Tag Archives: Non-Planar Printing

3D Printing: Slicing with Non-Planar Geometries


  • 2022/04/25: added single photo with various 20mm cube prints
  • 2022/04/01: rewording to avoid confusion of “planar slicing” with non-planar geometries
  • 2022/03/26: finally published
  • 2022/03/25: adding “Benefits of Non-Planar Printing” and “Blind Spots of CAD Systems” and “Scale and Functional Quality”
  • 2022/02/18: getting ready to publish
  • 2022/02/15: adding different slicing geometries and the resulting G-code
  • 2022/02/12: starting write-up


After researching non-planar slicing using planar slicers it was obvious to find a way to slice with any kind of geometry, and it meant to step back and formalize slicing procedure in a general manner like “Universal Slicing” – and look at the procedure of slicing itself.

Two classes were defined:

  • Class 1: using a geometry, either planar or non-planar, and slicing with a static slicing path
  • Class 2: slicing with variable slicing path and/or variable slicing geometry while slicing

This document/blog-post features a solution for Class 1 Universal Slicing.

My video Non-Planar 3D Printing: Slicing with Non-Planar Geometries goes through this information in an animated form, this is the textual form.

Slicing with Non-Planar Geometry (Class 1 Universal Slicing)

When using a static planar slicing vector one usually uses a plane, hence the term “planar slicing”, yet, there is also the possibility to use a non-planar geometry and slice in a planar direction (introducing ambiguity what planar and non-planar slicing actually mean). Regardless which slicing geometry is used in this procedure, the thickness of the sliced layer stays the same.

Slicing 20mm cube with wave-like geometry

In order to explore non-planar slices, using a wave-like geometry composed by Bezier curves and slice a 20mm cube:

Note: OpenSCAD is used solely used as 3D viewer, the slicing itself is performed by an experimental slicer.

Routing a single non-planar slice

A single slice is routed to wall/perimeter and infill extrusion:

There are several approaches to achieve this:

  • slice non-planar, map single slice 3d to 2d, route with 2d offsetting, and map back to 3d space (MetatronSlicer)
  • map entire mesh and slice planar, and map routes or resulting G-code back again (EnochSlicer)

and likely other more complex means.

Non-planar Printed Wave-like Sliced 20mm Cube

Preview of the complete G-code:

Preview the non-planar G-code of 20mm cube sliced with wave-like geometry

and a brief and fast printing simulation showing the entire print:

The computed G-code printed with a 3D printer, e.g. an ordinary 3-axis FDM:

Non-Planar 3D Printing: 20mm cube sliced with wave-like geometry (1x speed with a few skips)

and produces output like this:

left-to-right: wave-like geometry itself, progressive state of 20mm cube sliced with wave-like geometry at 0.25mm layer height

Implementing Non-Planar Slicing Geometries Slicer

The illustrations and actual G-code above were produced by two new in-house slicers which are in early development (2022/03):

20mm cube sliced with wave-like geometry
left-to-right: MetatronSlicer (0.0.7), EnochSlicer (0.0.2)
  • MetatronSlicer: boundary-based (BREP / OpenCASCADE) and voxel-based (OpenVDB) geometry engine, performing true non-planar slicing, and LabSlicer performing routing and G-code creation; slower slicing yet precise G-code
  • EnochSlicer: mesh and G-code transformation approach, fast slicing yet less accurate G-code

The extrusion precision is still rough, but overall concept and algorithms have been proven to work.

Results & Achievement

This work as presented here resolves a long pending issue of slicing meshs “non-planar”, or general “non-planar slicing” with all its inherent ambiguity – consider it as given that

one can use any 3D geometry with sufficient upper “surface” to slice a mesh with

and create printable G-code for 3- and 5-axis FDM:

  1. using a block as planar blueprint
  2. hemisphere, convex
  3. hemisphere reverse, concave
  4. cone, slicing conical like for Rotating Tilted Nozzle
  5. wave-like defined via Bezier curves
  6. wave-like defined via NURBS (Non-Uniform Rational B-Splines) curves
  7. tilted plane, slicing for belt printer with 45° tilted XY frame toward Z belt
  8. pimple-like

Along with volume segmentation as presented previously and conical, cylindrical and spherical slicing now any kind of slicing geometry can be used.

As pointed out in Universal Slicing, this “Planar Slicing with Non-Planar Geometries” is Class 1 of Universal Slicing whereas Class 2 covers changing slicing geometry and/or flexible slicing path along the slicing.

Limiting Non-Planar Height for 3-axis FDM

When using non-planar geometries to slice a model also non-planar G-code is produced and possibly significant Z motion occurs, and when printing with an ordinary 3-axis FDM 3D printer it may be suitable to limit the Z motion aka Z amplitude to 2-3mm in order to avoid part-cooler or other parts of the print head to collide with the already printed part:

left column: wave-like slicing, right column: hemisphere slicing
top row: full range, bottom row: limited to ~3mm Z amplitude

Future blog-posts will go into further details implementing Universal Slicing using those two slicers MetatronSlicer and EnochSlicer.

Regarding naming the slicers: Metatron is an archangel in jewish mythology – consider an “angel” as a fundamental intelligence, and in esoteric context Metatron is the being responsible for Form or Geometry itself – separating one into many in a spatial manner; whereas Enoch as a human, who ascended to become the archangel Metatron. I use those names in deep reverence for these two projects.

