December 2023 Challenge: 3D Glastonbury Tor

[Redrobes]

I wrote a bit of script for Image Magick and generated some images:

Test_Cut1_800.png Test_Cut2_800.png

Then laser cut these in thin card. The cuts went well...

Tes_Cut_Real1.jpg

... but they both absolutely do not stretch in the Z direction. Not even a bit - which I found quite surprising. They are both like card as though it were not cut at all. On the one with the radial lines you can press into the cut areas a bit but the center circle does not move.

So there is no stretch at all in these with cuts in.

The next step is to make finer spaced cuts and get the cuts closer to the edges. It should be obvious that if I cut a pure spiral to the center circle then it would move but would have no structure. So there must be a point in between the two extremes where it moves the right amount.

So back to the scripting...

[Redrobes]

Made some more circles where they are joined at a single tab somewhere on the circle. Started where the tab alternates side left and right. Then next tried one where the tab was moved around at a fixed angle. Both of these worked almost too well and there is very little resistance in the Z direction. So then I tried adding a two tabs per circle and alternating them NS and EW. That produced a result which was pretty good and the resistance in the Z direction is about right leaving us with a better shape when draped over a post.

Test_Cut3_800.png Test_Cut4_800.png Test_Cut5_800.png

The three cut bits of card draped over small objects like erasers. You can see that the middle one especially the outer loops drop to the desk and are not being pulled up enough.

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Tes_Cut_Real2.jpg

The one closest to the camera is not too bad. So next up is to try something similar on the contours of the Tor and see how that plays out.

[ChickPea]

This is so cool, Red. Really enjoying watching you develop your process, and excited to see how the Tor works out.

[Redrobes]

Thanks. I was getting a bit nervous that it was all at a dead end for a bit but I think its alright again and still has some possibilities. Its just a case of fine tuning the settings. Maybe those settings only apply to this specific card I am using and I will need different patterns for thicker card. But if it works out for one type then its just trial and error until we home in on it for another.

[ChickPea]

It's fun to experiment and get a feel for what works and what doesn't.... assuming the card isn't too expensive of course!

[Redrobes]

I have ate all my mince pies so its time I started getting back to this...

I clipped out a section of the unsmoothed banded painted contours map where I captured the middle bit with just the Tor in it. Then put that into my 3d app and smoothed out those contours. My app uses floating point math for the heights so we can get rid of all those jaggies in the heights.

Getting a reasonably smoothed out height map I then textured it with black and white bands and applied that back onto the 3D model as a texture which is shown here.

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Contours4.png

So I know I have the right contours matching the Tor at 5m height intervals.

If I take that image and do an edge detection then I am back to the contours again but these are nicer than my hand drawn ones I did in order to get to the first shaded model. I now have nice smooth lines all of the same thin pixel widths which is much better for me to use as the source for the laser.

Contours5.png

So next I need to put the tabs into this image and try this one out on some card. One issue I can immediately see is that the base, or the edge of the image needs to be all of the same height but the Tor has a lower height to the South than the North so its going to come out leaning to the North unless I do something about that.

I am going to have to get a copy of the base / edge heights and build an inverted platform and then add that to the height model to flatten it. That wont be real world accurate but we need to start the 3D model on a flat bit of card.

I was in the vicinity and took a trip to the Tor a couple of weeks ago and climbed up to the top and had a look around. At the time we have been having a lot of rain and the landscape around has become very flooded. I think this is normal and I read that in very old times the place name of Glastonbury was called the Isle of Glass when all of the region used to flood and turn to ice in the winter. Whether that is true or not I cannot be sure but its an interesting idea.

[Straf]

I haven't had any mince pies yet.

This is so innovative. It's like Star Trek, but with card, boldly going where no [hu]man has gone before. From the contours I, too, can see the potential tilt to the NNW. Perhaps slightly raise the elevation on that side to compensate so the base of the model is actually a plane on a slant?

Wasn't it around Glastonbury that King Alfred burnt those cakes while hiding in the marshes?

[Redrobes]

I think it will look a lot better when its done on printed card but I dont have a colour printer so the end result might be black and white. The Tor has got one side steeper than the other so the height map is correct its just that the base is all at different heights. What I am planning now is to just ignore the base and only cut from a certain height up. At least lets start that way and see how it pans out.

