klipper/docs/Bed_Mesh.md

The Bed Mesh module may be used to compensate for bed surface irregularties to
achieve a better first layer across the entire bed.  It should be noted that
software based correction will not achieve perfect results, it can only
approximate the shape of the bed.  Bed Mesh also cannot compensate for
mechanical and electrical issues.  If an axis is skewed or a probe is not
accurate then the bed_mesh module will not receive accurate results from
the probing process.

Prior to Mesh Calibration you will need to be sure that your Probe's
Z-Offset is calibrated.  If using an endstop for Z homing it will need
to be calibrated as well.  See [Probe_Calibrate](Probe_Calibrate.md)
and Z_ENDSTOP_CALIBRATE in [Manual_Level](Manual_Level.md) for more
information.

## Basic Configuration

### Rectangular Beds
This example assumes a printer with a 250 mm x 220 mm rectangular
bed and a probe with an x-offset of 24 mm and y-offset of 5 mm.

```
[bed_mesh]
speed: 120
horizontal_move_z: 5
mesh_min: 35,6
mesh_max: 240, 198
probe_count: 5,3
```

- `speed: 120`\
  _Default Value: 50_\
  The speed in which the tool moves between points.

- `horizontal_move_z: 5`\
  _Default Value: 5_\
  The Z coordinate the probe rises to prior to traveling between points.

- `mesh_min: 35,6`\
  _Required_\
  The first probed coordinate, nearest to the origin.  This coordinate
  is relative to the probe's location.

- `mesh_max: 240,198`\
  _Required_\
  The probed coordinate farthest farthest from the origin.  This is not
  necessarily the last point probed, as the probing process occurs in a
  zig-zag fashion.  As with `mesh_min`, this coordiante is relative to
  the probe's location.

- `probe_count: 5,3`\
  _Default Value: 3,3_\
  The number of points to probe on each axis, specified as x,y integer
  values.  In this example 5 points will be probed along the X axis, with
  3 points along the Y axis, for a total of 15 probed points.  Note that
  if you wanted a square grid, for example 3x3, this could be specified
  as a single integer value that is used for both axes, ie `probe_count: 3`.
  Note that a mesh requires a minimum probe_count of 3 along each axis.

The illustration below demonstrates how the `mesh_min`, `mesh_max`, and
`probe_count` options are used to generate probe points.  The arrows indicate
the direction of the probing procedure, beginning at `mesh_min`.  For reference,
when the probe is at `mesh_min` the nozzle will be at (11, 1), and when the probe
is at `mesh_max`, the nozzle will be at (206, 193).

![bedmesh_rect_basic](img/bedmesh_rect_basic.svg)

### Round beds
This example assumes a printer equipped with a round bed radius of 100mm.
We will use the same probe offsets as the rectangular example, 24 mm on X
and 5 mm on Y.

```
[bed_mesh]
speed: 120
horizontal_move_z: 5
mesh_radius: 75
mesh_origin: 0,0
round_probe_count: 5
```

- `mesh_radius: 75`\
  _Required_\
  The radius of the probed mesh in mm, relative to the `mesh_origin`.  Note
  that the probe's offsets limit the size of the mesh radius.  In this example,
  a radius larger than 76 would move the tool beyond the range of the printer.

- `mesh_origin: 0,0`\
  _Default Value: 0,0_\
  The center point of the mesh.  This coordinate is relative to the probe's
  location. While the default is 0,0, it may be useful to adjust the origin
  in an effort to probe a larger portion of the bed.  See the illustration
  below.

- `round_probe_count: 5`\
  _Default Value: 5_\
  This is an integer value that defines the maximum number of probed points
  along the X and Y axes.  By "maximum", we mean the number of points probed
  along the mesh origin.  This value must be an odd number, as it is required
  that the center of the mesh is probed.

The illustration below shows how the probed points are generated.  As you can see,
setting the `mesh_origin` to (-10, 0) allows us to specifiy a larger mesh radius
of 85.

![bedmesh_round_basic](img/bedmesh_round_basic.svg)

## Advanced Configuration

Below the more advanced configuration options are explained in detail.  Each
example will build upon the basic rectangular bed configuration shown above.
Each of the advanced options apply to round beds in the same manner.