Blind Spot of CAD Systems

Current CAD systems (2022) neglect or actually are unaware of the inner vs outer structure – because only one kind of the “structure” is known, e.g. a piece is designed because of a certain function, which defines its outer form, e.g. a wrench to use a simple example – but how about the inner structure? This isn’t defined in the CAD, it is defined at the manufacturing stage, yet with 3D printing this can be described and designed even in a parametric way as well, the slicing or general 3D printing stage with different materials.

We require 2 or 3 abstraction layers to design a functional piece:

  1. the functional description (doesn’t exist yet)
  2. the inner structure (description how material is deposited in Additive Manufacturing, e.g. the infill geometry as of with FDM, incl. non-planar printing, or lattice structures as with SLA or SLS)
  3. the outer structure (e.g. mesh, boundaries)

So far CAD systems only covers the 3rd point, the outer structure.

The functional description is almost non-existent in the CAD world, and only becomes some attention when Finite Element Analysis is made and the form is changed, it is kind of hidden in plain sight.

In future blog-posts I will address and elaborate on these issues further.

Scale and Functional Qualities

To put the flexible slicing geometry in the grander context of 3D printing engineering:

3D printing engineering starts at nanometer scale (10-6mm) with material science level, over to filament composition at 1 to 10 micrometer scale (10-2mm) such as fibers, inner geometry where slicing geometry & procedure and infill geometry define strength properties at millimeter scale (100mm), and outer geometry with the shape of the object itself provide the final stage of mechanical properties.

This entire “scale chain” as a whole defines the mechanical property of the final 3D printed object.

That’s it.



Status: early development, not yet available


  • 2022/04/01: bringing terms/wording in-sync with Universal Slicing
  • 2022/02/26: published finally with basic information
  • 2022/02/18: copying content from “Universal Slicing” page start to focus on the slicer itself


MetatronSlicer aims to become full functional Universal Slicer:

Universal slicing means free slicing geometry along a free path.

“free (definable) slicing geometry”: any kind of geometry, may it may a solid or just a surface defining the slicing geometry.

“free (definable) path”: the slicing procedure can go in any direction, curvature and steps.

See Universal Slicing for more thorough description and theoretical examples.

Implementing Universal Slicing

As I was proposing the concept of “Universal Slicing”, I had the impulse to start an implementation right away in order to produce illustrations for the concept.

  • MetatronSlicer aims to become full Universal Slicer, it’s not optimized for speed but to be capable as of completeness.
  • EnochSlicer is a sister project which takes research results from development of MetatronSlicer and tries to find a more efficient way to achieve the same or a subset.

Universal Slicer: MetatronSlicer

MetatronSlicer is the first attempt of an Universal Slicer (2022/02), which implements for a start planar-slicing of non-planar slicing geometries, for example a wave-like geometry:

The wave-like geometry was defined via Bezier curves.

Via some transformations back and forth the in-house LabSlicer and g-code produced non-planar slice:

  • the green represents the ideal 3D slice,
  • the yellow/golden are the extrusions,
  • the red dots indicate the start of a G1 extrusion segment.

As of MetatronSlicer 0.0.8 (still very experimental as of 2022/02) it was possible to produce printable G-code:

and then printed on a 3-axis FDM (Ashtar K #2 Prusa-Mendel style) machine with apprx. 3mm vertical nozzle spacing 2), the wave-like reference geometry was slighted scaled in Z to comply to this physical contraint:

full print at 1x speed with a few skips
MetatronSlicer: toward implementing Universal Slicing capabilities

A few samples of non-planar geometries slicing 20mm cube:

Class 1 Universal Slicing: Planar Slicing with Non-Planar Geometries: cube (planar), hemisphere (convex), hemisphere inverse (concave), conic, wave-like, nurbs, tilted, pimple-like

Convex hemispherical slice geometry slicing 20mm cube:

Concave hemispherical slice geometry slicing 20mm cube:

Conic slice geometry slicing 20mm cube:

which essentially replaces Slicer4RTN.

As of 2022/02 MetatronSlicer is still in very early development, but eventually aims to implement also variable slicing geometries and variable slicing vector such as:

Class 2 Universal Slicing: Variable Slice Geometry / Variable Slicing Path

MetatronSlicer vs EnochSlicer

MetatronSlicer implements true non-planar slicing and routes each slice exact, whereas EnochSlicer using pre- and post transformation of mesh and routes (pre g-code).

As development of an Universal Slicer is in early stage (2022/03), both projects are pushed forward to see which one is more fit and suitable and cross-fertilize each other.

routededicated 1)
gcodededicated 1)native 2)
post processingplaintransformation


  1. utilizing LabSlicerCore library
  2. native via planar slicer (direct mesh to gcode) like CuraEngine


MetatronSlicer and alike EnochSlicer are in early development, and will be tuned for industrial 3D printing applications for 3- and 5-axis FDM.

Sometime during 2022 one or both might become available as commercial products in order to fund future development, unless I find another way to fund the research and development – in that case an open source “community edition” is possible.


