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diff --git a/src/sp-spiral.cpp b/src/sp-spiral.cpp
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+++ b/src/sp-spiral.cpp
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+#define __SP_SPIRAL_C__
+
+/** \file
+ * <sodipodi:spiral> implementation
+ */
+/*
+ * Authors:
+ * Mitsuru Oka <oka326@parkcity.ne.jp>
+ * Lauris Kaplinski <lauris@kaplinski.com>
+ *
+ * Copyright (C) 1999-2002 Lauris Kaplinski
+ * Copyright (C) 2000-2001 Ximian, Inc.
+ *
+ * Released under GNU GPL, read the file 'COPYING' for more information
+ */
+
+#include "config.h"
+
+
+#include "svg/svg.h"
+#include "attributes.h"
+#include "display/bezier-utils.h"
+#include "display/curve.h"
+#include <glibmm/i18n.h>
+#include "xml/repr.h"
+
+#include "sp-spiral.h"
+
+static void sp_spiral_class_init (SPSpiralClass *klass);
+static void sp_spiral_init (SPSpiral *spiral);
+
+static void sp_spiral_build (SPObject * object, SPDocument * document, Inkscape::XML::Node * repr);
+static Inkscape::XML::Node *sp_spiral_write (SPObject *object, Inkscape::XML::Node *repr, guint flags);
+static void sp_spiral_set (SPObject *object, unsigned int key, const gchar *value);
+static void sp_spiral_update (SPObject *object, SPCtx *ctx, guint flags);
+
+static gchar * sp_spiral_description (SPItem * item);
+static void sp_spiral_snappoints(SPItem const *item, SnapPointsIter p);
+static void sp_spiral_set_shape (SPShape *shape);
+
+static NR::Point sp_spiral_get_tangent (SPSpiral const *spiral, gdouble t);
+
+static SPShapeClass *parent_class;
+
+/**
+ * Register SPSpiral class and return its type number.
+ */
+GType
+sp_spiral_get_type (void)
+{
+ static GType spiral_type = 0;
+
+ if (!spiral_type) {
+ GTypeInfo spiral_info = {
+ sizeof (SPSpiralClass),
+ NULL, /* base_init */
+ NULL, /* base_finalize */
+ (GClassInitFunc) sp_spiral_class_init,
+ NULL, /* class_finalize */
+ NULL, /* class_data */
+ sizeof (SPSpiral),
+ 16, /* n_preallocs */
+ (GInstanceInitFunc) sp_spiral_init,
+ NULL, /* value_table */
+ };
+ spiral_type = g_type_register_static (SP_TYPE_SHAPE, "SPSpiral", &spiral_info, (GTypeFlags)0);
+ }
+ return spiral_type;
+}
+
+/**
+ * SPSpiral vtable initialization.
+ */
+static void
+sp_spiral_class_init (SPSpiralClass *klass)
+{
+ GObjectClass * gobject_class;
+ SPObjectClass * sp_object_class;
+ SPItemClass * item_class;
+ SPShapeClass *shape_class;
+
+ gobject_class = (GObjectClass *) klass;
+ sp_object_class = (SPObjectClass *) klass;
+ item_class = (SPItemClass *) klass;
+ shape_class = (SPShapeClass *) klass;
+
+ parent_class = (SPShapeClass *)g_type_class_ref (SP_TYPE_SHAPE);
+
+ sp_object_class->build = sp_spiral_build;
+ sp_object_class->write = sp_spiral_write;
+ sp_object_class->set = sp_spiral_set;
+ sp_object_class->update = sp_spiral_update;
+
+ item_class->description = sp_spiral_description;
+ item_class->snappoints = sp_spiral_snappoints;
+
+ shape_class->set_shape = sp_spiral_set_shape;
+}
+
+/**
+ * Callback for SPSpiral object initialization.
