Re: Contourline values

*To*: mathgroup at smc.vnet.net*Subject*: [mg20062] Re: Contourline values*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Wed, 29 Sep 1999 03:33:23 -0400*References*: <7se5tl$qrp@smc.vnet.net> <7sho0u$1jq@smc.vnet.net> <7sjl4l$ef6$1@dragonfly.wolfram.com>*Sender*: owner-wri-mathgroup at wolfram.com

Kevin, When we enter cgo=ContourPlot[1/((x - 1)(x + 1)), {x, -2, 2}, {y, 0, 1},ContourShading -> False, Contours -> 3]; Mathematica generates the ContourGraphics object ( containing a matrix of heights); uses this to generate the displayed picture (a side efffect); returns ContourGraphics object as its value and assigns it to cgo. Mathematica knows what to do with a ContourGraphics object, and if we enter Show[cgo] then it again generates the display, and outputs cgo When Graphics[cgo] is evaluated it generates a Graphics object containing the the explicit Line objects that make the contour lines ( and if we allow contour shading it includes the polygons that provide this) The way that this is done is indicated briefly in Mathematica Graphics by Tom Wickham-Jones For a contour lines, interpolation is used to find crossings of the rectangles defined by the grid. When the lines have been constructed the polygons are made. But I have not seen the details. -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 Kevin J. McCann <kevinmccann at Home.com> wrote in message news:7sjl4l$ef6$1 at dragonfly.wolfram.com... > Allan, > > I had a look at your example and wonder if you could elaborate a bit on what > happened. If I look at cg with FullForm, I get stuff like: > > cg = ContourPlot[1/((x - 1)(x + 1)), {x, -2, 2}, {y, 0, 1},ContourShading -> > False, Contours -> 3]; > > cg//FullForm > > Produces: > ContourGraphics[List[List[0.333333, 0.515789, ... > > > On the other hand > > Graphics[cg]//FullForm > > Produces: > > Graphics[List[ > List[GrayLevel[0.], AbsoluteThickness[0.5], > Line[List[List[1.37445, 1.], List[1.37445, 0.928571],... > > I don't see the correlation. In particular, I don't see how the first {x,y} > point in the Line, viz. {1.37445,1.}, is produced from the earlier > ContourGraphics. > > Thanks, > > Kevin > > > Allan Hayes <hay at haystack.demon.co.uk> wrote in message > news:7sho0u$1jq at smc.vnet.net... > > > > Rita Bijlsma <R.Bijlsma at iri.tudelft.nl> wrote in message > > news:7se5tl$qrp at smc.vnet.net... > > > Hi! > > > > > > I can not find a way to get contourline values in contour plots. > > > > > > Can it be done (automatically) ? > > > > > > Thanks! > > > Rita > > > > > > -- > > > .-. || Drs. Rita Bijlsma tel: +31-15-2787109 > > > / \|| IRI dept of Radiation Physics fax: +31-15-2786422 > > > | ||| Delft University of Technology email: rita at iri.tudelft.nl > > > | |||_The Netherlands ______________ http://www.iri.tudelft.nl/~rita > > > > > > > Rita, > > > > cg = ContourPlot[1/((x - 1)(x + 1)), {x, -2, 2}, {y, 0, 1}, > > ContourShading -> False, Contours -> 3]; > > > > ContourGraphics[] > > > > > > Contour graphics stores a matriex of heights - no explicit lines. To get > the > > lines we convert the contour graphics object to a Graphics object and then > > use Cases to gert a list of the result of passing the first point > > coordinates for each line to the expression being plotted. Since there may > > be, as here, more than one line at the same height, we then use Union to > > remove duplicates. > > > > Cases[Graphics[cg], > > Line[{{x_, y_}, ___}] :> (1/((x - 1)(x + 1))), > > Infinity] // Union > > > > > > Out[28]= > > {-10175.9, -10175.9, -7.48556, -7.48556, -1.63844, -1.63844, 1.1247, > 1.1247, > > \ > > 6.99341, 6.99341} > > > > > > -- > > Allan > > --------------------- > > Allan Hayes > > Mathematica Training and Consulting > > Leicester UK > > www.haystack.demon.co.uk > > hay at haystack.demon.co.uk > > Voice: +44 (0)116 271 4198 > > Fax: +44 (0)870 164 0565 > > > > > > > > > >