In-House Slicers

– full planar slicer
– 4 stages: mesh, slice, route, gcode
– experimental
– API defined
– LabSlicerCore library
– import/export data of each stage
– voxel-based planar slicer
– fast slicing
– uses LabSlicerCore library for route and gcode stage
– OpenGL based planar slicer
– fast slicing
– uses LabSlicerCore library for route and g-code stage
– non-planar slicer
– implements Class 1 + 21) Universal Slicing
– uses OpenZCAD2) engine to slice non-planar
– non-planar slicer
– implements Class 1 + 21) Universal Slicing
– uses mesh & gcode transformation


  1. Class 2 Universal Slicing only partially implemented (status 2022/03)
  2. OpenZCAD is alike OpenSCAD but with Python as base-language with multiple backends (OpenCASCADE, LibFive, Fogleman’s SDF)

Universal Slicing


  • 2022/04/01: changing wording of “non-planar” vs “planar” slicing but describe actual slicing vector and geometry
  • 2022/03/26: published finally
  • 2022/03/24: added “Tensile & Shearing Force” illustration
  • 2022/03/10: added “Scale & Functional Qualities”
  • 2022/02/27: added Class 2 example
  • 2022/02/18: removed MetatronSlicer example and move to new page, keeping page focused on general and theoretical aspect of Universal Slicing
  • 2022/02/12: adding MetatronSlicer example as first attempt of an Universal Slicer
  • 2022/01/28: separating from another blog-post, solely focusing on Universal Slicing
  • 2022/01/16: starting write-up


While conceptualizing the in-house LabSlicer (2021/2022) and the two subsequent slicers afterwards (Vox3lSlicer & VoxGLSlicer), I realized it would be useful to formulate a general or universal description of slicing, hence I propose an universal definition of slicing as such:

Universal slicing means free slicing geometry along a free path.

“free (definable) slicing geometry”: any kind of geometry, may it be a solid or just a surface defining the slicing geometry.

“free (definable) path”: the slicing procedure can go in any direction, curvature and steps.

To put this in context:

  • “planar slicing” is plane or quasi box geometry with layer height thickness, sliced along a static 3D path vector of [ 0, 0, 1 ], aka “planar” or “Z-planar” with vector steps of [ 0, 0, layer height ], whereas layer height can change in that case it’s “variable” or “adaptive layer height”
  • “conic slicing” is a cone geometry with layer height thickness, sliced along a static path vector of [ 0, 0, 1 ] with vector steps of [ 0, 0, cos( layer height )] or scaling a stationary conic to match layer height
  • “cylindrical slicing” is a cylinder which stays positioned static at [ 0, 0, 0 ] and variable scaled to match layer height with [ s, s, 1 ], slicing pipe-like layers
  • “spherical slicing” is a sphere geometry with scales in size to match layer height, the position stays [ 0, 0, 0 ], whereas the geometry is scaled by [ s, s, s ], slicing thin sphere layers
SlicingSlicing GeometrySlicing VectorVector StepsGeometry Scale
planarplane[ 0, 0, 1 ][ 0, 0, t ][ 1, 1, 1 ]
coniccone[ 0, 0, 1 ][ 0, 0, t ][ 1, 1, 1 ]
cone[ 0, 0, 0 ][ 0, 0, 0 ][ s, s, s ]
cylindricalcylinder[ 0, 0, 0 ][ 0, 0, 0 ][ s, s, 1 ]
sphericalsphere[ 0, 0, 0 ][ 0, 0, 0 ][ s, s, s ]

The actual implementation, how slices are routed and then G-code is created, is up to the slicer; an Universal Slicer is a slicer which implements Universal Slicing paradigm.

Class 1: Static Slicing Vector, Static Slicing Geometry

There are two distinct cases of class 1 slicing:

  • slicing with planar geometry, a plane – also known as “planar slicing”
  • slicing with non-planar geometry, like a wave, a hemisphere, a cone, etc.

Static slicing vector means here, there is an equal distance among all points of a slice to the next or previous slice at the same [ x, y ] position according the slicing vector:

Class 1 Universal Slicing: Static Slicing Vector with Planar and Non-Planar Geometries

Regardless of the slicing geometry, the layer height or thickness remains the same along the slice or layer itself.

The layer height or thickness may vary from layer to layer, this is known as “variable layer height” or “adaptive layer height” but only means among layers or slices, but not within a single layer or slice.

Class 1 Examples

Examples of Class 1 Universal Slicing with planar and non-planar geometries and the respective G-code outputs (produced by MetatronSlicer and EnochSlicer):

Class 1 Universal Slicing: Planar Slicing with Non-Planar Geometries: planar, hemisphere convex, hemisphere concave, conic, wave-like Bezier & NURBS, tilted, pimple-like
  1. using a block as planar blueprint
  2. hemisphere, convex
  3. hemisphere reverse, concave
  4. cone, slicing conical like for Rotating Tilted Nozzle
  5. wave-like defined via Bezier curves
  6. wave-like defined via NURBS (Non-Uniform Rational B-Splines) curves
  7. tilted plane, slicing for belt printer with 45° tilted XY frame toward Z belt
  8. pimple-like

Class 2: Variable Slicing Vector or Variable Slicing Geometry

Variable slicing vector or changing slicing geometry (often refered as “non-planar slicing” without the specifics) means the slice itself has variable layer height or thickness – to be more precise:

  • change of slicing geometry, e.g. transitioning from one slicing geometry to another
  • change of slicing vector, e.g. change in steps, or curvature
Class 2 Universal Slicing: Variable Slicing Geometry, Variable Slicing Vector

It may not be always clear at first sight whether there is a transition of a slicing geometry or a change of slicing vector, as the changed slicing vector can also be looked as another slicing geometry – yet I think it makes more sense to differentiate between a slicing vector and slicing geometry when laying out a slicing procedure.

