Adding that trefoil knot a repeating pattern along the loop turns out to be more challenging than I thought first.
Wouldn't be much of a problem if only conic gradients were involved. But as a gradient that follows all along? Or a really repeating element? The joins messes up the structure.
Like, how would it be drawn with a brush? If thinking of the imprint is repeated along the path, at the joins you would need to lift the brush, and rotate.
But then, even if the brush is rotated, the imprint's shape wouldn't be matching with the previous stroke -assuming the shape of the brush doesn't change along.
So coming to the conclusion, that the shape needs to be changed along the path in order for a smooth flow.
There are two ways to make it work -one, if the imprint is of the same width as of the knot,
and the other when it's only a path segment with 0 width.
The latter is unrealistically "perfect", while the other wouldn't give a full symmetry if those imprint's colours were changing along the path.
Will try drawing those to make this more sense.
Here is the trefoil with a Wulff net overlay, to represent the idea.
The gradient joins weren't a visible issue with the endless knot. However, this time the knot's fill is much wider so that's also a part where a compromise will be necessary to have.
Strokes redrawn as brush strokes fading. Constructed it by the render circumcircle extension alone thus the node placement is not the best -yet it's more consistent tthan using spiro-paths.
Here is a midstep in construction, to get the idea:
After some Booleans operations, z-order reversing and interpolating attribute in group, as 3 brush strokes using white paint:
-yellow overlay showing one instance of the imprint at a random position-
Later on this can be used as a masking for other kinds of fills. Tried the previous spectrum but it certainly will need some readjustment later.
ok a tut would be awesome for the circle circumcircle extension! that is so cool. I need to go play with that. my pc isn't loading the grunge totally, they look good from what I can see anyway, lol.
It's not a new extension (and certainly I'm not up to date with all the ffeatures since like 0.91?); it is described in the manual here.
Runs too slow anyway. Drawing a spito-path with 3 nodes, making the middle one smooth will generate almost the same thing. Used that previously on the Wulff net in #8.
these are wonderfull, I like #18, 19. In case of the last one do you have the filter for it. I tried your site as suggested by @brynn which has those filters but they link to open clipart website which is now under maintenance.
Problem with the svg is that these filters are rather resource heavy and embedding them straight to the forum didn't work. Never worked in fact, from previous experience browsers crawl compared to rendering a raster double.
If I wanted to attach the svg straigh it would get embedded. Will check if the svg zipped first can work instead.
On this trefoil thingy-or triquetra to be more precise I'm far from satisfied. Yet it's already at around the 50th version and losing the track of orgaisation. Will get back to it eventually but at the moment I'm too busy with other projects.
Attaching the svg zipped. Edit: didn't work. Adding a wetransfer link -take it while it's hot:
Wow Lazur, these are awesome!! I love all of the different versions, especially #14b (greyscale with the light background). I also love the circumcircle piece (#12), and the finished square endless knot (#4). The series as a whole reminds me of Andy Worhol's work, where he makes a bunch of variations on a theme. These trefoils would look nice as a large-scale print, with four different versions occupying the respective corners. Very, very cool. Thanks for sharing.
Lucienne, your question marks also looks pretty cool!
It'll get complicated when width is added into the equation -because by offsetting the stroke edges the proportions change from square and equilateral triangle.
I didn't practice filters enough to do this in a single pass, but I guess as you said it must be possible. Cast shadow on and from note will always be a problem to solve by hand, as thread loops won't be always as the same apparent distance to the note.
For rope pattern, I think it's pretty dead. Methods I know would properly render only in top view... But there's and alternative method to LPE for pattern along path : Extension > Generate from path > pattern along path
This one has a "ribbon" option that flatten pattern when curve direction horizontally changes. That can't help for rope, but if it's a ribbon...
However, Your note'n'thread has already all presence needed as it !
Seing the blue thread version, I realize I prefer the previous black. Maybe the too flashy color... In fact, the flat black one renders oddly more volume than the blue shadowed. It's almost a game designer joke : "when you have graphic elements which cannot make illusion, just let the mess in the dark".
Your wire texture on second screenshot makes already a good job on screenshot. And what a filter scaffolding ! I'm already lost when there's more than 3-4 of them.
The pattern itself probably have a little offset between its extreme nodes. Optically, it occurs a ghost line at the junctions that seems to be amplified across filters.
To be more realistic, even if pattern along path performs pretty well radial distortions, it lacks some alternative distortion methods. Ribbon is one of them. In this case, we need something to shrink/stretch pattern dynamically, according for example either :
curve intensity/radius,
tengency to a specific direction,
space variation between nodes (around mean) ?
