometric equations.How can we get sure regarding which of the line segments are becoming parallel to each other or not until some visualization is possible (after doing Trigonometric multiplications)

I was searching some tool or at least some algorithm which will help us to visualize these geometric shapes(possible arrangements) from given Trigonometric expression

Lets give some more examples here

((Sin(Θ))^2  + (Cos(Θ))^2)=1

What does this mean geometrically? From childhood , we know this is Pythagoras Theorem

But which Software will draw pictures (Geometric pictures) to prove or display the effect on Right Angled Triangle?

((Sin(Θ))^2  + (Cos(Θ))^2)=1         Geometrically becomes like this

https://geometrifyingtrigonometry.quora.com/Interpretation-of-Pythagoras-Theorem-in-Geometrifying-Tr...

Similarly Geometric arrangement(Only one Single arrangement hand drawn here)

For

((Cosec(Θ))^2  - (Cot(Θ))^2)=1         Geometrically becomes like this

https://geometrifyingtrigonometry.quora.com/Corollary-Geometrifying-Trigonometry-Cosec-%CE%98-x-Cose...

Other references (My hand drawn struggles) are given in the links above.It is impossible to draw all such configurations in Hand Drawn way.I think Some tool is there or some algorithm is there which i dont know.

[SanjoyNath]

Dear Lee,

I got one equation from our Architect which looked like

(Cos(Θ))^6

And he is very good visualizer of things.He was claiming that this equation looks like a truss but i could not understand. How an equation of (Cos(Θ))^6 looks like a truss.

Then this picture came(This is only one possible option out of 6 x 4 =24 possible options of the pictures truss like structures) we can generate out of the given equation.

I got frustrated that i cannot visualize like an architect.So i started searching to find some software which will give me all possible 24 (possibly more , i dont know)options of pictures from given Trigonometric equations.Possibly can prove any  trigonometric identity through geometric way

https://geometrifyingtrigonometry.quora.com/Geometrifying-Trigonometry-Cos-%CE%98-6-Representations

[SanjoyNath]

Dear Lee,

One more interesting fact we can know from very old Architects and Civil Engineers (Who used to visualize lots of things without softwares) has more insights than our todays Software dependent persons(we need fast shortcuts) to design good geometries through CAD.

Very experienced Architects or 1920 Civil Engineers or 1860 Mechanical Engineers used some thumb rules of geometry like

Assume 25% of cases equality in Trigonometric Identity

For example

There is only 25% chance (Geometrically) that Sin(Θ) x Cos (Θ) = Cos(Θ) x Sin (Θ)

These are always equal in calculated data(scalar values)

But position of final line segments (Geometrically) has only 25% chance that these line segments will overlap on each other

https://geometrifyingtrigonometry.quora.com/Corollary-Geometrifying-Trigonometry-Cos-%CE%98-x-Sin-%C...

SanjoyNath(c) 25% chance of equality so not commutative Geometrically

[SanjoyNath]

Please help

If i have to go through any special course or book or site , please guide(Atleast) I am developing this good software on CAD.Need your help

I dont know if this is under Topological Problem or in some other kind of mathematics.I dont know which books to study to achieve this more efficiently(I am software developer for CAD Systems , not studied these mathematics too much)

GeometrifyingTrigonometry

SanjoyNath/GeometrifyingTrigonometry

[Alfred.NESWADBA]

Hi,

I'm not sure to understand all that, but from the small part I think I do understand ... isn't >>>MathCad<<< the software you need then?

- alfred -

[leeminardi]

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Dear Sanjoy, 

Please see my comments below. 

@SanjoyNath wrote:

Dear Lee,

One more interesting fact we can know from very old Architects and Civil Engineers (Who used to visualize lots of things without softwares) has more insights than our todays Software dependent persons(we need

fast shortcuts) to design good geometries through CAD.

This is not a "fact" but  purely conjecture on your part.   Do you have data of the "insights" of architects and engineers of old as compared to today?  I have found that the instant feedback that is provided in the dynamic manipulation of 3D CAD models enhances the spatial visualization skills of the user but I could not say if the result is better or worse than those who did  not use CAD.  Be careful not to confuse and then generalize subjective observations with facts.  Your observation may be fact but the conclusion may be something else.

Very experienced Architects or 1920 Civil Engineers or 1860 Mechanical Engineers used some thumb rules of geometry like

Assume 25% of cases equality in Trigonometric Identity

For example

There is only 25% chance (Geometrically) that Sin(Θ) x Cos (Θ) = Cos(Θ) x Sin (Θ)

I agree with your statement: These are always equal in calculated data(scalar values) but it is not clear what you are referencing with the 25% condition.  WHat lines are you referring to that overlap?

But position of final line segments (Geometrically) has only 25% chance that these line segments will overlap on each other

https://geometrifyingtrigonometry.quora.com/Corollary-Geometrifying-Trigonometry-Cos-%CE%98-x-Sin-%C...

It is not clear what you want to do with this illustration but it may be of interest to you that such a configuration can benefit from the use of parametric constraints as found in AutoCAD.  You would be able to easily change the distance between the two circles and the related geometry would automatically update.

SanjoyNath(c) 25% chance of equality so not commutative Geometrically

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[SanjoyNath]

Thanking @CodeDing

He has done a great thing here . Geometrifying Trigonometry(C) has started its journey

https://forums.autodesk.com/t5/visual-lisp-autolisp-and-general/is-there-any-lisp-routine-to-align-a...