+ */
+static void
+sp_spiral_init (SPSpiral * spiral)
+{
+ spiral->cx = 0.0;
+ spiral->cy = 0.0;
+ spiral->exp = 1.0;
+ spiral->revo = 3.0;
+ spiral->rad = 1.0;
+ spiral->arg = 0.0;
+ spiral->t0 = 0.0;
+}
+
+/**
+ * Virtual build: set spiral properties from corresponding repr.
+ */
+static void
+sp_spiral_build (SPObject * object, SPDocument * document, Inkscape::XML::Node * repr)
+{
+ if (((SPObjectClass *) parent_class)->build)
+ ((SPObjectClass *) parent_class)->build (object, document, repr);
+
+ sp_object_read_attr (object, "sodipodi:cx");
+ sp_object_read_attr (object, "sodipodi:cy");
+ sp_object_read_attr (object, "sodipodi:expansion");
+ sp_object_read_attr (object, "sodipodi:revolution");
+ sp_object_read_attr (object, "sodipodi:radius");
+ sp_object_read_attr (object, "sodipodi:argument");
+ sp_object_read_attr (object, "sodipodi:t0");
+}
+
+/**
+ * Virtual write: write spiral attributes to corresponding repr.
+ */
+static Inkscape::XML::Node *
+sp_spiral_write (SPObject *object, Inkscape::XML::Node *repr, guint flags)
+{
+ SPSpiral *spiral = SP_SPIRAL (object);
+
+ if ((flags & SP_OBJECT_WRITE_BUILD) && !repr) {
+ repr = sp_repr_new ("svg:path");
+ }
+
+ if (flags & SP_OBJECT_WRITE_EXT) {
+ /* Fixme: we may replace these attributes by
+ * sodipodi:spiral="cx cy exp revo rad arg t0"
+ */
+ repr->setAttribute("sodipodi:type", "spiral");
+ sp_repr_set_svg_double(repr, "sodipodi:cx", spiral->cx);
+ sp_repr_set_svg_double(repr, "sodipodi:cy", spiral->cy);
+ sp_repr_set_svg_double(repr, "sodipodi:expansion", spiral->exp);
+ sp_repr_set_svg_double(repr, "sodipodi:revolution", spiral->revo);
+ sp_repr_set_svg_double(repr, "sodipodi:radius", spiral->rad);
+ sp_repr_set_svg_double(repr, "sodipodi:argument", spiral->arg);
+ sp_repr_set_svg_double(repr, "sodipodi:t0", spiral->t0);
+ }
+
+ //Duplicate the path
+ SPCurve *curve = ((SPShape *) spiral)->curve;
+ //Nulls might be possible if this called iteratively
+ if ( !curve ) {
+ //g_warning("sp_spiral_write(): No path to copy\n");
+ return NULL;
+ }
+ NArtBpath *bpath = curve->bpath;
+ if ( !bpath ) {
+ //g_warning("sp_spiral_write(): No path to copy\n");
+ return NULL;
+ }
+ char *d = sp_svg_write_path ( bpath );
+ repr->setAttribute("d", d);
+ g_free (d);
+
+ if (((SPObjectClass *) (parent_class))->write)
+ ((SPObjectClass *) (parent_class))->write (object, repr, flags | SP_SHAPE_WRITE_PATH);
+
+ return repr;
+}
+
+/**
+ * Virtual set: change spiral object attribute.
+ */
+static void
+sp_spiral_set (SPObject *object, unsigned int key, const gchar *value)
+{
+ SPSpiral *spiral;
+ SPShape *shape;
+
+ spiral = SP_SPIRAL (object);
+ shape = SP_SHAPE (object);
+
+ /// \todo fixme: we should really collect updates
+ switch (key) {
+ case SP_ATTR_SODIPODI_CX:
+ if (!sp_svg_length_read_computed_absolute (value, &spiral->cx)) {
+ spiral->cx = 0.0;
+ }
+ object->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
+ break;
+ case SP_ATTR_SODIPODI_CY:
+ if (!sp_svg_length_read_computed_absolute (value, &spiral->cy)) {
+ spiral->cy = 0.0;
+ }
+ object->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
+ break;
+ case SP_ATTR_SODIPODI_EXPANSION:
+ if (value) {
+ /** \todo
+ * FIXME: check that value looks like a (finite)
+ * number. Create a routine that uses strtod, and
+ * accepts a default value (if strtod finds an error).
