Vaseinator

A Windows desktop app that designs vases that print without supports – as an ordinary print with a few walls, in any colours, or seamless in the slicer's spiral vase mode. Every vase it makes is a closed, watertight model, every layer is one single loop, and no part of the wall leans further than you allow.

Simple mode is a handful of choices made from pictures – easy enough for anyone – and one big Save for printing button; Advanced has every setting.

Use it in your browser – nothing to install: https://rickusinggithub.github.io/vaseinator/. The web version is the whole app – Simple and Advanced, every setting, the curves, drawing your own cross-section, the views and the exports – built by the app's own Python running right in the browser.

Shape the outline, pick a cross-section and what it turns into on the way up, spin it, cover it in ribs, rings, bumps, organic lumps or your own formula, and colour it in bands, stripes or a gradient spool. Cut holes through it, open it at the bottom, close it over at the top – or give it a face and make a mask or a helmet, sized for the head it fits, or a tissue box cover sized for the box of tissues it goes over. The app shows the vase in 3D as it will print, cuts it in half to show the wall, colours every face by how far it leans, plays the print back in real print time, and exports an STL or 3MF ready to slice.

Advanced: draw how things change up the vase	Section: the printed wall
Overhangs: green is easy, red needs support	Watch it print, in real print time
Draw any cross-section, sharp corners and all	Draw one lobe, repeat it: three bulbs become six

