exporting patch:
# HG changeset patch
# User Daniel J Sebald <address@hidden>
# Date 1470943121 18000
#      Thu Aug 11 14:18:41 2016 -0500
# Node ID e05e5775f7736d7bed7a2203f68edfeda95dedf5
# Parent  16efd0403698c1736db5aeeeadf08738cfece1a8
Use non-trig formula for rendering a circle

* gl-render.cc (make_marker_list): Sweep across the x-axis pixel resolution
  rather than arc angle when rendering circle symbol.

diff --git a/libinterp/corefcn/gl-render.cc b/libinterp/corefcn/gl-render.cc
--- a/libinterp/corefcn/gl-render.cc
+++ b/libinterp/corefcn/gl-render.cc
@@ -3841,15 +3841,14 @@ opengl_renderer::make_marker_list (const
       break;
     case 'o':
       {
-        int div = static_cast <int> (M_PI * sz / 4);
-        if (! (div % 2))
-          div += 1;               // ensure odd number for left/right symmetry
-        div = std::max (div, 5);  // ensure at least a few vertices are drawn
-        double ang_step = M_PI / div;
+        int x_limit = sz/2;
+        double x_limit_squared = x_limit * x_limit;
 
         glBegin (filled ? GL_POLYGON : GL_LINE_LOOP);
-        for (double ang = 0; ang < 2*M_PI; ang += ang_step)
-          glVertex2d (sz/2*cos (ang), sz/2*sin (ang));
+        for (int x = x_limit; x > -x_limit; x--)
+          glVertex2d (x, sqrt (x_limit_squared - x*x));
+        for (int x = -x_limit; x < x_limit; x++)
+          glVertex2d (x, -sqrt (x_limit_squared - x*x));
         glEnd ();
       }
       break;