+ * N.B. atof/sscanf/strtod consider "nan" and "inf"
+ * to be valid numbers.
+ */
+ spiral->exp = g_ascii_strtod (value, NULL);
+ spiral->exp = CLAMP (spiral->exp, 0.0, 1000.0);
+ } else {
+ spiral->exp = 1.0;
+ }
+ object->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
+ break;
+ case SP_ATTR_SODIPODI_REVOLUTION:
+ if (value) {
+ spiral->revo = g_ascii_strtod (value, NULL);
+ spiral->revo = CLAMP (spiral->revo, 0.05, 1024.0);
+ } else {
+ spiral->revo = 3.0;
+ }
+ object->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
+ break;
+ case SP_ATTR_SODIPODI_RADIUS:
+ if (!sp_svg_length_read_computed_absolute (value, &spiral->rad)) {
+ spiral->rad = MAX (spiral->rad, 0.001);
+ }
+ object->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
+ break;
+ case SP_ATTR_SODIPODI_ARGUMENT:
+ if (value) {
+ spiral->arg = g_ascii_strtod (value, NULL);
+ /** \todo
+ * FIXME: We still need some bounds on arg, for
+ * numerical reasons. E.g., we don't want inf or NaN,
+ * nor near-infinite numbers. I'm inclined to take
+ * modulo 2*pi. If so, then change the knot editors,
+ * which use atan2 - revo*2*pi, which typically
+ * results in very negative arg.
+ */
+ } else {
+ spiral->arg = 0.0;
+ }
+ object->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
+ break;
+ case SP_ATTR_SODIPODI_T0:
+ if (value) {
+ spiral->t0 = g_ascii_strtod (value, NULL);
+ spiral->t0 = CLAMP (spiral->t0, 0.0, 0.999);
+ /** \todo
+ * Have shared constants for the allowable bounds for
+ * attributes. There was a bug here where we used -1.0
+ * as the minimum (which leads to NaN via, e.g.,
+ * pow(-1.0, 0.5); see sp_spiral_get_xy for
+ * requirements.
+ */
+ } else {
+ spiral->t0 = 0.0;
+ }
+ object->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
+ break;
+ default:
+ if (((SPObjectClass *) parent_class)->set)
+ ((SPObjectClass *) parent_class)->set (object, key, value);
+ break;
+ }
+}
+
+/**
+ * Virtual update callback.
+ */
+static void
+sp_spiral_update (SPObject *object, SPCtx *ctx, guint flags)
+{
+ if (flags & (SP_OBJECT_MODIFIED_FLAG | SP_OBJECT_STYLE_MODIFIED_FLAG | SP_OBJECT_VIEWPORT_MODIFIED_FLAG)) {
+ sp_shape_set_shape ((SPShape *) object);
+ }
+
+ if (((SPObjectClass *) parent_class)->update)
+ ((SPObjectClass *) parent_class)->update (object, ctx, flags);
+}
+
+/**
+ * Return textual description of spiral.
+ */
+static gchar *
+sp_spiral_description (SPItem * item)
+{
+ // TRANSLATORS: since turn count isn't an integer, please adjust the
+ // string as needed to deal with an localized plural forms.
+ return g_strdup_printf (_("<b>Spiral</b> with %3f turns"), SP_SPIRAL(item)->revo);
+}
+
+
+/**
+ * Fit beziers together to spiral and draw it.
+ *
+ * \pre dstep \> 0.