Features

• Outline from twelve presets (classic, bulb, tulip, amphora, bottle, gourd, trumpet, …) or drawn by hand: drag points on the outline curve; the curve through them never overshoots.
• Cross-section: circle, polygon (with rounded corners), rectangle, star, flower, gear, ellipse or pebble – and a second shape it turns into on the way up – evenly, early, late, back and forth as many times as you like (circle → pentagon → circle → pentagon), or along your own curve.
• Draw any cross-section: a spline editor with smooth points and sharp cusps, for shapes no formula makes – lobes that swell past their necks, a crescent, a claw, a heart, nothing symmetrical at all. Draw one lobe and repeat it around – up to 100 times – start from a built-in shape, or trace a picture. Draw close up on one repeat, or in a full window with zoom.
• Spin: twist the shape round as it rises – evenly, easing in and out, speeding up, slowing down, back and forth, or along your own curve – or both ways at once for a lattice of crossing ridges.
• Surface patterns: ribs (that can spiral, or cross for diamond knurling), rings, staggered bumps and smooth organic lumps, each with its own depth and shape, a strength that can change up the vase, and a plain foot and rim.
• Low-poly facets: the whole vase from flat triangles, like a cut gem, with an optional rough cut.
• Your own function: type a formula in millimetres – 1.5 * sin(6*theta + 4*pi*h) – added to the radius everywhere. Variables for the angle, the angle turning with the twist (on a box with Evenly round the wall, counted along the wall, so patterns are even round a rectangle), height, share of the height and the radius so far; trig, waves, steps and smooth noise. A long formula can go over several lines – they are read as one, so start each new line with + - * or / – with notes after a #. It is checked and run safely: numbers, the listed variables and functions only; a mistake is pointed out by line and character.
• A normal print, or seamless: a vase prints like any other print, and is exported as the hollow pot it is – the wall as thick as it prints, the floor and the rim – so the slicer needs no special settings: sturdy, watertight and in colour. Or, in one colour (or a gradient spool), seamless in the slicer's spiral vase mode: one line climbing round and round, with no seam and a single wall that glows when lit. Spiral vase mode is hardly any quicker, so a normal print is the usual.
• Holes right through the wall: Voronoi cells (a honeycomb when regular), round holes, diamonds or slots, as big and as far apart as you like, kept clear of a plain foot and rim, and turning with the twist. Every hole's top comes to a point that closes no faster than the overhang limit, so it prints without support – with at most a short bridge, a few millimetres, at its very tip. Voronoi holes are ovals instead, each as long, as wide and as tilted as its cell and as big as fits inside it, so the wall between them is thin where two holes come close and thick in the corners; their round tops close over a bridge of at most 14 mm. Rounded edges swells the wall round every hole, so it curves smoothly from the outside, through the hole, to the inside. And open at the bottom too, for lampshades, sleeves and holders.
• Closed at the top: the top comes in to a point, leaning no more than the overhang limit, over a ceiling a few millimetres across that the printer bridges – a helmet, a dome, a bell, a sealed egg. The outline is rounded in to meet the point.
• Part way round: the wall goes only so far round – about 200° makes a mask – with the gap at the back.
• Masks and helmets: a face at the front – eyes (almond or round, apart, tilted), a raised nose, a mouth (open, a grille of slots that can smile, or open down to the chin like an old Greek helmet's) and slots for an elastic strap – every hole with a pointed top, so it prints without support. Head size fits one to a head: measure round it above the eyebrows and ears, as for a hat, and the whole design – height, outline and face – is scaled so the inside fits with a centimetre to spare. Stylised, not anatomical.
• Tissue box covers: measure the box of tissues – long, wide, tall – and the cover is made to go over it, with a little room to spare (more inside rounded corners, so a square-cornered box still fits). Pick the hole the tissues come out of – a long slot, an oval or a round hole – and any pattern, holes or colours. It is made the way it prints: upside down, the hole through its first layers on the bed and the open end at the top, so nothing needs supports. The hole's edge is rounded, both sides, for the tissues to slide over. Turn it over to put it on. Its ribs, bumps and lumps are spread evenly round the wall, as close together on the long sides as round the ends.
• A lid for a tissue box cover, printed on its own – with the cover, or later: a flat frame (or a solid plate) the shape of the rim, which the cover stands on. It goes on like a battery cover: laid on the rim 8 mm along from home, then pushed along till it clicks. Four rigid hooks slide in behind short rails inside the cover's long sides, by its corners – where a thin wall is stiff – and draw the lid tight; a latch by the pull tab springs up inside the cover's end. Nothing has to bend to hold it, so a box of tissues can't lever it off when the cover is carried. Lift the pull tab and slide it back to change the tissues. Gentle, Snug or Firm sets how tightly the hooks fit. It is made from the cover's own design; a cover printed before 1.16 has no rails.
• A fine mesh, a light file: the surface is built every 0.2 mm, and saving for the slicer simplifies it – triangles are merged wherever that moves the surface by no more than a few hundredths of a millimetre – so the file stays small and the slicer opens it quickly. A box's flat sides need only a few rows and columns of points to begin with.
• Colours: one colour or a gradient spool – shown where its colours will really land, worked out from the filament each height uses – and, printed normally, up to four filaments in bands (even, or thicker at the top or the bottom) or stripes, with palettes.
• Colours by a function: a second formula, with the same variables and functions as your own function, picks the filament at each point of the wall – below 1 filament 1, 1 to 2 filament 2, and so on. Made from the same terms as the texture, it colours the texture: for the Zigzag ribs, 1.2 * tri(12*theta + 3*tri(2*pi*z/25)), the colours 2 + 2*tri(2*pi*z/25) climb up and down with their zigzag. Each colour is a part of its own in the 3MF, cut just where the formula changes, and the 3D view shows them.
• Looks: matte, silk, glossy or translucent in the 3D view.
• Printable, always: each layer of the wall rests on the one below it, so it may lean neither out nor in further than the limit (45° by default). Soften to fit reshapes only what leans too far – and tells you by how much – and every triangle is checked afterwards.
• Views: the vase, a section through the printed wall, an overhang check, and the print layout on your bed inside the printer's build volume. Spin turns it on a turntable; Watch it print builds it up in real print time (wide layers take longer).
• The sums: size, base and opening, how much water it holds, filament in grams and metres, print time, steepest overhang, and the mesh – closed and watertight.
• Gallery of twenty-seven ready-made designs – lampshades and baskets with holes among them, three masks and a helmet – a plain cylinder to start from blank, Surprise me (a new random vase that still prints), and undo / redo of everything.
• Save for printing: a 3MF in the middle of the bed – each colour band its own part, set to its filament (one solid for a seamless vase) – as Lenticular Sign Maker and Maze Tube Designer do, with plain steps to print it and Open in slicer (Flash Studio, OrcaSlicer, Bambu Studio, PrusaSlicer, Cura… – whichever is installed). Also a solid STL. Designs save as .vase files (JSON).
• Simple: a design chosen from pictures, how big (in centimetres – or, for a mask or helmet, the head size), the shape from above and from the side, the twist, a pattern and a colour – each a picture to click. Advanced has every setting and the curves, your own function among them. Bigger text and a light theme are in the View menu.

