Blind Miter & Hidden Spline

Ninety degree joints with 90 degree V bits and minimal voids

While modern adhesives are surprisingly able to allow one to simply cut and glue miters (esp. if one is willing to add a few nails), adding a hidden spline will create a much stronger joint (and one which has the added benefit of being self-aligning).

Drawing the Joint

The miter itself is of course simply a bisecting of the junction of the two boards:

Basic Miter Joint (overhead view)

In order to cut the miter and the void for the spline a V endmill which is narrower in diameter than the boards are in thickness will be necessary:

Blind Miter Joint and profile of smaller V endmill

In order to leave a reasonable amount of material, the endmill should cut so that it is positioned closer to the interior than the exterior of the box ― making the cuts for the spline equal in width to one-half the board thickness and positioning them one-eighth the board thickness in from the interior edge results in a reasonable arrangement which is easily calculated:

Blind Miter Joint with smaller V endmill positioned

Which may then be drawn up:

Blind Miter Joint and hidden spline profile

Rotating the components and arranging them flat on the working area for cutting out shows them in profile as:

Blind Miter Joint and hidden spline profile unfolded

Modeling the Box

Box with parameters/dimensions

Cutting the Joint

Box parts with side profiles
Parts preview with miters
Pockets for hidden splines

Cut the file:

With a downcut endmill the parts need minimal cleanup:

And the box fits together, self-aligning: