RE: 2D to 3D graphics? and Thickness of Lines and Arcs

*To*: mathgroup at smc.vnet.net*Subject*: [mg31367] RE: [mg31284] 2D to 3D graphics? and [mg31288] Thickness of Lines and Arcs*From*: "Ingolf Dahl" <f9aid at fy.chalmers.se>*Date*: Wed, 31 Oct 2001 03:30:57 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Comment to the answers I have got about how to convert 2D graphics to 3D graphics: The reason why I wrote the question was that I became a bit frustrated when I found that some of the 2D graphic primitives (Rectangle, Circle, Disk, Raster, RasterArray, PostScript) lack a direct three-dimensional counterpart. In most parts, Mathematica is created with quite a good internal consistency and agreement, but evidently that has been difficult to achieve here. Mark Westwood, Allan Hayes and David Park (private communication) has all suggested simple replacement rules to replace the two dimensional coordinates in the primitives by three dimensional coordinates, and that can work for the primitives that are common for 2D and 3D coordinates, namely Point, Line, Polygon and Text, but not for the other. For Rectangle, Circle and Disk it should be quite easy to write functions, that build up the 3D counterparts from the 3D primitives. For Raster and RasterArray it should be more difficult, but maybe the result would be fun to play with. For PostScript code it might be possible to add extra Postscript commands to perform the 3D-projection. Maybe something for David Park to include in his DrawGraphics package (see http://home.earthlink.net/~djmp/)? (To me it seems as David Park have thought a bit deeper about these things than Wolfram.) In version 4.1 of Mathematica, the routine StackGraphics is able to transform a 2D circle to a 3D object (built by lines), normal to the y-axis, but the same routine does not seem to be able to handle 2D rectangles. Consistent? I would prefer to have available a 2D-to-3D routine that is more primitive and more well-defined for the user than StackGraphics. On a wishing list for a more user-friendly Mathematica I would also like to add more user-friendly versions of Rotate3D, RotationMatrix3D, and RotateShape. These routines use Euler angles as arguments. How many of us have a clear understanding of the ad hoc definition of the Euler angles? I suggest modifications of these routines, where the rotation axis and angle could be inserted directly as arguments. Also Will Self in message 31288 asks for the possibility to specify the thickness of lines and arcs in the units he is using. I want to add a wish for the same possibility with font sizes. Then text and thicknesses will be resized in the same way as the figure. I agree with Will Self that this is very basic. Ingolf Dahl Chalmers University -----Original Message----- From: Ingolf Dahl [mailto:f9aid at fy.chalmers.se] To: mathgroup at smc.vnet.net Subject: [mg31367] [mg31284] 2D to 3D graphics? Dear Mathgroup, Is there any way to transform a general (2D) Graphics objects to a Graphics3D object (with zero z coordinates)? I have a feeling that it is either very simple or very complicated. Have I missed something in the Book? Then I of course also want to be able to rotate the graphics in three dimensions, by RotateShape, but that is maybe to ask too much. I have experimented a bit with StackGraphics, since it seems to take 2D graphics as input, and 3D as output, but have not yet managed to manipulate the output of StackGraphics in any way. Ingolf Dahl Chalmers University