Download and run

Design library and profiles (desktop and web)

Open Designs → Library, profiles and Surprise locks on desktop or in the browser. Both interfaces use the same Python rules and portable library format:

• Surprise locks: preserve Dimensions (height and widest diameter), Silhouette (including its width), Cross-section, Twist, or Colours while exploring new random variations. Printer settings are always kept. Locks preserve the requested settings; softening can still alter the printable surface. Existing masks and tissue-box modes are not locks: Surprise me still creates a vase.
• My designs: save named variants, browse silhouette sketches, mark favourites, restore, or remove them. Restoring a variant remains undoable. These are silhouette thumbnails, not full 3D renders.
• Printer and material profiles: name and apply printer settings separately from material properties. Printer profiles store bed/build height, line/layer widths, bottom, walls, overhang limit and mesh detail. Material profiles store filament diameter, density, speed and maximum flow. Applying a profile keeps the design's shape and colours and can be undone.
• Recovery: retains up to 30 settled snapshots, beyond the current session's undo history. It is local to this computer/browser. Export a library backup before clearing browser storage or moving computers.
• Export/import library: transfer variants, profiles, recovery and locks between desktop and browser. Import merges entries by identity, leaves existing entries intact, and combines locks. Each library can hold up to 500 saved designs and 500 profiles. There is no automatic cloud synchronisation.

In View → Compare original and softened, blue shows the requested side envelope and orange shows the softened envelope. Connecting strokes highlight changed widths; the maximum surface movement is also reported. This side view can overlap where changes are angular rather than changes in outer width.

File → Save clearance samples exports five socket-and-pin pairs as one 3MF. Left to right, the radial clearances are 0.1, 0.2, 0.3, 0.4 and 0.5 mm (diametral clearances are double those values). Print with the intended material and settings, keep the pairs in order, and test the fit before committing to a larger print. These are general clearance samples, not replicas of the lid latches; they do not change a design's clearance automatically. The sample layout is approximately 92 × 33 × 3 mm.

Regression checks

python -m tests.test_vase
python -m unittest tests.test_workspace -v
node tests/test_web_state.cjs
python -m tests.test_app
python -m unittest tests.test_design_tools -v

The desktop tests require the packages in requirements.txt. They can run with QT_QPA_PLATFORM=offscreen. The optional node tests/test_browser.cjs end-to-end test needs Playwright, a Chrome/Chromium executable in BROWSER_PATH, and a built site served at http://127.0.0.1:8765 (or VASE_URL). Shared geometry, library and browser-state regressions run before Pages deployment.

• In your browser: https://rickusinggithub.github.io/vaseinator/ – the whole app, Simple and Advanced: every setting, the curves, drawing and tracing your own cross-section (in a full window too), your own function, the Vase, Section, Overhangs and Print layout views, Spin and Watch it print, the side and from-above pictures, and Save for printing (3MF), STL, a picture and .vase designs – which the Windows app opens too, and back. The first visit takes a little while to load; after that it starts quickly. The one thing only the Windows app does is open the file in your slicer for you.
• Windows app (no Python needed): download Vaseinator.exe from the Releases page and run it. It is a single file: nothing to unzip or install. It isn't code-signed, so Windows SmartScreen may ask once; choose More info → Run anyway.
• From source (Python 3.10+, any OS with OpenGL):

  git clone https://github.com/RickUsingGitHub/vaseinator.git
  cd vaseinator
  python -m venv .venv
  .venv\Scripts\pip install -r requirements.txt      # macOS/Linux: .venv/bin/pip
  .venv\Scripts\python main.py
  

  On Windows you can also just double-click run.bat, which sets everything up on first run.
• Build the Windows app yourself: build_exe.bat (uses PyInstaller; the result is dist\Vaseinator.exe).

Vaseinator is free. If it has made you something you like, you can buy me a coffee.

examples\ holds the gallery as .vase designs to open. tools\make_examples.py writes them again, and six of them to examples\stl\ as finished STLs, checked and ready to slice: Lagoon Twist, Star to Moon, Lattice Lantern, Gem Facets, Coral Reef and Claw Shell. (STLs are big, so they are not kept in git.)

On first run the app borrows your printer's bed size and height from Maze Tube Designer or Lenticular Sign Maker, if you have used them. Printer settings are remembered for new designs.

Using it

In Simple mode, click Choose a design… (every ready-made vase as a picture) or Surprise me, then click the pictures to change it: the shape from above, the shape from the side, a pattern, a colour; Tall and Wide size it – for a mask or helmet, Head size; for a tissue box cover, the box of tissues it goes over, and the hole for the tissues, and Save a lid for it… – and the slider twists it. Draw my own shape… opens a big window to draw the shape from above yourself. When it looks right, Save for printing… saves it for the slicer and says, in plain steps, how to print it – with a button to open it in your slicer (File ▸ Choose slicer program picks a different one).

