211 lines
6.9 KiB
Groff
211 lines
6.9 KiB
Groff
From d6d6c61c8d0e336c34ba3f5d9adbe923ffa1cbe3 Mon Sep 17 00:00:00 2001
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From: Behdad Esfahbod <behdad@behdad.org>
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Date: Thu, 6 Aug 2015 15:34:38 +0100
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Subject: [PATCH 2/6] Implement more robust winding-direction algorithm
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Fixes 'p' in Comic Sans Bold for example. That font has many
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self-intersecting contours. The one in 'p' was causing complete
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winding direction reversal using old algorithm. Implement area-based
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algorithm.
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---
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src/glyphy-outline.cc | 67 ++++++++++-----------------------------------------
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1 file changed, 13 insertions(+), 54 deletions(-)
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diff --git a/src/glyphy-outline.cc b/src/glyphy-outline.cc
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index 3543f3b..ef71247 100644
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--- a/src/glyphy-outline.cc
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+++ b/src/glyphy-outline.cc
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@@ -55,65 +55,24 @@ winding (const glyphy_arc_endpoint_t *endpoints,
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/*
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* Algorithm:
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*
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- * - Find the lowest-x part of the contour,
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- * - If the point is an endpoint:
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- * o compare the angle of the incoming and outgoing edges of that point
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- * to find out whether it's CW or CCW,
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- * - Otherwise, compare the y of the two endpoints of the arc with lowest-x point.
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- *
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- * Note:
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- *
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- * We can use a simpler algorithm here: Act as if arcs are lines, then use the
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- * triangle method to calculate the signed area of the contour and get the sign.
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- * It should work for all cases we care about. The only case failing would be
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- * that of two endpoints and two arcs. But we can even special-case that.
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+ * - Approximate arcs with triangles passing through the mid- and end-points,
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+ * - Calculate the area of the contour,
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+ * - Return sign.
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*/
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- unsigned int corner = 1;
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- for (unsigned int i = 2; i < num_endpoints; i++)
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- if (endpoints[i].p.x < endpoints[corner].p.x ||
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- (endpoints[i].p.x == endpoints[corner].p.x &&
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- endpoints[i].p.y < endpoints[corner].p.y))
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- corner = i;
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-
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- double min_x = endpoints[corner].p.x;
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- int winner = -1;
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- Point p0 (0, 0);
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- for (unsigned int i = 0; i < num_endpoints; i++) {
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- const glyphy_arc_endpoint_t &endpoint = endpoints[i];
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- if (endpoint.d == GLYPHY_INFINITY || endpoint.d == 0 /* arcs only, not lines */) {
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- p0 = endpoint.p;
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- continue;
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- }
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- Arc arc (p0, endpoint.p, endpoint.d);
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- p0 = endpoint.p;
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+ double area = 0;
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+ for (unsigned int i = 1; i < num_endpoints; i++)
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+ {
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+ const glyphy_point_t &p0 = endpoints[i - 1].p;
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+ const glyphy_point_t &p1 = endpoints[i].p;
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+ double d = endpoints[i].d;
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- Point c = arc.center ();
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- double r = arc.radius ();
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- if (c.x - r < min_x && arc.wedge_contains_point (c - Vector (r, 0))) {
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- min_x = c.x - r;
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- winner = i;
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- }
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- }
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+ assert (d != GLYPHY_INFINITY);
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- if (winner == -1)
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- {
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- // Corner is lowest-x. Find the tangents of the two arcs connected to the
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- // corner and compare the tangent angles to get contour direction.
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- const glyphy_arc_endpoint_t ethis = endpoints[corner];
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- const glyphy_arc_endpoint_t eprev = endpoints[corner - 1];
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- const glyphy_arc_endpoint_t enext = endpoints[corner < num_endpoints - 1 ? corner + 1 : 1];
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- double in = (-Arc (eprev.p, ethis.p, ethis.d).tangents ().second).angle ();
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- double out = (+Arc (ethis.p, enext.p, enext.d).tangents ().first ).angle ();
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- return out > in;
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+ area += p0.x*p1.y - p0.y*p1.x;
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+ area -= .5 * d * ((p1.x-p0.x)*(p1.x-p0.x) + (p1.y-p0.y)*(p1.y-p0.y));
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}
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- else
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- {
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- // Easy.