### Mesh Interpolation

While its possible to sample the probed matrix directly using simple bilinear
interpolation to determine the Z-Values between probed points, it is often
useful to interpolate extra points using more advanced interpolation algorithms
to increase mesh density.  These algorithms add curvature to the mesh,
attempting to simulate the material properties of the bed.  Bed Mesh offers
lagrange and bicubic interpolation to accomplish this.

```
[bed_mesh]
speed: 120
horizontal_move_z: 5
mesh_min: 35,6
mesh_max: 240, 198
probe_count: 5,3
mesh_pps: 2,3
algorithm: bicubic
bicubic_tension: 0.2
```

- `mesh_pps: 2,3`\
  _Default Value: 2,2_\
  The `mesh_pps` option is shorthand for Mesh Points Per Segment.  This
  option specifies how many points to interpolate for each segment along
  the x and y axes.  Consider a 'segment' to be the space between each
  probed point. Like `probe_count`, `mesh_pps` is specified as an x,y
  integer pair, and also may be specified a single integer that is applied
  to both axes.  In this example there are 4 segments along the X axis
  and 2 segments along the Y axis.  This evaluates to 8 interpolated
  points along X, 6 interpolated points along Y, which results in a 13x8
  mesh.  Note that if mesh_pps is set to 0 then mesh interpolation is
  disabled and the probed matrix will be sampled directly.

- `algorithm: lagrange`\
  _Default Value: lagrange_\
  The algorithm used to interpolate the mesh.  May be `lagrange` or `bicubic`.
  Lagrange interpolation is capped at 6 probed points as oscillation tends to
  occur with a larger number of samples.  Bicubic interpolation requires a
  minimum of 4 probed points along each axis, if less than 4 points are
  specified then lagrange sampling is forced.  If `mesh_pps` is set to 0 then
  this value is ignored as no mesh interpolation is done.

- `bicubic_tension: 0.2`\
  _Default Value: 0.2_\
  If the `algorithm` option is set to bicubic it is possible to specify the
  tension value.  The higher the tension the more slope is interpolated.  Be
  careful when adjusting this, as higher values also create more overshoot,
  which will result in interpolated values higher or lower than your probed
  points.

The illustration below shows how the options above are used to generate an
interpolated mesh.

![bedmesh_interpolated](img/bedmesh_interpolated.svg)

### Move Splitting

Bed Mesh works by intercepting gcode move commands and applying a transform
to their Z coordinate. Long moves must be and split into smaller moves
to correctly follow the shape of the bed. The options below control the
splitting behavior.

```
[bed_mesh]
speed: 120
horizontal_move_z: 5
mesh_min: 35,6
mesh_max: 240, 198
probe_count: 5,3
move_check_distance: 5
split_delta_z: .025
```

- `move_check_distance: 5`\
  _Default Value: 5_\
  The minimum distance to check for the desired change in Z before performing
  a split.  In this example, a move longer than 5mm will be traversed by the
  algorithm.  Each 5mm a mesh Z lookup will occur, comparing it with the Z
  value of the previous move.  If the delta meets the threshold set by
  `split_delta_z`, the move will be split and traversal will continue.  This
  process repeats until the end of the move is reached, where a final
  adjustment will be applied.  Moves shorter than the `move_check_distance`
  have the correct Z adjustment applied directly to the move without
  traversal or splitting.

- `split_delta_z: .025`\
  _Default Value: .025_\
  As mentioned above, this is the minimum deviation required to trigger a
  move split.  In this example, any Z value with a deviation +/- .025mm
  will trigger a split.

Generally the default values for these options are sufficient, in fact the
default value of 5mm for the `move_check_distance` may be overkill. However an
advanced user may wish to experiment with these options in an effort to squeeze
out the optimial first layer.

### Mesh Fade

When "fade" is enabled Z adjustment is phased out over a distance defined
by the configuration.  This is accomplished by applying small adjustments
to the layer height, either increasing or decreasing depending on the shape
of the bed. When fade has completed, Z adjustment is no longer applied,
allowing the top of the print to be flat rather than mirror the shape of the
bed.  Fade also may have some undesirable traits, if you fade too quickly it
can result in visible artifacts on the print.  Also, if your bed is
significantly warped, fade can shrink or stretch the Z height of the print.
As such, fade is disabled by default.

```
[bed_mesh]
speed: 120
horizontal_move_z: 5
mesh_min: 35,6
mesh_max: 240, 198
probe_count: 5,3
fade_start: 1
fade_end: 10
fade_target: 0
```

- `fade_start: 1`\
  _Default Value: 1_\
  The Z height in which to start phasing out adjustment.  It is a good idea
  to get a few layers down before starting the fade process.