Or start blank: Plain cylinder, first in the gallery (or File ▸ New plain cylinder, Ctrl+Shift+N), is a cylinder 200 mm across and 200 mm tall with everything else off, ready for your own function or a drawn cross-section; your printer settings are kept. Every change rebuilds the vase at once; while you drag a point on a curve, a quicker rough version follows your hand.

The curves for the twist, the change of shape and the pattern strength are ordinary graphs: the vase from bottom to top runs left to right, and the value runs up – drag a point up for more, down for less. Double-click to add a point (a few make a wave), right-click to take one away. The outline's curve is drawn upright and mirrored instead, like the vase from the side.

Group	What it does
Size	Height, the widest diameter (scales the whole outline), and the outline: a preset, or your own curve – diameter at each height, drawn as the vase seen from the side.
Shape	The cross-section at the bottom, and what it turns into at the top. Each shape has its own settings: sides, points, petals or teeth; how deep it cuts in; how sharp it is; how far it is turned. Drawn – any outline gives you the cross-section editor instead (below). Change happens says how the first shape becomes the second on the way up – including back and forth, as many Changes as you like, and your own curve.
Spin	How far the shape turns from bottom to top, and how the turning is spread up the vase – including back and forth, and your own curve. Both ways twists it both ways at once.
Surface	Ribs, rings, bumps and organic lumps; whether they turn with the twist; whether they are spread evenly round the wall (by distance along it, not by angle – for boxes, rectangles and ovals); how strong they are up the vase; and a plain foot and rim.
Low-poly	Flat facets: how many round and up, and how rough the cut.
Holes and openings	The holes – none, Voronoi, round, diamonds or slots – their size, the wall between them, how irregular the Voronoi cells are and their pattern, how much plain wall to keep at the foot and the rim, and rounded edges round them; open at the bottom; closed at the top; and how far the wall goes round. Holes, an open bottom and a wall part way round are printed normally.
Masks and helmets	For a head and its head size; the eyes – almond or round, their size, how far apart, how high and tilted; a raised nose – its width, length, how far it sticks out and how high its tip is; the mouth – open, a grille of slots (how many, and how much they smile) or open down to the chin; and strap slots. Sizes and heights are in millimetres along the face, from the bottom.
Tissue box	Tissue box cover; the box of tissues it goes over – its length, width and height; how rounded the cover's corners are; and the tissue hole – a long slot, an oval, a round hole or none – and its length and width; and its lid (File ▸ Save the lid for printing): how tightly its hooks fit the cover's rails, and whether it is a frame open in the middle or a solid plate.
Your own function	A formula added to the radius. Examples has eight to try; Help… lists the variables and functions.
Colours	The colour, or – printed normally – a palette or four filament colours, and how they go on the vase: one colour, bands, stripes, a gradient spool, or by a function – a formula for the filament at each point, with examples and help. How it looks: matte, silk, glossy, translucent.
Printing	Print as: a normal print (walls, any colours – the usual) or seamless (spiral vase mode, one colour). For a normal print, how many walls. The steepest overhang allowed and Soften to fit; the line width and layer height; the solid bottom; the printer's height and bed; speed and flow (for the print time); filament diameter and density (for the weight); and the mesh detail (0.2 mm; saving simplifies the mesh, so the file stays small).

The mouse wheel scrolls the panel: a drop-down list only changes with it once it is dropped down, a number box only over its arrows, and a slider never. Click a group's heading – ▾ Size, ▾ Shape and so on – to fold it away (▸) and keep the panel short; it stays folded next time, in the app and in the web version.

3D view: left-drag turns it, right-drag or shift-drag moves it, the wheel zooms, double-click or F goes back to the chosen view. S spins it, F5 watches it print, Ctrl+1–4 switch views, Ctrl+R is Surprise me, Ctrl+Z / Ctrl+Y undo and redo.

Drawing a cross-section: the middle of the editor is the vase's axis and the dashed circle its widest (the outline is scaled so its furthest point touches it). Drag a point; double-click the line to add one, and double-click a point to switch it between smooth (a circle) and a sharp corner (a diamond); right-click a point to take it away. Repeat around copies what you draw round the axis – draw one lobe, get five, or up to a hundred; change the number and the lobe narrows or widens to fit, just as deep. Close up shows one repeat big, turned to point upwards (above 8 repeats the editor starts that way), and double-clicking any copy adds the point to the lobe you draw. Full window… opens the editor as big as the screen: the wheel zooms, a right or middle drag moves it, F fits it again, and the vase follows as you draw. Start from has ready-made outlines – a claw, bulbs, a heart – and Trace a picture… (a dark closed line or filled shape on a light ground). Switching a built-in shape to Drawn starts from it: a five-petalled flower becomes one petal, repeated five times. Twist, the change into a second shape, the patterns and colour bands all work on a drawn outline; it turns red if it crosses itself.

