commit 7c5ebcb01b183d37d0c4aebc5d1a1469ce8dd241
parent bb8be43f20d2e2b4200ba5d97ef040ab9cde2a78
Author: Kyle Milz <kyle@getaddrinfo.net>
Date: Sat, 19 Mar 2016 16:31:49 -0600
glyphy: initial import
Diffstat:
17 files changed, 3357 insertions(+), 1 deletion(-)
diff --git a/Makefile b/Makefile
@@ -1,4 +1,4 @@
-SUBDIR= instrument lib viewer
+SUBDIR= glyphy instrument lib viewer
test: all
prove
diff --git a/glyphy/Makefile b/glyphy/Makefile
@@ -0,0 +1,10 @@
+LIB= glyphy
+SRCS= glyphy-arc.cxx glyphy-arcs.cxx glyphy-blob.cxx glyphy-extents.cxx
+SRCS += glyphy-outline.cxx glyphy-sdf.cxx glyphy-shaders.cxx
+
+CFLAGS += -I. -DPKGDATADIR=""
+LDADD += -lstdc++
+
+NOPROFILE=1
+NO_PROFILE=1
+.include <bsd.lib.mk>
diff --git a/glyphy/glyphy-arc-bezier.hh b/glyphy/glyphy-arc-bezier.hh
@@ -0,0 +1,228 @@
+/*
+ * Copyright 2012,2013 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju
+ */
+
+#ifndef GLYPHY_ARC_BEZIER_HH
+#define GLYPHY_ARC_BEZIER_HH
+
+#include "glyphy-common.hh"
+#include "glyphy-geometry.hh"
+
+namespace GLyphy {
+namespace ArcBezier {
+
+using namespace Geometry;
+
+
+class MaxDeviationApproximatorExact
+{
+ public:
+ /* Returns 3 max(abs(d₀ t (1-t)² + d₁ t² (1-t)) for 0≤t≤1. */
+ static double approximate_deviation (double d0, double d1)
+ {
+ double candidates[4] = {0,1};
+ unsigned int num_candidates = 2;
+ if (d0 == d1)
+ candidates[num_candidates++] = .5;
+ else {
+ double delta = d0*d0 - d0*d1 + d1*d1;
+ double t2 = 1. / (3 * (d0 - d1));
+ double t0 = (2 * d0 - d1) * t2;
+ if (delta == 0)
+ candidates[num_candidates++] = t0;
+ else if (delta > 0) {
+ /* This code can be optimized to avoid the sqrt if the solution
+ * is not feasible (ie. lies outside (0,1)). I have implemented
+ * that in cairo-spline.c:_cairo_spline_bound(). Can be reused
+ * here.
+ */
+ double t1 = sqrt (delta) * t2;
+ candidates[num_candidates++] = t0 - t1;
+ candidates[num_candidates++] = t0 + t1;
+ }
+ }
+
+ double e = 0;
+ for (unsigned int i = 0; i < num_candidates; i++) {
+ double t = candidates[i];
+ double ee;
+ if (t < 0. || t > 1.)
+ continue;
+ ee = fabs (3 * t * (1-t) * (d0 * (1 - t) + d1 * t));
+ e = std::max (e, ee);
+ }
+
+ return e;
+ }
+};
+
+
+
+template <class MaxDeviationApproximator>
+class ArcBezierErrorApproximatorBehdad
+{
+ public:
+ static double approximate_bezier_arc_error (const Bezier &b0, const Arc &a)
+ {
+ assert (b0.p0 == a.p0);
+ assert (b0.p3 == a.p1);
+
+ double ea;
+ Bezier b1 = a.approximate_bezier (&ea);
+
+ assert (b0.p0 == b1.p0);
+ assert (b0.p3 == b1.p3);
+
+ Vector v0 = b1.p1 - b0.p1;
+ Vector v1 = b1.p2 - b0.p2;
+
+ Vector b = (b0.p3 - b0.p0).normalized ();
+ v0 = v0.rebase (b);
+ v1 = v1.rebase (b);
+
+ Vector v (MaxDeviationApproximator::approximate_deviation (v0.dx, v1.dx),
+ MaxDeviationApproximator::approximate_deviation (v0.dy, v1.dy));
+
+ /* Edge cases: If d*d is too close too large default to a weak bound. */
+ if (a.d * a.d > 1. - 1e-4)
+ return ea + v.len ();
+
+ /* If the wedge doesn't contain control points, default to weak bound. */
+ if (!a.wedge_contains_point (b0.p1) || !a.wedge_contains_point (b0.p2))
+ return ea + v.len ();
+
+ /* If straight line, return the max ortho deviation. */
+ if (fabs (a.d) < 1e-6)
+ return ea + v.dy;
+
+ /* We made sure that fabs(a.d) < 1 */
+ double tan_half_alpha = fabs (tan2atan (a.d));
+
+ double tan_v = v.dx / v.dy;
+
+ double eb;
+ if (fabs (tan_v) <= tan_half_alpha)
+ return ea + v.len ();
+
+ double c2 = (a.p1 - a.p0).len () * .5;
+ double r = a.radius ();
+
+ eb = Vector (c2 + v.dx, c2 / tan_half_alpha + v.dy).len () - r;
+ assert (eb >= 0);
+
+ return ea + eb;
+ }
+};
+
+
+
+template <class ArcBezierErrorApproximator>
+class ArcBezierApproximatorMidpointSimple
+{
+ public:
+ static const Arc approximate_bezier_with_arc (const Bezier &b, double *error)
+ {
+ Arc a (b.p0, b.p3, b.midpoint (), false);
+
+ *error = ArcBezierErrorApproximator::approximate_bezier_arc_error (b, a);
+
+ return a;
+ }
+};
+
+template <class ArcBezierErrorApproximator>
+class ArcBezierApproximatorMidpointTwoPart
+{
+ public:
+ static const Arc approximate_bezier_with_arc (const Bezier &b, double *error, double mid_t = .5)
+ {
+ Pair<Bezier > pair = b.split (mid_t);
+ Point m = pair.second.p0;
+
+ Arc a0 (b.p0, m, b.p3, true);
+ Arc a1 (m, b.p3, b.p0, true);
+
+ double e0 = ArcBezierErrorApproximator::approximate_bezier_arc_error (pair.first, a0);
+ double e1 = ArcBezierErrorApproximator::approximate_bezier_arc_error (pair.second, a1);
+ *error = std::max (e0, e1);
+
+ return Arc (b.p0, b.p3, m, false);
+ }
+};
+
+template <class ArcBezierErrorApproximator>
+class ArcBezierApproximatorQuantized
+{
+ public:
+ ArcBezierApproximatorQuantized (double _max_d = GLYPHY_INFINITY, unsigned int _d_bits = 0) :
+ max_d (_max_d), d_bits (_d_bits) {};
+
+ protected:
+ double max_d;
+ unsigned int d_bits;
+
+ public:
+ const Arc approximate_bezier_with_arc (const Bezier &b, double *error) const
+ {
+ double mid_t = .5;
+ Arc a (b.p0, b.p3, b.point (mid_t), false);
+ Arc orig_a = a;
+
+ if (isfinite (max_d)) {
+ assert (max_d >= 0);
+ if (fabs (a.d) > max_d)
+ a.d = a.d < 0 ? -max_d : max_d;
+ }
+ if (d_bits && max_d != 0) {
+ assert (isfinite (max_d));
+ assert (fabs (a.d) <= max_d);
+ int mult = (1 << (d_bits - 1)) - 1;
+ int id = round (a.d / max_d * mult);
+ assert (-mult <= id && id <= mult);
+ a.d = id * max_d / mult;
+ assert (fabs (a.d) <= max_d);
+ }
+
+ /* Error introduced by arc quantization */
+ double ed = fabs (a.d - orig_a.d) * (a.p1 - a.p0).len () * .5;
+
+ ArcBezierApproximatorMidpointTwoPart<ArcBezierErrorApproximator>
+ ::approximate_bezier_with_arc (b, error, mid_t);
+
+ if (ed) {
+ *error += ed;
+
+ /* Try a simple one-arc approx which works with the quantized arc.
+ * May produce smaller error bound. */
+ double e = ArcBezierErrorApproximator::approximate_bezier_arc_error (b, a);
+ if (e < *error)
+ *error = e;
+ }
+
+ return a;
+ }
+};
+
+typedef MaxDeviationApproximatorExact MaxDeviationApproximatorDefault;
+typedef ArcBezierErrorApproximatorBehdad<MaxDeviationApproximatorDefault> ArcBezierErrorApproximatorDefault;
+typedef ArcBezierApproximatorMidpointTwoPart<ArcBezierErrorApproximatorDefault> ArcBezierApproximatorDefault;
+typedef ArcBezierApproximatorQuantized<ArcBezierErrorApproximatorDefault> ArcBezierApproximatorQuantizedDefault;
+
+} /* namespace ArcBezier */
+} /* namespace GLyphy */
+
+#endif /* GLYPHY_ARC_BEZIER_HH */
diff --git a/glyphy/glyphy-arc.cxx b/glyphy/glyphy-arc.cxx
@@ -0,0 +1,137 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju, Wojciech Baranowski
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "glyphy-common.hh"
+#include "glyphy-geometry.hh"
+#include "glyphy-arc-bezier.hh"
+
+using namespace GLyphy::Geometry;
+using namespace GLyphy::ArcBezier;
+
+
+
+/*
+ * Circular arcs
+ */
+
+
+/* Build from a conventional arc representation */
+void
+glyphy_arc_from_conventional (const glyphy_point_t *center,
+ double radius,
+ double angle0,
+ double angle1,
+ glyphy_bool_t negative,
+ glyphy_arc_t *arc)
+{
+ *arc = Arc (*center, radius, angle0, angle1, negative);
+};
+
+/* Convert to a conventional arc representation */
+void
+glyphy_arc_to_conventional (glyphy_arc_t arc,
+ glyphy_point_t *center /* may be NULL */,
+ double *radius /* may be NULL */,
+ double *angle0 /* may be NULL */,
+ double *angle1 /* may be NULL */,
+ glyphy_bool_t *negative /* may be NULL */)
+{
+ Arc a (arc);
+ if (radius) *radius = a.radius ();
+ if (center || angle0 || angle1) {
+ Point c = a.center ();
+ if (center) *center = c;
+ if (angle0) *angle0 = (a.p0 - c).angle ();
+ if (angle1) *angle1 = (a.p1 - c).angle ();
+ if (negative) *negative = a.d < 0;
+ }
+}
+
+glyphy_bool_t
+glyphy_arc_is_a_line (glyphy_arc_t arc)
+{
+ return arc.d == 0;
+}
+
+void
+glyphy_arc_extents (glyphy_arc_t arc,
+ glyphy_extents_t *extents)
+{
+ Arc(arc).extents (*extents);
+}
+
+
+/*
+ * Approximate single pieces of geometry to/from one arc
+ */
+
+
+void
+glyphy_arc_from_line (const glyphy_point_t *p0,
+ const glyphy_point_t *p1,
+ glyphy_arc_t *arc)
+{
+ *arc = Arc (*p0, *p1, 0);
+}
+
+void
+glyphy_arc_from_conic (const glyphy_point_t *p0,
+ const glyphy_point_t *p1,
+ const glyphy_point_t *p2,
+ glyphy_arc_t *arc,
+ double *error)
+{
+ Point p1_ (Point (*p0).lerp (2/3., *p1));
+ Point p2_ (Point (*p2).lerp (2/3., *p1));
+ glyphy_arc_from_cubic (p0,
+ &p1_,
+ &p2_,
+ p2,
+ arc,
+ error);
+}
+
+void
+glyphy_arc_from_cubic (const glyphy_point_t *p0,
+ const glyphy_point_t *p1,
+ const glyphy_point_t *p2,
+ const glyphy_point_t *p3,
+ glyphy_arc_t *arc,
+ double *error)
+{
+ *arc = ArcBezierApproximatorDefault::approximate_bezier_with_arc (Bezier (*p0, *p1, *p2, *p3), error);
+}
+
+void
+glyphy_arc_to_cubic (const glyphy_arc_t *arc,
+ glyphy_point_t *p0,
+ glyphy_point_t *p1,
+ glyphy_point_t *p2,
+ glyphy_point_t *p3,
+ double *error)
+{
+ Bezier b = Arc (*arc).approximate_bezier (error);
+ *p0 = arc->p0;
+ *p1 = b.p1;
+ *p2 = b.p2;
+ *p3 = arc->p1;
+}
diff --git a/glyphy/glyphy-arcs-bezier.hh b/glyphy/glyphy-arcs-bezier.hh
@@ -0,0 +1,153 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju
+ */
+
+#ifndef GLYPHY_ARCS_BEZIER_HH
+#define GLYPHY_ARCS_BEZIER_HH
+
+#include "glyphy-common.hh"
+#include "glyphy-geometry.hh"
+#include "glyphy-arc-bezier.hh"
+
+namespace GLyphy {
+namespace ArcsBezier {
+
+using namespace Geometry;
+using namespace ArcBezier;
+
+template <class ArcBezierApproximator>
+class ArcsBezierApproximatorSpringSystem
+{
+ static inline void calc_arcs (const Bezier &b,
+ const std::vector<double> &t,
+ const ArcBezierApproximator &appx,
+ std::vector<double> &e,
+ std::vector<Arc > &arcs,
+ double &max_e, double &min_e)
+ {
+ unsigned int n = t.size () - 1;
+ e.resize (n);
+ arcs.clear ();
+ max_e = 0;
+ min_e = GLYPHY_INFINITY;
+ for (unsigned int i = 0; i < n; i++)
+ {
+ Bezier segment = b.segment (t[i], t[i + 1]);
+ arcs.push_back (appx.approximate_bezier_with_arc (segment, &e[i]));
+
+ max_e = std::max (max_e, e[i]);
+ min_e = std::min (min_e, e[i]);
+ }
+ }
+
+ static inline void jiggle (const Bezier &b,
+ const ArcBezierApproximator &appx,
+ std::vector<double> &t,
+ std::vector<double> &e,
+ std::vector<Arc > &arcs,
+ double &max_e, double &min_e,
+ double tolerance,
+ unsigned int &n_jiggle)
+ {
+ unsigned int n = t.size () - 1;
+ double conditioner = tolerance * .01;
+ //fprintf (stderr, "candidate n %d max_e %g min_e %g\n", n, max_e, min_e);
+ unsigned int max_jiggle = log2 (n) + 1;
+ unsigned int s;
+ for (s = 0; s < max_jiggle; s++)
+ {
+ double total = 0;
+ for (unsigned int i = 0; i < n; i++) {
+ double l = t[i + 1] - t[i];
+ double k_inv = l * pow (e[i] + conditioner, -.3);
+ total += k_inv;
+ e[i] = k_inv;
+ }
+ for (unsigned int i = 0; i < n; i++) {
+ double k_inv = e[i];
+ double l = k_inv / total;
+ t[i + 1] = t[i] + l;
+ }
+ t[n] = 1.0; // Do this to get real 1.0, not .9999999999999998!