It's a too dirty and approximate solution, but with Lattice deformation 2 and pattern along path LPEs combination, some of these non-radial deformations seem reachable.
Made another screenshot and posted on the chat before:
Essentially there are no gaps in between those patterns along the path.
The diffuse filter uses the alpha channel as a bump map, which is derived from the luminance this case.
For that, the pattern is layered from multiple shades on the greyscale.
Now, to make it repeat, instead of pattern along path path effect, the bend path effect was used on a group.
Could do it properly with compound paths and a single backdrop, but was lazy enough not to do so just repeat the same group nex to eachother.
The filter rendering made it worse -well it was just a quick testing.
The filtering part got more complicated, so now it's a composite of two diffuse shading.
One uses the bent greyscale pattern, to "shade" the thin threads, while there is anotherone,
which uses the overall shape and some blurring to give a general "roundness".
It's a hack which isn't so cheap either. Because atop of having a rather complex group to bend as a start, the filter even uses blurring to stall the rendering further.
It'd be much better if it was done in one go, just by using a single diffuse filter primitive.
For that, a better "bump map" should be constructed.
The method isn't much complicated but rather tedious and repetitive, constructing isolines on a 3D rope shape.
I'll give it a go sometime because I'm too curious, yet want to get back to the knot ideas - it's all work in progress.
Got finished with 6 basic variants including the previous one above.
All tiles are separate paths with appropriate overlaps, taking z-order into account; like roof shingles.
Colouring wise there is no improvement yet. Need to come up with a good colour scheme and then implement that by using 2 gradients only;
maybe a black and white too for some additional masking, if going really fancy.
In the mean time, the tiling can be turned into outlines only, creating colouring book layouts.
Still not so satisfied with it though for at least 2 reasons.
For one, the miters "front face" with t he tiling looks as it had an additional edge.
The other issue is, the fill isn't symmetric, making the knot have 2 polar opposites, which is not intended -at least not by the tiling pattern; maybe by the colouring.
As usual, next to these half-a dozen variants, have two dozen more ideas I haven't explored.
At least it's in the work in progress thread, and not in the finished artwork section...
Work in Progress Knots, loops, impossible objects
Inkscape.org
It has always been an interesting topic to me. Will dedicate this topic to arrannge some of my related works -before reaching their "finished" state.
Recently started a challenge on a basic trefoil knot here.
Now, let's see how it can evolve beyond that level.
For start, redrawn one from scratch. Now it has a more polished geometry regaring the knot's proportions.
Here is a variant showing the underlying geometric structure -based on squares and equilateral triangles:
White stroke shows how a trefoil knot would look the best with zero thickness, all constructed from semi-circle arcs.
Note that those arcs are aligned to be parallel to the blue knot design, but it doesn't fall on the centerline.
Digging up some of the older ones.
Endless knot:
Also available with an animated filter, as an animated svg.
Embedding that would hault this page so check the source in the gallery.
endless knot svg
That was more of a finished work -just a direction this trefoil knot can spread.
Thanks for doing this thread. I really love the last square one above! Is that a mesh gradient, can't quite figure out how you did the gradients.
That's only linear gradient. Otherwise browsers wouldn't render it.
Check the original svg in inkscape.
Here is an even more straightforward url for the source:
https://media.inkscape.org/media/resources/file/endless15_cU8Yu1s.svg
Adding that trefoil knot a repeating pattern along the loop turns out to be more challenging than I thought first.
Wouldn't be much of a problem if only conic gradients were involved. But as a gradient that follows all along? Or a really repeating element? The joins messes up the structure.
Like, how would it be drawn with a brush? If thinking of the imprint is repeated along the path, at the joins you would need to lift the brush, and rotate.
But then, even if the brush is rotated, the imprint's shape wouldn't be matching with the previous stroke -assuming the shape of the brush doesn't change along.
So coming to the conclusion, that the shape needs to be changed along the path in order for a smooth flow.
There are two ways to make it work -one, if the imprint is of the same width as of the knot,
and the other when it's only a path segment with 0 width.
The latter is unrealistically "perfect", while the other wouldn't give a full symmetry if those imprint's colours were changing along the path.
Will try drawing those to make this more sense.
Here is the trefoil with a Wulff net overlay, to represent the idea.
The gradient joins weren't a visible issue with the endless knot. However, this time the knot's fill is much wider so that's also a part where a compromise will be necessary to have.
ah, so woth the compromise. I am loving the last blue one. hatch marks perhaps?
Not sure about that. A conic gradient centered to the knot is the most fluent regarding the colour change.
Quick mockup.
However the distortion of a possible repeating pattern alon the loop is way larger in this layout.
