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From: Emil Persson <humus@co...>  20090522 18:28:31

I'm tired and I have a headache, but if I understand your problem right then it sounds like a special case of a problem I just solved last night and wrote a tool for: http://www.humus.name/index.php?page=News <http://www.humus.name/index.php?page=News&ID=266>; &ID=266 So you'd just input your polygon directly (instead of inputting a particle texture and generate a polygon from that) and optimize for 4 vertices and that would solve it, no? Emil From: Stefan.Daenzer@... [mailto:Stefan.Daenzer@...] Sent: 22 May 2009 14:59 To: Game Development Algorithms Subject: [Algorithms] Best fit of polygon inside another polygon Hi, I've been thinking about an algorithm which fits a given polygon into a quad. I've stumbled upon this while trying to fit the largest possible polygon out of a set of different polygons into a quadliteral. What I want to find is the bestfitpolygon which can be contained completely in the quadliteral. The polygon and quad can be assumed to be convex. An nice feature would be to calculate the error as a function of the area which doesn't fit into the quad for every polygon I throw at the quad. I'm working in 2D right now, but might want to expand the problem for a later application into a 3D case (fit a polyhedra into a hexahedron). Any ideas how to solve this problem? Stefan 
From: Robin Green <robin.green@gm...>  20090522 17:33:41

On Fri, May 22, 2009 at 8:41 AM, Peter Lipson <peter@...> wrote: > sounds like a question from one of my takehome final exams.... > > Welcome to the world of R&D, where it's like taking an exam every day of the week. Only there are no right answers, no scores at the end, and it's not clear whether the question is even possible.  R. 
From: Peter Lipson <peter@to...>  20090522 16:08:17

sounds like a question from one of my takehome final exams.... Stefan.Daenzer@... wrote: > Hi, > > I've been thinking about an algorithm which fits a given polygon into > a quad. I've stumbled upon this while trying to fit the largest > possible polygon out of a set of different polygons into a > quadliteral. What I want to find is the bestfitpolygon which can be > contained completely in the quadliteral. The polygon and quad can be > assumed to be convex. An nice feature would be to calculate the error > as a function of the area which doesn't fit into the quad for every > polygon I throw at the quad. > > I'm working in 2D right now, but might want to expand the problem for > a later application into a 3D case (fit a polyhedra into a hexahedron). > > Any ideas how to solve this problem? > > Stefan >  > >  > Register Now for Creativity and Technology (CaT), June 3rd, NYC. CaT > is a gathering of techside developers & brand creativity professionals. Meet > the minds behind Google Creative Lab, Visual Complexity, Processing, & > iPhoneDevCamp asthey present alongside digital heavyweights like Barbarian > Group, R/GA, & Big Spaceship. http://www.creativitycat.com >  > > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist 
From: Fabian Giesen <f.giesen@49...>  20090522 13:15:13

Stefan.Daenzer@... wrote: > Hi, > > I've been thinking about an algorithm which fits a given polygon into a > quad. I've stumbled upon this while trying to fit the largest possible > polygon out of a set of different polygons into a quadliteral. What I > want to find is the bestfitpolygon which can be contained completely > in the quadliteral. The polygon and quad can be assumed to be convex. An > nice feature would be to calculate the error as a function of the area > which doesn't fit into the quad for every polygon I throw at the quad. > > I'm working in 2D right now, but might want to expand the problem for a > later application into a 3D case (fit a polyhedra into a hexahedron). > > Any ideas how to solve this problem? > > Stefan Which transformations are allowed? "Only translations", "translations and rotations", "translations, rotations and uniform scaling" and "general affine transformation" are all sensible choices but lead to very different approaches. Also, is the quad a general convex quad, or is it a rectangle or parallelogram? Kind regards, Fabian Giesen 
From: Stefan.D<aenzer@gm...>  20090522 12:58:57

Hi, I've been thinking about an algorithm which fits a given polygon into a quad. I've stumbled upon this while trying to fit the largest possible polygon out of a set of different polygons into a quadliteral. What I want to find is the bestfitpolygon which can be contained completely in the quadliteral. The polygon and quad can be assumed to be convex. An nice feature would be to calculate the error as a function of the area which doesn't fit into the quad for every polygon I throw at the quad. I'm working in 2D right now, but might want to expand the problem for a later application into a 3D case (fit a polyhedra into a hexahedron). Any ideas how to solve this problem? Stefan 