+
+ calc_arcs (b, t, appx, e, arcs, max_e, min_e);
+
+ //fprintf (stderr, "n %d jiggle %d max_e %g min_e %g\n", n, s, max_e, min_e);
+
+ n_jiggle++;
+ if (max_e < tolerance || (2 * min_e - max_e > tolerance))
+ break;
+ }
+ //if (s == max_jiggle) fprintf (stderr, "JIGGLE OVERFLOW n %d s %d\n", n, s);
+ }
+
+ public:
+ static void approximate_bezier_with_arcs (const Bezier &b,
+ double tolerance,
+ const ArcBezierApproximator &appx,
+ std::vector<Arc> &arcs,
+ double *perror,
+ unsigned int max_segments = 100)
+ {
+ /* Handle fully-degenerate cases. */
+ Vector v1 (b.p1 - b.p0);
+ Vector v2 (b.p2 - b.p0);
+ Vector v3 (b.p3 - b.p0);
+ if (fabs (v1.cross(v2)) < GLYPHY_EPSILON && fabs (v2.cross(v3)) < GLYPHY_EPSILON)
+ {
+ /* Curve has no area. If endpoints are NOT the same, replace with single
+ * line segment. Otherwise fully skip. */
+ arcs.clear ();
+ if (b.p0 != b.p1)
+ arcs.push_back (Arc (b.p0, b.p1, 0));
+ return;
+ }
+
+ std::vector<double> t;
+ std::vector<double> e;
+ double max_e, min_e;
+ unsigned int n_jiggle = 0;
+
+ /* Technically speaking we can bsearch for n. */
+ for (unsigned int n = 1; n <= max_segments; n++)
+ {
+ t.resize (n + 1);
+ for (unsigned int i = 0; i < n; i++)
+ t[i] = double (i) / n;
+ t[n] = 1.0; // Do this out of the loop to get real 1.0, not .9999999999999998!
+
+ calc_arcs (b, t, appx, e, arcs, max_e, min_e);
+
+ for (unsigned int i = 0; i < n; i++)
+ if (e[i] <= tolerance) {
+ jiggle (b, appx, t, e, arcs, max_e, min_e, tolerance, n_jiggle);
+ break;
+ }
+
+ if (max_e <= tolerance)
+ break;
+ }
+ if (perror)
+ *perror = max_e;
+ //fprintf (stderr, "n_jiggle %d\n", n_jiggle);
+ }
+};
+
+} /* namespace ArcsBezier */
+} /* namespace GLyphy */
+
+#endif /* GLYPHY_ARCS_BEZIER_HH */
diff --git a/glyphy/glyphy-arcs.cxx b/glyphy/glyphy-arcs.cxx
@@ -0,0 +1,320 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju, Wojciech Baranowski
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "glyphy-common.hh"
+#include "glyphy-geometry.hh"
+#include "glyphy-arcs-bezier.hh"
+
+using namespace GLyphy::Geometry;
+using namespace GLyphy::ArcsBezier;
+
+
+
+/*
+ * Approximate outlines with multiple arcs
+ */
+
+
+struct glyphy_arc_accumulator_t {
+ unsigned int refcount;
+
+ double tolerance;
+ double max_d;
+ unsigned int d_bits;
+ glyphy_arc_endpoint_accumulator_callback_t callback;
+ void *user_data;
+
+ glyphy_point_t start_point;
+ glyphy_point_t current_point;
+ bool need_moveto;
+ unsigned int num_endpoints;
+ double max_error;
+ glyphy_bool_t success;
+};
+
+
+glyphy_arc_accumulator_t *
+glyphy_arc_accumulator_create (void)
+{
+ glyphy_arc_accumulator_t *acc = (glyphy_arc_accumulator_t *) calloc (1, sizeof (glyphy_arc_accumulator_t));
+ acc->refcount = 1;
+
+ acc->tolerance = 5e-4;
+ acc->max_d = GLYPHY_MAX_D;
+ acc->d_bits = 8;
+ acc->callback = NULL;
+ acc->user_data = NULL;
+
+ glyphy_arc_accumulator_reset (acc);
+
+ return acc;
+}
+
+void
+glyphy_arc_accumulator_reset (glyphy_arc_accumulator_t *acc)
+{
+ acc->start_point = acc->current_point = Point (0, 0);
+ acc->need_moveto = true;
+ acc->num_endpoints = 0;
+ acc->max_error = 0;
+ acc->success = true;
+}
+
+void
+glyphy_arc_accumulator_destroy (glyphy_arc_accumulator_t *acc)
+{
+ if (!acc || --acc->refcount)
+ return;
+
+ free (acc);
+}
+
+glyphy_arc_accumulator_t *
+glyphy_arc_accumulator_reference (glyphy_arc_accumulator_t *acc)
+{
+ if (acc)
+ acc->refcount++;
+ return acc;
+}
+
+
+/* Configure acc */
+
+void
+glyphy_arc_accumulator_set_tolerance (glyphy_arc_accumulator_t *acc,
+ double tolerance)
+{
+ acc->tolerance = tolerance;
+}
+
+double
+glyphy_arc_accumulator_get_tolerance (glyphy_arc_accumulator_t *acc)
+{
+ return acc->tolerance;
+}
+
+void
+glyphy_arc_accumulator_set_callback (glyphy_arc_accumulator_t *acc,
+ glyphy_arc_endpoint_accumulator_callback_t callback,
+ void *user_data)
+{
+ acc->callback = callback;
+ acc->user_data = user_data;
+}
+
+void
+glyphy_arc_accumulator_get_callback (glyphy_arc_accumulator_t *acc,
+ glyphy_arc_endpoint_accumulator_callback_t *callback,
+ void **user_data)
+{
+ *callback = acc->callback;
+ *user_data = acc->user_data;
+}
+
+void
+glyphy_arc_accumulator_set_d_metrics (glyphy_arc_accumulator_t *acc,
+ double max_d,
+ double d_bits)
+{
+ acc->max_d = max_d;
+ acc->d_bits = d_bits;
+}
+
+void
+glyphy_arc_accumulator_get_d_metrics (glyphy_arc_accumulator_t *acc,
+ double *max_d,
+ double *d_bits)
+{
+ *max_d = acc->max_d;
+ *d_bits = acc->d_bits;
+}
+
+
+/* Accumulation results */
+
+unsigned int
+glyphy_arc_accumulator_get_num_endpoints (glyphy_arc_accumulator_t *acc)
+{
+ return acc->num_endpoints;
+}
+
+double
+glyphy_arc_accumulator_get_error (glyphy_arc_accumulator_t *acc)
+{
+ return acc->max_error;
+}
+
+glyphy_bool_t
+glyphy_arc_accumulator_successful (glyphy_arc_accumulator_t *acc)
+{
+ return acc->success;
+}
+
+
+/* Accumulate */
+
+static void
+emit (glyphy_arc_accumulator_t *acc, const Point &p, double d)
+{
+ glyphy_arc_endpoint_t endpoint = {p, d};
+ acc->success = acc->success && acc->callback (&endpoint, acc->user_data);
+ if (acc->success) {
+ acc->num_endpoints++;
+ acc->current_point = p;
+ }
+}
+
+static void
+accumulate (glyphy_arc_accumulator_t *acc, const Point &p, double d)
+{
+ if (Point (acc->current_point) == p)
+ return;
+ if (d == GLYPHY_INFINITY) {
+ /* Emit moveto lazily, for cleaner outlines */
+ acc->need_moveto = true;
+ acc->current_point = p;
+ return;
+ }
+ if (acc->need_moveto) {
+ emit (acc, acc->current_point, GLYPHY_INFINITY);
+ if (acc->success) {
+ acc->start_point = acc->current_point;
+ acc->need_moveto = false;
+ }
+ }
+ emit (acc, p, d);
+}
+
+static void
+move_to (glyphy_arc_accumulator_t *acc, const Point &p)
+{
+ if (!acc->num_endpoints || p != acc->current_point)
+ accumulate (acc, p, GLYPHY_INFINITY);
+}
+
+static void
+arc_to (glyphy_arc_accumulator_t *acc, const Point &p1, double d)
+{
+ accumulate (acc, p1, d);
+}
+
+static void
+bezier (glyphy_arc_accumulator_t *acc, const Bezier &b)
+{
+ double e;
+
+ std::vector<Arc> arcs;
+ typedef ArcBezierApproximatorQuantizedDefault _ArcBezierApproximator;
+ _ArcBezierApproximator appx (acc->max_d, acc->d_bits);
+ ArcsBezierApproximatorSpringSystem<_ArcBezierApproximator>
+ ::approximate_bezier_with_arcs (b, acc->tolerance, appx, arcs, &e);
+
+ acc->max_error = std::max (acc->max_error, e);
+
+ move_to (acc, b.p0);
+ for (unsigned int i = 0; i < arcs.size (); i++)
+ arc_to (acc, arcs[i].p1, arcs[i].d);
+}
+
+static void
+close_path (glyphy_arc_accumulator_t *acc)
+{
+ if (!acc->need_moveto && Point (acc->current_point) != Point (acc->start_point))
+ arc_to (acc, acc->start_point, 0);
+}
+
+void
+glyphy_arc_accumulator_move_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p0)
+{
+ move_to (acc, *p0);
+}
+
+void
+glyphy_arc_accumulator_line_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p1)
+{
+ arc_to (acc, *p1, 0);
+}
+
+void
+glyphy_arc_accumulator_conic_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p1,
+ const glyphy_point_t *p2)
+{
+ bezier (acc, Bezier (acc->current_point,
+ Point (acc->current_point).lerp (2/3., *p1),
+ Point (*p2).lerp (2/3., *p1),
+ *p2));
+}
+
+void
+glyphy_arc_accumulator_cubic_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p1,
+ const glyphy_point_t *p2,
+ const glyphy_point_t *p3)
+{
+ bezier (acc, Bezier (acc->current_point, *p1, *p2, *p3));
+}
+
+void
+glyphy_arc_accumulator_arc_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p1,
+ double d)
+{
+ arc_to (acc, *p1, d);
+}
+
+void
+glyphy_arc_accumulator_close_path (glyphy_arc_accumulator_t *acc)
+{
+ close_path (acc);
+}
+
+
+
+/*
+ * Outline extents from arc list
+ */
+
+
+void
+glyphy_arc_list_extents (const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ glyphy_extents_t *extents)
+{
+ Point p0 (0, 0);
+ glyphy_extents_clear (extents);
+ for (unsigned int i = 0; i < num_endpoints; i++) {
+ const glyphy_arc_endpoint_t &endpoint = endpoints[i];
+ if (endpoint.d == GLYPHY_INFINITY) {
+ p0 = endpoint.p;
+ continue;
+ }
+ Arc arc (p0, endpoint.p, endpoint.d);
+ p0 = endpoint.p;
+
+ glyphy_extents_t arc_extents;
+ arc.extents (arc_extents);
+ glyphy_extents_extend (extents, &arc_extents);
+ }
+}
diff --git a/glyphy/glyphy-blob.cxx b/glyphy/glyphy-blob.cxx
@@ -0,0 +1,328 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju, Wojciech Baranowski
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "glyphy-common.hh"
+#include "glyphy-geometry.hh"
+
+#define GRID_SIZE 24
+
+using namespace GLyphy::Geometry;
+
+
+#define UPPER_BITS(v,bits,total_bits) ((v) >> ((total_bits) - (bits)))
+#define LOWER_BITS(v,bits,total_bits) ((v) & ((1 << (bits)) - 1))
+
+#define MAX_X 4095
+#define MAX_Y 4095
+
+static inline glyphy_rgba_t
+arc_endpoint_encode (unsigned int ix, unsigned int iy, double d)
+{
+ glyphy_rgba_t v;
+
+ /* 12 bits for each of x and y, 8 bits for d */
+ assert (ix <= MAX_X);
+ assert (iy <= MAX_Y);
+ unsigned int id;
+ if (isinf (d))
+ id = 0;
+ else {
+ assert (fabs (d) <= GLYPHY_MAX_D);
+ id = 128 + lround (d * 127 / GLYPHY_MAX_D);
+ }
+ assert (id < 256);
+
+ v.r = id;
+ v.g = LOWER_BITS (ix, 8, 12);
+ v.b = LOWER_BITS (iy, 8, 12);
+ v.a = ((ix >> 8) << 4) | (iy >> 8);
+ return v;
+}
+
+static inline glyphy_rgba_t
+arc_list_encode (unsigned int offset, unsigned int num_points, int side)
+{
+ glyphy_rgba_t v;
+ v.r = 0; // unused for arc-list encoding
+ v.g = UPPER_BITS (offset, 8, 16);
+ v.b = LOWER_BITS (offset, 8, 16);
+ v.a = LOWER_BITS (num_points, 8, 8);
+ if (side < 0 && !num_points)
+ v.a = 255;
+ return v;
+}
+
+static inline glyphy_rgba_t
+line_encode (const Line &line)
+{
+ Line l = line.normalized ();
+ double angle = l.n.angle ();
+ double distance = l.c;
+
+ int ia = lround (-angle / M_PI * 0x7FFF);
+ unsigned int ua = ia + 0x8000;
+ assert (0 == (ua & ~0xFFFF));
+
+ int id = lround (distance * 0x1FFF);
+ unsigned int ud = id + 0x4000;
+ assert (0 == (ud & ~0x7FFF));
+
+ /* Marker for line-encoded */
+ ud |= 0x8000;
+
+ glyphy_rgba_t v;
+ v.r = ud >> 8;
+ v.g = ud & 0xFF;
+ v.b = ua >> 8;
+ v.a = ua & 0xFF;
+ return v;
+}
+
+
+/* Given a cell, fills the vector closest_arcs with arcs that may be closest to some point in the cell.