Class 2 Examples

Example of Class 2 of Universal Slicing (produced by EnochSlicer):

It is important to realize, that change of slicing geometry and/or slicing vector implies the slice or layer has variable thickness, hence, might have to comply with physical limits like maximum layer height printable with FDM and a given nozzle diameter – the actual implementation of an Universal Slicer has to adhere this.

Slicing Vector vs Slicing Geometry

Slicing VectorSlicing GeometrySlices / 3D PrintingSlice Thickness

Implementing Universal Slicing

The implementation of such Universal Slicing can be achieved in many ways and procedures. It is important to name features and describe what it they mean, such as:

  • Universal Slicing: is the ability to choose slice geometry and slice path freely
  • Universal Slicer: slicer which implements Universal Slicing in parts or fully – if it only implements part it shall be declared so
  • Class 1 Universal Slicing: static slicing path of [ 0, 0, 1 ], but with any kind of slicing geometry, static planar or static non-planar
  • Class 2 Universal Slicing: flexible slicing path, ability to change slicing geometry while slicing
ClassSlicing PathSlicing Geometry
Class 1staticstatic (planar or non-planar)
Class 2flexibleflexible (planar or non-planar)

Universal Slicers

  • MetatronSlicer (in-house XYZdims, status 2022/03):
    • slicing with (non-)planar geometries (Class 1)
    • partial support for slicing with change of slicing geometry (Class 2)
  • EnochSlicer (in-house XYZdims, status 2022/03):
    • slicing with (non-)planar geometries (Class 1)
    • partial support for slicing with change of slicing path & geometry (Class 2)
  • DotXControl 5-Axis Slicer (status 2022/03): supposedly supports Class 1 + 2 based on illustrations on the web-site
  • AI-Build (AI Build): requires NDA to even see a demo (!!) therefore difficult to conclude capabilities, might supports Class 1 + 2 based on illustrations and brief videos
MetatronSlicer: slicing with wave-like geometry a 20mm cube, printed with 3-axis FDM

Benefits of Non-Planar 3D Printing FDM

Layer adhesion tensile and shearing forces of planar and non-planar FDM
Fa = attacking force; Ft = tensile component of Fa; Fs = shearing component of Fa; β = tangent angle

One advantage resides in the ability to address FDM Z-layer adhesion issues by distributing force or stress vectors along any kind of trajectory and optimize material vs strength of the overall printed piece, e.g. when using continuous fiber filament and lay it along most stressed locations.

Further, the ability to have top layers align to object’s surface directly, no more layer lines. Essentially being able to define and manufacture a piece based on inner structure requirements and its outer form requirements.


3D Printing: Non-Planar “Balcony” Overhang with 3-axis FDM Printer


  • 2021/05/02: adding overhang-inout with 5 segments, with conic inside- and outside-cone mode
  • 2021/05/01: adding tilt sliced overhang segment variant as comparison
  • 2021/04/29: video uploaded and blog-post published
  • 2021/04/27: first successful tests with vertical nozzle (3-axis FDM printer)


The past few months and weeks I focused on the non-planar slicing, and the first tests with sub-volume segmenting and thereby mixing planar and non-planar sliced G-code worked as simulation, and now in actual prints.

One of the benchmarks are 90° overhangs in different directions, and I printed with vertical nozzle on an ordinary 3-axis FDM printer, therefore I prepared the G-code with a new tool (in-development) which coordinates segmenting and planar/non-planar slicing of sub-volumes, and the conic sliced segment was sliced with 25° conic angle so it remains printable with the vertical nozzle unlike the simulation where a 4- or 5-axis FDM printer is required:


Conic Sliced Overhang Segment

The simulation as reference:

and the actual print process with vertical nozzle on a low-cost 3-axis FDM printer:

Excerpt of the actual printing process with brief annotations:

Tilt Sliced Overhang Segment

Just for sake trying out, instead of conic sliced overhang segment, tilt sliced and 45° Z rotated to nicely extend to the maximum overhang position:

and the actual print of a slightly lower model but with the same features:

Comparing Tilted Sliced vs Conic Sliced Overhang Underside

Overhang In/Out: 2 Overhang Conic Segments

5 segments (bottom to top): z-planar, conic (inside-cone), z-planar, conic (outside-cone), z-planar

And revisiting the Overhang In/Out Model, which features ingoing and outgoing overhang, segmented into 5 sub-volumes:

  1. bottom: z-planar
  2. ingoing1) overhang: conic (inside-cone mode)
  3. middle: z-planar
  4. outgoing1) overhang: conic (outside-code mode)
  5. upper: z-planar

1) when dealing with conic slicing, the direction of overhang matters when deciding the mode of conic slicing, e.g. outside-cone or inside-cone.

and the actual print, a half of the model so the printing of inner overhang on the lower part of the model is visible:


It took me a few days to tune the 3-axis FDM printer to print in acceptable quality of this Overhang Model No 5 and also Overhang In/Out Model. A strong part-cooler was mandatory, well adjusted print temperature and slow perimeter as those extrusions align horizontally without vertical support; and it worked: the main idea is to segment and limit the overhang part to ~2mm thickness – a quasi “balcony” – which still allows a classic vertical nozzle with part-cooler to print such, and then switch back to planar printing again.