+ * \pre is_unit_vector(*hat1).
+ * \post is_unit_vector(*hat2).
+ **/
+static void
+sp_spiral_fit_and_draw (SPSpiral const *spiral,
+ SPCurve *c,
+ double dstep,
+ NR::Point darray[],
+ NR::Point const &hat1,
+ NR::Point &hat2,
+ double *t)
+{
+#define BEZIER_SIZE 4
+#define FITTING_MAX_BEZIERS 4
+#define BEZIER_LENGTH (BEZIER_SIZE * FITTING_MAX_BEZIERS)
+ g_assert (dstep > 0);
+ g_assert (is_unit_vector (hat1));
+
+ NR::Point bezier[BEZIER_LENGTH];
+ double d;
+ int depth, i;
+
+ for (d = *t, i = 0; i <= SAMPLE_SIZE; d += dstep, i++) {
+ darray[i] = sp_spiral_get_xy(spiral, d);
+
+ /* Avoid useless adjacent dups. (Otherwise we can have all of darray filled with
+ the same value, which upsets chord_length_parameterize.) */
+ if ((i != 0)
+ && (darray[i] == darray[i - 1])
+ && (d < 1.0)) {
+ i--;
+ d += dstep;
+ /** We mustn't increase dstep for subsequent values of
+ * i: for large spiral.exp values, rate of growth
+ * increases very rapidly.
+ */
+ /** \todo
+ * Get the function itself to decide what value of d
+ * to use next: ensure that we move at least 0.25 *
+ * stroke width, for example. The derivative (as used
+ * for get_tangent before normalization) would be
+ * useful for estimating the appropriate d value. Or
+ * perhaps just start with a small dstep and scale by
+ * some small number until we move >= 0.25 *
+ * stroke_width. Must revert to the original dstep
+ * value for next iteration to avoid the problem
+ * mentioned above.
+ */
+ }
+ }
+
+ double const next_t = d - 2 * dstep;
+ /* == t + (SAMPLE_SIZE - 1) * dstep, in absence of dups. */
+
+ hat2 = -sp_spiral_get_tangent (spiral, next_t);
+
+ /** \todo
+ * We should use better algorithm to specify maximum error.
+ */
+ depth = sp_bezier_fit_cubic_full (bezier, NULL, darray, SAMPLE_SIZE,
+ hat1, hat2,
+ SPIRAL_TOLERANCE*SPIRAL_TOLERANCE,
+ FITTING_MAX_BEZIERS);
+ g_assert(depth * BEZIER_SIZE <= gint(G_N_ELEMENTS(bezier)));
+#ifdef SPIRAL_DEBUG
+ if (*t == spiral->t0 || *t == 1.0)
+ g_print ("[%s] depth=%d, dstep=%g, t0=%g, t=%g, arg=%g\n",
+ debug_state, depth, dstep, spiral->t0, *t, spiral->arg);
+#endif
+ if (depth != -1) {
+ for (i = 0; i < 4*depth; i += 4) {
+ sp_curve_curveto (c,
+ bezier[i + 1],
+ bezier[i + 2],
+ bezier[i + 3]);
+ }
+ } else {
+#ifdef SPIRAL_VERBOSE
+ g_print ("cant_fit_cubic: t=%g\n", *t);
+#endif
+ for (i = 1; i < SAMPLE_SIZE; i++)
+ sp_curve_lineto (c, darray[i]);
+ }
+ *t = next_t;
+ g_assert (is_unit_vector (hat2));
+}
+
+static void
+sp_spiral_set_shape (SPShape *shape)
+{
+ NR::Point darray[SAMPLE_SIZE + 1];
+ double t;
+
+ SPSpiral *spiral = SP_SPIRAL(shape);
+
+ SP_OBJECT (spiral)->requestModified(SP_OBJECT_MODIFIED_FLAG);
+
+ SPCurve *c = sp_curve_new ();
+
+#ifdef SPIRAL_VERBOSE