+ * Uses idea that all close arcs to cell must be ~close to center of cell.
+ */
+static void
+closest_arcs_to_cell (Point c0, Point c1, /* corners */
+ double faraway,
+ const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ std::vector<glyphy_arc_endpoint_t> &near_endpoints,
+ int *side)
+{
+ // Find distance between cell center
+ Point c = c0.midpoint (c1);
+ double min_dist = glyphy_sdf_from_arc_list (endpoints, num_endpoints, &c, NULL);
+
+ *side = min_dist >= 0 ? +1 : -1;
+ min_dist = fabs (min_dist);
+ std::vector<Arc> near_arcs;
+
+ // If d is the distance from the center of the square to the nearest arc, then
+ // all nearest arcs to the square must be at most almost [d + half_diagonal] from the center.
+ double half_diagonal = (c - c0).len ();
+ double radius_squared = pow (min_dist + half_diagonal, 2);
+ if (min_dist - half_diagonal <= faraway) {
+ Point p0 (0, 0);
+ for (unsigned int i = 0; i < num_endpoints; i++) {
+ const glyphy_arc_endpoint_t &endpoint = endpoints[i];
+ if (endpoint.d == GLYPHY_INFINITY) {
+ p0 = endpoint.p;
+ continue;
+ }
+ Arc arc (p0, endpoint.p, endpoint.d);
+ p0 = endpoint.p;
+
+ if (arc.squared_distance_to_point (c) <= radius_squared)
+ near_arcs.push_back (arc);
+ }
+ }
+
+ Point p1 = Point (0, 0);
+ for (unsigned i = 0; i < near_arcs.size (); i++)
+ {
+ Arc arc = near_arcs[i];
+
+ if (i == 0 || p1 != arc.p0) {
+ glyphy_arc_endpoint_t endpoint = {arc.p0, GLYPHY_INFINITY};
+ near_endpoints.push_back (endpoint);
+ p1 = arc.p0;
+ }
+
+ glyphy_arc_endpoint_t endpoint = {arc.p1, arc.d};
+ near_endpoints.push_back (endpoint);
+ p1 = arc.p1;
+ }
+}
+
+
+glyphy_bool_t
+glyphy_arc_list_encode_blob (const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ glyphy_rgba_t *blob,
+ unsigned int blob_size,
+ double faraway,
+ double avg_fetch_desired,
+ double *avg_fetch_achieved,
+ unsigned int *output_len,
+ unsigned int *nominal_width, /* 8bit */
+ unsigned int *nominal_height, /* 8bit */
+ glyphy_extents_t *pextents)
+{
+ glyphy_extents_t extents;
+ glyphy_extents_clear (&extents);
+
+ glyphy_arc_list_extents (endpoints, num_endpoints, &extents);
+
+ if (glyphy_extents_is_empty (&extents)) {
+ *pextents = extents;
+ if (!blob_size)
+ return false;
+ *blob = arc_list_encode (0, 0, +1);
+ *avg_fetch_achieved = 1;
+ *output_len = 1;
+ *nominal_width = *nominal_height = 1;
+ return true;
+ }
+
+ /* Add antialiasing padding */
+ extents.min_x -= faraway;
+ extents.min_y -= faraway;
+ extents.max_x += faraway;
+ extents.max_y += faraway;
+
+ double glyph_width = extents.max_x - extents.min_x;
+ double glyph_height = extents.max_y - extents.min_y;
+ double unit = std::max (glyph_width, glyph_height);
+
+ unsigned int grid_w = GRID_SIZE;
+ unsigned int grid_h = GRID_SIZE;
+
+ if (glyph_width > glyph_height) {
+ while ((grid_h - 1) * unit / grid_w > glyph_height)
+ grid_h--;
+ glyph_height = grid_h * unit / grid_w;
+ extents.max_y = extents.min_y + glyph_height;
+ } else {
+ while ((grid_w - 1) * unit / grid_h > glyph_width)
+ grid_w--;
+ glyph_width = grid_w * unit / grid_h;
+ extents.max_x = extents.min_x + glyph_width;
+ }
+
+ double cell_unit = unit / std::max (grid_w, grid_h);
+
+ std::vector<glyphy_rgba_t> tex_data;
+ std::vector<glyphy_arc_endpoint_t> near_endpoints;
+
+ unsigned int header_length = grid_w * grid_h;
+ unsigned int offset = header_length;
+ tex_data.resize (header_length);
+ Point origin = Point (extents.min_x, extents.min_y);
+ unsigned int total_arcs = 0;
+
+ for (unsigned int row = 0; row < grid_h; row++)
+ for (unsigned int col = 0; col < grid_w; col++)
+ {
+ Point cp0 = origin + Vector ((col + 0) * cell_unit, (row + 0) * cell_unit);
+ Point cp1 = origin + Vector ((col + 1) * cell_unit, (row + 1) * cell_unit);
+ near_endpoints.clear ();
+
+ int side;
+ closest_arcs_to_cell (cp0, cp1,
+ faraway,
+ endpoints, num_endpoints,
+ near_endpoints,
+ &side);
+
+#define QUANTIZE_X(X) (lround (MAX_X * ((X - extents.min_x) / glyph_width )))
+#define QUANTIZE_Y(Y) (lround (MAX_Y * ((Y - extents.min_y) / glyph_height)))
+#define DEQUANTIZE_X(X) (double (X) / MAX_X * glyph_width + extents.min_x)
+#define DEQUANTIZE_Y(Y) (double (Y) / MAX_Y * glyph_height + extents.min_y)
+#define SNAP(P) (Point (DEQUANTIZE_X (QUANTIZE_X ((P).x)), DEQUANTIZE_Y (QUANTIZE_Y ((P).y))))
+
+ if (near_endpoints.size () == 2 && near_endpoints[1].d == 0) {
+ Point c (extents.min_x + glyph_width * .5, extents.min_y + glyph_height * .5);
+ Line line (SNAP (near_endpoints[0].p), SNAP (near_endpoints[1].p));
+ line.c -= line.n * Vector (c);
+ line.c /= unit;
+ tex_data[row * grid_w + col] = line_encode (line);
+ continue;
+ }
+
+ /* If the arclist is two arcs that can be combined in encoding if reordered,
+ * do that. */
+ if (near_endpoints.size () == 4 &&
+ isinf (near_endpoints[2].d) &&
+ near_endpoints[0].p.x == near_endpoints[3].p.x &&
+ near_endpoints[0].p.y == near_endpoints[3].p.y)
+ {
+ glyphy_arc_endpoint_t e0, e1, e2;
+ e0 = near_endpoints[2];
+ e1 = near_endpoints[3];
+ e2 = near_endpoints[1];
+ near_endpoints.resize (0);
+ near_endpoints.push_back (e0);
+ near_endpoints.push_back (e1);
+ near_endpoints.push_back (e2);
+ }
+
+ for (unsigned i = 0; i < near_endpoints.size (); i++) {
+ glyphy_arc_endpoint_t &endpoint = near_endpoints[i];
+ tex_data.push_back (arc_endpoint_encode (QUANTIZE_X(endpoint.p.x), QUANTIZE_Y(endpoint.p.y), endpoint.d));
+ }
+
+ unsigned int current_endpoints = tex_data.size () - offset;
+
+ if (current_endpoints)
+ {
+ /* See if we can fulfill this cell by using already-encoded arcs */
+ const glyphy_rgba_t *needle = &tex_data[offset];
+ unsigned int needle_len = current_endpoints;
+ const glyphy_rgba_t *haystack = &tex_data[header_length];
+ unsigned int haystack_len = offset - header_length;
+
+ bool found = false;
+ while (haystack_len >= needle_len) {
+ /* Trick: we don't care about first endpoint's d value, so skip one
+ * byte in comparison. This works because arc_encode() packs the
+ * d value in the first byte. */
+ if (0 == memcmp (1 + (const char *) needle,
+ 1 + (const char *) haystack,
+ needle_len * sizeof (*needle) - 1)) {
+ found = true;
+ break;
+ }
+ haystack++;
+ haystack_len--;
+ }
+ if (found) {
+ unsigned int new_offset = haystack - &tex_data[0];
+ tex_data.resize (offset);
+ haystack = needle = NULL; /* Invalidated by the resize. */
+ offset = new_offset;
+ }
+ }
+ else
+ offset = 0;
+
+ tex_data[row * grid_w + col] = arc_list_encode (offset, current_endpoints, side);
+ offset = tex_data.size ();
+
+ total_arcs += current_endpoints;
+ }
+
+ if (avg_fetch_achieved)
+ *avg_fetch_achieved = 1 + double (total_arcs) / (grid_w * grid_h);
+
+ *pextents = extents;
+
+ if (tex_data.size () > blob_size)
+ return false;
+
+ memcpy (blob, &tex_data[0], tex_data.size () * sizeof(tex_data[0]));
+ *output_len = tex_data.size ();
+ *nominal_width = grid_w;
+ *nominal_height = grid_h;
+
+ return true;
+}
diff --git a/glyphy/glyphy-common-glsl.h b/glyphy/glyphy-common-glsl.h
@@ -0,0 +1,224 @@
+static const char *glyphy_common_glsl =
+"/*\n"
+" * Copyright 2012 Google, Inc. All Rights Reserved.\n"
+" *\n"
+" * Licensed under the Apache License, Version 2.0 (the \"License\");\n"
+" * you may not use this file except in compliance with the License.\n"
+" * You may obtain a copy of the License at\n"
+" *\n"
+" * http://www.apache.org/licenses/LICENSE-2.0\n"
+" *\n"
+" * Unless required by applicable law or agreed to in writing, software\n"
+" * distributed under the License is distributed on an \"AS IS\" BASIS,\n"
+" * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n"
+" * See the License for the specific language governing permissions and\n"
+" * limitations under the License.\n"
+" *\n"
+" * Google Author(s): Behdad Esfahbod, Maysum Panju\n"
+" */\n"
+"\n"
+"\n"
+"#ifndef GLYPHY_INFINITY\n"
+"# define GLYPHY_INFINITY 1e9\n"
+"#endif\n"
+"#ifndef GLYPHY_EPSILON\n"
+"# define GLYPHY_EPSILON 1e-5\n"
+"#endif\n"
+"\n"
+"#ifndef GLYPHY_RGBA\n"
+"# ifdef GLYPHY_BGRA\n"
+"# define GLYPHY_RGBA(v) glyphy_bgra (v)\n"
+"# else\n"
+"# define GLYPHY_RGBA(v) glyphy_rgba (v)\n"
+"# endif\n"
+"#endif\n"
+"\n"
+"vec4\n"
+"glyphy_rgba (const vec4 v)\n"
+"{\n"
+" return v.rgba;\n"
+"}\n"
+"\n"
+"vec4\n"
+"glyphy_bgra (const vec4 v)\n"
+"{\n"
+" return v.bgra;\n"
+"}\n"
+"\n"
+"\n"
+"struct glyphy_arc_t {\n"
+" vec2 p0;\n"
+" vec2 p1;\n"
+" float d;\n"
+"};\n"
+"\n"
+"struct glyphy_arc_endpoint_t {\n"
+" /* Second arc endpoint */\n"
+" vec2 p;\n"
+" /* Infinity if this endpoint does not form an arc with the previous\n"
+" * endpoint. Ie. a \"move_to\". Test with glyphy_isinf().\n"
+" * Arc depth otherwise. */\n"
+" float d;\n"
+"};\n"
+"\n"
+"struct glyphy_arc_list_t {\n"
+" /* Number of endpoints in the list.\n"
+" * Will be zero if we're far away inside or outside, in which case side is set.\n"
+" * Will be -1 if this arc-list encodes a single line, in which case line_* are set. */\n"
+" int num_endpoints;\n"
+"\n"
+" /* If num_endpoints is zero, this specifies whether we are inside (-1)\n"
+" * or outside (+1). Otherwise we're unsure (0). */\n"
+" int side;\n"
+" /* Offset to the arc-endpoints from the beginning of the glyph blob */\n"
+" int offset;\n"
+"\n"
+" /* A single line is all we care about. It's right here. */\n"
+" float line_angle;\n"
+" float line_distance; /* From nominal glyph center */\n"
+"};\n"
+"\n"
+"bool\n"
+"glyphy_isinf (const float v)\n"
+"{\n"
+" return abs (v) >= GLYPHY_INFINITY * .5;\n"
+"}\n"
+"\n"
+"bool\n"
+"glyphy_iszero (const float v)\n"
+"{\n"
+" return abs (v) <= GLYPHY_EPSILON * 2.;\n"
+"}\n"
+"\n"
+"vec2\n"
+"glyphy_ortho (const vec2 v)\n"
+"{\n"
+" return vec2 (-v.y, v.x);\n"
+"}\n"
+"\n"
+"int\n"
+"glyphy_float_to_byte (const float v)\n"
+"{\n"
+" return int (v * (256. - GLYPHY_EPSILON));\n"
+"}\n"
+"\n"
+"ivec4\n"
+"glyphy_vec4_to_bytes (const vec4 v)\n"
+"{\n"
+" return ivec4 (v * (256. - GLYPHY_EPSILON));\n"
+"}\n"
+"\n"
+"ivec2\n"
+"glyphy_float_to_two_nimbles (const float v)\n"
+"{\n"
+" int f = glyphy_float_to_byte (v);\n"
+" return ivec2 (f / 16, int(mod (float(f), 16.)));\n"
+"}\n"
+"\n"
+"/* returns tan (2 * atan (d)) */\n"
+"float\n"
+"glyphy_tan2atan (const float d)\n"
+"{\n"
+" return 2. * d / (1. - d * d);\n"
+"}\n"
+"\n"
+"glyphy_arc_endpoint_t\n"
+"glyphy_arc_endpoint_decode (const vec4 v, const ivec2 nominal_size)\n"
+"{\n"
+" vec2 p = (vec2 (glyphy_float_to_two_nimbles (v.a)) + v.gb) / 16.;\n"
+" float d = v.r;\n"
+" if (d == 0.)\n"
+" d = GLYPHY_INFINITY;\n"
+" else\n"
+"#define GLYPHY_MAX_D .5\n"
+" d = float(glyphy_float_to_byte (d) - 128) * GLYPHY_MAX_D / 127.;\n"
+"#undef GLYPHY_MAX_D\n"
+" return glyphy_arc_endpoint_t (p * vec2(nominal_size), d);\n"
+"}\n"
+"\n"
+"vec2\n"
+"glyphy_arc_center (const glyphy_arc_t a)\n"
+"{\n"
+" return mix (a.p0, a.p1, .5) +\n"
+" glyphy_ortho (a.p1 - a.p0) / (2. * glyphy_tan2atan (a.d));\n"
+"}\n"
+"\n"
+"bool\n"
+"glyphy_arc_wedge_contains (const glyphy_arc_t a, const vec2 p)\n"
+"{\n"
