Re: plotted circle is regular decagon on opengl graphics

[Daniel J Sebald]

On 08/12/2016 12:13 AM, Daniel J Sebald wrote:
> On 08/11/2016 03:28 PM, Robert Funnell wrote:
> > On Thu, 11 Aug 2016, Rik wrote:
>
> > > > The performance cost is the cos/sin computations, not the underlying
> > > > driver.  The driver essentially sweeps out the same arc no matter how
> > > > fine the angular resolution is (i.e., it may draw more polygon lines,
> > > > but
> > > > the individual polygon lines are shorter so don't need as many
> > > > computations to complete).
> > >
> > > I'm happy to have something different in place.  The procedure here
> > > (http://slabode.exofire.net/circle_draw.shtml) uses only multiplications
> > > and additions and is possibly faster than either the trig approach or
> > > the
> > > sqrt approach.  Probably easy to benchmark all three options since the
> > > only
> > > thing that needs testing is the creation of the vertex points, not the
> > > actual calls to OpenGL.
>
> These are nice Rik.  It's sort of a differential approach.  I actually
> like the vector rotation at first blush, and since you already have the
> increment-angle calculation code you'd just need to compute the angular
> rotation matrix at the start.  The tangent-subtraction algorithm
> probably works fine with floating point precision, the risk being that
> any inaccuracy of the computation could accumulate and the start and end
> points don't quite meet up correctly.

Here's a patch that uses rotation matrix

[xnew]   [m11  m12] [x]
|    | = |        | | |
[ynew]   [m21  m22] [y]

Here's my very rough estimate for drawing three million circles:

graphics_toolkit ('qt');
plot(rand(3000000,1), rand(3000000,1), 'or');
set(get(gca,'children'),'MarkerSize',10);  ## Start counting until 
figure refresh
set(get(gca,'children'),'MarkerSize',100);  ## Start counting until 
figure refresh

                  3M size 10   3M size 100
                  ----------   -----------
rotation matrix:     15 s          24 s
  trigonometric:     15 s          27 s
           sqrt:     18 s          25 s

OpenGL must store the polygon vertices for redraw because this consumes 
a lot of memory.  By my guess, the sqrt method uses about 40% more 
memory, so it is probably more granulation than necessary.

One could play games of trying to minimize the number of vertices, but I 
don't think it is too critical as it seems to me the underlying OpenGL 
routines are what's consuming the most CPU time.  All of the above 
routines seem adequately efficient.

Dan

octave-nontrig_circle_symbol-djs2016aug12.patch
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