Skip to main content

graphics - Drawing Rotated views while ignoring the Bounding box


I am trying to make an animation of a rotating cube using the following code:


cube = GraphicsComplex[
{{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}},
Polygon[{{1, 2, 4, 3}, {5, 6, 8, 7}, {1, 2, 6, 5}, {3, 4, 8, 7}, {1, 3, 7, 5}, {2, 4, 8, 6}}]
]

cubes = Table[
Graphics3D[{Rotate[cube, x, {1, 1, 1}, {0, 0, 0}]}, 

ViewPoint -> {3, 1/2, -2}, ViewVertical -> {1, 1, 1}, 
Boxed -> False], {x, 0, 2 Pi/3 - Pi/48, Pi/24}]

However, as the cube rotates, the bounding box (which is not drawn because Boxed->False) causes the image of the cube to be shrunk to fit the larger bounding box in the field of view. Is there a way to keep the scale constant and not vary with the varying size of the bounding box?


I've gone through the list of options for Graphics3D, yet none seem to help.



Edit:

Heike's answer works like a charm! For those interested, here is the finished code, used to create the illustration for this answer on math.SE.


cube =
GraphicsComplex[

{{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}},
Polygon[{{1, 2, 4, 3}, {5, 6, 8, 7}, {1, 2, 6, 5}, {3, 4, 8, 7}, {1, 3, 7, 5}, {2, 4, 8, 6}}]
];

envelope[t_] := If[t < 1, t, If[t < 2, Sqrt[(2 t - 3)^2 + 3]/2, 3 - t]]

lozenge = 
Rotate[
RevolutionPlot3D[{Sqrt[2/3] envelope[t], t/Sqrt[3]}, {t, 0, 3}, MaxRecursion -> 5][[1]],
{{0, 0, 1}, {1, 1, 1}}];


enveloped = 
Table[
Graphics3D[{Rotate[cube, x, {1, 1, 1}, {0, 0, 0}],  Opacity[1/2], lozenge},
ViewVector -> {3, 1/2, -2}, ViewAngle -> 30 Degree, ViewCenter -> {1/2, 1/2, 1/2}, 
ViewVertical -> {1, 1, 1}, Boxed -> False, ImageSize -> 300],
{x, 0, 2 Pi/3 - Pi/48, Pi/24}];

Export["enveloped.gif", enveloped, "GraphicsList", "DisplayDurations" -> {.05}]

Answer




The variation in size is due to variation in camera position and viewing angle. Since ViewPoint uses special coordinates which depend on the bounding box it's better to use ViewVector instead (or even ViewMatrix if you can make it work). To keep the viewing angle fixed you should give an explicit value for ViewAngle. To place the object at the right position in the field of view you could use ViewCentre. For the example above you could do something like


cubes = Table[
  Graphics3D[{Rotate[cube, x, {1, 1, 1}, {0, 0, 0}]}, 
   ViewVector -> {3, 1/2, -2}, 
   ViewAngle -> 35 Degree,
   ViewCenter -> {.5, .5, .5},
   ViewVertical -> {1, 1, 1}, Boxed -> False],
  {x, 0, 2 Pi/3 - Pi/48, Pi/24}]

Comments

Post a Comment

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[ ...
Post a Comment
Read more

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...
Post a Comment
Read more

Is there a way to do conditional matrix loop using 'continue'

I have the following: n = 3; m = 5; ww = RandomReal[{0, 0.1}, {n, n}]; uu = RandomReal[{0, 1}, {m, n}]; pp = RandomReal[{0, 1}, {n, n}]; ss = RandomInteger[{0, 5}, {m, n}]; Grid[{{"ww", "uu", "pp", "ss"}, {ww // TableForm, uu // TableForm, pp // TableForm, ss // TableForm}}, Spacings -> {5, 2}, Dividers -> All] where I would like to look at every element of matrix ss and produce a matrix tt , with zeroes at the locations in ss which have zeroes, and in all other positions do the following: tt = (-1/Subscript[ww, m]) Log[(1 - uu)/(Subscript[pp, m - 1])], where Subscript[ww, m] is the value at index of ww matrix and where Subscript[pp, m - 1] is the value at index-1 of pp matrix. So for example if the first value ever read from matrix ss happens to be 2, then value taken from matrix ww would be from the row 2, but from pp would be from row 1. Also how to tell difference between a 0 as a valid value from within the matrix elemen...
Post a Comment
Read more