From 0795e76a6c286d58aa910d83eef8fb34c945f6d6 Mon Sep 17 00:00:00 2001 From: Joe Ardent Date: Wed, 18 Jan 2023 23:56:54 -0800 Subject: [PATCH] checkpoint post, almost done --- .../PXL_20220723_214758454.jpg | Bin 2403735 -> 0 bytes .../blending_california.png | Bin 0 -> 526799 bytes .../ca_topo_crappy_test_print.png | Bin 0 -> 1982066 bytes .../crappy_test_print_close_up.jpg | Bin 0 -> 168718 bytes .../exponential_plot.png | Bin 0 -> 5546 bytes .../final_ca_topo_blend.png | Bin 0 -> 906263 bytes .../final_heightmap.png | Bin 0 -> 234477 bytes .../a-very-digital-artifact/final_printed.jpg | Bin 0 -> 909264 bytes .../a-very-digital-artifact/final_shasta.png | Bin 0 -> 308196 bytes .../sundries/a-very-digital-artifact/index.md | 198 +++++++++++++++++- .../lo-rez_exp_blurred.png | Bin 0 -> 782505 bytes .../non-linear_scaling_of_ca_height_data.png | Bin 0 -> 577034 bytes .../a-very-digital-artifact/plot.gnuplot | 9 + .../wood_ca_on_table.jpg | Bin 0 -> 454828 bytes 14 files changed, 205 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If you were to view the file as though it were an image, it would -look like this: +look like this: ![the ca_topo image; it's hard to make out details and very dark][small_ca_topo] *
    if you squint, you can kinda see the mountains
    * @@ -477,8 +477,181 @@ this: With that version, I was able to produce some reasonably smooth-looking geometry in Blender: +![a slightly smoother mesh][smoother-california-mesh] + +Or so I thought. + +As you can see, it's still very pointy. A lot of the high-frequency detail has been removed, which +means it's not rough and jagged, but Shasta still looks ridiculous. + +## A matter of scale + +The problem was that I was doing a linear scaling of the height of features in the data, and the +required factors were so enormous that it distorted the geometry in an ugly way. + +The State of California is very large, but for the sake of argument, let's pretend it's exactly 700 +miles tall, from the southern tip to the northern border's latitude, going straight north; the real +length is close to that. Also for the sake of argument, let's say that the tallest mountain is 3 +miles tall; the actual height is less than that, but that's OK. That means the ratio of height to +length is 3/700, or 0.0043-ish. + +If you had a physically accurate topographic carving of California that was a foot long, the tallest +peak on the carving would be 0.0043 feet high, which is about 1/20th of an inch, or about 1.3 +millimeters. You'd probably be able to tell with your fingers and even your eyes where Shasta was, +and see that there was a faint line from the Sierra Nevadas, but that would be it. That's why it's +so hard to see the details in the raw elevation data geotiff. + +In order to be able to see any detail, and to meet expectations about what a topographic carving is +supposed to look like, the height of the highest peaks needs to be exaggerated by something like +10-20x. My problem was that I was doing a linear scale; I was making *everything* 10-20x taller than +it "should" be, which was causing everything to look stretched and weird. + +And even with that amount of exaggeration, some features were not showing up. For example, [this +2,000-foot tall mound in the Sacramento Valley](https://en.wikipedia.org/wiki/Sutter_Buttes), which +is faintly visible in the heightmap, is almost not there in the resulting mesh. It's about 1/7th the +height of Shasta, which is not all that much, when Shasta was represented by something 0.75 inches +tall. + +What I really needed was some non-linear way to scale the height, some way to exaggerate lower +altitudes more than higher ones. The highest points should stay as they were; they determine the +ultimate overall height, but as we saw, they overshadow lower features without a little help. An +easy way to do this is to take some fractional root (raise it to a power between 0.0 and 1.0) of the +linear scaling factor, and use that new value instead. For example, the graph of *x* raised to the +0.41th[^zero-forty-oneth] power looks like this: + +![y = x^0.41 between 0 and 1][exp-plot] + +Notice how values *at* 0 and 1 are the same as they would be with linear scaling, values *near* 0 +rapidly get scaled upward, and by the time you get near 1, it looks almost linear again. + +Luckily, `gdal_translate` has an option to do this kind of scaling, so it was a quick + +> `gdal_translate -of PNG -ot UInt16 -scale -130 4412 0 65535 -exponent 0.41 ca_topo.tif +exponentially_scaled_heightmap.png` + +and a couple rounds of blurring, and I had the following heightmap: + +![a non-linearly scaled heightmap][lo-rez_exp_blurred] + +which resulted in a mesh that looked something like this inside Blender: + +![3D viewport in Blender showing a topo-displaced mesh that looks like +California][exp-scaled-blending] + +Doesn't that look nicer? Notice how a bunch of things that were nearly invisible before, like that +mound near Sacramento, are easily visible. Check out the [Channel +Islands](https://en.wikipedia.org/wiki/Channel_Islands_(California)) now plain as day! I was feeling +pretty good about having this whole thing wrapped up shortly, only a little late for the birthday. + +# A dark period + +What followed was two frustrating weeks attempting to get a manifold mesh out of Blender that was +small enough, by which I mean number of vertices and edges, so that +[FreeCAD](https://www.freecadweb.org/) could turn it into an STP file. Unfortunately, FreeCAD was +not a good tool for working with meshes, like creating them from a heightmap, so I had to use two +different tools. + +This also meant that I would run into limits due to translation overhead when going between +them. Let me explain. I'd get a mesh in Blender, export it to a neutral mesh format like +[OBJ](https://en.wikipedia.org/wiki/Wavefront_.obj_file) that both programs understand well, and it +would be a 60 megabyte file. My computer has 32 **giga**bytes, more 500 times more memory than +that, so you'd think it would not be a problem. + +The act of asking FreeCAD to import that OBJ file as a *mesh*, and not even as a solid body, caused +the memory use to go to 21 gigabytes. This is a lot, but the computer still had plenty of room left +in memory for things like "responding to the keyboard and mouse" or "redrawing the +screen". Everything at this point is still perfectly usable. + +When I attempted to convert that mesh into a solid body, though, memory use ballooned up to +encompass all available RAM, and my system slowed to a nearly imperceptible crawl until my frantic +`ctrl-c`s were finally registered by the [signal +handlers](https://www.gnu.org/software/libc/manual/html_node/Termination-Signals.html) in FreeCAD +before I could use it again. This happened a lot. + +I went through many rounds of attempting to clean up the mesh and reduce its complexity, but I don't +have many notes or intermediate artifacts from this time. A lot of that was being a beginner at both +Blender **and** FreeCAD, though there's so much educational material that I was rarely held back by +not knowing how to do a particular thing inside each program. A lot was inexperience in the domain; +I did not know how much detail was essential, and I did not have a lot of experience with digital +modeling in the first place. The workflow was very manual, and cycles were fairly long, which made +it hard to try a bunch of things in quick succession as experiments. All those things and more +conspired to make this portion of the process a total slog with very little to show of. + # Test prints +Finally, after a couple weeks of trying and failing to get something into FreeCAD that I could then +work with (like melding it with a thick base and trimming that base to follow the shape of the +state), I had had enough. I have some notes from the time: + +> I'm finally printing something out. I've given up on converting it into a parametric +CAD-like object; it seems this is a Hard Problem, but I'm not sure why. My goal with doing that was +to give a parametric CAD file to a local CNC milling shop, per their request, since when I suggested +a mesh-based file (STL), the guy was like "I can't do much manipulation with that to make it more +manufacturable, so a real CAD file would be best". +> +> But at least with an STL file, I can print it myself. So that's going now, we'll see how it turns +out in no less than eight hours. +> +> I haven't really done anything else with my computer besides this for a while. + +When that print was done, here's what it looked like: + +![a piece of literal dogshit][crappy_test_print] + +In case you were not revolted enough, I invite you to cast your gaze upon this eldritch abomination: + +![close-up of extremely bad print results][crappy-close-up] + +As bad as it looked, it felt even worse to touch. Setting aside the hideous base with its