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- return endpoints[winner].d < 0;
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- }
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-
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- return false;
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+ return area < 0;
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}
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--
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2.5.0
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From 644c5bab6e7f0e5af8f42fa7a8075372716c66d3 Mon Sep 17 00:00:00 2001
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From: Behdad Esfahbod <behdad@behdad.org>
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Date: Thu, 6 Aug 2015 15:49:37 +0100
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Subject: [PATCH 3/6] Start handling fully-degenerate curves
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---
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src/glyphy-arcs-bezier.hh | 7 +++++++
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src/glyphy-geometry.hh | 4 ++++
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2 files changed, 11 insertions(+)
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diff --git a/src/glyphy-arcs-bezier.hh b/src/glyphy-arcs-bezier.hh
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index ab729cb..32b7c8c 100644
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--- a/src/glyphy-arcs-bezier.hh
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+++ b/src/glyphy-arcs-bezier.hh
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@@ -103,6 +103,13 @@ class ArcsBezierApproximatorSpringSystem
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double *perror,
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unsigned int max_segments = 100)
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{
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+ /* Handle fully-degenerate cases. */
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+ Vector v1 (b.p1 - b.p0);
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+ Vector v2 (b.p2 - b.p0);
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+ Vector v3 (b.p3 - b.p0);
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+ if (fabs (v1.cross(v2)) < GLYPHY_EPSILON && fabs (v2.cross(v3)) < GLYPHY_EPSILON)
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+ ;//TODO
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+
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std::vector<double> t;
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std::vector<double> e;
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double max_e, min_e;
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diff --git a/src/glyphy-geometry.hh b/src/glyphy-geometry.hh
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index f5f6003..3c60856 100644
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--- a/src/glyphy-geometry.hh
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+++ b/src/glyphy-geometry.hh
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@@ -99,6 +99,7 @@ struct Vector {
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inline const Vector normal (void) const; /* ortho().normalized() */
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inline double angle (void) const;
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+ inline double cross (const Vector &other) const;
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inline const Vector rebase (const Vector &bx, const Vector &by) const;
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inline const Vector rebase (const Vector &bx) const;
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@@ -345,6 +346,9 @@ inline double Vector::angle (void) const {
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return atan2 (dy, dx);
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}
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+inline double Vector::cross (const Vector &other) const {
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+ return dx * other.dy - dy * other.dx;
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+}
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inline const Vector Vector::rebase (const Vector &bx,
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const Vector &by) const {
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return Vector (*this * bx, *this * by);
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--
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2.5.0
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From 5667ab11a3d5f57bb89c4e8970d26b940d36964a Mon Sep 17 00:00:00 2001
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From: Behdad Esfahbod <behdad@behdad.org>
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Date: Thu, 6 Aug 2015 15:51:15 +0100
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Subject: [PATCH 4/6] Simplify winding()
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---
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src/glyphy-outline.cc | 4 ++--
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1 file changed, 2 insertions(+), 2 deletions(-)
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diff --git a/src/glyphy-outline.cc b/src/glyphy-outline.cc
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index ef71247..7fded28 100644
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--- a/src/glyphy-outline.cc
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+++ b/src/glyphy-outline.cc
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@@ -69,8 +69,8 @@ winding (const glyphy_arc_endpoint_t *endpoints,
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assert (d != GLYPHY_INFINITY);
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- area += p0.x*p1.y - p0.y*p1.x;
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- area -= .5 * d * ((p1.x-p0.x)*(p1.x-p0.x) + (p1.y-p0.y)*(p1.y-p0.y));
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+ area += Vector(p0).cross (Vector(p1));
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+ area -= .5 * d * (Point(p1) - Point(p0)).len2 ();
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}
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return area < 0;
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}
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--
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2.5.0
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From 16fa0a713295a76f3075e6732007dca2dd38d11e Mon Sep 17 00:00:00 2001
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From: Behdad Esfahbod <behdad@behdad.org>
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Date: Thu, 6 Aug 2015 16:00:19 +0100
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Subject: [PATCH 5/6] Better handle fully-degenerate curves
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---
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src/glyphy-arcs-bezier.hh | 9 ++++++++-
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1 file changed, 8 insertions(+), 1 deletion(-)
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diff --git a/src/glyphy-arcs-bezier.hh b/src/glyphy-arcs-bezier.hh
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index 32b7c8c..ac210c0 100644
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--- a/src/glyphy-arcs-bezier.hh
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+++ b/src/glyphy-arcs-bezier.hh
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@@ -108,7 +108,14 @@ class ArcsBezierApproximatorSpringSystem
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Vector v2 (b.p2 - b.p0);
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Vector v3 (b.p3 - b.p0);
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if (fabs (v1.cross(v2)) < GLYPHY_EPSILON && fabs (v2.cross(v3)) < GLYPHY_EPSILON)
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- ;//TODO
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+ {
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+ /* Curve has no area. If endpoints are NOT the same, replace with single
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+ * line segment. Otherwise fully skip. */
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+ arcs.clear ();
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+ if (b.p0 != b.p1)
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+ arcs.push_back (Arc (b.p0, b.p1, 0));
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+ return;
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+ }
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std::vector<double> t;
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std::vector<double> e;
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--
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2.5.0
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