Skip to main content

plotting - Ad hoc graphics primitives-like objects


Sphere is one of the three-dimensional graphics primitives available in Mathematica and can be easily used to created very useful images. For instance, in the figure below I created three images of an ellipsoidal object that is lit from a fixed direction and it is then just rotated around the z-axis.



GraphicsRow[
Table[
Graphics3D[
Rotate[Scale[{GrayLevel[.7], Sphere[]}, {1, 1.5, 1}, {0, 0, 0}],
i Degree, {0, 0, 1}], PlotRange -> {{-2, 2}, {-2, 2}, {-2, 2}},
AspectRatio -> 1, Background -> Black, Boxed -> False,
ViewPoint -> Front, SphericalRegion -> True,
Lighting -> {{"Directional", White, ImageScaled[{0, 0, 1}]}}
], {i, {0, 45, 90}}]]


ellipsoidalObject


Suppose that instead of using the ellipsoidal object I would like to use an object like this bump:


Plot3D[Exp[-(x^2 + y^2)], {x, -2, 2}, {y, -2, 2}]

bump


Is there a way to create a "graphics primitive" object of the bump, so as to just use it instead of Sphere in the above example?


I suppose there should be a way to extract all the polygons specifying the shape of the bump, but I couldn't find a way to do it. Any other approach is also more than welcome.



Answer



The result of Plot3D and related functions is something of the form Graphics3D[primitives, options], so to extract the graphics primitives you can simply take the first part of the plot. These can then be manipulated similar to Sphere[] in your example, e.g.


plot = Plot3D[Exp[-(x^2 + y^2)], {x, -2, 2}, {y, -2, 2}][[1]];


GraphicsRow[
Table[Graphics3D[
Rotate[Scale[{GrayLevel[.7], plot}, {1, 1.5, 1}, {0, 0, 0}],
i Degree, {0, 0, 1}], PlotRange -> {{-2, 2}, {-2, 2}, {-2, 2}},
AspectRatio -> 1, Background -> Black, Boxed -> False,
ViewPoint -> Front, SphericalRegion -> True,
Lighting -> {{"Directional", White,
ImageScaled[{0, 0, 1}]}}], {i, {0, 45, 90}}]]


Mathematica graphics


Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...