+" float d2 = glyphy_tan2atan (a.d);\n"
+" return dot (p - a.p0, (a.p1 - a.p0) * mat2(1, d2, -d2, 1)) >= 0. &&\n"
+" dot (p - a.p1, (a.p1 - a.p0) * mat2(1, -d2, d2, 1)) <= 0.;\n"
+"}\n"
+"\n"
+"float\n"
+"glyphy_arc_wedge_signed_dist_shallow (const glyphy_arc_t a, const vec2 p)\n"
+"{\n"
+" vec2 v = normalize (a.p1 - a.p0);\n"
+" float line_d = dot (p - a.p0, glyphy_ortho (v));\n"
+" if (a.d == 0.)\n"
+" return line_d;\n"
+"\n"
+" float d0 = dot ((p - a.p0), v);\n"
+" if (d0 < 0.)\n"
+" return sign (line_d) * distance (p, a.p0);\n"
+" float d1 = dot ((a.p1 - p), v);\n"
+" if (d1 < 0.)\n"
+" return sign (line_d) * distance (p, a.p1);\n"
+" float r = 2. * a.d * (d0 * d1) / (d0 + d1);\n"
+" if (r * line_d > 0.)\n"
+" return sign (line_d) * min (abs (line_d + r), min (distance (p, a.p0), distance (p, a.p1)));\n"
+" return line_d + r;\n"
+"}\n"
+"\n"
+"float\n"
+"glyphy_arc_wedge_signed_dist (const glyphy_arc_t a, const vec2 p)\n"
+"{\n"
+" if (abs (a.d) <= .03)\n"
+" return glyphy_arc_wedge_signed_dist_shallow (a, p);\n"
+" vec2 c = glyphy_arc_center (a);\n"
+" return sign (a.d) * (distance (a.p0, c) - distance (p, c));\n"
+"}\n"
+"\n"
+"float\n"
+"glyphy_arc_extended_dist (const glyphy_arc_t a, const vec2 p)\n"
+"{\n"
+" /* Note: this doesn't handle points inside the wedge. */\n"
+" vec2 m = mix (a.p0, a.p1, .5);\n"
+" float d2 = glyphy_tan2atan (a.d);\n"
+" if (dot (p - m, a.p1 - m) < 0.)\n"
+" return dot (p - a.p0, normalize ((a.p1 - a.p0) * mat2(+d2, -1, +1, +d2)));\n"
+" else\n"
+" return dot (p - a.p1, normalize ((a.p1 - a.p0) * mat2(-d2, -1, +1, -d2)));\n"
+"}\n"
+"\n"
+"int\n"
+"glyphy_arc_list_offset (const vec2 p, const ivec2 nominal_size)\n"
+"{\n"
+" ivec2 cell = ivec2 (clamp (floor (p), vec2 (0.,0.), vec2(nominal_size - 1)));\n"
+" return cell.y * nominal_size.x + cell.x;\n"
+"}\n"
+"\n"
+"glyphy_arc_list_t\n"
+"glyphy_arc_list_decode (const vec4 v, const ivec2 nominal_size)\n"
+"{\n"
+" glyphy_arc_list_t l;\n"
+" ivec4 iv = glyphy_vec4_to_bytes (v);\n"
+" l.side = 0; /* unsure */\n"
+" if (iv.r == 0) { /* arc-list encoded */\n"
+" l.offset = (iv.g * 256) + iv.b;\n"
+" l.num_endpoints = iv.a;\n"
+" if (l.num_endpoints == 255) {\n"
+" l.num_endpoints = 0;\n"
+" l.side = -1;\n"
+" } else if (l.num_endpoints == 0)\n"
+" l.side = +1;\n"
+" } else { /* single line encoded */\n"
+" l.num_endpoints = -1;\n"
+" l.line_distance = float(((iv.r - 128) * 256 + iv.g) - 0x4000) / float (0x1FFF)\n"
+" * max (float (nominal_size.x), float (nominal_size.y));\n"
+" l.line_angle = float(-((iv.b * 256 + iv.a) - 0x8000)) / float (0x7FFF) * 3.14159265358979;\n"
+" }\n"
+" return l;\n"
+"}\n"
+;
diff --git a/glyphy/glyphy-common.hh b/glyphy/glyphy-common.hh
@@ -0,0 +1,60 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju
+ */
+
+#ifndef GLYPHY_COMMON_HH
+#define GLYPHY_COMMON_HH
+
+#include <glyphy.h>
+
+#include <math.h>
+#include <string.h>
+#include <assert.h>
+#include <stdio.h>
+#include <vector>
+#include <algorithm>
+#include <iostream>
+
+#ifndef GLYPHY_EPSILON
+# define GLYPHY_EPSILON 1e-5
+#endif
+#ifndef GLYPHY_INFINITY
+# define GLYPHY_INFINITY INFINITY
+#endif
+
+
+static inline bool
+iszero (double v)
+{
+ return fabs (v) < 2 * GLYPHY_EPSILON;
+}
+
+
+#define GLYPHY_MAX_D .5
+
+#undef ARRAY_LENGTH
+#define ARRAY_LENGTH(__array) ((signed int) (sizeof (__array) / sizeof (__array[0])))
+
+#define _ASSERT_STATIC1(_line, _cond) typedef int _static_assert_on_line_##_line##_failed[(_cond)?1:-1]
+#define _ASSERT_STATIC0(_line, _cond) _ASSERT_STATIC1 (_line, (_cond))
+#define ASSERT_STATIC(_cond) _ASSERT_STATIC0 (__LINE__, (_cond))
+
+#ifdef __ANDROID__
+#define log2(x) (log(x) / log(2.0))
+#endif
+
+#endif /* GLYPHY_COMMON_HH */
diff --git a/glyphy/glyphy-extents.cxx b/glyphy/glyphy-extents.cxx
@@ -0,0 +1,89 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "glyphy-common.hh"
+
+
+void
+glyphy_extents_clear (glyphy_extents_t *extents)
+{
+ extents->min_x = GLYPHY_INFINITY;
+ extents->min_y = GLYPHY_INFINITY;
+ extents->max_x = -GLYPHY_INFINITY;
+ extents->max_y = -GLYPHY_INFINITY;
+}
+
+glyphy_bool_t
+glyphy_extents_is_empty (const glyphy_extents_t *extents)
+{
+ return isinf (extents->min_x);
+}
+
+void
+glyphy_extents_add (glyphy_extents_t *extents,
+ const glyphy_point_t *p)
+{
+ if (glyphy_extents_is_empty (extents)) {
+ extents->min_x = extents->max_x = p->x;
+ extents->min_y = extents->max_y = p->y;
+ return;
+ }
+ extents->min_x = std::min (extents->min_x, p->x);
+ extents->min_y = std::min (extents->min_y, p->y);
+ extents->max_x = std::max (extents->max_x, p->x);
+ extents->max_y = std::max (extents->max_y, p->y);
+}
+
+void
+glyphy_extents_extend (glyphy_extents_t *extents,
+ const glyphy_extents_t *other)
+{
+ if (glyphy_extents_is_empty (other))
+ return;
+ if (glyphy_extents_is_empty (extents)) {
+ *extents = *other;
+ return;
+ }
+ extents->min_x = std::min (extents->min_x, other->min_x);
+ extents->min_y = std::min (extents->min_y, other->min_y);
+ extents->max_x = std::max (extents->max_x, other->max_x);
+ extents->max_y = std::max (extents->max_y, other->max_y);
+}
+
+glyphy_bool_t
+glyphy_extents_includes (const glyphy_extents_t *extents,
+ const glyphy_point_t *p)
+{
+ return extents->min_x <= p->x && p->x <= extents->max_x &&
+ extents->min_y <= p->y && p->y <= extents->max_y;
+}
+
+void
+glyphy_extents_scale (glyphy_extents_t *extents,
+ double x_scale,
+ double y_scale)
+{
+ extents->min_x *= x_scale;
+ extents->max_x *= x_scale;
+ extents->min_y *= y_scale;
+ extents->max_y *= y_scale;
+}
diff --git a/glyphy/glyphy-freetype.h b/glyphy/glyphy-freetype.h
@@ -0,0 +1,102 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju
+ */
+
+/* Intentionally doesn't have include guards */
+
+#include "glyphy.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+#include <ft2build.h>
+#include FT_FREETYPE_H
+#include FT_OUTLINE_H
+
+
+
+#ifndef GLYPHY_FREETYPE_PREFIX
+#define GLYPHY_FREETYPE_PREFIX glyphy_freetype_
+#endif
+
+#ifndef glyphy_freetype
+#define glyphy_freetype(name) GLYPHY_PASTE (GLYPHY_FREETYPE_PREFIX, name)
+#endif
+
+
+
+static int
+glyphy_freetype(move_to) (FT_Vector *to,
+ glyphy_arc_accumulator_t *acc)
+{
+ glyphy_point_t p1 = {(double) to->x, (double) to->y};
+ glyphy_arc_accumulator_close_path (acc);
+ glyphy_arc_accumulator_move_to (acc, &p1);
+ return glyphy_arc_accumulator_successful (acc) ? FT_Err_Ok : FT_Err_Out_Of_Memory;
+}
+
+static int
+glyphy_freetype(line_to) (FT_Vector *to,
+ glyphy_arc_accumulator_t *acc)
+{
+ glyphy_point_t p1 = {(double) to->x, (double) to->y};
+ glyphy_arc_accumulator_line_to (acc, &p1);
+ return glyphy_arc_accumulator_successful (acc) ? FT_Err_Ok : FT_Err_Out_Of_Memory;
+}
+
+static int
+glyphy_freetype(conic_to) (FT_Vector *control, FT_Vector *to,
+ glyphy_arc_accumulator_t *acc)
+{
+ glyphy_point_t p1 = {(double) control->x, (double) control->y};
+ glyphy_point_t p2 = {(double) to->x, (double) to->y};
+ glyphy_arc_accumulator_conic_to (acc, &p1, &p2);
+ return glyphy_arc_accumulator_successful (acc) ? FT_Err_Ok : FT_Err_Out_Of_Memory;
+}
+
+static int
+glyphy_freetype(cubic_to) (FT_Vector *control1, FT_Vector *control2, FT_Vector *to,
+ glyphy_arc_accumulator_t *acc)
+{
+ glyphy_point_t p1 = {(double) control1->x, (double) control1->y};
+ glyphy_point_t p2 = {(double) control2->x, (double) control2->y};
+ glyphy_point_t p3 = {(double) to->x, (double) to->y};
+ glyphy_arc_accumulator_cubic_to (acc, &p1, &p2, &p3);
+ return glyphy_arc_accumulator_successful (acc) ? FT_Err_Ok : FT_Err_Out_Of_Memory;
+}
+
+static FT_Error
+glyphy_freetype(outline_decompose) (const FT_Outline *outline,
+ glyphy_arc_accumulator_t *acc)
+{
+ const FT_Outline_Funcs outline_funcs = {
+ (FT_Outline_MoveToFunc) glyphy_freetype(move_to),
+ (FT_Outline_LineToFunc) glyphy_freetype(line_to),
+ (FT_Outline_ConicToFunc) glyphy_freetype(conic_to),
+ (FT_Outline_CubicToFunc) glyphy_freetype(cubic_to),
+ 0, /* shift */
+ 0, /* delta */
+ };
+
+ return FT_Outline_Decompose ((FT_Outline *) outline, &outline_funcs, acc);
+}
+
+#ifdef __cplusplus
+}
+#endif
diff --git a/glyphy/glyphy-geometry.hh b/glyphy/glyphy-geometry.hh
@@ -0,0 +1,742 @@
+/*
+ * Copyright 2012,2013 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju
+ */
+
+#ifndef GLYPHY_GEOMETRY_HH
+#define GLYPHY_GEOMETRY_HH
+
+#include "glyphy-common.hh"
+
+namespace GLyphy {
+namespace Geometry {
+
+template <typename Type> struct Pair;
+struct Vector;
+struct SignedVector;
+struct Point;
+struct Line;
+struct Segment;
+struct Arc;
+struct Bezier;
+
+/* returns tan (2 * atan (d)) */
+inline double tan2atan (double d) { return 2 * d / (1 - d*d); }
+
+/* returns sin (2 * atan (d)) */
+inline double sin2atan (double d) { return 2 * d / (1 + d*d); }
+
+/* returns cos (2 * atan (d)) */
+inline double cos2atan (double d) { return (1 - d*d) / (1 + d*d); }
+
+template <typename Type>
+struct Pair {
+ typedef Type ElementType;
+
+ inline Pair (const Type &first_, const Type &second_) : first (first_), second (second_) {}
+
+ Type first, second;
+};
+
+struct Point : glyphy_point_t {
+ inline Point (double x_, double y_) { x = x_; y = y_; }
+ inline explicit Point (const Vector &v);
+ inline Point (const glyphy_point_t &p) { *(glyphy_point_t *)this = p; }
+
+ inline bool operator == (const Point &p) const;
+ inline bool operator != (const Point &p) const;
+ inline Point& operator+= (const Vector &v);
+ inline Point& operator-= (const Vector &v);
+ inline const Point operator+ (const Vector &v) const;
+ inline const Point operator- (const Vector &v) const;
+ inline const Vector operator- (const Point &p) const;
+ inline const Point midpoint (const Point &p) const;
+ inline const Line bisector (const Point &p) const;
+ inline double distance_to_point (const Point &p) const; /* distance to point! */
+ inline double squared_distance_to_point (const Point &p) const; /* square of distance to point! */
+
+ inline bool is_finite (void) const;
+ inline const Point lerp (const double &a, const Point &p) const;
+};
+
+struct Vector {
+ inline Vector (double dx_, double dy_) : dx (dx_), dy (dy_) {}
+ inline explicit Vector (const Point &p) : dx (p.x), dy (p.y) {}
+
+ inline bool operator == (const Vector &v) const;
+ inline bool operator != (const Vector &v) const;
+ inline const Vector operator+ (void) const;
+ inline const Vector operator- (void) const;
+ inline Vector& operator+= (const Vector &v);
+ inline Vector& operator-= (const Vector &v);
+ inline Vector& operator*= (const double &s);
+ inline Vector& operator/= (const double &s);
+ inline const Vector operator+ (const Vector &v) const;
+ inline const Vector operator- (const Vector &v) const;
+ inline const Vector operator* (const double &s) const;
+ inline const Vector operator/ (const double &s) const;
+ inline double operator* (const Vector &v) const; /* dot product */
+ inline const Point operator+ (const Point &p) const;
+
+ inline bool is_nonzero (void) const;
+ inline double len (void) const;
+ inline double len2 (void) const;
+ inline const Vector normalized (void) const;
+ inline const Vector ortho (void) const;
+ inline const Vector normal (void) const; /* ortho().normalized() */
+ inline double angle (void) const;
+
+ inline double cross (const Vector &other) const;
+ inline const Vector rebase (const Vector &bx, const Vector &by) const;
+ inline const Vector rebase (const Vector &bx) const;
+
+ double dx, dy;
+};
+
+struct SignedVector : Vector {
+ inline SignedVector (const Vector &v, bool negative_) : Vector (v), negative (negative_) {}
+
+ inline bool operator == (const SignedVector &v) const;
+ inline bool operator != (const SignedVector &v) const;
+ inline const SignedVector operator- (void) const;
+
+ bool negative;
+};
+
+struct Line {
+ inline Line (double a_, double b_, double c_) : n (a_, b_), c (c_) {}
+ inline Line (Vector n_, double c_) : n (n_), c (c_) {}
+ inline Line (const Point &p0, const Point &p1) :
+ n ((p1 - p0).ortho ()), c (n * Vector (p0)) {}
+
+ inline const Point operator+ (const Line &l) const; /* line intersection! */
+ inline const SignedVector operator- (const Point &p) const; /* shortest vector from point to line */
+
+
+ inline const Line normalized (void) const;
+ inline const Vector normal (void) const;
+
+ Vector n; /* line normal */
+ double c; /* n.dx*x + n.dy*y = c */
+};
+
+struct Segment {
+ inline Segment (const Point &p0_, const Point &p1_) :
+ p0 (p0_), p1 (p1_) {}
+
+ inline const SignedVector operator- (const Point &p) const; /* shortest vector from point to ***line*** */
+ inline double distance_to_point (const Point &p) const; /* shortest distance from point to segment */
+ inline double squared_distance_to_point (const Point &p) const; /* shortest distance squared from point to segment */
+ inline bool contains_in_span (const Point &p) const; /* is p in the stripe formed by sliding this segment? */
+ inline double max_distance_to_arc (const Arc &a) const;
+
+
+ Point p0;
+ Point p1;
+};
+
+
+
+struct Arc {
+ inline Arc (const Point &p0_, const Point &p1_, const Point &pm, bool complement) :
+ p0 (p0_), p1 (p1_),
+ d (p0_ == pm || p1_ == pm ? 0 :
+ tan (((p1_-pm).angle () - (p0_-pm).angle ()) / 2 - (complement ? 0 : M_PI_2))) {}
+ inline Arc (const Point &p0_, const Point &p1_, const double &d_) :
+ p0 (p0_), p1 (p1_), d (d_) {}
+ inline Arc (const Point ¢er, double radius, const double &a0, const double &a1, bool complement) :
+ p0 (center + Vector (cos(a0),sin(a0)) * radius),
+ p1 (center + Vector (cos(a1),sin(a1)) * radius),
+ d (tan ((a1 - a0) / 4 - (complement ? 0 : M_PI_2))) {}
+ inline Arc (const glyphy_arc_t &a) : p0 (a.p0), p1 (a.p1), d (a.d) {}
+ inline operator glyphy_arc_t (void) const { glyphy_arc_t a = {p0, p1, d}; return a; }
+
+ inline bool operator == (const Arc &a) const;
+ inline bool operator != (const Arc &a) const;
+ inline const SignedVector operator- (const Point &p) const; /* shortest vector from point to arc */
+
+ inline double radius (void) const;
+ inline const Point center (void) const;
+ inline const Pair<Vector> tangents (void) const;
+
+ inline Bezier approximate_bezier (double *error) const;
+
+ inline bool wedge_contains_point (const Point &p) const;
+ inline double distance_to_point (const Point &p) const;
+ inline double squared_distance_to_point (const Point &p) const;
+ inline double extended_dist (const Point &p) const;
+
+ inline void extents (glyphy_extents_t &extents) const;
+
+ Point p0, p1;
+ double d; /* Depth */
+};
+
+struct Bezier {
+ inline Bezier (const Point &p0_, const Point &p1_,
+ const Point &p2_, const Point &p3_) :
+ p0 (p0_), p1 (p1_), p2 (p2_), p3 (p3_) {}
+
+ inline const Point point (const double &t) const;
+ inline const Point midpoint (void) const;
+ inline const Vector tangent (const double &t) const;
+ inline const Vector d_tangent (const double &t) const;
+ inline double curvature (const double &t) const;
+ inline const Pair<Bezier> split (const double &t) const;
+ inline const Pair<Bezier> halve (void) const;
+ inline const Bezier segment (const double &t0, const double &t1) const;
+
+ Point p0, p1, p2, p3;
+};
+
+
+/* Implementations */
+
+
+/* Point */
+
+inline Point::Point (const Vector &v) {
+ x = v.dx;
+ y = v.dy;
+}
+inline bool Point::operator == (const Point &p) const {
+ return x == p.x && y == p.y;
+}
+inline bool Point::operator != (const Point &p) const {
+ return !(*this == p);
+}
+inline Point& Point::operator+= (const Vector &v) {
+ x += v.dx;
+ y += v.dy;
+ return *this;
+}
+inline Point& Point::operator-= (const Vector &v) {
+ x -= v.dx;
+ y -= v.dy;
+ return *this;
+}
+inline const Point Point::operator+ (const Vector &v) const {
+ return Point (*this) += v;
+}
+inline const Point Point::operator- (const Vector &v) const {
+ return Point (*this) -= v;
+}
+inline const Vector Point::operator- (const Point &p) const {
+ return Vector (x - p.x, y - p.y);
+}
+
+inline const Point Point::midpoint (const Point &p) const {
+ return *this + (p - *this) / 2;
+}
+inline const Line Point::bisector (const Point &p) const {
+ Vector d = p - *this;
+ return Line (d.dx * 2, d.dy * 2, d * Vector (p) + d * Vector (*this));
+}
+
+inline double Point::distance_to_point (const Point &p) const {
+ return ((*this) - p).len ();
+}
+
+inline double Point::squared_distance_to_point (const Point &p) const {
+ return ((*this) - p).len2 ();
+}
+
+inline bool Point::is_finite (void) const {
+ return isfinite (x) && isfinite (y);
+}
+inline const Point Point::lerp (const double &a, const Point &p) const {
+ /* The following two cases are special-cased to get better floating
+ * point stability. We require that points that are the same be
+ * bit-equal. */
+ if (a == 0) return *this;
+ if (a == 1.0) return p;
+ return Point ((1-a) * x + a * p.x, (1-a) * y + a * p.y);
+}
+
+
+/* Vector */
+
+inline bool Vector::operator == (const Vector &v) const {
+ return dx == v.dx && dy == v.dy;
+}
+inline bool Vector::operator != (const Vector &v) const {
+ return !(*this == v);
+}
+inline const Vector Vector::operator+ (void) const {
+ return *this;
+}
+inline const Vector Vector::operator- (void) const {
+ return Vector (-dx, -dy);
+}
+inline Vector& Vector::operator+= (const Vector &v) {
+ dx += v.dx;
+ dy += v.dy;
+ return *this;
+}
+inline Vector& Vector::operator-= (const Vector &v) {
+ dx -= v.dx;
+ dy -= v.dy;
+ return *this;
+}
+inline Vector& Vector::operator*= (const double &s) {
+ dx *= s;
+ dy *= s;
+ return *this;
+}
+inline Vector& Vector::operator/= (const double &s) {
+ dx /= s;
+ dy /= s;
+ return *this;
+}
+inline const Vector Vector::operator+ (const Vector &v) const {
+ return Vector (*this) += v;
+}
+inline const Vector Vector::operator- (const Vector &v) const {
+ return Vector (*this) -= v;
+}
+inline const Vector Vector::operator* (const double &s) const {
+ return Vector (*this) *= s;
+}
+inline const Vector operator* (const double &s, const Vector &v) {
+ return v * s;
+}
+inline const Vector Vector::operator/ (const double &s) const {
+ return Vector (*this) /= s;
+}
+inline double Vector::operator* (const Vector &v) const { /* dot product */
+ return dx * v.dx + dy * v.dy;
+}
+inline const Point Vector::operator+ (const Point &p) const {
+ return p + *this;
+}
+
+inline bool Vector::is_nonzero (void) const {
+ return dx || dy;
+}
+inline double Vector::len (void) const {
+ return hypot (dx, dy);
+}
+inline double Vector::len2 (void) const {
+ return dx * dx + dy * dy;
+}
+inline const Vector Vector::normalized (void) const {
+ double d = len ();
+ return d ? *this / d : *this;
+}
+inline const Vector Vector::ortho (void) const {
+ return Vector (-dy, dx);
+}
+inline const Vector Vector::normal (void) const {
+ return ortho ().normalized ();
+}
+inline double Vector::angle (void) const {
+ return atan2 (dy, dx);
+}
+
+inline double Vector::cross (const Vector &other) const {
+ return dx * other.dy - dy * other.dx;
+}
+inline const Vector Vector::rebase (const Vector &bx,
+ const Vector &by) const {
+ return Vector (*this * bx, *this * by);
+}
+inline const Vector Vector::rebase (const Vector &bx) const {
+ return rebase (bx, bx.ortho ());
+}
+
+
+/* SignedVector */
+
+inline bool SignedVector::operator == (const SignedVector &v) const {
+ return (const Vector &)(*this) == (const Vector &)(v) && negative == v.negative;
+}
+inline bool SignedVector::operator != (const SignedVector &v) const {
+ return !(*this == v);
+}
+inline const SignedVector SignedVector::operator- (void) const {
+ return SignedVector (-(const Vector &)(*this), !negative);
+}
+
+
+/* Line */
+
+inline const Point Line::operator+ (const Line &l) const {
+ double det = n.dx * l.n.dy - n.dy * l.n.dx;
+ if (!det)
+ return Point (GLYPHY_INFINITY, GLYPHY_INFINITY);
+ return Point ((c * l.n.dy - n.dy * l.c) / det,
+ (n.dx * l.c - c * l.n.dx) / det);
+}
+inline const SignedVector Line::operator- (const Point &p) const {
+ double mag = -(n * Vector (p) - c) / n.len ();
+ return SignedVector (n.normalized () * mag, mag < 0); /******************************************************************************************* FIX. *************************************/
+}
+
+inline const SignedVector operator- (const Point &p, const Line &l) {
+ return -(l - p);
+}
+
+inline const Line Line::normalized (void) const {
+ double d = n.len ();
+ return d ? Line (n / d, c / d) : *this;
+}
+inline const Vector Line::normal (void) const {
+ return n;
+}
+
+/* Segment */
+inline const SignedVector Segment::operator- (const Point &p) const {
+ /* shortest vector from point to line */
+ return p - Line (p1, p0); /************************************************************************************************** Should the order (p1, p0) depend on d?? ***********************/
+}
+
+/* Segment */
+inline bool Segment::contains_in_span (const Point &p) const {
+ if (p0 == p1)
+ return false;
+
+ /* shortest vector from point to line */
+ Line temp (p0, p1);
+ double mag = -(temp.n * Vector (p) - temp.c) / temp.n.len ();
+ Vector y (temp.n.normalized () * mag);
+ Point z = y + p;
+
+ // Check if z is between p0 and p1.
+
+ if (fabs (p1.y - p0.y) > fabs (p1.x - p0.x)) {
+ return ((z.y - p0.y > 0 && p1.y - p0.y > z.y - p0.y) ||
+ (z.y - p0.y < 0 && p1.y - p0.y < z.y - p0.y));
+ }
+ else {
+ return ((0 < z.x - p0.x && z.x - p0.x < p1.x - p0.x) ||
+ (0 > z.x - p0.x && z.x - p0.x > p1.x - p0.x));
+ }
+}
+
+inline double Segment::distance_to_point (const Point &p) const {
+ if (p0 == p1)
+ return 0;
+
+ // Check if z is between p0 and p1.
+ Line temp (p0, p1);
+ if (contains_in_span (p))
+ return -(temp.n * Vector (p) - temp.c) / temp.n.len ();
+
+ double dist_p_p0 = p.distance_to_point (p0);
+ double dist_p_p1 = p.distance_to_point (p1);
+ return (dist_p_p0 < dist_p_p1 ? dist_p_p0 : dist_p_p1) * (-(temp.n * Vector (p) - temp.c) < 0 ? -1 : 1);
+}
+
+
+inline double Segment::squared_distance_to_point (const Point &p) const {
+ if (p0 == p1)
+ return 0;
+
+ // Check if z is between p0 and p1.