Under the 3D view, From the side shows the outline in the colour of each height (the dashed line is the narrowest radius, so you can see how deep the shape goes; an orange tick on the left marks heights that were softened, a red tick on the right anything still leaning too far), and Layers from above shows fifteen layers stacked, so the twist and the change of shape are easy to see.

Printing

Save for printing gives the steps for your vase. Advanced ▸ Printing ▸ Print as chooses a normal print (the usual) or seamless.

A normal print

• Leave spiral vase mode off, and otherwise print with your usual settings. The vase comes as the hollow pot it is – a wall as thick as Walls × Line width (1.2 mm as it comes), the floor, the rim and any holes – so the slicer simply fills it in: there is nothing to set.
• The colour bands and stripes, and colours by a function, are parts of their own filaments in the 3MF, so the slicer prints them in colour by itself; on a printer with several toolheads, like the Creator 5 Pro, each band uses its own head. It prints a layer at a time, with a seam.

Seamless (spiral vase mode)

• Slice with spiral vase mode on (Spiralize). The exported model is solid: the slicer prints only its outside, as one continuous line. Don't slice it normally with infill – it would print as a solid block.
• Set bottom layers to the number the panel gives (6 for a 1.2 mm bottom at 0.2 mm layers), 0 top layers, 0% infill, 1 wall.
• Set the outer wall line width to the app's line width. 0.6–0.8 mm on a 0.4 mm nozzle is much stronger and more watertight than 0.4 mm.
• It prints one filament. Flash Studio won't change filament in spiral vase mode (Change Filament is greyed out on the layer slider), and won't spiral an object made of parts of several filaments. A gradient spool is one filament, so it works.

Either way

• No supports. The panel shows the steepest lean of the wall; the Overhangs view shows where it is.
• To make sure it holds water: a little extra flow (103–105%), 5–10 °C hotter than usual for strong layer bonds, and a moderate speed (30–50 mm/s for the wall). PETG is more watertight than PLA; silk PLA looks lovely but bonds a little less well. Test it in a sink. A coat of clear epoxy or varnish inside seals any weep.
• A brim helps a vase with a narrow foot stay put – and a mask, which stands on the thin edge of its chin, or a helmet on its rim.

tools\verify_stl.py checks any STL for spiral vase printing, straight from the file: closed and watertight, faces outwards, one piece, flat on the bed, no wall leaning past the limit, and every layer one closed loop.

.venv\Scripts\python tools\verify_stl.py examples\stl\lagoon_twist_vase.stl

Opening the 3MF in your slicer

Save for printing (and Export 3MF) writes the vase as one object in the middle of the bed – the same kind of file as Lenticular Sign Maker and Maze Tube Designer. Open in slicer opens it for you; in Flash Studio or OrcaSlicer you can also use File ▸ Import (Ctrl+I).

• A normal print: the hollow pot, each colour band its own part, set to filaments 1, 2, 3… in the vase's colours; reassign them in the slicer as you like. Leave spiral vase mode off and print with your usual settings.
• Seamless: the vase is one solid part. Turn on spiral vase mode and print.

Project layout

File	What it holds
main.py	Starts the app.
vaseinator/app.py	The main window: the Advanced settings, views, animations, gallery, undo, exports.
vaseinator/simple_panel.py	Simple mode: the picture choices, and the gallery of pictures.
vaseinator/choices.py	What each of Simple mode's pictures sets – shared with the web version.
vaseinator/settings.py	Every Advanced setting, the rules for which are shown and what a change brings with it – shared with the web version.
vaseinator/report.py	The panel beside the 3D view, the steps to print it, and the help – shared with the web version.
vaseinator/slicers.py	Finding the slicers installed, to open a vase in one.
vaseinator/geometry.py	The vase itself: the surface, softening, the solid and the shown shell, and the sums.
vaseinator/shapes.py	Outlines, cross-sections, curves up the height, textures, palettes.
vaseinator/expr.py	Your own function: checked, then evaluated with numpy.
vaseinator/hollow.py	The hollow pot a normal print makes, the hole patterns, a face's eyes, nose, mouth and strap slots, and their pointed tops.
vaseinator/sections.py	Drawn cross-sections: the spline through the points, tracing a picture, filling and insetting outlines.
vaseinator/curves.py	The curve editor.
vaseinator/outline_editor.py	The cross-section editor.
vaseinator/plots.py	The side and from-above pictures.
vaseinator/viewer.py	The OpenGL 3D view.
vaseinator/presets.py	The gallery and Surprise me.
vaseinator/params.py	Settings, and saving and opening designs.
vaseinator/stl.py, threemf.py	The exports.
tests/test_vase.py, tests/test_app.py	Self-tests of the geometry and the window.
assets/gallery/	A picture of each ready-made vase, drawn by tools/make_thumbnails.py.
tools/	The icon, the gallery pictures, the example files, the STL checker, and build_web.py.
web/	The web version: the page (index.html, app.js, style.css), the 3D view (view.js), the curve and cross-section editors (curves.js, outline.js), the side and from-above pictures (plots.js), the worker that runs the Python (worker.js) and the Python it calls (bridge.py).
.github/workflows/pages.yml	Publishes the web version on GitHub Pages at every push to main.

