Primitive Disk Gradient Fills in Graphics
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From: M.Roellig on 14 Jul 2010 05:34 On 13 Jul., 11:28, Murta <rodrigomur...(a)gmail.com> wrote: > Hello All > > There is really no way to do a simple gradient fill inside a disk > in Mathematica? > I'm working in a BubbleChart, and would like to make a graphics > disk using ChartElements, going to color x to transparent using > opacity. > I get surprised to see that there is no way to work with gradient > fill inside primitives like Disk.. there is really this? > If it's true, please, correct it in Mathematica 8!... Hi, I agree, GradientFill would be nice, as well as TextureFill or any filling with arbitrary patterns. Until then you can try to construct it by yourself: GradientDisk[] := Graphics[Table[{Hue[r], Circle[{0, 0}, r]}, {r, 0, 1, 0.001}]] ; BubbleChart[RandomReal[1, {10, 3}], ChartElements -> {GradientDisk[]}] or BWGradientDisk[] := Graphics[Table[{GrayLevel[r], Circle[{0, 0}, r]}, {r, 0, 1, 0.001}]]; BubbleChart[RandomReal[1, {10, 3}], ChartElements -> {BWGradientDisk[]}] This takes quite some time, since many Circles are drawn. If somebody knows how to rasterize a circly without getting square image borders, one could use the rasterized image as Element. Maybe exporting to gif with transparent white background works. Of course, the same excercise also works with Rectangles etc.. Cheers, Markus
From: Murta on 15 Jul 2010 03:11 On 14 jul, 06:36, "David Park" <djmp...(a)comcast.net> wrote: > Here is a solution using Presentations. You should also be able to do this > using RegionPlot, Show and some graphics level jumping. > > Needs["Presentations`Master`"] > > gradientDisk::usage = > "gradientDisk[{xcenter, ycenter}, radius, color] will draw an \ > outlined colored disk with the color blended from White to full color \ > across the the horizontal dimension."; > SyntaxInformation[ > gradientDisk] = {"ArgumentsPattern" -> {{_, _}, _, _}}; > gradientDisk[{xcenter_, ycenter_}, radius_, color_] := > {RegionDraw[(x - xcenter)^2 + (y - ycenter)^2 < radius^2, {x, > xcenter - radius, xcenter + radius}, {y, ycenter - radius, > ycenter + radius}, > ColorFunctionScaling -> False, > ColorFunction -> > Function[{x, y}, > Blend[{White, color}, > Rescale[x, {xcenter - radius, xcenter + radius}]]]], > AbsoluteThickness[1], > Circle[{xcenter, ycenter}, radius]} > > Draw2D[ > {gradientDisk[{0, 0}, 1, Red], > gradientDisk[{2, 2}, 1/2, Green], > gradientDisk[{-2, 1}, .45, Blue]}, > Frame -> True, > PlotRange -> 4 > ] > > David Park > djmp...(a)comcast.nethttp://home.comcast.net/~djmpark/ > > From: Murta [mailto:rodrigomur...(a)gmail.com] > > Hello All > > There is really no way to do a simple gradient fill inside a disk > in Mathematica? > I'm working in a BubbleChart, and would like to make a graphics > disk using ChartElements, going to color x to transparent using > opacity. > I get surprised to see that there is no way to work with gradient > fill inside primitives like Disk.. there is really this? > If it's true, please, correct it in Mathematica 8!... Thanks for All the reply. I will construct it in the ways suggested. But I hope Mathematica 8 came better in this itens! tks Rodrigo Murta
From: David Park on 15 Jul 2010 03:11 Well, darn if there isn't a method for doing that within BubbleChart. Evaluate ChartElementData["BubbleChart"] {Bubble,FadingBubble,GradientBubble,MarkerBubble,NoiseBubble,OscillatingBubb le,PolyhedronBubble,SphereBubble,SquareWaveBubble,TriangleWaveBubble} for the various types of bubbles. Then, for example: BubbleChart[RandomReal[1, {10, 3}], ChartStyle -> "Pastel", ChartElementFunction -> "GradientBubble"] But how would we obtain different colors for the bubbles, say based on the radius? I don't know where we can feed it in. Instead of starting with high level, "set-piece" plot types, and then trying to screw them around with convoluted