[Commit] cairo ChangeLog, 1.65, 1.66 TODO, 1.6, 1.7 configure.in, 1.18, 1.19

[Carl Worth]

Committed by: cworth

Update of /local/src/CVS/cairo
In directory home.keithp.com:/tmp/cvs-serv7386

Modified Files:
	ChangeLog TODO configure.in 
Log Message:
Added cairo_arc and cairo_arc_negative.

Index: ChangeLog
===================================================================
RCS file: /local/src/CVS/cairo/ChangeLog,v
retrieving revision 1.65
retrieving revision 1.66
diff -u -d -r1.65 -r1.66
--- ChangeLog	27 Sep 2003 12:08:38 -0000	1.65
+++ ChangeLog	29 Sep 2003 15:36:29 -0000	1.66
@@ -1,4 +1,23 @@
-2003-09-27  Carl Worth  <cworth at isi.edu>
+2003-09-29  Carl Worth  <cworth at isi.edu>
+
+	* configure.in (CAIRO_VERSION): Bumpred version to 0.1.6 to
+	indicate new cairo_arc and cairo_arc_negative.
+
+	* src/cairo_gstate.c (_arc_error_normalized):
+	(_arc_max_angle_for_tolerance_normalized):
+	(_cairo_gstate_arc_segments_needed):
+	(_cairo_gstate_arc_segment):
+	(_cairo_gstate_arc_dir):
+	(_cairo_gstate_arc):
+	(_cairo_gstate_arc_negative): Several new functions to implement
+	arc support.
+
+	* src/cairo.h: Added cairo_arc and cairo_arc_negative.
+
+	* src/cairo.c (cairo_arc): 
+	(cairo_arc_negative): Added new arc support.
+
+2003-09-27  Carl Worth  <cworth at isi.edu>	
 
 	* src/cairoint.h: Fixed several enum symbols that had been
 	mistakenly converted to lowercase at some point.

Index: TODO
===================================================================
RCS file: /local/src/CVS/cairo/TODO,v
retrieving revision 1.6
retrieving revision 1.7
diff -u -d -r1.6 -r1.7
--- TODO	17 Sep 2003 15:48:41 -0000	1.6
+++ TODO	29 Sep 2003 15:36:29 -0000	1.7
@@ -11,12 +11,13 @@
 
 * Verification, profiling, optimization.
 
-
 Some notes on arc support
--------------------------
+=========================
 
-"Approximation of circular arcs by cubic poynomials", Michael Goldapp,
-Computer Aided Geometric Design 8 (1991) 227-238.
+Some general notions
+--------------------
+This is from "Approximation of circular arcs by cubic poynomials",
+Michael Goldapp, Computer Aided Geometric Design 8 (1991) 227-238.
 
 To draw a unit arc from 0 to A with 0 < A < pi/2:
 
@@ -37,9 +38,14 @@
 
 	e(t) = x^2(t) + y^2(t) - 1
 
-And from Dokken[cite]: e(t) ~ 2 abs( rho(t) )
+And from "Good approximation of circles by curvature-continuous Bezier
+curves", Tor Dokken and Morten Daehlen, Computer Aided Geometric
+Design 8 (1990) 22-41, we learn:
 
-A single cubic Bezier spline approximation must have the 4 control points:
+	e(t) ~ 2 abs( rho(t) )
+
+Continuing with Goldapp's analysis, a single cubic Bezier spline
+approximation must have the 4 control points:
 
 	(1, 0)
 	(1, h)
@@ -55,7 +61,38 @@
 
 	abs( max(e(t)) ) = 4/27 * (sin^6 (A/4)) / (cos^2 (A/4))
 	    t in [0,1]
-	
+
+-----
+
+Now, for Cairo we want to draw an arc of radius R from an angle A to
+an angle B, (where B > A). So the equations above have trivial
+modifications:
+
+The spline control points become
+
+	(R * cos(A), R * sin(A))
+	(R * cos(A) - h * sin(A), R * sin(A) + h * cos (A))
+	(R * cos(B) + h * sin(B), R * sin(B) - h * cos (B))
+	(R * cos(B), R * sin(B))
+
+where	h = 4/3 * R * tan ((B-A)/4)
+
+And the maximum deviation in radius is approximately:
+
+	2/27 * (sin^6 ((B-A)/4) / cos^2 ((B-A)/4))
+
+So now we can get down to writing some C code:
+
+double
+_arc_error_normalized (double angle)
+{
+    return 2/27 * pow (sin (angle / 4), 6) / pow (cos (angle / 4), 2);
+}
+
+And for accurate drawing the following must hold in device space:
+
+	tolerance/radius >= _arc_error_normalized (B-A)
+
 A comparison with PostScript
 ============================
 
@@ -190,4 +227,3 @@
 Type,Attribute,and Conversion Operators, File Operators, Resource
 Operators, Virtual Memory Operators, Miscellaneous Operators,
 Interpreter Parameter Operators, Errors
-

Index: configure.in
===================================================================
RCS file: /local/src/CVS/cairo/configure.in,v
retrieving revision 1.18
retrieving revision 1.19
diff -u -d -r1.18 -r1.19
--- configure.in	25 Sep 2003 22:01:28 -0000	1.18
+++ configure.in	29 Sep 2003 15:36:29 -0000	1.19
@@ -3,7 +3,7 @@
 dnl ===========================================================================
 
 # Package version number, (as distinct from shared library version)
-CAIRO_VERSION=0.1.5
+CAIRO_VERSION=0.1.6
 
 # libtool shared library version