Vertical nozzle with part-cooler printing conic sliced overhang – a “balcony” – working with narrow margins

Detail settings: the conic overhang was sliced with Slicer4RTN with following settings slicer4rtn --slicer=cura-slicer --speed_wall=10 --speed_wall_0=10 --speed_wall_x=10 ... and since the Z-axis motion is limited to 4mm/s (M6 threaded rod, 1 rotation => 1mm) the overall printing speed is slow enough to provide acceptable print quality.


3D Printing: Multi-Axis Printing & Overhangs


  • 2021/03/14: more detailed references, published
  • 2021/03/11: starting write-up with basic illustration


I thought to compose a summary of the features of 3 types of 3D printers I currently work on, and its relations to print 90° overhangs – main motivation to go beyond 3-axis 3D printing:

Functionality Commonalities

  • a 5-axis printer PAX has the same features as a 4-axis printer RTN and 3-axis printer plus it can print at any tilt angle, printing 90° or more overhangs
  • a 4-axis printer RTN prints conic- or angled sliced models so it can print 90° overhangs in all directions (conic slice) from a central point or single direction (angled slice); the tilt angle is fixed at 45°; Z sliced horizontal layers must be post-processed1) to be printable in acceptable quality but good quality cannot be achived in my opinion
  • a 3-axis printer by default cannot print 90° overhangs without support (unless it’s tilted 45° as for belt-printer, then only in one direction), but may print conic sliced models with 20-25° cone angle, hence print 90° overhangs from a central point, and behave partially like a 4-axis printer
  1. a suitable Zrot must be calculated and added to extrusion commands of the G-code, see this example.

Printing an Conic Sliced Overhang

Conic sliced, in this case 45° conic angle, model nr 6 (table-like), with 45° tilted nozzle (simulation, animation)

Conic Sliced on 3-axis

A well tuned and well designed part-cooler is prerequisite to print conic-sliced models at cone angle of 20-25°, and currently there is no conic slicer which can properly segment sub-volumes yet (2021/03) to switch from horizontal- and conic-slicing (with two modes of outside/inside cone) where suitable.

Conic Sliced on 4-axis RTN

Conic- or angled slicing is recommended in order to print with Rotating Tilted Nozzle (RTN) or post-processing of existing horizontal sliced G-code is required to provide additional Zrot information to print in good quality.

Conic Sliced on 5-axis PAX

and nearly the same with PAX90 (tilt angle 0..90° only) with shorter arm:

A 5-axis Penta Axis (PAX) supports other slice methods than horizontal-, angled- or conic-sliced, but any variable build-orientation, but will make the slicing software very complex to recognize those sub-volumes suitable for advanced slicing methods.

This also means, a 5-axis PAX slicer with proper settings can produce G-code for 5-, 4- and 3-axis 3D printers with combining the horizontal-, angled- and cone slicing for sub-volumes or segments.

Traditionally Horizontal Layers

Slic3r 1.2.9 and Ultimaker Cura 4.8 as comparison:


That’s it.

3D Printing: 90° Overhangs without Support Structure with Non-Planar Slicing on 3-axis Printer


  • 2021/03/22: slicer4rtn released, see announcement
  • 2021/03/19: some information on use of slicer4rtn (not yet released)
  • 2021/03/09: removed lengthy “Test Protocol” and extended “Gallery” section a bit
  • 2021/03/08: slicer4rtn at 0.2.4 (still unreleased) resulting in better prints, blog-post linked at hackaday
  • 2021/03/05: 95° and 100° overhangs are printable too, more bug-fixes in slicer4rtn
  • 2021/03/04: fixing various bugs in slicer4rtn as disovered printing more complex pieces, supporting prusa-slicer as well aside slic3r, pushing the limits with overhangs
  • 2021/03/02: documenting my findings, a few photos, some early conclusions (not even one day old), conic sliced and tilt sliced.
90° Overhangs without support structure on 3-axis 3D printer


It has been target of many efforts to print 90° overhangs without support on 3-axis 3D printers as with ordinary Z slicing, each layer requires a support underneath; hence, every overhang then needs a support structure if the model itself doesn’t provide it.

But if . . . one slices non-planar? That’s what I thought about for a couple of years and kept it in the back of my mind. In January 2021 I came across Rotating Tilted Nozzle (RTN) aka RotBot as developed by ZHAW University of Applied Sciences Zurich (Switzerland). I began to design my own approach of the printhead and then started to code my own conic slicer (slicer4rtn), as the paper which might explain it wasn’t published yet by ZHAW.

While reflecting on the output of the 4-axis conic sliced models, I thought what if I simply make the cone angle flatter than 45° but 15-25° so the vertical nozzle can print it?