- `fade_end: 10`\
  _Default Value: 0_\
  The Z height in which fade should complete.  If this value is lower than
  `fade_start` then fade is disabled.  This value may be adjusted depending
  on how warped the print surface is.  A significantly warped surface should
  fade out over a longer distance.  A near flat surface may be able to reduce
  this value to phase out more quickly.  10mm is a sane value to begin with if
  using the default value of 1 for `fade_start`.

- `fade_target: 0`\
  _Default Value:  The average Z value of the mesh_\
  The `fade_target` can be thought of as an additional Z offset applied to the
  entire bed after fade completes.  Generally speaking we would like this value
  to be 0, however there are circumstances where it should not be.  For
  example,  lets assume your homing position on the bed is an outlier, its
  .2 mm lower than the average probed height of the bed.  If the `fade_target`
  is 0, fade will shrink the print by an average of .2 mm across the bed.  By
  setting the `fade_target` to .2, the homed area will expand by .2 mm, however
  the rest of the bed will have an accurately sized.  Generally its a good idea
  to leave `fade_target` out of the configuration so the average height of the
  mesh is used, however it may be desirable to manually adjust the fade target
  if one wants to print on a specific portion of the bed.

### The Relative Reference Index

Most probes are suceptible to drift, ie: inaccuracies in probing introduced by
heat or interference.  This can make calculating the probe's z-offset
challenging, particuarly at different bed temperatures.  As such, some printers
use an endstop for homing the Z axis, and a probe for calibrating the mesh.
These printers can benefit from configuring the relative reference index.

```
[bed_mesh]
speed: 120
horizontal_move_z: 5
mesh_min: 35,6
mesh_max: 240, 198
probe_count: 5,3
relative_reference_index: 7
```

- `relative_reference_index: 7`\
  _Default Value: None (disabled)_\
  When the probed points are generated they are each assigned an index.  You
  can look up this index in klippy.log or by using BED_MESH_OUTPUT (see the
  section on Bed Mesh GCodes below for more information).  If you assign an
  index to the `relative_reference_index` option, the value probed at this
  coordinate will replace the probe's z_offset.  This effectively makes
  this coordinate the "zero" reference for the mesh.

When using the relative reference index, you should choose the index nearest
to the spot on the bed where Z endstop calibration was done.  Note that
when looking up the index using the log or BED_MESH_OUTPUT, you should use
the coordinates listed under the "Probe" header to find the correct index.

### Faulty Regions

It is possible for some areas of a bed to report inaccurate results when
probing due to a "fault" at specific locations.  The best example of this
are beds with series of integrated magnets used to retain removable steel
sheets.  The magnetic field at and around these magnets may cause an inductive
probe to trigger at a distance higher or lower than it would otherwise,
resulting in a mesh that does not accurately represent the surface at these
locations.  **Note: This should not be confused with probe location bias, which
produces inaccurate results across the entire bed.**

The `faulty_region` options may be configured to compensate for this affect.
If a generated point lies within a faulty region bed mesh will attempt to
probe up to 4 points at the boundaries of this region.  These probed values
will be averaged and inserted in the mesh as the Z value at the generated
(X, Y) coordinate.

```
[bed_mesh]
speed: 120
horizontal_move_z: 5
mesh_min: 35,6
mesh_max: 240, 198
probe_count: 5,3
faulty_region_1_min: 130.0, 0.0
faulty_region_1_max: 145.0, 40.0
faulty_region_2_min: 225.0, 0.0
faulty_region_2_max: 250.0, 25.0
faulty_region_3_min: 165.0, 95.0
faulty_region_3_max: 205.0, 110.0
faulty_region_4_min: 30.0, 170.0
faulty_region_4_max: 45.0, 210.0
```

- `faulty_region_{1...99}_min`\
  `faulty_region_{1..99}_max`\
  _Default Value: None (disabled)_\
  Faulty Regions are defined in a way similar to that of mesh itself, where
  minimum and maximum (X, Y) coordinates must be specified for each region.
  A faulty region may extend outside of a mesh, however the alternate points
  generated will always be within the mesh boundary.  No two regions may
  overlap.

