<h2>Degrees of freedom</h2>
<p>2D has <strong>3</strong> degrees of freedom: X, Y, and a single rotation. As a result, you can describe any object in 2D by defining its center position and the rotation its surface start point is at and then referencing its shape.</p>
<p>3D has <strong>6</strong> degrees of freedom: X, Y, and Z position, and the rotation around each of the axes. Describing a 3D object is much more complicated.</p>
<p>Printers usually work with fully constrained rotations after the slicing. Traditional machining has limited Z accessibility without a 4th axis or using a 5-axis arm, and is limited in depth by the length of tooling.</p>
<h2>Slicing is a number of mathematical 2D processes</h2>
<p>When slicing, the slicer creates slices of a layer thickness. These then are interpreted by projecting to the center the smallest outline that would fit everywhere in the body and raising that outline to the center of the slice.</p>
<p>The stack of outlines is pretty much the outer surface reduced to a number of 2D objects. As placing the object already fixed its rotation, this leaves each outline to be solved for 2 variables for the toolpath: X and Y.</p>
<p>Just stacking all these results in a 3D object in the end.</p>
<h2>2.5D is a machining term</h2>
<p>Traditional machining creates 3D objects. However, <a href="https://en.wikipedia.org/wiki/2.5D_(machining)" rel="nofollow noreferrer">machining with a 2.5D setup</a> does not create undercuts, as it only uses cylindrical tooling in most cases. This machining works by projecting the top item onto a plane and having at most one Z coordinate. That means one can easily create a &quot;height map&quot; of the item's surface.</p>
<p>The surfaces in nonplanar mapping are similar: the top examples have a lot of traditional 2D solved printing and a single top layer that follows a 2.5D machine path - which is, remind you, a simplified 3D coordinate system.</p>
<p>By only solving the last layer for X, Y, and Z path coordinates and banning undercuts, the solving time can be massively reduced, leading to faster slicing and allowing more time spent on refining the print paths. 2.5 D path solution algorithms also are much better explored from traditional machining, while true 3D machining requires the machining tool to move with all degrees of freedom.</p>
<h2>Layered 2.5 D</h2>
<p>Example (a) below breaks from traditional 2.5 D but can be reduced back to 2.5 D. Cutting the item in non-planar layers that follow the bottom geometry, that geometry can be solved as a 2.5 D machine path, and then the next layer is solved with an offset above that. However, cutting an item non-planarly can become very complicated, especially with more complex geometry than a simple arch.</p>

CC BY-SA 4.0
2024-02-02T09:34:25.423Z
2024-02-04T18:29:59.290Z
2024-02-04T18:29:59.290Z
Trish
<p>Why do most slicers slice, and printers print in 2.5D, a planar method, rather than an actual 3D non-planar method? Doesn't this mainly come down to slicer software limitations rather than hardware limitations?</p>
<p>The results, in many cases, seem so much better. As shown below:</p>
<p><a href="https://i.sstatic.net/dqaOx.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/dqaOx.jpg" alt="planar vs. non-planar prints" /></a>
<a href="https://i.sstatic.net/pK2MW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/pK2MW.png" alt="planar vs. non-planar prints" /></a></p>

<slicing><fdm><planar><non-planar>
Why is 'planar-2.5D-slicing' most commonly used instead of 'non-planar-3D-slicing'?
Bob Ortiz
# Why is 'planar-2.5D-slicing' most commonly used instead of 'non-planar-3D-slicing'?

(Asked by: username_0 on 2023-11-28)

Why do most slicers slice, and printers print in 2.5D, a planar method, rather than an actual 3D non-planar method? Doesn't this mainly come down to slicer software limitations rather than hardware limitations?

The results, in many cases, seem so much better. As shown below:

[![planar vs. non-planar prints](https://i.sstatic.net/dqaOx.jpg)](https://i.sstatic.net/dqaOx.jpg)
[![planar vs. non-planar prints](https://i.sstatic.net/pK2MW.png)](https://i.sstatic.net/pK2MW.png)

**Tags:** slicing, fdm, planar, non-planar

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## 1 answers

### Answer by username_1 on 2024-02-02. Score: 2 | Accepted answer

## Degrees of freedom

2D has **3** degrees of freedom: X, Y, and a single rotation. As a result, you can describe any object in 2D by defining its center position and the rotation its surface start point is at and then referencing its shape.

3D has **6** degrees of freedom: X, Y, and Z position, and the rotation around each of the axes. Describing a 3D object is much more complicated.

Printers usually work with fully constrained rotations after the slicing. Traditional machining has limited Z accessibility without a 4th axis or using a 5-axis arm, and is limited in depth by the length of tooling.

## Slicing is a number of mathematical 2D processes

When slicing, the slicer creates slices of a layer thickness. These then are interpreted by projecting to the center the smallest outline that would fit everywhere in the body and raising that outline to the center of the slice.

The stack of outlines is pretty much the outer surface reduced to a number of 2D objects. As placing the object already fixed its rotation, this leaves each outline to be solved for 2 variables for the toolpath: X and Y.

Just stacking all these results in a 3D object in the end.

## 2.5D is a machining term

Traditional machining creates 3D objects. However, [machining with a 2.5D setup](https://en.wikipedia.org/wiki/2.5D_(machining)) does not create undercuts, as it only uses cylindrical tooling in most cases. This machining works by projecting the top item onto a plane and having at most one Z coordinate. That means one can easily create a "height map" of the item's surface.

The surfaces in nonplanar mapping are similar: the top examples have a lot of traditional 2D solved printing and a single top layer that follows a 2.5D machine path - which is, remind you, a simplified 3D coordinate system.

By only solving the last layer for X, Y, and Z path coordinates and banning undercuts, the solving time can be massively reduced, leading to faster slicing and allowing more time spent on refining the print paths. 2.5 D path solution algorithms also are much better explored from traditional machining, while true 3D machining requires the machining tool to move with all degrees of freedom.

## Layered 2.5 D

Example (a) below breaks from traditional 2.5 D but can be reduced back to 2.5 D. Cutting the item in non-planar layers that follow the bottom geometry, that geometry can be solved as a 2.5 D machine path, and then the next layer is solved with an offset above that. However, cutting an item non-planarly can become very complicated, especially with more complex geometry than a simple arch.


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