Re: operator overloading with UpValues (eg, for shifting graphics)

*To*: mathgroup at smc.vnet.net*Subject*: [mg13642] Re: operator overloading with UpValues (eg, for shifting graphics)*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Fri, 07 Aug 1998 18:37:26 +0800*Organization*: University of Western Australia*References*: <6qbqkd$a67@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Daniel Reeves wrote: > I thought it would be nice to shift some graphics by just adding an x-y > pair. It seemed like this sort of thing should do that: > > Unprotect[Line]; > Line /: Line[pts_] + {x_,y_} := Line[pts+{x,y}] Protect[Line]; > > But it doesn't. The UpValue for Graphics doesn't get used. This does > work: > > Line /: Line[pts_] + shift[x_,y_] := Line[pts+{x,y}] > > but then I might as well just do this: > > shift[Line[pts_],{x_,y_}] := Line[pts+{x,y}] > > The idea is to be able to just say Line[...] + {x,y} and get a shifted > Line. > > Does anyone know a way to do that? > Also, if/why Mathematica is doing "the right thing" in defying my > expectations in the first example. Ie, should the Listable-ness of > Plus have precedence over my UpValue for Line? I think you'll find that all these questions (and many more) are answered in the excellent "Mathematica Graphics: Techniques and Applications" by Tom Wickham-Jones. Incidentally, the packages for this book are available from MathSource: http://www.mathsource.com/cgi-bin/MathSource/Enhancements/Graphics/3D/0208-976 BTW, a nice simple example of Affine transformations on graphics was given in The Mathematica Journal 4(3):38-39: An arbitrary affine transformation (that is, a composition of translation, rotation, and scaling) of a vector {x,y} in the plane can be be written in matrix notation as m.{x,y} + c, where m is a 2x2 matrix (generating rotation and scaling) and c is a constant (translation) vector. Here is a simple procedure that applies affine transformations to two-dimensional graphics: Affine[plot_Graphics,m_?MatrixQ,c_?VectorQ]:= Show[plot/.{x_?NumberQ,y_?NumberQ} -> m.{x,y}+c] Commencing with a basic plot: SinPlot=Plot[Sin[x],{x,0,6 Pi}]; one can rotate it about the z-axis by 90 degrees and then mirror it in the y-axis: Affine[SinPlot,{{0,1},{1,0}},{0,0}]; or display a more complicated combination of rotation, scaling, and translation: Affine[SinPlot,{{1,0},{1,3}},{-1,-2}]; > "This isn't right. This isn't even wrong." > -- Wolfgang Pauli, on a paper submitted by a physicist colleague Only a physicist would have such a sig ... Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.physics.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________