How the geometry works

The vase is a radial height map r(θ, z): one radius in each direction round the axis at each height, built on a grid of heights and angles. Because each height has exactly one radius in each direction, every layer is one simple closed loop – what spiral vase mode needs – and the mesh can't cross itself: each triangle lies in its own wedge of angle between two heights. The wall is joined to a flat bottom and a flat top, so the solid is closed, watertight and one piece, with no boolean operations.

A normal print is exported as the hollow pot: the outer face, an inner face moved in square to it by the wall's thickness, a flat floor (or an open bottom) and the rim, built row by row on the same grid as the surface. A hole pattern is a number at each grid point – how far inside a hole it is, in mm, below nought in the wall – from the nearest hole centres. A Voronoi cell's sides are the lines halfway to its neighbouring centres, and it leaves room for a hole half a strut in from them. Its hole is the oval with the same spread as that room – as long, as wide and as tilted, the tilt damped a little, the cells a little taller than a honeycomb's so most ovals stand upright – made as big as fits wholly inside it. Its round top closes over a bridge where its sides grow flatter than the overhang limit allows; an oval whose bridge would be too wide is made smaller. The wall is cut where that number is nought (marching squares), the same on both faces, with a side face joining them round each hole; each cut is one vertex shared by every face beside it, so the pot stays closed. Going up row by row, the wall over a hole may only reach in so far past the wall below it – measured from the point really below, so on a twisting vase the holes' sides lean no more than their tops – so every hole's top closes to a point at no more than the overhang limit. Where it finally closes between two grid points there is a short bridge (a Voronoi oval's is the width found for it), which the app measures and tells you about. Rounded edges moves the outer and inner faces apart round each hole, by a smooth curve of the distance from its edge that fades away a little further off and grows no faster going up than the overhang limit allows; the cut edge itself stays put, so the wall curves round through the hole. Colour bands of the pot are cut on rows put in at the band heights, each a closed part.

A face is more of the same: the eyes, mouth and strap slots are hole fields too, placed in millimetres along the surface from the front, and the gap at the back of a wall that goes only part way round is one more – so they all get pointed tops, and a pattern of holes keeps a strut's width of wall round them. The nose is added to the radius, and softening keeps its underside within the limit. A closed top caps the outline's radius with a cone leaning a little under the limit up to a point – the two blended where they meet, so the outline curves in – and the pot's inner face ends a floor's thickness under the point in a small flat ceiling (the app measures the widest circle that fits in it: the span the printer bridges). Head size measures round the inner face where the head goes in – the narrowest place below the widest, or for a mask the widest – less a centimetre to spare, and scales the whole design until that is the head asked for.

A tissue box cover is a vase too, upside down: a rectangle cross-section – its corners quarter circles – straight up, sized from the box of tissues: as wide and long inside as the box with room to spare each side (more where a rounded corner has to clear a square one, and more for patterns that reach in), and as tall as the box with a little over it plus the solid bottom, which is the cover's top. The hole for the tissues – a slot with round ends, an oval or a circle, kept clear of the walls – is cut through that bottom: the floor is filled between the wall and the hole, row by row round the middle, on the bed and on its top, with the hole's side between them, so the mesh stays closed. That side is rounded, 1.2 mm each side: the floor thickens round the hole to 2.4 mm and the round runs over its top. On the bed's side the round's bottom would lie flat over the hole, so it is a chamfillet – from the bed a chamfer leaning no more than the wall may (43°), then the round from where it is that steep – and the thickening slopes back down to the floor, facing up, so the edge prints without supports. The opening is the size set where it is narrowest, halfway up the round. Everything else – holes in the wall, rounded edges, colour bands – works as on any vase. Evenly round the wall lays the patterns out by how far along the wall each point is, as a share of the way round, rather than by its angle from the middle – which on a box would crowd them along the middles of the long sides.

