Challenge #161: Triangles, Triangles, Triangles

The idea of the challenge is simple, but it could be a little trick to execute!

Provided are a set of coordinates. With this set of triangles, you must create triangles. Each triangular spatial object must have exactly 3 non-collinear points. With this data set, you should create 516 unique triangles! How many of the 516 can you get?

This week's challenge was contributed by @CharlieS !

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challenge_161_solution.yxmd

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Spatial Analysis

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Advanced

Intermediate

Data Preparation

Accepted answers

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patrick_digan

Fun challenge @CharlieS

Spoiler

While I naturally reach for the spatial tools, the formula tools can accomplish the same tasks without transposing the data.

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T_Willins

Fun challenge! Last filter needed to match solution, but shouldn't tiny triangles still count? Investigation of original data indicates these are non-linear points (Thank you Mr. Coss - High School Geometry Teacher)

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challenge_161_solution.yxmd

CharlieS

I'm delighted that I could contribute to the awesome-ness that is the Weekly Challenges! I originally designed this with several sub-challenges if you want more:

- Draw a triangle using Spatial tools

- Draw a triangle without using Spatial tools

- Draw multiple triangles using only a single tool

- Draw multiple triangles using an iterative macro

- Draw all 516 unique triangles

A note on the "valid" solutions: due to how the points were drawn, it is possible to produce some very thin triangles that would be collinear if a grid was drawn on a Cartesian plane. Rather than adjusting the points, I was curious to see different approaches to handing these scenarios.

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Thableaus

Challenge #161, done.

Spoiler

I also removed the tiny triangles to get to the final answer - (unsure why they don't count)

Cheers,

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TerryT

Fun challenge! Thanks @CharlieS

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cplewis90

Fun challenge! I had to look up (as I couldn't remember back to high school trigonometry how to determine if 3 points were collinear.

Spoiler

After doing some digging (looking at 3 points that are seemingly a straight line), I understood why I couldn't use 0 as the collinearity check. Some of the areas are basically 0, but are not really triangles as they appear to be lines on the plane.
Challenge 161.PNG

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Ladarthure

Fun challenge, I had troubles for the final filter

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RolandSchubert

Interesting. Final filter was a challenge

Spoiler

First tried to filter triangles using ST_DIMENSION (should return 1 for lines)

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NicoleJohnson

OK so I got a bit hung up on the definition of "Non-Collinear", so my workflow actually has 2 solutions - one that gets 516 unique triangles (not the most efficient solution compared to others, but logically it got me there, and I feel like my high school math teacher wouldn't have been mortified, so I'm okay with it)... and then an alternate solution that I feel better matches the intention that all triangles be "non-collinear", which I defined to mean that there could be no point in the triangle that was at the same latitude or longitude plane as any other point in that triangle. Results in far fewer triangles (essentially, any triangle with a straight vertical or horizontal side is eliminated by this method).

Either way, super fun challenge @CharlieS!

Spoiler

Method #1: Create 516 unique triangles... realized after looking at a few other solutions that the Unique tool would have greatly simplified this, but it got me there eventually (basically reordered the points in ascending RecordID order and then grouped them to eliminate duplicates, achieving the same effect... with way too many tools haha).

Method #2: Create only triangles that do contain any points that are on the same plane (latitude or longitude). Again, a bit of a roundabout way to get there (once again finding an obscure reason to use one of my hidden favorite tools, Make Columns!)... but conceptually this one was actually easier for me to wrap my head around. And since I cheated a little by borrowing the Unique tool from other solutions as my method to get rid of duplicates, I opted to not use any Spatial tools for this method, using the Spatial formulas instead. BONUS: The resulting picture of triangles with this method is quite pretty!

Cheers,

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ggruccio

My plan to get the linear ones out didn't exactly work...but I found a workaround!

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RichoBsJ

Hi! Here my solution, nice challenge!