+ Line temp (p0, p1);
+ if (contains_in_span (p))
+ return (temp.n * Vector (p) - temp.c) * (temp.n * Vector (p) - temp.c) / (temp.n * temp.n);
+
+ double dist_p_p0 = p.squared_distance_to_point (p0);
+ double dist_p_p1 = p.squared_distance_to_point (p1);
+ return (dist_p_p0 < dist_p_p1 ? dist_p_p0 : dist_p_p1);
+}
+
+
+inline double Segment::max_distance_to_arc (const Arc &a) const {
+ double max_distance = fabs(a.distance_to_point(p0)) ;
+ return max_distance > fabs(a.distance_to_point(p1)) ? max_distance : fabs(a.distance_to_point(p1)) ;
+}
+
+
+
+/* Arc */
+
+inline bool Arc::operator == (const Arc &a) const {
+ return p0 == a.p0 && p1 == a.p1 && d == a.d;
+}
+inline bool Arc::operator != (const Arc &a) const {
+ return !(*this == a);
+}
+
+
+inline const SignedVector Arc::operator- (const Point &p) const {
+
+ if (fabs(d) < 1e-5) {
+ Segment arc_segment (p0, p1);
+ return arc_segment - p;
+ }
+ if (wedge_contains_point (p)){
+ Vector difference = (center () - p).normalized () * fabs (p.distance_to_point (center ()) - radius ());
+
+ return SignedVector (difference, ((p - center ()).len () < radius ()) ^ (d < 0));
+ }
+ double d0 = p.squared_distance_to_point (p0);
+ double d1 = p.squared_distance_to_point (p1);
+
+ Arc other_arc (p0, p1, (1.0 + d) / (1.0 - d)); /********************************* NOT Robust. But works? *****************/
+ Vector normal = center () - (d0 < d1 ? p0 : p1) ;
+
+ if (normal.len() == 0)
+ return SignedVector (Vector (0, 0), true); /************************************ Check sign of this S.D. *************/
+
+ return SignedVector (Line (normal.dx, normal.dy, normal * Vector ((d0 < d1 ? p0 : p1))) - p, !other_arc.wedge_contains_point(p));
+}
+
+inline const SignedVector operator- (const Point &p, const Arc &a) {
+ return -(a - p);
+}
+
+
+
+inline double Arc::radius (void) const
+{
+ return fabs ((p1 - p0).len () / (2 * sin2atan (d)));
+}
+
+inline const Point Arc::center (void) const
+{
+ return (p0.midpoint (p1)) + (p1 - p0).ortho () / (2 * tan2atan (d));
+}
+
+inline const Pair<Vector> Arc::tangents (void) const
+{
+ Vector dp = (p1 - p0) * .5;
+ Vector pp = dp.ortho () * -sin2atan (d);
+ dp = dp * cos2atan (d);
+ return Pair<Vector> (dp + pp, dp - pp);
+}
+
+
+
+inline Bezier Arc::approximate_bezier (double *error) const
+{
+ Vector dp = p1 - p0;
+ Vector pp = dp.ortho ();
+
+ if (error)
+ *error = dp.len () * pow (fabs (d), 5) / (54 * (1 + d*d));
+
+ dp *= ((1 - d*d) / 3);
+ pp *= (2 * d / 3);
+
+ Point p0s = p0 + dp - pp;
+ Point p1s = p1 - dp - pp;
+
+ return Bezier (p0, p0s, p1s, p1);
+}
+
+
+inline bool Arc::wedge_contains_point (const Point &p) const
+{
+ Pair<Vector> t = tangents ();
+ if (fabs (d) <= 1)
+ return (p - p0) * t.first >= 0 && (p - p1) * t.second <= 0;
+ else
+ return (p - p0) * t.first >= 0 || (p - p1) * t.second <= 0;
+}
+
+
+/* Distance may not always be positive, but will be to an endpoint whenever necessary. */
+inline double Arc::distance_to_point (const Point &p) const {
+ if (fabs(d) < 1e-5) {
+ Segment arc_segment (p0, p1);
+ return arc_segment.distance_to_point (p);
+ }
+
+ SignedVector difference = *this - p;
+
+ if (wedge_contains_point (p) && fabs(d) > 1e-5)
+ return fabs (p.distance_to_point (center ()) - radius ()) * (difference.negative ? -1 : 1);
+ double d1 = p.squared_distance_to_point (p0);
+ double d2 = p.squared_distance_to_point (p1);
+ return (d1 < d2 ? sqrt(d1) : sqrt(d2)) * (difference.negative ? -1 : 1);
+}
+
+/* Distance will be to an endpoint whenever necessary. */
+inline double Arc::squared_distance_to_point (const Point &p) const {
+ if (fabs(d) < 1e-5) {
+ Segment arc_segment (p0, p1);
+ return arc_segment.squared_distance_to_point (p);
+ }
+
+ //SignedVector difference = *this - p;
+
+ if (wedge_contains_point (p) && fabs(d) > 1e-5) {
+ double answer = p.distance_to_point (center ()) - radius ();
+ return answer * answer;
+ }
+ double d1 = p.squared_distance_to_point (p0);
+ double d2 = p.squared_distance_to_point (p1);
+ return (d1 < d2 ? d1 : d2);
+}
+
+inline double Arc::extended_dist (const Point &p) const {
+ Point m = p0.lerp (.5, p1);
+ Vector dp = p1 - p0;
+ Vector pp = dp.ortho ();
+ float d2 = tan2atan (d);
+ if ((p - m) * (p1 - m) < 0)
+ return (p - p0) * (pp + dp * d2).normalized ();
+ else
+ return (p - p1) * (pp - dp * d2).normalized ();
+}
+
+inline void Arc::extents (glyphy_extents_t &extents) const {
+ glyphy_extents_clear (&extents);
+ glyphy_extents_add (&extents, &p0);
+ glyphy_extents_add (&extents, &p1);
+ Point c = center ();
+ double r = radius ();
+ Point p[4] = {c + r * Vector (-1, 0),
+ c + r * Vector (+1, 0),
+ c + r * Vector ( 0, -1),
+ c + r * Vector ( 0, +1)};
+ for (unsigned int i = 0; i < 4; i++)
+ if (wedge_contains_point (p[i]))
+ glyphy_extents_add (&extents, &p[i]);
+}
+
+
+/* Bezier */
+
+inline const Point Bezier::point (const double &t) const {
+ Point p01 = p0.lerp (t, p1);
+ Point p12 = p1.lerp (t, p2);
+ Point p23 = p2.lerp (t, p3);
+ Point p012 = p01.lerp (t, p12);
+ Point p123 = p12.lerp (t, p23);
+ Point p0123 = p012.lerp (t, p123);
+ return p0123;
+}
+
+inline const Point Bezier::midpoint (void) const
+{
+ Point p01 = p0.midpoint (p1);
+ Point p12 = p1.midpoint (p2);
+ Point p23 = p2.midpoint (p3);
+ Point p012 = p01.midpoint (p12);
+ Point p123 = p12.midpoint (p23);
+ Point p0123 = p012.midpoint (p123);
+ return p0123;
+}
+
+inline const Vector Bezier::tangent (const double &t) const
+{
+ double t_2_0 = t * t;
+ double t_0_2 = (1 - t) * (1 - t);
+
+ double _1__4t_1_0_3t_2_0 = 1 - 4 * t + 3 * t_2_0;
+ double _2t_1_0_3t_2_0 = 2 * t - 3 * t_2_0;
+
+ return Vector (-3 * p0.x * t_0_2
+ +3 * p1.x * _1__4t_1_0_3t_2_0
+ +3 * p2.x * _2t_1_0_3t_2_0
+ +3 * p3.x * t_2_0,
+ -3 * p0.y * t_0_2
+ +3 * p1.y * _1__4t_1_0_3t_2_0
+ +3 * p2.y * _2t_1_0_3t_2_0
+ +3 * p3.y * t_2_0);
+}
+
+inline const Vector Bezier::d_tangent (const double &t) const {
+ return Vector (6 * ((-p0.x + 3*p1.x - 3*p2.x + p3.x) * t + (p0.x - 2*p1.x + p2.x)),
+ 6 * ((-p0.y + 3*p1.y - 3*p2.y + p3.y) * t + (p0.y - 2*p1.y + p2.y)));
+}
+
+inline double Bezier::curvature (const double &t) const {
+ Vector dpp = tangent (t).ortho ();
+ Vector ddp = d_tangent (t);
+ /* normal vector len squared */
+ double len = dpp.len ();
+ double curvature = (dpp * ddp) / (len * len * len);
+ return curvature;
+}
+
+inline const Pair<Bezier > Bezier::split (const double &t) const {
+ Point p01 = p0.lerp (t, p1);
+ Point p12 = p1.lerp (t, p2);
+ Point p23 = p2.lerp (t, p3);
+ Point p012 = p01.lerp (t, p12);
+ Point p123 = p12.lerp (t, p23);
+ Point p0123 = p012.lerp (t, p123);
+ return Pair<Bezier> (Bezier (p0, p01, p012, p0123),
+ Bezier (p0123, p123, p23, p3));
+}
+
+inline const Pair<Bezier > Bezier::halve (void) const
+{
+ Point p01 = p0.midpoint (p1);
+ Point p12 = p1.midpoint (p2);
+ Point p23 = p2.midpoint (p3);
+ Point p012 = p01.midpoint (p12);
+ Point p123 = p12.midpoint (p23);
+ Point p0123 = p012.midpoint (p123);
+ return Pair<Bezier> (Bezier (p0, p01, p012, p0123),
+ Bezier (p0123, p123, p23, p3));
+}
+
+inline const Bezier Bezier::segment (const double &t0, const double &t1) const
+{
+ Point p01 = p0.lerp (t0, p1);
+ Point p12 = p1.lerp (t0, p2);
+ Point p23 = p2.lerp (t0, p3);
+ Point p012 = p01.lerp (t0, p12);
+ Point p123 = p12.lerp (t0, p23);
+ Point p0123 = p012.lerp (t0, p123);
+
+ Point q01 = p0.lerp (t1, p1);
+ Point q12 = p1.lerp (t1, p2);
+ Point q23 = p2.lerp (t1, p3);
+ Point q012 = q01.lerp (t1, q12);
+ Point q123 = q12.lerp (t1, q23);
+ Point q0123 = q012.lerp (t1, q123);
+
+ return Bezier (p0123,
+ p0123 + (p123 - p0123) * ((t1 - t0) / (1 - t0)),
+ q0123 + (q012 - q0123) * ((t1 - t0) / t1),
+ q0123);
+}
+
+
+/* insertion operator */
+
+
+static inline std::ostream& operator<<(std::ostream& os, const Point& p)
+{
+ os << "Point(" << p.x << "," << p.y << ")";
+ return os;
+}
+static inline std::ostream& operator<<(std::ostream& os, const Vector& v)
+{
+ os << "Vector(" << v.dx << "," << v.dy << ")";
+ return os;
+}
+static inline std::ostream& operator<<(std::ostream& os, const Arc& a)
+{
+ os << "Arc(" << a.p0 << ", " << a.p1 << ", " << a.d << ")";
+ return os;
+}
+static inline std::ostream& operator<<(std::ostream& os, const Bezier& b)
+{
+ os << "Bezier(" << b.p0 << ", " << b.p1 << ", " << b.p2 << ", " << b.p3 << ")";
+ return os;
+}
+
+} /* namespace Geometry */
+} /* namespace GLyphy */
+
+#endif /* GLYPHY_GEOMETRY_HH */
diff --git a/glyphy/glyphy-outline.cxx b/glyphy/glyphy-outline.cxx
@@ -0,0 +1,327 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "glyphy-common.hh"
+#include "glyphy-geometry.hh"
+
+using namespace GLyphy::Geometry;
+
+
+void
+glyphy_outline_reverse (glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints)
+{
+ if (!num_endpoints)
+ return;
+
+ // Shift the d's first
+ double d0 = endpoints[0].d;
+ for (unsigned int i = 0; i < num_endpoints - 1; i++)
+ endpoints[i].d = endpoints[i + 1].d == GLYPHY_INFINITY ? GLYPHY_INFINITY : -endpoints[i + 1].d;
+ endpoints[num_endpoints - 1].d = d0;
+
+ // Reverse
+ for (unsigned int i = 0, j = num_endpoints - 1; i < j; i++, j--) {
+ glyphy_arc_endpoint_t t = endpoints[i];
+ endpoints[i] = endpoints[j];
+ endpoints[j] = t;
+ }
+}
+
+
+static bool
+winding (const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints)
+{
+ /*
+ * Algorithm:
+ *
+ * - Approximate arcs with triangles passing through the mid- and end-points,
+ * - Calculate the area of the contour,
+ * - Return sign.
+ */
+
+ double area = 0;
+ for (unsigned int i = 1; i < num_endpoints; i++)
+ {
+ const glyphy_point_t &p0 = endpoints[i - 1].p;
+ const glyphy_point_t &p1 = endpoints[i].p;
+ double d = endpoints[i].d;
+
+ assert (d != GLYPHY_INFINITY);
+
+ area += Vector(p0).cross (Vector(p1));
+ area -= .5 * d * (Point(p1) - Point(p0)).len2 ();
+ }
+ return area < 0;
+}
+
+
+static int
+categorize (double v, double ref)
+{
+ return v < ref - GLYPHY_EPSILON ? -1 : v > ref + GLYPHY_EPSILON ? +1 : 0;
+}
+
+static bool
+is_zero (double v)
+{
+ return fabs (v) < GLYPHY_EPSILON;
+}
+
+static bool
+even_odd (const glyphy_arc_endpoint_t *c_endpoints,
+ unsigned int num_c_endpoints,
+ const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints)
+{
+ /*
+ * Algorithm:
+ *
+ * - For a point on the contour, draw a halfline in a direction
+ * (eg. decreasing x) to infinity,
+ * - Count how many times it crosses all other contours,
+ * - Pay special attention to points falling exactly on the halfline,
+ * specifically, they count as +.5 or -.5, depending the direction
+ * of crossing.