+ g_print ("cx=%g, cy=%g, exp=%g, revo=%g, rad=%g, arg=%g, t0=%g\n",
+ spiral->cx,
+ spiral->cy,
+ spiral->exp,
+ spiral->revo,
+ spiral->rad,
+ spiral->arg,
+ spiral->t0);
+#endif
+
+ /* Initial moveto. */
+ sp_curve_moveto(c, sp_spiral_get_xy(spiral, spiral->t0));
+
+ double const tstep = SAMPLE_STEP / spiral->revo;
+ double const dstep = tstep / (SAMPLE_SIZE - 1);
+
+ NR::Point hat1 = sp_spiral_get_tangent (spiral, spiral->t0);
+ NR::Point hat2;
+ for (t = spiral->t0; t < (1.0 - tstep);) {
+ sp_spiral_fit_and_draw (spiral, c, dstep, darray, hat1, hat2, &t);
+
+ hat1 = -hat2;
+ }
+ if ((1.0 - t) > SP_EPSILON)
+ sp_spiral_fit_and_draw (spiral, c, (1.0 - t)/(SAMPLE_SIZE - 1.0),
+ darray, hat1, hat2, &t);
+
+ sp_shape_set_curve_insync ((SPShape *) spiral, c, TRUE);
+ sp_curve_unref (c);
+}
+
+/**
+ * Set spiral properties and update display.
+ */
+void
+sp_spiral_position_set (SPSpiral *spiral,
+ gdouble cx,
+ gdouble cy,
+ gdouble exp,
+ gdouble revo,
+ gdouble rad,
+ gdouble arg,
+ gdouble t0)
+{
+ g_return_if_fail (spiral != NULL);
+ g_return_if_fail (SP_IS_SPIRAL (spiral));
+
+ /** \todo
+ * Consider applying CLAMP or adding in-bounds assertions for
+ * some of these parameters.
+ */
+ spiral->cx = cx;
+ spiral->cy = cy;
+ spiral->exp = exp;
+ spiral->revo = revo;
+ spiral->rad = MAX (rad, 0.001);
+ spiral->arg = arg;
+ spiral->t0 = CLAMP(t0, 0.0, 0.999);
+
+ ((SPObject *)spiral)->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
+}
+
+/**
+ * Virtual snappoints callback.
+ */
+static void sp_spiral_snappoints(SPItem const *item, SnapPointsIter p)
+{
+ if (((SPItemClass *) parent_class)->snappoints) {
+ ((SPItemClass *) parent_class)->snappoints (item, p);
+ }
+}
+
+/**
+ * Return one of the points on the spiral.
+ *
+ * \param t specifies how far along the spiral.
+ * \pre \a t in [0.0, 2.03]. (It doesn't make sense for t to be much more
+ * than 1.0, though some callers go slightly beyond 1.0 for curve-fitting
+ * purposes.)
+ */
+NR::Point sp_spiral_get_xy (SPSpiral const *spiral, gdouble t)
+{
+ g_assert (spiral != NULL);
+ g_assert (SP_IS_SPIRAL(spiral));
+ g_assert (spiral->exp >= 0.0);
+ /* Otherwise we get NaN for t==0. */
+ g_assert (spiral->exp <= 1000.0);
+ /* Anything much more results in infinities. Even allowing 1000 is somewhat overkill. */
+ g_assert (t >= 0.0);
+ /* Any callers passing -ve t will have a bug for non-integral values of exp. */
+
+ double const rad = spiral->rad * pow(t, (double) spiral->exp);
+ double const arg = 2.0 * M_PI * spiral->revo * t + spiral->arg;
+
+ return NR::Point(rad * cos (arg) + spiral->cx,
+ rad * sin (arg) + spiral->cy);
+}
+
+
+/**
+ * Returns the derivative of sp_spiral_get_xy with respect to t,
+ * scaled to a unit vector.
