Sidecut and shape
Quotes are verbatim and attributed to their original authors.
A ski's outline is set by three widths — tip, waist, and tail — and where the waist (the narrowest point) sits along the length. Those choices give the ski its turn radius and its balance underfoot.
Where the waist goes
The common starting point is to work from the running length (the part in snow contact, i.e. the ski minus the tip and tail splay) and place the waist a little behind centre:
The parameters are linked
With a circular (single-radius) sidecut you cannot set the three widths and place the waist independently — geometry decides the rest:
As one builder summarised after learning it the hard way, "all the parameters are linked and the physical realities of geometry mean you can't define all the parameters independently" (falls). Turn radius follows directly from the widths and running length.
Mount point
Boot centre is usually placed at the waist, then set back a touch from true centre — commonly 2–5 cm, or a fixed ~50 mm setback — with more setback for powder and less (or none) for a park twin. It is ultimately personal preference.
Draw it in CAD
Rather than do the geometry by hand, builders draw the outline in a program that computes the waist and radius for you — SnoCAD-X and Boardcrafter are the community favourites, and AutoCAD is free for students. See CAD/CAM & CNC.