+ *
+ * All this counting is extremely tricky:
+ *
+ * - Floating point equality cannot be relied on here,
+ * - Lots of arc analysis needed,
+ * - Without having a point that we know falls /inside/ the contour,
+ * there are legitimate cases that we simply cannot handle using
+ * this algorithm. For example, imagine the following glyph shape:
+ *
+ * +---------+
+ * | +-----+ |
+ * | \ / |
+ * | \ / |
+ * +----o----+
+ *
+ * If the glyph is defined as two outlines, and when analysing the
+ * inner outline we happen to pick the point denoted by 'o' for
+ * analysis, there simply is no way to differentiate this case from
+ * the following case:
+ *
+ * +---------+
+ * | |
+ * | |
+ * | |
+ * +----o----+
+ * / \
+ * / \
+ * +-----+
+ *
+ * However, in one, the triangle should be filled in, and in the other
+ * filled out.
+ *
+ * One way to work around this may be to do the analysis for all endpoints
+ * on the outline and take majority. But even that can fail in more
+ * extreme yet legitimate cases, such as this one:
+ *
+ * +--+--+
+ * | / \ |
+ * |/ \|
+ * + +
+ * |\ /|
+ * | \ / |
+ * +--o--+
+ *
+ * The only correct algorithm I can think of requires a point that falls
+ * fully inside the outline. While we can try finding such a point (not
+ * dissimilar to the winding algorithm), it's beyond what I'm willing to
+ * implement right now.
+ */
+
+ const Point p = c_endpoints[0].p;
+
+ double count = 0;
+ Point p0 (0, 0);
+ for (unsigned int i = 0; i < num_endpoints; i++) {
+ const glyphy_arc_endpoint_t &endpoint = endpoints[i];
+ if (endpoint.d == GLYPHY_INFINITY) {
+ p0 = endpoint.p;
+ continue;
+ }
+ Arc arc (p0, endpoint.p, endpoint.d);
+ p0 = endpoint.p;
+
+ /*
+ * Skip our own contour
+ */
+ if (&endpoint >= c_endpoints && &endpoint < c_endpoints + num_c_endpoints)
+ continue;
+
+ /* End-point y's compared to the ref point; lt, eq, or gt */
+ unsigned s0 = categorize (arc.p0.y, p.y);
+ unsigned s1 = categorize (arc.p1.y, p.y);
+
+ if (is_zero (arc.d))
+ {
+ /* Line */
+
+ if (!s0 || !s1)
+ {
+ /*
+ * Add +.5 / -.5 for each endpoint on the halfline, depending on
+ * crossing direction.
+ */
+ Pair<Vector> t = arc.tangents ();
+ if (!s0 && arc.p0.x < p.x + GLYPHY_EPSILON)
+ count += .5 * categorize (t.first.dy, 0);
+ if (!s1 && arc.p1.x < p.x + GLYPHY_EPSILON)
+ count += .5 * categorize (t.second.dy, 0);
+ continue;
+ }
+
+ if (s0 == s1)
+ continue; // Segment fully above or below the halfline
+
+ // Find x pos that the line segment would intersect the half-line.
+ double x = arc.p0.x + (arc.p1.x - arc.p0.x) * ((p.y - arc.p0.y) / (arc.p1.y - arc.p0.y));
+
+ if (x >= p.x - GLYPHY_EPSILON)
+ continue; // Does not intersect halfline
+
+ count++; // Add one for full crossing
+ continue;
+ }
+ else
+ {
+ /* Arc */
+
+ if (!s0 || !s1)
+ {
+ /*
+ * Add +.5 / -.5 for each endpoint on the halfline, depending on
+ * crossing direction.
+ */
+ Pair<Vector> t = arc.tangents ();
+
+ /* Arc-specific logic:
+ * If the tangent has dy==0, use the other endpoint's
+ * y value to decide which way the arc will be heading.
+ */
+ if (is_zero (t.first.dy))
+ t.first.dy = +categorize (arc.p1.y, p.y);
+ if (is_zero (t.second.dy))
+ t.second.dy = -categorize (arc.p0.y, p.y);
+
+ if (!s0 && arc.p0.x < p.x + GLYPHY_EPSILON)
+ count += .5 * categorize (t.first.dy, 0);
+ if (!s1 && arc.p1.x < p.x + GLYPHY_EPSILON)
+ count += .5 * categorize (t.second.dy, 0);
+ }
+
+ Point c = arc.center ();
+ double r = arc.radius ();
+ if (c.x - r >= p.x)
+ continue; // No chance
+ /* Solve for arc crossing line with y = p.y */
+ double dy = p.y - c.y;
+ double x2 = r * r - dy * dy;
+ if (x2 <= GLYPHY_EPSILON)
+ continue; // Negative delta, no crossing
+ double dx = sqrt (x2);
+ /* There's two candidate points on the arc with the same y as the
+ * ref point. */
+ Point pp[2] = { Point (c.x - dx, p.y),
+ Point (c.x + dx, p.y) };
+
+#define POINTS_EQ(a,b) (is_zero (a.x - b.x) && is_zero (a.y - b.y))
+ for (unsigned int i = 0; i < ARRAY_LENGTH (pp); i++)
+ {
+ /* Make sure we don't double-count endpoints that fall on the
+ * halfline as we already accounted for those above */
+ if (!POINTS_EQ (pp[i], arc.p0) && !POINTS_EQ (pp[i], arc.p1) &&
+ pp[i].x < p.x - GLYPHY_EPSILON && arc.wedge_contains_point (pp[i]))
+ count++; // Add one for full crossing
+ }
+#undef POINTS_EQ
+ }
+ }
+
+ return !(int (floor (count)) & 1);
+}
+
+static bool
+process_contour (glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ const glyphy_arc_endpoint_t *all_endpoints,
+ unsigned int num_all_endpoints,
+ bool inverse)
+{
+ /*
+ * Algorithm:
+ *
+ * - Find the winding direction and even-odd number,
+ * - If the two disagree, reverse the contour, inplace.
+ */
+
+ if (!num_endpoints)
+ return false;
+
+ if (num_endpoints < 3) {
+ abort (); // Don't expect this
+ return false; // Need at least two arcs
+ }
+ if (Point (endpoints[0].p) != Point (endpoints[num_endpoints-1].p)) {
+ abort (); // Don't expect this
+ return false; // Need a closed contour
+ }
+
+ if (inverse ^
+ winding (endpoints, num_endpoints) ^
+ even_odd (endpoints, num_endpoints, all_endpoints, num_all_endpoints))
+ {
+ glyphy_outline_reverse (endpoints, num_endpoints);
+ return true;
+ }
+
+ return false;
+}
+
+/* Returns true if outline was modified */
+glyphy_bool_t
+glyphy_outline_winding_from_even_odd (glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ glyphy_bool_t inverse)
+{
+ /*
+ * Algorithm:
+ *
+ * - Process one contour at a time.
+ */
+
+ unsigned int start = 0;
+ bool ret = false;
+ for (unsigned int i = 1; i < num_endpoints; i++) {
+ const glyphy_arc_endpoint_t &endpoint = endpoints[i];
+ if (endpoint.d == GLYPHY_INFINITY) {
+ ret = ret | process_contour (endpoints + start, i - start, endpoints, num_endpoints, bool (inverse));
+ start = i;
+ }
+ }
+ ret = ret | process_contour (endpoints + start, num_endpoints - start, endpoints, num_endpoints, bool (inverse));
+ return ret;
+}
diff --git a/glyphy/glyphy-sdf-glsl.h b/glyphy/glyphy-sdf-glsl.h
@@ -0,0 +1,152 @@
+static const char *glyphy_sdf_glsl =
+"/*\n"
+" * Copyright 2012 Google, Inc. All Rights Reserved.\n"
+" *\n"
+" * Licensed under the Apache License, Version 2.0 (the \"License\");\n"
+" * you may not use this file except in compliance with the License.\n"
+" * You may obtain a copy of the License at\n"
+" *\n"
+" * http://www.apache.org/licenses/LICENSE-2.0\n"
+" *\n"
+" * Unless required by applicable law or agreed to in writing, software\n"
+" * distributed under the License is distributed on an \"AS IS\" BASIS,\n"
+" * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n"
+" * See the License for the specific language governing permissions and\n"
+" * limitations under the License.\n"
+" *\n"
+" * Google Author(s): Behdad Esfahbod, Maysum Panju\n"
+" */\n"
+"\n"
+"#ifndef GLYPHY_TEXTURE1D_FUNC\n"
+"#define GLYPHY_TEXTURE1D_FUNC glyphy_texture1D_func\n"
+"#endif\n"
+"#ifndef GLYPHY_TEXTURE1D_EXTRA_DECLS\n"
+"#define GLYPHY_TEXTURE1D_EXTRA_DECLS\n"
+"#endif\n"
+"#ifndef GLYPHY_TEXTURE1D_EXTRA_ARGS\n"
+"#define GLYPHY_TEXTURE1D_EXTRA_ARGS\n"
+"#endif\n"
+"\n"
+"#ifndef GLYPHY_SDF_TEXTURE1D_FUNC\n"
+"#define GLYPHY_SDF_TEXTURE1D_FUNC GLYPHY_TEXTURE1D_FUNC\n"
+"#endif\n"
+"#ifndef GLYPHY_SDF_TEXTURE1D_EXTRA_DECLS\n"
+"#define GLYPHY_SDF_TEXTURE1D_EXTRA_DECLS GLYPHY_TEXTURE1D_EXTRA_DECLS\n"
+"#endif\n"
+"#ifndef GLYPHY_SDF_TEXTURE1D_EXTRA_ARGS\n"
+"#define GLYPHY_SDF_TEXTURE1D_EXTRA_ARGS GLYPHY_TEXTURE1D_EXTRA_ARGS\n"
+"#endif\n"
+"#ifndef GLYPHY_SDF_TEXTURE1D\n"
+"#define GLYPHY_SDF_TEXTURE1D(offset) GLYPHY_RGBA(GLYPHY_SDF_TEXTURE1D_FUNC (offset GLYPHY_TEXTURE1D_EXTRA_ARGS))\n"
+"#endif\n"
+"\n"
+"#ifndef GLYPHY_MAX_NUM_ENDPOINTS\n"
+"#define GLYPHY_MAX_NUM_ENDPOINTS 32\n"
+"#endif\n"
+"\n"
+"glyphy_arc_list_t\n"
+"glyphy_arc_list (const vec2 p, const ivec2 nominal_size GLYPHY_SDF_TEXTURE1D_EXTRA_DECLS)\n"
+"{\n"
+" int cell_offset = glyphy_arc_list_offset (p, nominal_size);\n"
+" vec4 arc_list_data = GLYPHY_SDF_TEXTURE1D (cell_offset);\n"
+" return glyphy_arc_list_decode (arc_list_data, nominal_size);\n"
+"}\n"
+"\n"
+"float\n"
+"glyphy_sdf (const vec2 p, const ivec2 nominal_size GLYPHY_SDF_TEXTURE1D_EXTRA_DECLS)\n"
+"{\n"
+" glyphy_arc_list_t arc_list = glyphy_arc_list (p, nominal_size GLYPHY_SDF_TEXTURE1D_EXTRA_ARGS);\n"
+"\n"
+" /* Short-circuits */\n"
+" if (arc_list.num_endpoints == 0) {\n"
+" /* far-away cell */\n"
+" return GLYPHY_INFINITY * float(arc_list.side);\n"
+" } if (arc_list.num_endpoints == -1) {\n"
+" /* single-line */\n"
+" float angle = arc_list.line_angle;\n"
+" vec2 n = vec2 (cos (angle), sin (angle));\n"
+" return dot (p - (vec2(nominal_size) * .5), n) - arc_list.line_distance;\n"
+" }\n"
+"\n"
+" float side = float(arc_list.side);\n"
+" float min_dist = GLYPHY_INFINITY;\n"
+" glyphy_arc_t closest_arc;\n"
+"\n"
+" glyphy_arc_endpoint_t endpoint_prev, endpoint;\n"
+" endpoint_prev = glyphy_arc_endpoint_decode (GLYPHY_SDF_TEXTURE1D (arc_list.offset), nominal_size);\n"
+" for (int i = 1; i < GLYPHY_MAX_NUM_ENDPOINTS; i++)\n"
+" {\n"
+" if (i >= arc_list.num_endpoints) {\n"
+" break;\n"
+" }\n"
+" endpoint = glyphy_arc_endpoint_decode (GLYPHY_SDF_TEXTURE1D (arc_list.offset + i), nominal_size);\n"
+" glyphy_arc_t a = glyphy_arc_t (endpoint_prev.p, endpoint.p, endpoint.d);\n"
+" endpoint_prev = endpoint;\n"
+" if (glyphy_isinf (a.d)) continue;\n"
+"\n"
+" if (glyphy_arc_wedge_contains (a, p))\n"
+" {\n"
+" float sdist = glyphy_arc_wedge_signed_dist (a, p);\n"
+" float udist = abs (sdist) * (1. - GLYPHY_EPSILON);\n"
+" if (udist <= min_dist) {\n"
+" min_dist = udist;\n"
+" side = sdist <= 0. ? -1. : +1.;\n"
+" }\n"
+" } else {\n"
+" float udist = min (distance (p, a.p0), distance (p, a.p1));\n"
+" if (udist < min_dist) {\n"
+" min_dist = udist;\n"
+" side = 0.; /* unsure */\n"
+" closest_arc = a;\n"
+" } else if (side == 0. && udist == min_dist) {\n"
+" /* If this new distance is the same as the current minimum,\n"
+" * compare extended distances. Take the sign from the arc\n"
+" * with larger extended distance. */\n"
+" float old_ext_dist = glyphy_arc_extended_dist (closest_arc, p);\n"
+" float new_ext_dist = glyphy_arc_extended_dist (a, p);\n"
+"\n"
+" float ext_dist = abs (new_ext_dist) <= abs (old_ext_dist) ?\n"
+" old_ext_dist : new_ext_dist;\n"
+"\n"
+"#ifdef GLYPHY_SDF_PSEUDO_DISTANCE\n"
+" /* For emboldening and stuff: */\n"
+" min_dist = abs (ext_dist);\n"
+"#endif\n"
+" side = sign (ext_dist);\n"
+" }\n"
+" }\n"
+" }\n"
+"\n"
+" if (side == 0.) {\n"
+" // Technically speaking this should not happen, but it does. So try to fix it.\n"
+" float ext_dist = glyphy_arc_extended_dist (closest_arc, p);\n"
+" side = sign (ext_dist);\n"
+" }\n"
+"\n"
+" return min_dist * side;\n"
+"}\n"
+"\n"
+"float\n"
+"glyphy_point_dist (const vec2 p, const ivec2 nominal_size GLYPHY_SDF_TEXTURE1D_EXTRA_DECLS)\n"
+"{\n"
+" glyphy_arc_list_t arc_list = glyphy_arc_list (p, nominal_size GLYPHY_SDF_TEXTURE1D_EXTRA_ARGS);\n"
+"\n"
+" float side = float(arc_list.side);\n"
+" float min_dist = GLYPHY_INFINITY;\n"
+"\n"
+" if (arc_list.num_endpoints == 0)\n"
+" return min_dist;\n"
+"\n"
+" glyphy_arc_endpoint_t endpoint;\n"
+" for (int i = 0; i < GLYPHY_MAX_NUM_ENDPOINTS; i++)\n"
+" {\n"
+" if (i >= arc_list.num_endpoints) {\n"
+" break;\n"
+" }\n"
+" endpoint = glyphy_arc_endpoint_decode (GLYPHY_SDF_TEXTURE1D (arc_list.offset + i), nominal_size);\n"
+" if (glyphy_isinf (endpoint.d)) continue;\n"
+" min_dist = min (min_dist, distance (p, endpoint.p));\n"
+" }\n"
+" return min_dist;\n"
+"}\n"
+;
diff --git a/glyphy/glyphy-sdf.cxx b/glyphy/glyphy-sdf.cxx
@@ -0,0 +1,91 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju, Wojciech Baranowski
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "glyphy-common.hh"
+#include "glyphy-geometry.hh"
+
+using namespace GLyphy::Geometry;
+
+/*
+ * TODO
+ *
+ * Sync this with the shader sdf
+ */
+
+double
+glyphy_sdf_from_arc_list (const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ const glyphy_point_t *p,
+ glyphy_point_t *closest_p /* may be NULL; TBD not implemented yet */)
+{
+ Point c = *p;
+ Point p0 (0, 0);
+ Arc closest_arc (p0, p0, 0);
+ double min_dist = GLYPHY_INFINITY;
+ int side = 0;
+ for (unsigned int i = 0; i < num_endpoints; i++) {
+ const glyphy_arc_endpoint_t &endpoint = endpoints[i];
+ if (endpoint.d == GLYPHY_INFINITY) {
+ p0 = endpoint.p;
+ continue;
+ }
+ Arc arc (p0, endpoint.p, endpoint.d);
+ p0 = endpoint.p;
+
+ if (arc.wedge_contains_point (c)) {
+ double sdist = arc.distance_to_point (c); /* TODO This distance has the wrong sign. Fix */
+ double udist = fabs (sdist) * (1 - GLYPHY_EPSILON);
+ if (udist <= min_dist) {
+ min_dist = udist;
+ side = sdist >= 0 ? -1 : +1;
+ }
+ } else {
+ double udist = std::min ((arc.p0 - c).len (), (arc.p1 - c).len ());
+ if (udist < min_dist) {
+ min_dist = udist;
+ side = 0; /* unsure */
+ closest_arc = arc;
+ } else if (side == 0 && udist == min_dist) {
+ /* If this new distance is the same as the current minimum,
+ * compare extended distances. Take the sign from the arc
+ * with larger extended distance. */
+ double old_ext_dist = closest_arc.extended_dist (c);
+ double new_ext_dist = arc.extended_dist (c);
+
+ double ext_dist = fabs (new_ext_dist) <= fabs (old_ext_dist) ?