options, it would be much easier to start with primitives and build up the higher level plot types. Suppose I want a bubble fading from White to a color at the rim, and I want different colors depending on the radius of the bubble? Here is an easy way to build it up. Needs["Presentations`Master`"] First define the primitive. gradientDisk::usage = "gradientDisk[{xcenter, ycenter}, radius, color] will draw an \ outlined disk with the color blended from White to full color across \ the radius."; SyntaxInformation[ gradientDisk] = {"ArgumentsPattern" -> {{_, _}, _, _}}; gradientDisk[{xcenter_, ycenter_}, radius_, color_] := {RegionDraw[(x - xcenter)^2 + (y - ycenter)^2 < radius^2, {x, xcenter - radius, xcenter + radius}, {y, ycenter - radius, ycenter + radius}, ColorFunctionScaling -> False, ColorFunction -> Function[{x, y}, Blend[{White, color}, Rescale[Sqrt[(x - xcenter)^2 + (y - ycenter)^2], {0, radius}]]]], AbsoluteThickness[1], Circle[{xcenter, ycenter}, radius]} Adapt it to the WRI form of Bubble data with a particular color selection for the bubbles. myBubble[{x_, y_, r_}] := gradientDisk[{x, y}, r, ColorData["SolarColors"][Rescale[r, {0, 2}]]] Then draw the bubble chart. data = Array[{RandomReal[{-10, 10}], RandomReal[{-10, 10}], RandomReal[{0.1, 2}]} &, 20]; Draw2D[ {myBubble /@ data}, Frame -> True, ImageMargins -> 5, PlotRange -> 12 ] Also, since WRI must have defined a primitive for SquareWaveBubble, say, how could we obtain direct access to it? (I know how to program one but since WRI has done, and buried, the work how about getting it out?) David Park djmpark(a)comcast.net http://home.comcast.net/~djmpark/ From: M.Roellig [mailto:markus.roellig(a)googlemail.com] On 13 Jul., 11:28, Murta <rodrigomur...(a)gmail.com> wrote: > Hello All > > There is really no way to do a simple gradient fill inside a disk > in Mathematica? > I'm working in a BubbleChart, and would like to make a graphics > disk using ChartElements, going to color x to transparent using > opacity. > I get surprised to see that there is no way to work with gradient > fill inside primitives like Disk.. there is really this? > If it's true, please, correct it in Mathematica 8!... Hi, I agree, GradientFill would be nice, as well as TextureFill or any filling with arbitrary patterns. Until then you can try to construct it by yourself: GradientDisk[] := Graphics[Table[{Hue[r], Circle[{0, 0}, r]}, {r, 0, 1, 0.001}]] ; BubbleChart[RandomReal[1, {10, 3}], ChartElements -> {GradientDisk[]}] or BWGradientDisk[] := Graphics[Table[{GrayLevel[r], Circle[{0, 0}, r]}, {r, 0, 1, 0.001}]]; BubbleChart[RandomReal[1, {10, 3}], ChartElements -> {BWGradientDisk[]}] This takes quite some time, since many Circles are drawn. If somebody knows how to rasterize a circly without getting square image borders, one could use the rasterized image as Element. Maybe exporting to gif with transparent white background works. Of course, the same excercise also works with Rectangles etc.. Cheers, Markus
From: David Park on 16 Jul 2010 05:16 Many thanks for that Patrick. I don't think one has to Unprotect ChartElementData. At least, I had no problem. Here is an example of getting out these primitives and using them in your own custom plot. The possible types of primitives for BubbleChart: ChartElementData["BubbleChart"] {"Bubble", "FadingBubble", "GradientBubble", "MarkerBubble", \ "NoiseBubble", "OscillatingBubble", "PolyhedronBubble", \ "SphereBubble", "SquareWaveBubble", "TriangleWaveBubble"} Examine one of these with Manipulate. ChartElementData["SquareWaveBubble", "Manipulate"] Insert a specific case to see the form of the function. ChartElementDataFunction["SquareWaveBubble", "AngularFrequency" -> 20, "RadialAmplitude" -> 0.1`] Now design a custom primitive. This one specifies the location, size and color for a SquareWaveBubble. The RadialAmplitude varies with the size. (Look up ChartElementFunction for