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Re: Re: Fast interactive graphics

  • To: mathgroup at
  • Subject: [mg77713] Re: [mg77499] Re: Fast interactive graphics
  • From: John Fultz <jfultz at>
  • Date: Fri, 15 Jun 2007 04:39:31 -0400 (EDT)
  • Reply-to: jfultz at

Yes, your post brings up some important points about Manipulate which I'd like 
to address.

First, it's actually pretty uncommon that the speed of a Manipulate is affected 
by rendering time.  It can happen, but it's much more likely that the reason for
a Manipulate to slow down is because of computational time...i.e. it's doing theentire computation over again.  But whatever the cause, there's a lot you can doinside of Manipulate to affect the results.  Some illustrations...

 Show[Plot3D[Sin[x y], {x, 0, 5}, {y, 0, 5}, Filling -> Bottom, 
   PlotPoints -> 30], 
  Graphics3D[{PointSize[.1], Point[Append[xy, 1]]}]], {xy, {0, 0}, {5,

I've added the PlotPoints here to demonstrate the computational cost, and 
Filling to add rendering cost (you may remember a previous post where I 
indicated that adding transparency to a 3D graphic, as the default FillingStyle 
does, significantly increases rendering complexity).

The 2D slider in this example does nothing more than move the point around. 
But, in fact, whenever you're moving the slider, it's recomputing the entire
Show[] expression, including redoing the Plot3D from scratch every time.  
However, while you're moving the slider, the quality of the resulting graphic
is lower, which significantly reduces both computational and rendering complexity.  
This is because Manipulate is making a speed/quality tradeoff by applying the 
option PerformanceGoal to Plot3D.  We can manually override this by providing 
our own PerformanceGoal option to see how much better things look, and how much 
worse performance is...

 Show[Plot3D[Sin[x y], {x, 0, 5}, {y, 0, 5}, Filling -> Bottom, 
   PlotPoints -> 30, PerformanceGoal -> "Quality"], 
  Graphics3D[{PointSize[.1], Point[Append[xy, 1]]}]], {xy, {0, 0}, {5,

This looks wonderful, but the responsiveness is horrible.  We're now getting the 
full computational+rendering cost of the Plot3D every time we move the point.  
We can do better.  Since we know that the Plot3D is essentially a static 
element, we can direct Manipulate to only change the dynamic elements.  We do 
this by embedding Dynamic around the elements we want to be considered 
independently.  In this case, the only dynamic element is the coordinate of the 
Point (the fact that there is a point is static; only it's location is Dynamic). 
So, let's tweak the above by wrapping the Append in Dynamic...

 Show[Plot3D[Sin[x y], {x, 0, 5}, {y, 0, 5}, Filling -> Bottom, 
   PlotPoints -> 30, PerformanceGoal -> "Quality"], 
    Point[Dynamic[Append[xy, 1]]]}]], {xy, {0, 0}, {5, 5}}]

This is more responsive, but still pretty bad.  We're dealing here with less
time spent in the kernel and more time in the FE rebuilding the BSP tree and
using slower rendering methods because of the transparency.  Another stratagem 
to speed things up is to use the ControlActive function to change how things arebeing evaluated and/or rendered during the manipulation of a control.  So, in 
this case, we could use ControlActive to remove the Filling during the drag...

 Show[Plot3D[Sin[x y], {x, 0, 5}, {y, 0, 5}, 
   Filling -> ControlActive[xy; None, Bottom], PlotPoints -> 30, 
   PerformanceGoal -> "Quality"], 
    Point[Dynamic[Append[xy, 1]]]}]], {xy, {0, 0}, {5, 5}}]

Note that we had to make the ControlActive[] dependent upon the xy variable;
since Filling didn't have a natural dependency on xy, I added it to a 
CompoundExpression.  This, you'll find, is a good tradeoff of responsiveness and 
consistent quality.  There's a bit of a delay when you start and stop moving the 
control, but while you're moving it, the responsiveness is reasonable.

Finally, if you're willing to give up interactive updating, you could set 
ContinuousAction->False on the Manipulate.

Steve, you're absolutely right that sometimes you have to construct your own
Dynamic expressions and controls for maximum flexibility and performance.  
However, there's quite a lot which can be done with Manipulate, as well.

For more information on improving the performance of Manipulate, make sure to 
check out the Manipulate tutorials...


John Fultz
jfultz at
User Interface Group
Wolfram Research, Inc.