weird +artifacts due to those areas not being a single flat polygon, but rather several polygons that were +not parallel or co-planar (modeling artifact), there was just too much high-frequency detail in the +terrain, and it was a total mismatch with the 3D printed medium. + +The real thing was going to be carved out of wood by a [CNC +mill](https://all3dp.com/2/what-is-cnc-milling-simply-explained/), which uses a drill-like component +to carve away pieces of the material you're working with. This means that there's a tiny spinning +bit with a definite, finite size, and any detail in the model smaller than the end of that spinning +bit would likely be impossible to carve with it. This meant that all that high-frequency detail was +not only ugly, it was also completely unnecessary. + +## Just try harder + +I was eager to get something into the CNC shop's hands at this point, but I also knew that this +model was not acceptable. So, I resolved to brutally simplify the geometry until I got something +that was workable inside FreeCAD. + +First off, I made the heightmap even smaller, only 500 pixels wide. Fewer pixels means fewer details +for turning into a displacement map for a mesh! I also removed the Channel Islands from the +heightmap, resulting in this final mesh displacement input: + +![it's the final heightmap][final-heightmap] +*
    it's the final heightmap (doot-doot-doot-doot, +doot-doot-doot-doot-doot)
    * + +Inside Blender, I'd gotten quite proficient at running through the steps to generate a mesh from a +heightmap, and once I'd done that, I went through several rounds of [mesh +simplification](https://graphics.stanford.edu/courses/cs468-10-fall/LectureSlides/08_Simplification.pdf); +the geometry was practically homeopathic. + +![the final model in blender][final-model] + +Check out this close-up of Mt Shasta: + +![close-up of Shasta in the final model][final-shasta] +*
    a less lonely Mt Shasta
    * + +Present, but not obnoxious. I printed out another test print to make sure it looked as good in +physical reality: + +![the final test print of the final model][final-print] + +Verdict: yes. If you want, you can visit +[https://www.printables.com/model/240867-topographic-california](https://www.printables.com/model/240867-topographic-california) +and download the 3D printer file to print it yourself at home. If you don't have a 3D printer, you +can still look at and interact with a 3D model of it in the browser on that site, so it's still kind +of neat. A couple different strangers uploaded pictures of their prints of it, which I thought was +cool! + # Final cut # Thank yous, lessons learned, and open questions @@ -498,7 +671,17 @@ given how much I had to blur and decimate)? --- -[main_image]: PXL_20220723_214758454.jpg "A plywood slab carved with CNC into a topographic representation of California" +[final-print]: final_printed.jpg "the final test print of the final model" + +[final-shasta]: final_shasta.png "close-up of Shasta in the final model" + +[final-model]: final_ca_topo_blend.png "the final model in Blender" + +[final-heightmap]: final_heightmap.png "it's the final heightmap (sick synthesizer riff blasts)" + +[crappy-close-up]: crappy_test_print_close_up.jpg "close-up of extremely bad print results" + +[main_image]: wood_ca_on_table.jpg "A plywood slab carved with CNC into a topographic representation of California" [programmers_creed]: /images/programmers_creed.jpg "jfk overlaid with the programmer's creed: we do these things not because they are easy, but because we thought they were going to be easy" @@ -518,6 +701,16 @@ given how much I had to blur and decimate)? [blurry-linear-hm-smaller]: lo-rez_blurred_hm3.png "second round of blurring the heightmap" +[smoother-california-mesh]: blending_california.png "slightly smoother mesh in blender" + +[exp-plot]: exponential_plot.png "a graph of the function `y = x^0.41` between 0 and 1" + +[lo-rez_exp_blurred]: lo-rez_exp_blurred.png "nearly final heightmap, using exponential scaling to exaggerate lower altitudes" + +[exp-scaled-blending]: non-linear_scaling_of_ca_height_data.png "You can see how Shasta doesn't stick out so much when the other hills are brought up a bit relatively speaking" + +[crappy_test_print]: ca_topo_crappy_test_print.png "a piece of literal dogshit" + [^introspection]: The conclusion upon examination was, "I just wasn't thinking". 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