This discussion is becoming painful. What we have here is a failure to communicate.
Nancy is talking about a transform of coordinates that would, for example, take a 2D rectangle and wrap it around a cylinder (form the outside surface of a coffee can perhaps). This is a surface to surface transformation. Tom is talking about a calculation in 2D that has a 3D symmetric representation where a rectangle that lies on R=0 will map to the entire coffee can. It is a one to many mapping that, to my knowledge, is not simple in DX. It is possible, though somewhat crude. Another example of the technique in question is the one dimensional calculation that represents a sphere. For the numerical calculation, you have nodes on a line segment where the left most one is fixed as the center of the sphere and the others represent radial points outward. By tracking conditions at the nodes and/or elements between them, you can play games with spherical expansion and contraction (think birth or death of a star). For visualization purposes you want to show a cut-away of spherical shells rather than dots on a line segment. Now think about representing a velocity vector or the density gradient. I have been doing the surface modeling of 2D cylindrical calculations in DX for several years but I have never tried vector functions on the data. I've always taken the easy path and computed them outside DX. It would not be difficult to write a user module to calculate those functions. -Ned Piburn nancy collins wrote: > > it is true that dx won't draw curved lines between 2 vertices; > the spacing of the vertices will indeed control how smooth your > curve plots, but my point is that if you do your computation before > you convert from [r,z] to cartesian, it won't matter. it will be > doing a real linear interpolation in r and in z, without any loss > of accuracy because of sampling density. > > before i go any further, maybe a simple experiment will help? > > start with an empty dx session. > > add a Construct, set origin=[0,0] deltas=[0.68,0.68] counts=[10,10] > (these deltas are to make it easier to convert into approximately > 2 pi+ radians later on.) > > connect the output to ShowConnections, that output to Image. > look at it. a 2d grid. mentally, think of the bottom axis as r, > the vertical axis as z. > > now put 3 modules inline between the Construct & ShowConnections: > Mark, Compute, Unmark. Set the component of Mark to "positions". > set the expression for Compute to "[a.y * cos(a.x), a.y * sin(a.x)]" > > now rexecute and you'll hopefully see a circular grid now. it's not quite > closed - that last stitching between column 0 and column 10 is what > chris was talking about with his previous append. > > yes, there are straight lines between the verticies, but stay with me. > > last step - take a Refine module, set the level to 1, and place it inline > between the Unmark & ShowConnections. you get the same outline, > with each quad subdivided into 4 now. now reconnect Unmark & > ShowConnections and put the Refine between the Construct & Mark. > now you should see a rounder circle. the latter is doing linear > interpolation in r and z; the former is doing linear interpolation in x, y. > you get smoother & smoother approximations to a circle by making > more & more samples in r,z before converting to x,y. > > so until you do the conversion of the positions, any computations you > do are automatically in r,z space, using linear interpolation in r & z, so > you don't have to worry about sampling density until you are ready to > convert. > > i'm not sure i understand your question about the div & curl, but i'm > more than happy to point you to the source - look in > src/exec/dxmods/_divcurl.c > you'll have to skip a lot of dx structuring code at the top. there are > separate sections for computing div & curl in cubes/hexahedra, in > tets, etc - one per primitive type. it's pretty highly macro-fied i'm > afraid. > > sorry, i'm not sure i understand your geometry, but i think you are > saying that you have data at [r,z] and it should be rotated through all > phi's? so i think you'd do that by importing a 2d [r,z] plane of quads, > using something like CollectSeries to make a group consisting of > the same plane repeated N times, and then using the Stack module > to make a real 3d volume of cubes in which each 2d sheet is the same. > is that anywhere close? if so, then you may be able to just stack > 2 sheets to make a volume 1 cube thick, do all your computations > in that, and then refine it at whatever density you want for display > purposes. > > nancy
