====== Sweeping by a moving solid ======
{{frep:envel1.gif?nolink}}

We have reduced the problem of a swept solid description to a global extremum search by a parameter of movement. It allows the user to apply arbitrary variable-shape and CSG solids as generators, arbitrary parametrized movement and self-intersections. An example of sweeping by falling cup and spoon is shown below.

{{frep:encup0.gif?nolink}} {{frep:encup1.gif?nolink}} {{frep:encup2.gif?nolink}}

Simulation of NC machining uses time-dependent set-theoretic operations with a part and a cutter in relative motion:

[[http://hyperfun.org/nc1.gif|{{frep:nc1_100.gif?nolink}}]] [[http://hyperfun.org/nc2.gif|{{frep:nc2_100.gif?nolink}}]] [[http://hyperfun.org/nc3c.gif|{{frep:nc3c_100.gif?nolink}}]] [[http://hyperfun.org/nc3.gif|{{frep:nc3_100.gif?nolink}}]] [[http://hyperfun.org/nc4.gif|{{frep:nc4_100.gif?nolink}}]] \\ Click on an image to get its more large version. \\
[[http://www.ntu.edu.sg/home/assourin/Frep.htm|More sweeps]]

Details can be found in the paper:

Sourin A.I., Pasko A.A. "Function representation for sweeping by a moving solid", IEEE Transactions on Visualization and Computer Graphics, vol.2, No.1, March 1996, Special issue on solid modeling, pp.11-18.\\
Electronic version: [[http://hyperfun.org/Sweep.ps|PostScript (294K)]] and [[http://hyperfun.org/Sweep.ps.gz|PostScript + gzip (64K)]]