Overhang model conic sliced at 25° angle
slicer4rtn --angle=22.5 sliced overhang model, meant for 4-axis printer, but printed on 3-axis printer

Conic Slices Simulation

A simple overhang model (nr 3) conic sliced at 25° for 0.4mm nozzle, 0.2mm layer height:

Tilted Slices Simulation

The same overhang model (nr 3) tilt sliced at 25° for 0.4mm nozzle, 0.2mm layer height (like with belt printer):

Conic Slices Print Tests

And on the afternoon of March 1st 2021 I ran my G-code for the first time on an ordinary 3-axis printer, a cheap CTC DIY I3 Pro B (Prusa-i3 like), in the attempt to print 90° overhangs, with a conic sliced overhang model:

Wow – it seems to have worked! There were still some issues, like the nozzle without extrusion moved into the print as I forgot map linear motions without extrusion also to conic coordinates as well, and some other minor things.

You may consider this a “backport” of 4-axis slicing procedure back to a 3-axis 3D printing procedure.

Next Day Attempts

Conic Slices

The print is still pretty ugly due to the obvious under-extrusion, but the geometry seems to work overall. The overhang on the left-front isn’t evenly, as the outer wall print speed is still too high.

Tilted Slices

Very clean print so far but the overhang is limited to one direction (see below of overall considerations).


Well, it works, but here are some limitations of using non-planar slicing:

Conic Slices

  • conic sliced overhangs need to be going out- or inward from a central point
    • more complex pieces need to be volume decomposed or segmented, e.g. some sub-volume sliced ordinary vertically Z-wise, others conic sliced where needed – this is part of my research on 4-axis and 5-axis printers; and I was hoping some of the findings can be applied to 3-axis 3D printer as well (as this post shows)
  • the printhead geometry with heatblock sock, part-cooler, LED light they quickly come into way with larger pieces and larger overhangs
    • this might look minor, but part coolers play significant role for quality prints, so they need to be optimized for non-planar printing
  • cone angle
    • 15° works, sufficient space around the nozzle, but on the edge for overhangs, better surface quality
    • 20° works better, layers more stable beneath the overhang
    • 25° works too, but is the limit on my E3D V6 clone, poorer surface quality, but overhang prints better
  • print quality is sub-optiomal, as the nozzle runs over its own extruded filament and any “flat” surface becomes jittery as it’s not longer flat (toward Z) printed

Tilted Slices

  • single direction angled slice like with belt-printer
  • only one direction overhang possible, but good quality
  • tilt angle:
    • 25° works good, yet, the heatblock comes into the way rather quickly with my sample overhang model

Conic vs Tilted Slices

Issues to Resolve

  • more tests
  • more beautiful prints
    • fine tune extrusion rate: the current slicer4rtn does a simple/poor interpolation causing rough top surfaces (under- vs overextrusion)
    • fine tune outer wall of overhangs, slow them down
      • --slicer.external-perimeter-speed=10% (Slic3r)
  • support more slicers
    • Slic3r: supported since slicer4rtn 0.0.1
    • Prusa Slicer: supported since slicer4rtn 0.1.2 (0.1.1 was broken) but often refuses to slice model, e.g. cube fails in inverted cone space
    • Cura Engine: not yet
    • see Conic Slicing for RTN for up-to-date list
  • support skirts (again): due the slicer algorithm the skirt must omitted before pre-processing but be added at last stage or post-processing
  • redesign my part cooler so I can test print larger overhang pieces
  • find collision algorithm (along with given parametric printhead geometry), that’s part of the 4-axis and 5-axis slicing procedure
  • integrate it sub-volume segmenting framework to print complex pieces too


2-sided overhang model nr 4 (conic sliced)

Trying out an overhang model which extends -Y and Y (as side-ways the part-cooler comes into the way)

There are still inconsistencies with extrusion calculation, but the prints getting cleaner.

4-sided overhang model nr 6 (conic sliced)

Sample print comes soon as I need to redesign my part cooler so I can print this piece.

1-sided long 4mm thick overhang model nr 3 (conic sliced)

Long 40mm overhang, just 4mm thick extending nose . . .

1-sided long 2mm thick overhang model nr 3 (conic sliced)

Long 40mm overhang, just 2mm thin extending nose, let’s push the limits of what’s possible:

OK print so far, better than anticipated, but still a way to improve it. Reprint with a newer version of slicer4rtn (0.2.3):

  • better surface, no stringing anymore
  • faster print speed but also more geometric inconsistency like bending up
  • underside is more uneven but also cleaner than all the previous (pre- 0.2.0 of slicer4rtn)

1-sided short 2mm thick 95° overhang model nr 3 (conic sliced)

Just trying more overhang, let’s see.

Obviously there is more than 95° overhang possible, so let’s try …

1-sided short 2mm thick 100° overhang model nr 3 (conic sliced)

Even steeper overhang, let’s see.

This is truly promising, up to 100° overhangs printable with vertical nozzle as mounted on most 3-axis 3D printers . . .

Slicer4RTN Settings

As of the publication of this blog-post (2021/03) no slicer is available but slicer4rtn will be made available soon which was released 2021/03/22.