A thin-walled cover is stiff only by its corners: the middle of a side or an end bows out under a newton or so, and a catch there – on a sloping face, as any ledge inside a cover printed upside down must be – lets go as soon as a box of tissues leans on the lid. So the cover has four rails, short ledges inside its long sides, 9 mm along from each corner and 8 mm long: from 3 mm above the rim (the cover on) an upright face 1.2 mm tall, 1.6 mm in from the wall, then a side sloping back out to the wall at 40° from upright. Printed upside down, the flat side faces up and the sloping side down, so they need no supports. The rails' faces are straight – each rail fills the wall in as far as one line each side, 1.6 mm in from where the wall comes furthest in over the hooks' way – whatever a pattern does to the wall behind them. The long sides have at least 4.6 mm of room inside for the lid's hooks, the ends 2 mm more than the sides' usual; holes keep 13 mm clear of the rim, and their rounded edges' swell 8.5 mm.

Its lid is made from the cover as built: the plate is the outline of the rim, turned over as the cover is to go on, with a pull tab added at one end of the long way. It goes on 8 mm along from home, towards the tab, and slides back to lock:

• Four hooks, one behind each rail when the lid is home. Each is a post 2.4 mm thick, 0.3 mm in from its rail's face, with a claw reaching out over the rail to 0.35 mm from the wall; the claw's underside lies along the rail's sloping side. Where the lid is laid on there is no rail, and the hooks pass up beside the wall. Each claw's underside is 0.5 mm higher at its leading end, so the lid is drawn tight against the rim over the last of its slide; the grip is the gap left at home – 0.15, 0 or −0.15 mm, the last squeezing claw and rail together. For each hook the inside of the wall is measured at every row up from the rim, where it stands, where it goes in and all the way between; the hooks are then all one shape.
• A fence along each long side, 2 mm thick and 5 mm tall, which the hooks stand on: it keeps the plate from sagging under the box of tissues between the hooks. A lower one across the far end is the stop: it meets the inside of the cover's end, 0.15 mm off, when the lid is home.
• The latch: the plate's bar at the tab's end is narrow, clear of the box of tissues, and bends like a flat spring – printed flat, the strong way. On it is a ridge 1.8 mm tall, upright towards the cover's end and sloping the other way. As the lid slides on, the cover's rim rides up the slope, pressing the bar down, and the ridge springs up 0.35 mm inside the end: the lid can't slide back. Lifting the pull tab bends the bar away and frees it. A solid lid is the frame with a panel in it, a slit left between the panel and this bar.

So the lid hangs from rigid hooks on sloping faces that only wedge tighter, on the stiffest parts of the cover; it is kept from sliding by the stop and the latch; and nothing that holds it has to bend.

The pot is built on the grid, then the rows and columns that lie within 0.02 mm of the straight line between their neighbours are left out – on a box most of them, on a twisting vase few – and saving simplifies the mesh once more, merging triangles wherever the surface moves by no more than a few hundredths of a millimetre (pyfqmr in the app, meshoptimizer in the web version), keeping it closed.

Colours by a function are worked out at every point of the pot's grid, from the outer face, with the same variables as your own function. The grid keeps the rows and columns that hold where the colour changes as true as the wall, and no cell spans more than a fifth of a colour. Each filament's part is then the pot with the other colours cut away just as holes are – by how far, in mm, each point is from that filament's colours – so neighbouring parts share the edge between them and together hold the plastic of the whole. The floor, and a closed top's point, are a part each, in the colour most of the wall has where it meets them.

A drawn cross-section needn't have one radius in each direction – a lobe can swell past its neck – so it is built another way: as rows of points up the vase, each row the outline (blended into the second one, sized by the outline curve and turned by the twist) cut into the same number of points at even distances along it, the patterns pushed out square to it. Neighbouring rows join point to point, the bottom and top are filled by ear clipping, and any outline that crosses itself is refused, so every layer is still one simple loop. Softening limits how fast the size, the twist and the change of shape may go at any height where a face leans too far, and fades the patterns there gently.

Shapes are smoothed to the grid's own spacing, so sharp points and valleys that twist across it don't alias into rows of little teeth.

How far the wall leans is measured on the true surface normal: tan(lean) = r·|∂r/∂z| / √(r² + (∂r/∂θ)²), out or in alike. Soften to fit works in two steps. A shape twisting faster than its flanks can follow first has its flanks softened round each layer (a flank carried sideways at r·ω leans by r·ω·|r_θ| / √(r² + r_θ²)), so it stays one clean twisted shape. Then each column up the vase is limited to the slope the lean allows there – the largest surface under it and the smallest over it that keep within the limit, averaged – with the correction smoothed round the vase so neighbouring columns agree. Every finished triangle is then checked, and the limit tightened just round any that still lean too far.

.venv\Scripts\python -m tests.test_vase builds every gallery vase, a dozen surprises and some hard cases – drawn outlines among them – and checks that each is closed and watertight with outward faces, flat on the bed, within the overhang limit, and one closed loop at every height tested; that leans are measured right; that a cylinder has the right volume and capacity; that STL and 3MF files read back the same; that designs save and open; that your own function can reach nothing it shouldn't; that colour changes land on layers; and that a drawn outline goes through its points, matches the built-in shape it came from, holds what a round vase holds, is refused if it crosses itself, can be traced from a picture, and repeated a hundred times – narrowed to fit, checked, filled and built closed in a few seconds; that a normal print is the hollow pot, with the right volume, its colour bands parts that make it up exactly; and that every pattern of holes, on round and drawn shapes, twisting or not, makes a closed pot whose holes' sides lean no more than the limit but for short bridges at their points, that holds nothing, with an open bottom too – and Voronoi ovals that leave every wall between them as thick as set, and rounded edges that swell as set and keep within the limit; and that a closed top comes to a point over a small ceiling (drawn and banded too), a wall part way round stops where it should, a face's holes and nose are where they should be and print without support, and a design sized for a head fits it – the masks and helmet a head 57 cm round; that a tissue box cover clears its box of tissues by the room to spare everywhere inside, with its hole through the bottom layers alone, holes and bands and all, and that its lid, tried against the cover as it prints – plain, lace and lumpy – goes in beside the rails and lifts off there, slides home touching nothing but by its latch, and once home is caught by all four rails when pulled down, by the latch when pushed back, by the stop when pushed on and by the rails sideways; that colours by a function come as closed parts, one per filament, each just where the formula puts it and together the plastic of the whole – on a plain box, a textured twist and Voronoi lace – and that a seamless vase or facets stay one colour; and that the web version's Python, put together as the site has it, runs with no Qt at all – it starts, builds a mask, fits it to a head and makes the slicer's file. .venv\Scripts\python -m tests.test_app drives the window itself: edits, curves, undo, the gallery, Surprise me, every view, the print animation, saving and exporting, and drawing (with the mouse, close up and in a full window, zoomed with the wheel), repeating up to a hundred times and tracing a cross-section, and Simple mode: each kind of picture, the gallery of pictures, Save for printing with its steps and Open in slicer, bigger text and the light theme, and a mask sized by the head it fits, its face's settings and Undo. Test windows open on the second screen, if there is one.

Either can run just part of itself, for a quick check after a small change: name a word, and only the tests (or the window's sections) with it in their names run – tests.test_vase lid box runs the tissue box cover's and its lid's tests, tests.test_app box the window's tissue box section. The window's sections are edits, gallery, morph, views, saving, colours, drawn, simple, holes, masks, box, look and function; each starts from a design of its own, so any can run alone. A name that matches nothing lists them all.

The web version

The page runs the same Python as the desktop app – the parts of vaseinator that need no Qt: the geometry, the designs, the settings and their rules, the report and the exports – in the browser with Pyodide and numpy. It runs two web workers, so the page stays smooth: one builds the vase, the other answers everything else at once – what a change of setting brings with it, which settings to show, tracing a picture, fitting a head. web/bridge.py is the little bit between them and the page: it builds a vase and hands back its mesh as raw arrays, which the page draws with three.js, along with the desktop app's own report, the pictures' data and the print's timing, and makes the 3MF, STL and .vase files the page saves. The Advanced panel is made from the desktop app's own list of settings. A quick draft shows at once – and follows the hand while a curve or an outline is dragged – and the full detail follows a moment later. Nothing is sent anywhere: the vase is built on your own computer.

tools\build_web.py puts the site together in site\: the page, the Python and the gallery pictures, the page's files stamped with a version so that after an update a browser never mixes old files with new. To try it locally:

.venv\Scripts\python tools\build_web.py
.venv\Scripts\python -m http.server 8000 -d site

and open http://localhost:8000. GitHub Pages builds and publishes it the same way on every push to main.

License

MIT – see LICENSE.