Spoiler

In order to have the unique 516 triangles, I gave a number to each point (starting value is 101), so I can multiply the three values and have a unique number per triangle (as I'm starting in 101, there won't be any number representing two different triangles, there will be always a unique number per triangle):

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danilang

Fun Challenge! Thanks for the idea @CharlieS

As for the tiny triangles, they would be collinear if drawn on a flat plane, as CharlieS mentioned, but since they're mapped to a sphere, they end up having a small area. Here's a plot of the 24 thin ones

thin ones.png

Here's one of vertical ones zoomed in

The length(height) of this triangle is 19.3 km, but it's width is only .008 KM.

Spoiler

Dan

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pasccout

This was a fun one... I have the same number of items but not exactly the same order so the drawing is a bit different.

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sprodger

my solution:

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pjdit

My Solution. had to remove the small ones, but did get the 516. also made some pretty pictures in the process of trial and error.. :-)

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Reesetrain2

Nicole,

I was thinking the same thing in that non-collinear would mean the opposite of Collinear, which is usually defined as all points on the same line. Furthermore, when dealing with modeling, co-llinear is generally referred to as non-desired trait in a model as you likely have two variables that that are essentially the same, just changed by a scalar. A good example would be weight and volume. If you have the volume of water in Gallons in your model and you have the Weight in pounds, you will have two variables that are Collinear (Water weighs 8.5 lbs per gallon assuming the temperature stays the same). With geometry, I understood the definition of a Triangle to mean that it was Non-Collinear in nature...

-This lead me to originally think that I would have to find all combination possibilities and then eliminate those that were CO-Linnear.

Anyway, semantics aside, I had a hard time with this one, as i had to peek at others examples, as I got stuck with way more than 516 Triangles.

Reesetrain2

My Submission...Very Messy, as you are forewarned!

-Cheers!

Reese

challenge_161_Submission_Reesetrain.yxzp

Reesetrain2

Pasccout,

Excellent Workflow that you have there!

-I had a few questions regarding the Sort and Subsequent Multi-Row Formula.

-Why is the Sort Required for the Workflow to run? What changes as I got stuck with something like 1800 Triangles...

-Multi-Row Formula with OrderID: I really like the idea of the Internal Order piece as I think that is a great method of having a Grouped Id for all kinds of applications.

-Cheers!

Matt

DavidThorpe

Fun challenge!

My solution:

challenge_161_solution_DT.yxmd

DawnDuong

I used a non-macro approach, mainly relying on the geometrical rules. I initially had 544 instead of 516. The difference is due to very thin triangles. So it is an interesting case of which tolerance level to set to test for linearity.

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kelly_gilbert

Interesting! I definitely never would have thought to use that method for creating the triangle shapes (or for finding unique combos!) My method was definitely more steps (but works).

Spoiler

I initially tried to exclude invalid triangles (where the points were all collinear) by using the side lengths, but spatial length/area don't work because these are lat/lons rather than cartesian coordinates!

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AmandaCarew

Great challenge! So many different ways to solve.

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GiuseppeC

Nice one!

Not sure why people are filtering out small triangles at the end. I have used...

Spoiler

the Spatial Info tool to tell polygons (i.e. triangles) from lines and I get 540 triangles!

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JosephSerpis

Challenge Completed

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LukeM

Some clever logic required!

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Verakso

Thanks to @CharlieS for fun challenge

I do love a great Spatial

So all though this was super fun, I did have some minor challenges with it

Spoiler

My result does not completely match the provided output, and I cannot quite figure out how to match it 100%, but I do get 516 unique triangles

My WorklowAs mentioned there is a difference

The Provided Result

My Result

so I guess I will have to take a look at some of the other solutions to see, it there is a more clever way to do this

Still Climbing

/Verakso

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estherb47

Really fun challenge!!

Spoiler

Had to wrap my head around how to get the points connected in a unique way, and then the ideas flew quickly.

Decided to go the non-spatial tool route to practice spatial formulae. The workflow:

Lots of triangles!

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philipmannering

Very nice challenge. I got my 516 triangles

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Challenge 161 - How many traingles.yxmd

dimark

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NancyS

@JoeM, @CharlieS

Interesting Challenge!

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Eleonora

My solution. Took much longer than usual to solve: I had the right picture but with 540 triangles. Had to read others' comments to come up with the right final filer.