more details.) myBubble[x_, y_, size_, color_] := {color, ChartElementDataFunction["SquareWaveBubble", "AngularFrequency" -> 20, "RadialAmplitude" :> Rescale[size, {.2, 3}, {1, 0}]][{{x - size/2, x + size/2}, {y - size/2, y + size/2}}, {x, y}]} Here is some data and a plot done outside of BubbleChart. data = Table[{RandomReal[{-10, 10}], RandomReal[{-10, 10}], s = RandomReal[{.2, 3}], ColorData["DarkRainbow"][Rescale[s, {.2, 3}]]}, {i, 15}]; Graphics[ {myBubble @@@ data}, AspectRatio -> Automatic, Frame -> True, PlotRange -> 13] However, this does depend on having an Automatic AspectRatio. David Park djmpark(a)comcast.net http://home.comcast.net/~djmpark/ From: Patrick Scheibe [mailto:pscheibe(a)trm.uni-leipzig.de] Hi all, just clear the protection attributes of ChartElementData and find out that ChartElementData["GradientBubble", "Manipulate"] should help. Cheers Patrick On Thu, 2010-07-15 at 03:10 -0400, David Park wrote: > > Also, since WRI must have defined a primitive for SquareWaveBubble, say, how > could we obtain direct access to it? (I know how to program one but since > WRI has done, and buried, the work how about getting it out?) > > > David Park > djmpark(a)comcast.net > http://home.comcast.net/~djmpark/ >
From: Patrick Scheibe on 16 Jul 2010 05:16 Hi again, > I don't think one has to Unprotect ChartElementData. At least, I had no > problem. Here is an example of getting out these primitives and using them > in your own custom plot. what I meant was, that there is here (Linux 64, Mathematica 7.0.1) no direct documentation of ChartElementData. Unprotecting (read protection) the symbol and using ?? for looking at the definition was the way I found out about the usage. Of course you can use it without unprotecting the symbol. Cheers Patrick > The possible types of primitives for BubbleChart: > > ChartElementData["BubbleChart"] > > {"Bubble", "FadingBubble", "GradientBubble", "MarkerBubble", \ > "NoiseBubble", "OscillatingBubble", "PolyhedronBubble", \ > "SphereBubble", "SquareWaveBubble", "TriangleWaveBubble"} > > Examine one of these with Manipulate. > > ChartElementData["SquareWaveBubble", "Manipulate"] > > Insert a specific case to see the form of the function. > > ChartElementDataFunction["SquareWaveBubble", "AngularFrequency" -> 20, > "RadialAmplitude" -> 0.1`] > > Now design a custom primitive. This one specifies the location, size and > color for a SquareWaveBubble. The RadialAmplitude varies with the size. > (Look up ChartElementFunction for more details.) > > myBubble[x_, y_, size_, color_] := {color, > ChartElementDataFunction["SquareWaveBubble", > "AngularFrequency" -> 20, > "RadialAmplitude" :> Rescale[size, {.2, 3}, {1, 0}]][{{x - size/2, > x + size/2}, {y - size/2, y + size/2}}, {x, y}]} > > Here is some data and a plot done outside of BubbleChart. > > data = Table[{RandomReal[{-10, 10}], RandomReal[{-10, 10}], > s = RandomReal[{.2, 3}], > ColorData["DarkRainbow"][Rescale[s, {.2, 3}]]}, {i, 15}]; > Graphics[ > {myBubble @@@ data}, > AspectRatio -> Automatic, > Frame -> True, > PlotRange -> 13] > > However, this does depend on having an Automatic AspectRatio. > > David Park > djmpark(a)comcast.net > http://home.comcast.net/~djmpark/ > > > > > > > > > > > > From: Patrick Scheibe [mailto:pscheibe(a)trm.uni-leipzig.de] > > Hi all, > > just clear the protection attributes of ChartElementData and find out > that > > ChartElementData["GradientBubble", "Manipulate"] > > should help. > > Cheers > Patrick > > On Thu, 2010-07-15 at 03:10 -0400, David Park wrote: > > > > Also, since WRI must have defined a primitive for SquareWaveBubble, say, > how > > could we obtain direct access to it? (I know how to program one but since > > WRI has done, and buried, the work how about getting it out?) > > > > > > David Park > > djmpark(a)comcast.net > > http://home.comcast.net/~djmpark/ > > >
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