Blade grinds seem easy until you think about them. Once you realize that there are convex, concave and flat planes all intersecting each other in multiple places and along a curving profile that must remain a constant width; not to mention the fact that for aesthetics, you are trying to control how and where all those lines intersect...well, most peoples minds blank-out. Before you look at the rest of the pictures, take a moment and see what you come up with first. If you have time, try to model it then look at the rest of this project.
The biggest challenge is keeping the edge a constant thickness. If that edge isn't a constant thickness then the honed edge (or secondary edge) will vary in height along the blade and just look awful. On more complicated grind like a tanto the intersection of the tip, top and belly need to be tightly controlled for the engineered performance of the blade (the belly is hollow* (*concave) ground with a very thin honed edge for perfection in slicing while the tip is a thick flat or apple-seed* (*convex like) grind for puncture). Tight control is also needed for the aesthetics, all three grind need to converge at the sharp transition points otherwise the blade just looks wrong.
I'll use this knife as an example. it is composed of two hollow grinds, (a top and belly that converge at the tip). Followed by a triangular secondary grind for the honed edge.
The most elegant solution I have found so far is to use a simple sweep-cut. I create a simple profile that contains all the critical information. I then make a path that follows the blade profile. This produces a double faceted feature that can change in up to 5 degrees of freedom and yet is controlled by 2-3 dimensions.
The secondary grind is a much simpler form of the primary.
The top grind is another variation on the same theme. It does however require a bit of playing with to get it to converge perfectly but it is limited to a single dimension.
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3D Solid Modeling of Complex Angles

One tricky thing I had to figure out when I started working at SOG was how do I model a complex faceted surface such as a knife blade in 3D? And then, how do I model it elegantly enough so that it is easy to use and modify.

Beren McKay
Sr. Director of Product Development at SOG Seattle, WA