Strokes redrawn as brush strokes fading. Constructed it by the render circumcircle extension alone thus the node placement is not the best -yet it's more consistent tthan using spiro-paths.
Here is a midstep in construction, to get the idea:
After some Booleans operations, z-order reversing and interpolating attribute in group, as 3 brush strokes using white paint:
-yellow overlay showing one instance of the imprint at a random position-
Later on this can be used as a masking for other kinds of fills. Tried the previous spectrum but it certainly will need some readjustment later.
Another variant from the grunge department:
ok a tut would be awesome for the circle circumcircle extension! that is so cool. I need to go play with that. my pc isn't loading the grunge totally, they look good from what I can see anyway, lol.
It's not a new extension (and certainly I'm not up to date with all the ffeatures since like 0.91?); it is described in the manual here.
Runs too slow anyway. Drawing a spito-path with 3 nodes, making the middle one smooth will generate almost the same thing. Used that previously on the Wulff net in #8.
Back to #12 and #13.
Hi @Lazur ,
these are wonderfull, I like #18, 19. In case of the last one do you have the filter for it. I tried your site as suggested by @brynn which has those filters but they link to open clipart website which is now under maintenance.
Hi Raghavendra Kamath,
thank you!
Yes, unfortunately openclipart cannot be accessed as it used to be. Could dig up this pack from kisscc0 -as someone reuploaded it before.
chalk pack
Problem with the svg is that these filters are rather resource heavy and embedding them straight to the forum didn't work. Never worked in fact, from previous experience browsers crawl compared to rendering a raster double.
If I wanted to attach the svg straigh it would get embedded. Will check if the svg zipped first can work instead.
On this trefoil thingy-or triquetra to be more precise I'm far from satisfied. Yet it's already at around the 50th version and losing the track of orgaisation. Will get back to it eventually but at the moment I'm too busy with other projects.
Attaching the svg zipped.Edit: didn't work. Adding a wetransfer link -take it while it's hot:https://www.kisscc0.com/clipart/computer-icons-icon-design-etiquette-drawing-chalk-0hln0c/
Not completely satisfied with the filter however tweaking it is very slow and cannot afford any more fine-tuning on it.
Probably would redo it from scratch as it takes some time to grasp what was going on in the previous filter chain.
Hello, this is my first contribution, I only draw with Inkscape since one year, and tried to make this questionmark impossible?
Lucienne😏
Wow Lazur, these are awesome!! I love all of the different versions, especially #14b (greyscale with the light background). I also love the circumcircle piece (#12), and the finished square endless knot (#4). The series as a whole reminds me of Andy Worhol's work, where he makes a bunch of variations on a theme. These trefoils would look nice as a large-scale print, with four different versions occupying the respective corners. Very, very cool. Thanks for sharing.
Lucienne, your question marks also looks pretty cool!
Hmm so much stuff postponed here.
One of these days, I'm gonna get organizized.
Saw someone recently posting a triquerta interlaced witha circle at openclipart which was another direction I wasnted to explore sometime.
Seems the basic proportions follows along with the layout in https://inkscape.org/forums/wip/knots-loops-impossible-objects/#c7040.
It'll get complicated when width is added into the equation -because by offsetting the stroke edges the proportions change from square and equilateral triangle.
Performing yet another necromancy on this topic.
In the challenge of 2021 September on the forum -https://inkscape.org/forums/competitions/new-challenge-21-september-2021-04-october-2021/-
the theme was to draw a glass object.
Came across this image by HenryM at openclipart:
https://openclipart.org/detail/333437/rotating-tumbling-geometry
Thought the original was a bit sloppy but had the potential.
Ended up redrawing it for the challenge as a glass donut.
For what it's worth, it uses the same principals as any other impossible ring, so guess it als ofits in here.
https://openclipart.org/detail/333546/hexagonal-ring-from-glass
Also, created an animated version out of it -which has some errors here and there. Better luck next time I guess.
https://openclipart.org/download/333547/loop22-glass-animated.svg
Redrawn another knot image before that, by HenryM at openclipart.
-original image, "Ming knot"-> https://openclipart.org/detail/333258/ming-knot-as-geometry-and-image-when-made-with-wood-veneers
-redrawn version:
https://openclipart.org/detail/333260/wooden-knot-intarsia
More recently. came across a variation on a Penrose trident, by rygle at openclipart
Original image was morphed into musical notes, depicted by using a black outline only.
https://openclipart.org/detail/337238/notable-trident
Gave it another spin, by using no outlines but clean fills:
https://openclipart.org/detail/337444/impossible-musical-triplet
Was playing with the thought that a thread could be interwowen into the trident and/or turning it into a glass object.
