Fix bed mesh algorithm for 3 point bicubic algorightm

[igiannakas]

Description

Fixes #4875, #4694

Checks the below conditions for Klipper firmware:

1. If the total number of mesh points is 6 -> use Lagrange interpolation
2. If the total number of mesh points is greater than 6, use Bicubic
3. If bicubic is used, ensure that at least 4 points are present in both X and Y.

This appears consistent with the Klipper documentation below and the KAMP implementation.

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.

[igiannakas]

So I've been checking out how KAMP does it

    {% if (([points_x, points_y]|max) > 6) %}                                                                                       # 
        {% set algorithm = "bicubic" %}                                                                                             # 
        {% set min_points = 4 %}                                                                                                    # 
    {% else %}                                                                                                                      # Calculate if algorithm should be bicubic or lagrange
        {% set algorithm = "lagrange" %}                                                                                            # 
        {% set min_points = 3 %}                                                                                                    # 
    {% endif %}  

So they take the max of points X and points Y and if either is >6 -> use Bicubic. So for Orca should this snippet be?

        auto bed_mesh_algo = "bicubic";
        int min_points = 4; // bicubic needs 4 probe points per axis
        if (std::max(probe_count_x, probe_count_y) <= 6) { // lagrange needs up to a total of 6 mesh points
            bed_mesh_algo = "lagrange";
            min_points = 3;
        }

[SoftFever]

So I've been checking out how KAMP does it

    {% if (([points_x, points_y]|max) > 6) %}                                                                                       # 
        {% set algorithm = "bicubic" %}                                                                                             # 
        {% set min_points = 4 %}                                                                                                    # 
    {% else %}                                                                                                                      # Calculate if algorithm should be bicubic or lagrange
        {% set algorithm = "lagrange" %}                                                                                            # 
        {% set min_points = 3 %}                                                                                                    # 
    {% endif %}  

So they take the max of points X and points Y and if either is >6 -> use Bicubic. So for Orca should this snippet be?

        auto bed_mesh_algo = "bicubic";
        int min_points = 4; // bicubic needs 4 probe points per axis
        if (std::max(probe_count_x, probe_count_y) <= 6) { // lagrange needs up to a total of 6 mesh points
            bed_mesh_algo = "lagrange";
            min_points = 3;
        }

According to Klipper doc, this is also wrong.

I think the previous probe_count_x * probe_count_y <= 6 logic is correct.

Just that the min points check need to be changed.
Something like following?

        auto bed_mesh_algo = "bicubic";
        if (probe_count_x * probe_count_y <= 6) { // lagrange needs up to a total of 6 mesh points
            bed_mesh_algo = "lagrange";
        }
        else {
          if(print.config().gcode_flavor == gcfKlipper){
              // bicubic needs 4 probe points per axis
              probe_count_x = std::max(probe_count_x,4);
              probe_count_y = std::max(probe_count_y,4);
            }
          //no-op
          }

[igiannakas]

OK I think it's done (?). Git has been a bit slow and difficult this evening for some reason

[SoftFever]

LGTM