The image below illustrates how replacement points are generated when
a generated point lies within a faulty region.  The regions shown match those
in the sample config above.  The replacement points and their coordinates
are identified in green.

![bedmesh_interpolated](img/bedmesh_faulty_regions.svg)

## Bed Mesh Gcodes

### Calibration

`BED_MESH_CALIBRATE METHOD=[manual | automatic] [<probe_parameter>=<value>]
 [<mesh_parameter>=<value>]`\
_Default Method:  automatic if a probe is detected, otherwise manual_

Initiates the probing procedure for Bed Mesh Calibration.  If `METHOD=manual`
is selected then manual probing will occur.  When switching between automatic
and manual probing the generated mesh points will automatically be adjusted.

It is possible to specify mesh parameters to modify the probed area.  The
following parameters are available:
- Rectangular beds (cartesian):
  - `MESH_MIN`
  - `MESH_MAX`
  - `PROBE_COUNT`
- Round beds (delta):
  - `MESH_RADIUS`
  - `MESH_ORIGIN`
  - `ROUND_PROBE_COUNT`
- All beds:
  - `RELATIVE_REFERNCE_INDEX`
  - `ALGORITHM`
See the configuration documentation above for details on how each parameter
applies to the mesh.

### Profiles

`BED_MESH_PROFILE SAVE=name LOAD=name REMOVE=name`

After a BED_MESH_CALIBRATE has been performed, it is possible to save the
current mesh state into a named profile.  This makes it possible to load
a mesh without re-probing the bed.  After a profile has been saved using
`BED_MESH_PROFILE SAVE=name` the `SAVE_CONFIG` gcode may be executed
to write the profile to printer.cfg.

Profiles can be loaded by executing `BED_MESH_PROFILE LOAD=name`.

It should be noted that each time a BED_MESH_CALIBRATE occurs, the current
state is automatically saved to the _default_ profile.  If this profile
exists it is automatically loaded when Klipper starts.  If this behavior
is not desirable the _default_ profile can be removed as follows:

`BED_MESH_PROFILE REMOVE=default`

Any other saved profile can be removed in the same fashion, replacing
_default_ with the named profile you wish to remove.

### Output

`BED_MESH_OUTPUT PGP=[0 | 1]`

Outputs the current mesh state to the terminal.  Note that the mesh itself
is output

The PGP parameter is shorthand for "Print Generated Points".  If `PGP=1` is
set, the generated probed points will be output to the terminal:

```
// bed_mesh: generated points
// Index | Tool Adjusted | Probe
// 0 | (11.0, 1.0) | (35.0, 6.0)
// 1 | (62.2, 1.0) | (86.2, 6.0)
// 2 | (113.5, 1.0) | (137.5, 6.0)
// 3 | (164.8, 1.0) | (188.8, 6.0)
// 4 | (216.0, 1.0) | (240.0, 6.0)
// 5 | (216.0, 97.0) | (240.0, 102.0)
// 6 | (164.8, 97.0) | (188.8, 102.0)
// 7 | (113.5, 97.0) | (137.5, 102.0)
// 8 | (62.2, 97.0) | (86.2, 102.0)
// 9 | (11.0, 97.0) | (35.0, 102.0)
// 10 | (11.0, 193.0) | (35.0, 198.0)
// 11 | (62.2, 193.0) | (86.2, 198.0)
// 12 | (113.5, 193.0) | (137.5, 198.0)
// 13 | (164.8, 193.0) | (188.8, 198.0)
// 14 | (216.0, 193.0) | (240.0, 198.0)
```

The "Tool Adjusted" points refer to the nozzle location for each point, and
the "Probe" points refer to the probe location.  Note that when manually
probing the "Probe" points will refer to both the tool and nozzle locations.

### Clear Mesh State

`BED_MESH_CLEAR`

This gcode may be used to clear the internal mesh state.

### Apply X/Y offsets

`BED_MESH_OFFSET [X=<value>] [Y=<value>]`

This is useful for printers with multiple independent extruders, as an offset
is necessary to produce correct Z adjustment after a tool change.  Offsets
should be specified relative to the primary extruder.  That is, a positive
X offset should be specified if the secondary extruder is mounted to the
right of the primary extruder, and a positive Y offset should be specified
if the secondary extruder is mounted "behind" the primary extruder.