However so far all I got was this far:
Drawing a realistic thread seems a bigger challenge than I can just pull off in a reasonable time frame - besides a simple pattern along path effect.
So this one is put on hold.
However, that image gave an offspring idea as a throwback with the impossible knot that I'm working on at the moment.
So far, got to the basic layout and thinking of ways to colour it in.
The shadows need reworking too - if done right, they should work flawlessly without those black outlines.
Which is yet another challenge by itself.
To avoid rendering issues of double edges atop eachother, the shadows need to be clipped.
And because they will have some miter corners, masking will be necessary too. Or the using of gradient meshes. Whichever is more convenient.
Still enjoying these figures! And making them.😊
Here is a more advanced version of that impossible endless knot.
Took way longer than I care to share and ended up downloading the latest stabile version. I'll definitely need to adapt and relearn using it.
So far, the reason behind was knowing how the layer panel got merged into the objects panel.
Not sure how to change a layer's transparency or blending mode, however I used the new feature to crop multiple layers at once.
This way, 7 fill layers atop eachother produce the result with the same visible edge -without any anti-aliasing issues!
Meaning, it should work just as polished without any black outlines.
So be it, let see how it turns out just like that.
Added a dark background as I had in mind printing it on a T-shirt sometime.
Logo and high-res image not provided yet; will get back to it and polishing up the svg later.
Have to admit the new dithering in the gradient alone was worth updating to the current stabile.
Glad you like what you see Lucienne @Maargot!
If you care to share your images, maybe you can start your own dedicated work in progress/finished work topic on the forum.
Can bet you have more to showcase of how far behind I got implementing these old ideas.
Actually it would be interesting to see your thought process, how you come up with your impossible object images.
Interference adds noise to this topic's "work in progress" theme so a separate topic would be much preferred.
Just
finishedpublished as they are two variants to that endless knot.With the knot drawn having a glass material and some animated balls inside.
Animation may lag -it's a 800/800 px image, if you zoom out 50% it will appear smooth.
https://inkscape.org/~Lazur/%E2%98%85glass-endless-knot-animated-01
https://inkscape.org/~Lazur/%E2%98%85glass-endless-knot-animated-02
More variants after some adjustments, with the logotype from 2017 updated.
Second one, with a bit of Vasarely influence.
Larger versions are available on my deviantart page.
https://www.deviantart.com/lazururh/art/Impossible-knot-924577775
https://www.deviantart.com/lazururh/art/endless-knot-924578357
Your impossible note version with thread is sooo cool !
For the thread, I can suggest a trick to to give it some volume and basic grainy texture without spending too much time on it :
Thank you @m1981!
If you look into filtering, all those grouped, layered-masked visuals can be substituted with a single filter chain.
Then a diffuse filter primitive could be involved too, for more "realism".
Problem is, after that it'd still be necessary adding cast shadows from the note.
I was thinking more of a rope pattern along a path. However then the bending, tight curves would look "a bit" off.
Maybe if the thread would consist of three thinner ones it would be more convincing with all the overlaps.
That case the cast shadows would be a nightmare.
Maybe I'll get back to it, after that impossoble knot.
There are a dozen ideas on that one I haven't realised yet.
I didn't practice filters enough to do this in a single pass, but I guess as you said it must be possible.
Cast shadow on and from note will always be a problem to solve by hand, as thread loops won't be always as the same apparent distance to the note.
For rope pattern, I think it's pretty dead. Methods I know would properly render only in top view...
But there's and alternative method to LPE for pattern along path : Extension > Generate from path > pattern along path
This one has a "ribbon" option that flatten pattern when curve direction horizontally changes. That can't help for rope, but if it's a ribbon...
However, Your note'n'thread has already all presence needed as it !
Here is a quick go at a diffuse filter:
In my opinion the lack of fresnel is a giveaway -how a "perfectly round" surface has no distortion in the roughness of the texture towards the edges.
It just looks flat despite the more or less good diffuse lights.
On the thread, I'd still consider it a challenge making it realistic.
For example, this one uses some repeating pattern with a gradient fill, plus more diffuse filters.
There would be cast shadows necessary and what not to make it pop.
Previously had spent alot of time working on a tileable houndstooth pattern, figuring out how to achieve a thread looking "good".
Didn't turn out as good as expected, but for a fabric pattern that was acceptable.
If that was the main part of the composition, it'd take way more studying and experimenting.
It's a bit older and attached the thumbnail from openclipart, which is rendered a bit off.
