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How to properly retopo from Boolean to Quads (using mitered bevels to contain boolean guide edges)
[ALT-W] Select Boxcutter tool
Select an object
Hold LMB drag to draw a shape
Release LMB to finalize shape and enter next step
[LMB] or [SPACE] to execute
[RMB] or [ESC] to cancel
[W] Exit Boxcutter tool
Before drawing, you can press [D] to select Box, Circle or Ngon cutter.
Draw starting from inside your object outward. If you start from the outside inward, auto ortho will kick in. Press [NUM5] to return to perspective view.
When you are Drawing or Extruding (= default), you can switch to:
( Drawing [D] )
Extruding [E] – Lower bottom of cutter. [E] toggles between Offsetting and Extruding.
Offsetting [O] – Raise top of cutter.
Array [V] – Repeat for circular array. Use scroll wheel to increase numbers.
Solidify [T] – Gives it “thickness”
Bevel [B] – [Q] sides only <> top/bottom also.
Mirror [1,2,3] – Mirror, Bisect mirror (= remove geometry if / where it overlaps) or No mirror for X, Y and Z.
Cutting [X] – Remove cutter from object (“difference”)
Slicing [X] – The drawn shape will be cut from the object(“intersect”). You may need to apply non-destructively as overlapping faces look weird in viewport.
Insetting [Z] – Inset shape. Combine [T] for solidify. Use [CTRL-D] to fine tune amounts.
Joining [J] – Join cutter to object. Grows the object.
Using Knife [K] – Cutter verts and edges become part of object. Works best in Edit mode.
Extracting [Y] – No idea…
Making [A] – No idea…
Cycle cutter [C] !!!
Lock shape [TAB]
When you are in the middle of stuff, press [TAB] to lock the Boxcutter shape.
– Manipulate the Dots to Extrude, Offset, Bevel or change the shape.
– Use scroll wheel to rotate view.
– Press [CTRL-D] for popup menu. Only works when locked [TAB] and not hovering over a dot.
To exit menu, hover outside of menu. Menu will dissappear. Press [E] to continue (extruding).
Whenever I return to an active unfinished Boxcutter operation I like to press [TAB] to lock or [E] to resume (extruding). Do not press [LMB], [SPACE], [RMB] or [ESC] to resume as this will execute or cancel [!]
[LMB] pull a corner.
[+SHIFT] keep square constraint.
[+ALT] keep center constraint.
[+SHIFT+ALT] keep square and keep center constraint
If the Boxcutter top menu does not appear, just press [ALT-W].
Creating a wedge shaped cutter
1. Create a box cut taking a bite out of the midpoint of an edge of a cube.
2. When finilizing, hold [SHIFT] to keep the cutter live (= visible in Outliner).
3. In Edit mode, dissolve an edge [DEL] of the cutter to create a wedge shaped cutter.
4. When boxcutting, use [C] to cycle your cutters and reuse the wedge shaped cutter.
Ignore Blender snap options; use Boxcutter snap when inside Boxcutter.
[ALT-W] to select Boxcutter tool.
Enable all Boxcutter snap options.
Hold [CTRL] whilst hovering over selected object or over grid.
You should see snapping dots appear.
Hold [CTRL] when drawing to move in increments.
Hold [CTRL+ALT] to draw from center in increments(!)
You can edit your cutter like any other shape.
Simply make visible in Outliner and modify in Edit mode.
[N] > Item tab > Transform > X, Y, Z values.
Move [G], Rotate [R], Scale [S] as per usual along axis [X], [Y], [Z] and use [+SHIFT] for XY, XZ, YZ plane.
Enter exact numeric values in popup when complete.
Use Blender snapping aides.
[ALT-Z] for X Ray mode + Face mode 
Making a custom cutter
[~] or [R] to rotate.
2. Add a Bevel of 0.01m.
3. Boxcutter Cut a number of boxes.
4. Press ‘T’ (solidify, or ‘thickness’) to make the cutter hollow and only cut the wall thickness.
Note how the Bevel modifier is kept last in the stack. This is part of the workflow.
Note the box cutter goes through the interior of the cube.
If you want your surface line art to only sit on the surface, you will need to use Knife rectangle 2D shapes instead of Cutter 3D boxes:
2. Edit mode.
3. Boxcutter Knife cut a number of random rectangles. The intersecting line art is imprinted onto the surface of the cube. Interior of the cube is not affected. Exit Boxcutter.
4. Select edge rings [ALT-LMB] + [SHIFT] of imprinted box line art.
5. Bevel [CTRL-B].
6. Extrude along normals to push in slightly.
Tip: Use Ngon instead of Rectangle shape.