| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Can anyone point me to information about Minkowski addition? I've
run across references to this in papers which relate this to
convolution, in that both are useful in describing the result of
"dragging" a polygon (e.g., a brush) along some path (i.e., a
trajectory). This brush-trajectory model is encountered in computer
graphics, and has become the subject of some recent efforts to build
a framework for computational geometry around it.
I'm not a mathematician, but I'm willing to do some work to understand
what Minkowski addition is. Any pointers to papers or text, preferably
one that do NOT require extensive math background, would be greatly
appreciated.
Thanks very much.
-pd
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 459.1 | ENGINE::ROTH | Tue Mar 25 1986 09:16 | 10 | ||
Could you provide a reference; I've just started to work in a graphics related area and would find it interesting. Minknowski did some good work on the 'geometry of numbers' - the number theoretic relationships that arise on integer lattices in various dimensions, and I can well imagine this being useful for raster display graphics. I have not heard of the term 'Minkowski addition' though. - Jim | |||||
| 459.2 | PDVAX::P_DAVIS | really SARAH::P_DAVIS | Tue Mar 25 1986 13:41 | 17 | |
I've seen "Minkowski sum" or "Minkowski addition" referred to in
two papers, neither of which provided a general reference on the
subject. On was entitled "A Kinetic Framework for Computational
Geometry", by Leo Guibas, Lyle Ramshaw, and Jorge Stolfi. This
paper can be found in volume 15 of the SIGGRAPH '84 Course Notes:
Mathematics of Computer Graphics. Another reference was in a paper
I don't have in front of me, but it was by Pijush K. Ghosh and S.
P. Mudur, and appeared in a collection of papers published by
Springer-Verlag under the title "Fundamental Algorithms for Computer
Graphics." The title also had some reference to frameworks for
computational geometry, or some such thing.
Can you point me to a reference on Minkowski's "Geometry of Numbers"
work?
Thanks.
-pd
| |||||
| 459.3 | Hardy & Wright is the usual reference | ENGINE::ROTH | Tue Mar 25 1986 14:45 | 13 | |
Most books on number theory would have some information on Minkowski, for example the classic 'Introduction to the Theory of Numbers' by Hardy and Wright. When I get home I'll take a look and see what may be relevent. You mentioned convolution - that certainly sounds like a plausable connection in terms of moving a 'brush' (2D distribution) of some sort over a plane of lattice points. There probably is some neat method for leaving behind a pattern efficiently, perhaps via a sort of fast convolution algorithm. And fast convolution algorithms are based on number theoretic ideas... - Jim | |||||