exporting patch:
# HG changeset patch
# User Daniel J Sebald <address@hidden>
# Date 1470990389 18000
#      Fri Aug 12 03:26:29 2016 -0500
# Node ID e6b3a5fcd3ee4c71e4e42da15f33a0858dce72f7
# Parent  16efd0403698c1736db5aeeeadf08738cfece1a8
Use rotation matrix multiplication for rendering a circle

* gl-render.cc (make_marker_list): Rotate a vector starting at (sz/2,0)
  incrementally rather than use trig functions.

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
@@ -3845,11 +3845,21 @@ opengl_renderer::make_marker_list (const
         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;
+        float m11 = cos (M_PI/div);
+        float m21 = sin (M_PI/div);
+        float m12 = -m21;
+        float m22 = m11;
+        float x = sz/2;
+        float y = 0;
+        div *= 2;
 
         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 i = 0; i < div; i++) {
+          glVertex2d (x, y);
+          float xx = x;
+          x = m11*xx + m12*y;
+          y = m21*xx + m22*y;
+        }
         glEnd ();
       }
       break;