Re: plotted circle is regular decagon on opengl graphics

[Daniel J Sebald]

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.


> > --Rik
>
> FWIW, your mention of using only multiplications and additions reminded
> me of the algorithm that I've been using since 1985, from Van Aken
> (1984) (http://dx.doi.org/10.1109/MCG.1984.275994). It uses only additions.
>
> - Robert

Looks like a classic paper Robert.  These types of algorithms are what I 
meant by graphics hardware optimization, trying to find the utmost 
minimum calculations with simple computations (thereby not requiring a 
general purpose CPU, floating point co-processor unit, etc.) and still 
retain accuracy given pixel resolution.

Dan