  • Caution: you need to be an experienced 3D printing enthusiast to proceed, you need to know and realize what you do:
    • pay close attention of the printhead geometry, such as the nozzle and heatblock, and the part cooler which limits the non-planar printing
    • depending on the angle, and the direction of extrusion more or less extrusion distortion will occur
Issues to look at when printing conic sliced models with vertical nozzle on a 3-axis 3D printer

  • --angle=20 is a good start, you may go as low as 15°, and perhaps at max at 30° depending on your nozzle and heatblock, if you aim to print 90° overhangs
  • --layer-height=0.2 is a good start too, the thinner the layers the better overhangs can be printed
  • if you have trouble with over- or under-extrusion and your printer otherwise well tuned, then use --erate=f as extrusion-rate tuning, whereas f = 0.5..1.5 or so, if you have to go below or above, something else is wrong.
  • conic slicing is complex(er), you need to think in new terms:
    • the slicing procedure requires a conic slicing center
      • to and from that center overhangs can be printed well
      • if you have multiple centers, slicer4rtn does not yet support volume segmenting to support multiple centers
      • slicer4rtn requires manually entered conic slicing center
    • it requires fine-grained faces so the slicing works well, use --subdivide=5 or higher for simple pieces, e.g. like a cube or low-poly models in generals

Tuning 3-axis 3D Printer

Following changes are recommended:

  • increase Z axis speed: within the start G-code the line M203 Z.. (replace .. with an actual number) to increase speed of Z-axis
    • depending on the pitch of your Z-lead screw or threaded rods, you may set it to Z4, Z6, or higher, so the motion speed comes close to X- and Y-axis to improve print quality
    • if it’s set too high, your stepper motor will block and not move at all
      • my setup with M6 threaded rod for Z (200 full steps = 1mm):
        • M203 Z8, 8mm/s => 8 revolutions/s => 1600 full steps/s: FAILED (blocked motor)
        • M203 Z6, 6mm/s => 6 revolutions/s => 1200 full steps/s: FAILED (stuttering motor at times, mechanical not reliable)
        • M203 Z4, 4mm/s => 4 revolutions/s => 800 full steps/s: OK
        • M203 Z3, 3mm/s -> 3 revolutions/s => 600 full steps/s: OK
    • leadscrew T8x2 (2mm lead per revolution) might support ~12mm/s
    • leadscrew T8x8 (8mm lead per revolution) might support ~50mm/s (ideal, matching X and Y)
  • slow down perimeter (overhangs): use --external-perimeter-speed=20% or a bit more, it prints overhangs better, leave it at 50% if prints look good
  • X- and Y axis speed: try to match your Z speed, so the overall printing is evenly:
    • Slic3r
      • perimeter-speed
      • bridge-speed
      • infill-speed
  • miscellaneous hints:
    • slicer setting solid-infill-below-area = 10 (make infill work at small(er) pieces too)



That’s it.

3D Printing: Conic Slicing for Rotating Tilted Nozzle (RTN) / 4 Axis

State: early draft, mostly simulations with a few tests with 3-axis printer only

Conic sliced overhang model with two overhangs, printing with Rotating Tilted Nozzle (RTN) 90° overhang structure without support structure


  • 2021/09/28: added reference to paper by ZHAW describing slicing procedure
  • 2021/03/22: slicer4rtn released, see dedicated page Slicer4RTN
  • 2021/03/16: removing details on slicer4rtn as a new dedicated page is in the working (coming soon)
  • 2021/03/08: slicer4rtn 0.2.3 reached (still unreleased), better prints, documenting various settings in more details
  • 2021/03/05: added proper ZHAW reference in the introduction and a few notes
  • 2021/02/27: removed some redundant illustrations and remade some of them, outside-cone vs inside-cone mode & printing
  • 2021/02/26: added inside-cone printing example for inner overhang mode, also early information of slicer4rtn; more animations to observe details of produced G-code, using now also OpenSCAD to simulate G-code and actual nozzle position
  • 2021/02/24: better tests with 20mm cube and overhang structure, included two short G-code simulations as videos, added 20mm sphere and 3D Benchy and discover first issues with volume decomposition and overhang recognition
  • 2021/02/23: first write up, pseudo code and first attempt to conic slice 20mm cube

As I progress I will update this blog-post.


The main idea is to utilize existing 3D printing slicers but create conic slices for the Rotating Tilted Nozzle (RTN) 4 Axis Printer. ZHAW published in their announcement in 2021/01 something about utilizing existing slicers, but the details remained concealed and later published as a paper but I did not want to wait and pondered on the problem, and came up with a solution. In its current state it’s purely theoretical and untested for now (2021/02) barely tested yet.

Michael Wüthrich confirmed my solution is comparable with their solution. ZHAW planned their paper to be published sometime 2021. So, the main credit goes to ZHAW and the researchers (Prof. Dr. Wilfried Elspass, Dr. Christian Jaeger, Michael Wüthrich, Maurus Gubser, Philip Bos and Simon Holdener) there, I was just impatient and tried to find a solution with the information available.

I also adapted some of the notions Wüthrich introduced in the Novel 4-Axis 3D Printing Process to Print Overhangs Without Support Material paper, e.g. “outside-cone” and “inside-cone” printing as featured in an earlier blog-post already.

Non-Planar Conic Slices

The 4-axis Rotating Tilted Nozzle (RTN) physical setup implies its slices are of non-planar conic shape, allowing to print overhangs without support structure, such as:

Conic slices of an overhang model

I also like to master the conic slices properly as they promise to become a subset of 5 axis printhead (PAX) features too – so it’s worth the effort even if the RTN itself might be too limited in its application with its fixed tilt – we will see.