As for the cakes, your right. In about 878AD or something around then we were in the midst of a Viking invasion and they were pushing across the country and were at about a line that cuts Britain from Exeter across up to the North East. The Anglo Saxon King Alfred was holding them back and being pushed back to Somerset where it was all a marsh and had a secret abbey and stronghold in the marshes which had no obvious access.

He gathered up forces in the marshes at this small place called Athelney (where incidentally there is similar, smaller sort of Tor called Burrow Mump) and the story goes he got distracted whist planning the raids that he burnt the cakes in the oven. He set out across Somerset to Wiltshire to a place called Edington and fought the Viking King Guthram and defeated him and captured a few dozen of his top generals. He took them back and as part of the surrender terms forced them to convert to Christianity at a church in a place called Aller which is not too far from the Tor. He then went to his "palace" at Wedmore and Cheddar. The church at Aller still has an Anglo Saxon font which could have been the one used only I am told it is one of three and only one of them survives so its a 33% chance its the one. I must go there and have a look at that one day. There is a monument to Alfred at Athelney only its not on public land so you can take a photo of it but not get up close.

There is a cross at Wedmore in the church yard which celebrates his victory put there in 880's era which looks pretty battered now. In Cheddar there are the remains of the Saxon palace which in the school yard which is itself in front of Cheddar Gorge, the large fissure in the rock which have the famous caves in the depths of them.

I tell you this bit because it is a fact that J.R.R. Tolkien has his honeymoon with Edith in Somerset. Being a professor of Anglo Saxon I imagine he had a lot of interest in the area because of all of this Alfred stuff. In his letters he says that Helms deep is based on the palace at Cheddar and that in the book they retreat back to the stronghold with the caves in the background. In the Jackson films, Helms deep butts up against the caves, but in the book there is like a half a mile from the fortification back to the walled fortress in the rock which matches up much better to Cheddar.

Also incidentally there is a pathway up from Cheddar Gorge to the top of the cliffs where there used to be a tower that had a big fire on it that was lit in times of distress during the first / second world war. I am not certain he nicked that idea from there specifically, but its a good bet. Also the lake around here used to be called Faramere. I think he stole a lot of stuff from this area personally. I have a hunch that the Tor might also be the inspiration for the lonely mountain but that's a bit more speculative. But it does stand out as this big hill across the levels of Somerset and is pretty striking. There is another local story (which predates Tolkien by a large number of years) of a dragon which lives in the hills. Not the Tor specifically but I think around Shepton Mallet area which is about 10 miles East of the Tor. But that story was bound to be known to Tolkien.

EDIT: Just looking up this dragon, its supposed to be in Dinder which is to the East of the Tor but is not nearly as far as Shepton Mallet and is in sight of the Tor. So a dragon was supposed to be around the Tor which is a hill all on its own in the levels. Hmm, the lonely mountain doesn't seem quite so speculative any more.

Anyway, the plan today is cut this:

[Redrobes]

I cut that one and it looked ok but its very floppy at the base and too rigid at the top. So I made up another cut where I added more tabs near to the base and cut it too. But this one was too rigid at the base now.

I think I know what the problem is. I was thinking that the amount of length on the laser lines would determine the amount of movement it would show on the card. But I dont think that is the case any more.

In the first cuts I had the tabs at opposing sides of the hill and the card bends at the tabs and the bit between the tabs is an arc which bends up and flexes the model. In the second cut the tabs are around the contour such that the laser lines are mostly straight between them and in this situation the flex needs to stretch the card which we know from the previous experiments that it wont. So I think its really important that its the angle between the tabs that is more important than the length of line between them. I reckon we need about 120 degrees or so minimum between the tabs in order for the part to bend and at 180 its really flexible. The length makes a difference as well but its the angle that makes more difference. A spiral is like having the tabs at 360 degrees so its super flexible to the point of being useless.

CardTor1.png

Test_Cut7_800.png

CardTor2.png

[Redrobes]

Keep going... I made a new cut with the tabs on opposing sides until the last few contours then I changed to a 3 tabs per contour system. This one, when cut, was much better and I think I am happy with this one. The only improvement would be that I could have done with a tab on that slope running down to the base on the left side to pull up the last ring of card. The image doesnt look a lot different but holding it you notice it more.

So I think I know enough now to make up the artwork and the cut path for it. Then I will make a full sized card and see how it pans out.

Test_Cut8_800.png

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CardTor3.png