+ old_ext_dist : new_ext_dist;
+
+ /* For emboldening and stuff: */
+ // min_dist = fabs (ext_dist);
+ side = ext_dist >= 0 ? +1 : -1;
+ }
+ }
+ }
+
+ if (side == 0) {
+ // Technically speaking this should not happen, but it does. So try to fix it.
+ double ext_dist = closest_arc.extended_dist (c);
+ side = ext_dist >= 0 ? +1 : -1;
+ }
+
+ return side * min_dist;
+}
diff --git a/glyphy/glyphy-shaders.cxx b/glyphy/glyphy-shaders.cxx
@@ -0,0 +1,39 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju, Wojciech Baranowski
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include "glyphy-common.hh"
+
+/*
+ * Shader source code
+ */
+
+/* TODO path separator */
+#define SHADER_PATH(File) PKGDATADIR "/" File
+
+#include "glyphy-common-glsl.h"
+#include "glyphy-sdf-glsl.h"
+
+const char * glyphy_common_shader_source (void) { return glyphy_common_glsl; }
+const char * glyphy_sdf_shader_source (void) { return glyphy_sdf_glsl; }
+
+const char * glyphy_common_shader_source_path (void) { return SHADER_PATH ("glyphy-common.glsl"); }
+const char * glyphy_sdf_shader_source_path (void) { return SHADER_PATH ("glyphy-sdf.glsl"); }
diff --git a/glyphy/glyphy.h b/glyphy/glyphy.h
@@ -0,0 +1,354 @@
+/*
+ * Copyright 2012 Google, Inc. All Rights Reserved.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Google Author(s): Behdad Esfahbod, Maysum Panju
+ */
+
+#ifndef GLYPHY_H
+#define GLYPHY_H
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+#define GLYPHY_PASTE_ARGS(prefix, name) prefix ## name
+#define GLYPHY_PASTE(prefix, name) GLYPHY_PASTE_ARGS (prefix, name)
+
+
+
+typedef int glyphy_bool_t;
+
+
+typedef struct {
+ double x;
+ double y;
+} glyphy_point_t;
+
+
+
+/*
+ * Geometry extents
+ */
+
+typedef struct {
+ double min_x;
+ double min_y;
+ double max_x;
+ double max_y;
+} glyphy_extents_t;
+
+void
+glyphy_extents_clear (glyphy_extents_t *extents);
+
+glyphy_bool_t
+glyphy_extents_is_empty (const glyphy_extents_t *extents);
+
+void
+glyphy_extents_add (glyphy_extents_t *extents,
+ const glyphy_point_t *p);
+
+void
+glyphy_extents_extend (glyphy_extents_t *extents,
+ const glyphy_extents_t *other);
+
+glyphy_bool_t
+glyphy_extents_includes (const glyphy_extents_t *extents,
+ const glyphy_point_t *p);
+
+void
+glyphy_extents_scale (glyphy_extents_t *extents,
+ double x_scale,
+ double y_scale);
+
+
+
+/*
+ * Circular arcs
+ */
+
+
+typedef struct {
+ glyphy_point_t p0;
+ glyphy_point_t p1;
+ double d;
+} glyphy_arc_t;
+
+
+/* Build from a conventional arc representation */
+void
+glyphy_arc_from_conventional (const glyphy_point_t *center,
+ double radius,
+ double angle0,
+ double angle1,
+ glyphy_bool_t negative,
+ glyphy_arc_t *arc);
+
+/* Convert to a conventional arc representation */
+void
+glyphy_arc_to_conventional (glyphy_arc_t arc,
+ glyphy_point_t *center /* may be NULL */,
+ double *radius /* may be NULL */,
+ double *angle0 /* may be NULL */,
+ double *angle1 /* may be NULL */,
+ glyphy_bool_t *negative /* may be NULL */);
+
+glyphy_bool_t
+glyphy_arc_is_a_line (glyphy_arc_t arc);
+
+void
+glyphy_arc_extents (glyphy_arc_t arc,
+ glyphy_extents_t *extents);
+
+
+
+/*
+ * Approximate single pieces of geometry to/from one arc
+ */
+
+
+void
+glyphy_arc_from_line (const glyphy_point_t *p0,
+ const glyphy_point_t *p1,
+ glyphy_arc_t *arc);
+
+void
+glyphy_arc_from_conic (const glyphy_point_t *p0,
+ const glyphy_point_t *p1,
+ const glyphy_point_t *p2,
+ glyphy_arc_t *arc,
+ double *error);
+
+void
+glyphy_arc_from_cubic (const glyphy_point_t *p0,
+ const glyphy_point_t *p1,
+ const glyphy_point_t *p2,
+ const glyphy_point_t *p3,
+ glyphy_arc_t *arc,
+ double *error);
+
+void
+glyphy_arc_to_cubic (const glyphy_arc_t *arc,
+ glyphy_point_t *p0,
+ glyphy_point_t *p1,
+ glyphy_point_t *p2,
+ glyphy_point_t *p3,
+ double *error);
+
+
+
+/*
+ * Approximate outlines with multiple arcs
+ */
+
+
+typedef struct {
+ glyphy_point_t p;
+ double d;
+} glyphy_arc_endpoint_t;
+
+typedef glyphy_bool_t (*glyphy_arc_endpoint_accumulator_callback_t) (glyphy_arc_endpoint_t *endpoint,
+ void *user_data);
+
+
+typedef struct glyphy_arc_accumulator_t glyphy_arc_accumulator_t;
+
+glyphy_arc_accumulator_t *
+glyphy_arc_accumulator_create (void);
+
+void
+glyphy_arc_accumulator_destroy (glyphy_arc_accumulator_t *acc);
+
+glyphy_arc_accumulator_t *
+glyphy_arc_accumulator_reference (glyphy_arc_accumulator_t *acc);
+
+
+void
+glyphy_arc_accumulator_reset (glyphy_arc_accumulator_t *acc);
+
+
+/* Configure accumulator */
+
+void
+glyphy_arc_accumulator_set_tolerance (glyphy_arc_accumulator_t *acc,
+ double tolerance);
+
+double
+glyphy_arc_accumulator_get_tolerance (glyphy_arc_accumulator_t *acc);
+
+void
+glyphy_arc_accumulator_set_callback (glyphy_arc_accumulator_t *acc,
+ glyphy_arc_endpoint_accumulator_callback_t callback,
+ void *user_data);
+
+void
+glyphy_arc_accumulator_get_callback (glyphy_arc_accumulator_t *acc,
+ glyphy_arc_endpoint_accumulator_callback_t *callback,
+ void **user_data);
+
+void
+glyphy_arc_accumulator_set_d_metrics (glyphy_arc_accumulator_t *acc,
+ double max_d,
+ double d_bits);
+
+void
+glyphy_arc_accumulator_get_d_metrics (glyphy_arc_accumulator_t *acc,
+ double *max_d,
+ double *d_bits);
+
+
+/* Accumulation results */
+
+unsigned int
+glyphy_arc_accumulator_get_num_endpoints (glyphy_arc_accumulator_t *acc);
+
+double
+glyphy_arc_accumulator_get_error (glyphy_arc_accumulator_t *acc);
+
+glyphy_bool_t
+glyphy_arc_accumulator_successful (glyphy_arc_accumulator_t *acc);
+
+
+/* Accumulate */
+
+void
+glyphy_arc_accumulator_move_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p0);
+
+void
+glyphy_arc_accumulator_line_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p1);
+
+void
+glyphy_arc_accumulator_conic_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p1,
+ const glyphy_point_t *p2);
+
+void
+glyphy_arc_accumulator_cubic_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p1,
+ const glyphy_point_t *p2,
+ const glyphy_point_t *p3);
+
+void
+glyphy_arc_accumulator_arc_to (glyphy_arc_accumulator_t *acc,
+ const glyphy_point_t *p1,
+ double d);
+
+void
+glyphy_arc_accumulator_close_path (glyphy_arc_accumulator_t *acc);
+
+void
+glyphy_arc_list_extents (const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ glyphy_extents_t *extents);
+
+
+
+/*
+ * Modify outlines for proper consumption
+ */
+
+void
+glyphy_outline_reverse (glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints);
+
+/* Returns true if outline was modified */
+glyphy_bool_t
+glyphy_outline_winding_from_even_odd (glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ glyphy_bool_t inverse);
+
+
+
+/*
+ * Encode an arc outline into binary blob for fast SDF calculation
+ */
+
+
+typedef struct {
+ unsigned char r;
+ unsigned char g;
+ unsigned char b;
+ unsigned char a;
+} glyphy_rgba_t;
+
+
+/* TODO make this callback-based also? */
+/* TODO rename to glyphy_blob_encode? */
+glyphy_bool_t
+glyphy_arc_list_encode_blob (const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ glyphy_rgba_t *blob,
+ unsigned int blob_size,
+ double faraway,
+ double avg_fetch_desired,
+ double *avg_fetch_achieved,
+ unsigned int *output_len,
+ unsigned int *nominal_width, /* 6bit */
+ unsigned int *nominal_height, /* 6bit */
+ glyphy_extents_t *extents);
+
+/* TBD _decode_blob */
+
+
+
+/*
+ * Calculate signed-distance-field from (encoded) arc list
+ */
+
+
+double
+glyphy_sdf_from_arc_list (const glyphy_arc_endpoint_t *endpoints,
+ unsigned int num_endpoints,
+ const glyphy_point_t *p,
+ glyphy_point_t *closest_p /* may be NULL; TBD not implemented yet */);
+
+/* TBD */
+double
+glyphy_sdf_from_blob (const glyphy_rgba_t *blob,
+ unsigned int nominal_width,
+ unsigned int nominal_height,
+ const glyphy_point_t *p,
+ glyphy_point_t *closest_p /* may be NULL; TBD not implemented yet */);
+
+
+
+/*
+ * Shader source code
+ */
+
+
+/* TODO make this enum-based? */
+
+const char *
+glyphy_common_shader_source (void);
+
+const char *
+glyphy_common_shader_source_path (void);
+
+const char *
+glyphy_sdf_shader_source (void);
+
+const char *
+glyphy_sdf_shader_source_path (void);
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* GLYPHY_H */