On Mon, 11 Jun 2007 04:17:02 -0400 (EDT), Steve Luttrell wrote:
> I have been experimenting to try to find a way of answering my own
> question.
> It seems that part of the problem was that using Manipulate introduuces
> some
> overheads that can be avoided by writing your own interactive graphics
> code.
> The code below is the result of some experimentation that shows a useful
> level of interactive manipulation of a 2-dimensional manifold.
> Define a cut-out region. This is a "window" within which the manifold is
> being interactively manipulated.
> cutout[\[Phi]_, \[Theta]_] := (9 \[Pi])/8 < \[Phi] < (13 \[Pi])/
> 8 && \[Pi]/4 < \[Theta] < (3 \[Pi])/4;
> Basic spherical region with a cut-out. This is a background graphic
> showing
> everything except the part that is being manipulated.
> g0 = ParametricPlot3D[{Sin[\[Theta]] Cos[\[Phi]],
> Sin[\[Theta]] Sin[\[Phi]], Cos[\[Theta]]}, {\[Phi], 0,
> 2 \[Pi]}, {\[Theta], 0, \[Pi]},
> RegionFunction -> (Not[cutout[#4, #5]] &)];
> Define a fiducial point. This is the location of the tip of a "nose"-like
> protrusion that is being manipulated around the manifold.
> {\[Phi]1, \[Theta]1} = {(11 \[Pi])/8, \[Pi]/2};
> Slider2D[Dynamic[{\[Phi]1, \[Theta]1}], {{0, \[Pi]}, {2 \[Pi], 0}}]
> Dynamically updated display of everything.
> Dynamic[
> u = (1 +
> 0.5 Exp[-((\[Theta] - \[Theta]1)/0.25)^2 - ((\[Phi] - \[Phi]1)/
> 0.25)^2]) {Sin[\[Theta]] Cos[\[Phi]],
> Sin[\[Theta]] Sin[\[Phi]], Cos[\[Theta]]};
> p = 1.01 u /. {\[Theta] -> \[Theta]1, \[Phi] -> \[Phi]1};
> g1 = ParametricPlot3D[u, {\[Phi], 0, 2 \[Pi]}, {\[Theta], 0, \[Pi]},
> RegionFunction -> (cutout[#4, #5] &)];
> g2 = Graphics3D[{Red, PointSize[0.05], Point[p]}];
> Show[g0, g1, g2, PlotRange -> 2 {{-1, 1}, {-1, 1}, {-1, 1}},
> AxesLabel -> {"x", "y", "z"}]
> ]
> Now you can move the 2D slider around (slowly!) to adjust the position of
> the "nose" on the sphere. On my version of Mathematica (Windows XP 32-bit)
> as you move the slider you get a continuously updated fiducial point and
> "nose", but the mesh on the nose doesn't get drawn in until you release
> the
> mouse button. Also the border of the "nose" is not drawn in during the
> continuous updates.
> This code produces results that are a LOT better than the situation was
> when
> I wrote my original posting, and this approach may be a worthwhile
> starting
> point for this type of interactive manipulation.
> Steve Luttrell
> West Malvern, UK
> "Steve Luttrell" <steve at> wrote in message
> news:f4gmui$hpj$1 at
>> In version 6 I want to do interactive graphics where I use a controller
>> to
>> manipulate the shape of a curved 2-dimensional manifold (for instance).
>> This
>> is a type of interaction with Mathematica that should be of interest to
>> lots
>> of people.
>> The main problem that I have is that the redraw time after each
>> controller
>> movement is quite long. I need continuous feedback so that I can
>> immediately
>> see the effect of making various controller movements, so using
>> ContinuousAction->False in Manipulate (for instance) doesn't solve this
>> problem. I have tried various shortcuts such as skeletonising the
>> graphic
>> during updates so that it redraws quicker, but it is still too slow, and
>> will get worse for the more complicated graphics that I really want to
>> work
>> on.
>> As a general solution it would be great if it was possible to control
>> the
>> redrawing of graphics so that only those parts that need to be redrawn
>> are
>> actually redrawn, with the user taking responsibility for any
>> consequential
>> errors in the accumulated graphics rendering. Here I don't want to
>> simply
>> zoom the graphic to limit the rendered region, because I want to
>> interactively see the impact of my manipulations in the context of the
>> whole
>> graphic.
>> Does anyone know a way of imposing this type of control (see above) on
>> graphics rendering, or is it not actually possible in Mathematica? I
>> think
>> the answer is no, but I just want to make sure that I haven't
>> overlooked a
>> trick here.
>> Steve Luttrell
>> West Malvern, UK

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