Intersect command should work with Curve objects

Swulf shared this idea 9 years ago
Completed

Hello,


In the attached file you will see a curve that can be rotated using a slider. I am working on a problem where it is necessary to determine the intersection(s) between this curve and various Lines. In the file, for example, this might be Curve 'aa' and Line 'e'. I was hoping to have exactly the functionality of the current Intersect tool but with support for Curves (I was a bit downcast :cry: when it didn't work).


As it seems that this is not (yet? :) ) a feature of Geogebra, would it be possible for it to be added in a future release? It would be tremendously useful.


Thanks,


Swulf

https://ggbm.at/553211

Comments (14)

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1

I agree. This is much needed. Also tools to find local extrema etc should work with curves and loci.


As it is I'm having problems doing certain types of investigations. If I measure how an angle changes when a point moves I can show this function as a trace or a locus in graphics view 2 but I cannot find the maxima of the trace or locus. As a workaround I copy traces to the spreadsheet and make a 3rd- or 4th-degree polynomial regression round the extremum and then I can find the extremum of the polynomial. But when I change the conditions of the constructions with another slider I would very much like to se the extremum of the locus move as the locus itself shifts. Currently, however, I an frequently unable to crate the locus, let alone find its extremum, and certainly not exploring this dynamically.

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1

I am also having difficulties completing some investigations that I need to do, typically because I am using Geogebra 5 (for the excellent 3D feature) and I have found on several occasions that needed functionality was not working yet. As I normally only find this out once I have gone some way into setting up a problem, it is pretty frustrating.


A few examples:


a) Investigations into reflections from conic surfaces - stalled because 1) multiple intersections of lines with a conic are really slow down performance, 2) a rotated function or conic gets turned into a 'curve' and you can't calculate intersections with a curve,


b) Investigation into reflections from an articulated plane mirror in a 3D environment - stalled because of no support in 3D for angle bisector.


I fully realize that Geogebra 5 is in development and is a work in progress. For example, I was stalled by the lack of the ability to calculate the angle between two arbitrary lines in G5 for a while, but this has been added in recent versions. So, I am not complaining at all, but I do want to point out that some of us are really relying on the maybe less exciting but fundamental functionality to get our stuff done.


Swulf

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1

I've not tried version 5 yet, so I can't suggest any workarounds unless you're able to do what I tried with capturing a trace and fitting a polynomial. Reaosonably, it should be possible to find intersections of curves - other software packages like Cabri can do this.

photo
1

Are there any openings on this (intersection of curves/loci/paths and other objects, extremas and roots of curves/loci/paths etc)?


As stated above - it would open up for multiple step investigations like: "Ok - so I see from the locus/trace that the maximum is here, but what happens when I change this parameter...? Which path will the maximum follow?"

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1

determine the intersection(s) between this curve and various Lines

if the lines pass through the origin (0,0), is easy:

y = mx

m = tan(t)

t = atan(m)

aa(t)

...

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1

And you can do this:

list1 = Sequence[aa(t), t, 0, 6.28319, pi/100]

g = PolyLine[list1]

Intersect[line,g]

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1

Yes, I agree, you and I can do that, but it is not obvious how to do this for students (or for me for that matter). Also it takes time and diverts the focus from the mathematical investigation to the technique of creating the intersection. And if we can do it like that I suggest it be implemented in some fashion so that anyone can do the intuitive thing: find the intersection with the ordinary intersection tool.

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1

it's just a workaround ...

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1

Absolutely, and thank you for it and excuse my tone, which was not intended. :flushed:

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1

would it be possible for it to be added in a future release?


Intersect[ <Line>, <Curve> ] works from 4.1.108.0

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1

And when will Extremum[ <Locus> ] work? :smiley_cat:


It's a definite wish for version 5.

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1

As the summer is comming near and development projects are getting planned, I thought I'd re-iterate this particular point on my wish list.


Extremum[ <Locus> ] would allow for multiple-step investigations: "Aha - the maximum point is here, but how will this change if I change this parameter?"


Finding the locus of the maximum of a locus... Extreme power :D

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1

You can place a point on locus and do Minimize / Maximize to find extrema of the locus.

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