+ *
+ * \pre spiral != 0.
+ * \pre 0 \<= t.
+ * \pre p != NULL.
+ * \post is_unit_vector(*p).
+ */
+static NR::Point
+sp_spiral_get_tangent (SPSpiral const *spiral, gdouble t)
+{
+ NR::Point ret(1.0, 0.0);
+ g_return_val_if_fail (( ( spiral != NULL )
+ && SP_IS_SPIRAL(spiral) ),
+ ret);
+ g_assert (t >= 0.0);
+ g_assert (spiral->exp >= 0.0);
+ /* See above for comments on these assertions. */
+
+ double const t_scaled = 2.0 * M_PI * spiral->revo * t;
+ double const arg = t_scaled + spiral->arg;
+ double const s = sin (arg);
+ double const c = cos (arg);
+
+ if (spiral->exp == 0.0) {
+ ret = NR::Point(-s, c);
+ } else if (t_scaled == 0.0) {
+ ret = NR::Point(c, s);
+ } else {
+ NR::Point unrotated(spiral->exp, t_scaled);
+ double const s_len = L2 (unrotated);
+ g_assert (s_len != 0);
+ /** \todo
+ * Check that this isn't being too hopeful of the hypot
+ * function. E.g. test with numbers around 2**-1070
+ * (denormalized numbers), preferably on a few different
+ * platforms. However, njh says that the usual implementation
+ * does handle both very big and very small numbers.
+ */
+ unrotated /= s_len;
+
+ /* ret = spiral->exp * (c, s) + t_scaled * (-s, c);
+ alternatively ret = (spiral->exp, t_scaled) * (( c, s),
+ (-s, c)).*/
+ ret = NR::Point(dot(unrotated, NR::Point(c, -s)),
+ dot(unrotated, NR::Point(s, c)));
+ /* ret should already be approximately normalized: the
+ matrix ((c, -s), (s, c)) is orthogonal (it just
+ rotates by arg), and unrotated has been normalized,
+ so ret is already of unit length other than numerical
+ error in the above matrix multiplication. */
+
+ /** \todo
+ * I haven't checked how important it is for ret to be very
+ * near unit length; we could get rid of the below.
+ */
+
+ ret.normalize();
+ /* Proof that ret length is non-zero: see above. (Should be near 1.) */
+ }
+
+ g_assert (is_unit_vector (ret));
+ return ret;
+}
+
+/**
+ * Compute rad and/or arg for point on spiral.
+ */
+void
+sp_spiral_get_polar (SPSpiral const *spiral, gdouble t, gdouble *rad, gdouble *arg)
+{
+ g_return_if_fail (spiral != NULL);
+ g_return_if_fail (SP_IS_SPIRAL(spiral));
+
+ if (rad)
+ *rad = spiral->rad * pow(t, (double) spiral->exp);
+ if (arg)
+ *arg = 2.0 * M_PI * spiral->revo * t + spiral->arg;
+}
+
+/**
+ * Return true if spiral has properties that make it invalid.
+ */
+bool
+sp_spiral_is_invalid (SPSpiral const *spiral)
+{
+ gdouble rad;
+
+ sp_spiral_get_polar (spiral, 0.0, &rad, NULL);
+ if (rad < 0.0 || rad > SP_HUGE) {
+ g_print ("rad(t=0)=%g\n", rad);
+ return TRUE;
+ }
+ sp_spiral_get_polar (spiral, 1.0, &rad, NULL);
+ if (rad < 0.0 || rad > SP_HUGE) {
+ g_print ("rad(t=1)=%g\n", rad);
+ return TRUE;
+ }
+ return FALSE;
+}
+
+/*
+ Local Variables:
+ mode:c++
+ c-file-style:"stroustrup"
+ c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+ indent-tabs-mode:nil
+ fill-column:99
+ End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
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