In a nutshell the steps are following:

  1. sub-divide faces of the model (fine-grained)
  2. map model to inverse conic space
  3. send to slicer
  4. remap G-code to conic space
  5. adding Zrot to G-code

Conic Space Mapping

(x1,y1,z1,rot) = conicSpaceMapping(cx,cy,x,y,z,dir);


  • cx, cy are the conic axis coordinates
  • x, y, z are the input coordinates
  • x1, y1, z1 are the output coordinates
  • rot the rotation angle x,y vs cx,cy
  • dir is either direct (default) or inverse
function conicSpaceMapping(cx,cy,x,y,z,dir='direct') {
   dx = x-cx; 
   dy = y-cy;
   d = sqrt(dx*dx + dy*dy);
   rot = atan2(dy,dx);
   return (x,y,dir=="direct" ? z-d : z+d,rot);


The entire procedure goes like this:

m = loadModel("cube.stl");
m = subDivide(m,5);
for(p of m.vertices) {
    m.vertices[i] = conicSpaceMapping(cx,cy,p.x,p.y,p.z,'inverse');

gcode = sliceModel(m);

foreach(line of gcode) {
   (code,x,y,z,e) = extractCoordsExtrusion(line);
   (x1,y1,z1,zrot) = conicSpaceMapping(cx,cy,x,y,z,'direct');

Note: the pseuco-code is incomplete as extrusion E is not yet taken care of, as soon I found a definitive solution I will write it up.


I implemented the pseudo-code with some more details like taking care of G-code E extrusion as well and fine-step linear extrusion – here some early tests using OpenSCAD as STL & G-code viewer and Slic3r as actual slicer:

20mm Cube Conic Sliced

Snapshots of progress of conic sliced 20mm cube:

20mm cube conic sliced G-code
20mm cube conic sliced with rotating tilted nozzle simulation

Overhang Conic Sliced

Snapshots of progress of conic sliced Overhang:

Conic sliced overhang model
Conic sliced overhang model including rotating tilted nozzle simulation

Gallery of Conic Sliced Models

Detailed snapshots of overhang nr 3

Detailed snapshots of model nr 6 (table-like)

Some more models with their in-between states, using Cura as model and G-code viewer:

Issues to Resolve

  • test actual G-code in real life
  • find good pre-processing face sub-division strategy
    • in its current form the algorithm requires fine-grained sub-divided faces otherwise inaccurate G-code is created which cannot be recovered
  • slice more complex parts
  • document all details
  • release source code to public


Some close-ups of conic sliced models:

Outside- vs Inside-Cone Printing

As pointed out in the previous blog-post, the RTN has two main modes of operation, outside-cone and inside-cone printing to cover outside overhangs and inside overhangs – the slicer must recognize those and switch operation mode. Further, these two modes cannot easily be mixed, and need to be segmented or separated, hence speaking of volume segmentation.

This poses significant grow of complexity from just planar slicing, the 4-axis RTN provides features to print 90° overhangs without support structure, but only when the part can be properly analysed and segmented so that those operational mode can be applied.

The difference between inside- and outside-cone printing is to change the order of conic mapping for the model and post slicing:

outside-cone mode

  1. map model inverse conic
  2. slice model
  3. map G-code direct conic

inside-cone mode

  1. map model direct conic
  2. slice model
  3. map G-code inverse conic, Zrot + 180°


The pseudo-code turned into an actual application I named slicer4rtn and is a command-line tool, slicing STL into G-code:

% slicer4rtn --subdivide=5 --recenter cube.stl
== Slicer4RTN 0.4.1 ==
processing 'cube.stl':
   1/5 read stl
      1/5 subdivide (44 vertices)
      2/5 subdivide (188 vertices)
      3/5 subdivide (764 vertices)
      4/5 subdivide (3068 vertices)
      5/5 subdivide (12284 vertices)
   2/5 map vertices
   3/5 write temporary stl
   4/5 slice (slic3r) stl
=> Processing triangulated mesh
=> Generating perimeters
=> Preparing infill
=> Infilling layers
=> Exporting G-code to ./temp-603919.gcode
Done. Process took 0 minutes and 1.362 seconds
Filament required: 710.9mm (5.0cm3)
   5/5 remap gcode to 'cube.gcode' (16214 lines)
== took 3 secs total, done.

I gonna released Slicer4RTN eventually 2021/03/22, in its early version the model currently can only be sliced for outside-cone or inside-cone printing, so the volume decomposition or segmentation needs to be done separately. For now it helps me to verify some of the 4-axis and 5-axis printer designs I work on.

Ashtar K RTN printing conic sliced 20mm cube (close up, animation)
Ashtar K RTN printing conic sliced overhang model without support structure (close up, animation)
Ashtar K RTN printing conic sliced overhang model nr 6 (table-like) without support structure (close up, animation)

Test Prints

As soon I built the RTN printhead on one of my printers I will post photos of the first prints. For now (2021/03) I only printed conic sliced pieces on a 3-axis 3D printer.


See Also

With conic sliced G-code there are many first layers . . .

That’s it.