Haven't checked that svg for a while, probably it'd take some optimisation.
https://openclipart.org/detail/289287/houndstooth-15
Seing the blue thread version, I realize I prefer the previous black. Maybe the too flashy color... In fact, the flat black one renders oddly more volume than the blue shadowed. It's almost a game designer joke : "when you have graphic elements which cannot make illusion, just let the mess in the dark".
Your wire texture on second screenshot makes already a good job on screenshot. And what a filter scaffolding ! I'm already lost when there's more than 3-4 of them.
The pattern itself probably have a little offset between its extreme nodes. Optically, it occurs a ghost line at the junctions that seems to be amplified across filters.
To be more realistic, even if pattern along path performs pretty well radial distortions, it lacks some alternative distortion methods. Ribbon is one of them. In this case, we need something to shrink/stretch pattern dynamically, according for example either :
It's a too dirty and approximate solution, but with Lattice deformation 2 and pattern along path LPEs combination, some of these non-radial deformations seem reachable.
Can agree on that.
Made another screenshot and posted on the chat before:
Essentially there are no gaps in between those patterns along the path.
The diffuse filter uses the alpha channel as a bump map, which is derived from the luminance this case.
For that, the pattern is layered from multiple shades on the greyscale.
Now, to make it repeat, instead of pattern along path path effect, the bend path effect was used on a group.
Could do it properly with compound paths and a single backdrop, but was lazy enough not to do so just repeat the same group nex to eachother.
The filter rendering made it worse -well it was just a quick testing.
The filtering part got more complicated, so now it's a composite of two diffuse shading.
One uses the bent greyscale pattern, to "shade" the thin threads, while there is anotherone,
which uses the overall shape and some blurring to give a general "roundness".
It's a hack which isn't so cheap either. Because atop of having a rather complex group to bend as a start, the filter even uses blurring to stall the rendering further.
It'd be much better if it was done in one go, just by using a single diffuse filter primitive.
For that, a better "bump map" should be constructed.
The method isn't much complicated but rather tedious and repetitive, constructing isolines on a 3D rope shape.
I'll give it a go sometime because I'm too curious, yet want to get back to the knot ideas - it's all work in progress.
Speaking of the knot, a few days ago submitted a variation into the current challenge, showing the tile layout from front to back.
https://inkscape.org/forums/competitions/inkscape-challenge-1-august-2022-31-august-2022/#c45459
That one was built up by 372 "rhombus-shaped" tiles - but in actuality the look is deceiving.
To avoid the rendering gap issue, every tile has additional space and overlaps the other.
Just recently finished another rhombus tile layout, where the individual tile appears to be scaled 50% compared to the previous variation.
It is built up by 1352 tiles.
The layout again is inspired by Vasarely, and experimenting with the colouring.
It's not yet tuned for easy handling, just used random colours from the basic bottom palette.
OK, this version is now showing tiles coloured with flat fills only, without any cheap overlay effects.
A larger version is available here:
https://www.deviantart.com/lazururh/art/endless-knot-926053186
More of this parallelogram tiling.
Got finished with 6 basic variants including the previous one above.
All tiles are separate paths with appropriate overlaps, taking z-order into account; like roof shingles.
Colouring wise there is no improvement yet. Need to come up with a good colour scheme and then implement that by using 2 gradients only;
maybe a black and white too for some additional masking, if going really fancy.
In the mean time, the tiling can be turned into outlines only, creating colouring book layouts.
Still not so satisfied with it though for at least 2 reasons.
For one, the miters "front face" with t he tiling looks as it had an additional edge.
The other issue is, the fill isn't symmetric, making the knot have 2 polar opposites, which is not intended -at least not by the tiling pattern; maybe by the colouring.
As usual, next to these half-a dozen variants, have two dozen more ideas I haven't explored.
At least it's in the work in progress thread, and not in the finished artwork section...
Some of those fancier variants mentioned, as part of an experimentation.
Put that endless knot aside for other work yet came across another related inspiration to the theme of this in progression topic.
edisonpalomo made a looping animation in blender showing a Penrose triangle with a ball rolling along on its side.
https://www.instagram.com/edisonpalomo/?fbclid=IwAR3zQzZFl-hWCbd2tajiUZeLvnJ7x6uRr7kAF2sUi_fYYHLB7rCVHpzG_-k
Was wondering how that could be achieved in a 2D environment.
So far created the basic Penrose triangle shape -from 3 groups, 6 paths in total (with proper overlapping and no rendering gaps)-
and a motionpath animation following the sides.
From now on, it's about how to slice everything up in the z-order and compositing.
Svg is also shared at openclipart:
https://openclipart.org/detail/338729/penrose-triangle-animated