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   on karl’s interrupted walking algorithm from 2016 or whatnot during
   chemotherapy

   we’ve been over this before. but it could be fun to actually put it
   together. what are the parts?

   the next part was modelling a concave orthographic projection onto the
   floor showing what regions the center of mass was stable in.

   how to model this? it’s in 2d space. a basic query might be whether or
   not a point is within it.

   i remember the code already existed for paths. could a concave
   projection be a closed path? does it matter? 1847 i’m thinking it’s
   pretty normal to assume a polygon. one can always add curves to the
   polygon with a separate edge class or something.

   how to tell if a point is within a convex polygon? shouldn’t i know
   this?

   there is probably optimized code somewhere, but would it maybe help to
   order the coordinates clockwise or such, and then take the dot product
   of one of those vectors with another?

   i’m thinking maybe for each side, if a point is within the polygon, it
   will be on the same side of that line or line segment, if they are all
   treated clockwise or such. then i’m somehow thinking thisncould be
   tested with a dot product. is this true?

   considering: identifying side of point from line between two other
   points using dot product.

   dot product is same-sign when two vectors are <90 degrees different,
   for them being on left or right of the other, then opposite-sign when
   two vectors are >90 different, and is 0 at 90 and product magnitude or
   1 at 0 and 180 (-1). so if i were to check side using dot product, i
   might consider valuing the change at 90 degrees. the 0 value is also
   appropriately ambiguous if a point lays entirely on an edge.

   so, we could take the tangent or right angle to the edge, and then dot
   product that with a vector to the point in question. i guess if all
   their signs are the same, they’ll be on the same side. it’s an idea