inkscape/src/sp-spiral.cpp

	sp-spiral.cpp revision 4bd9cc13b0264b6577fd94bbbd737c4608b3466d
/** \file
 * <sodipodi:spiral> implementation
 */
/*
 * Authors:
 *   Mitsuru Oka <oka326@parkcity.ne.jp>
 *   Lauris Kaplinski <lauris@kaplinski.com>
 *   Abhishek Sharma
 *   Jon A. Cruz <jon@joncruz.org>
 *
 * 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 <2geom/bezier-utils.h>
#include <2geom/pathvector.h>
#include "display/curve.h"
#include <glibmm/i18n.h>
#include "xml/repr.h"
#include "document.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::Document *doc, 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, std::vector<Inkscape::SnapCandidatePoint> &p, Inkscape::SnapPreferences const *snapprefs);

static void sp_spiral_set_shape (SPShape *shape);
static void sp_spiral_update_patheffect (SPLPEItem *lpeitem, bool write);

static Geom::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)
{
    SPObjectClass *sp_object_class = reinterpret_cast<SPObjectClass *>(klass);
    SPItemClass *item_class = reinterpret_cast<SPItemClass *>(klass);
    SPLPEItemClass *lpe_item_class = reinterpret_cast<SPLPEItemClass *>(klass);
    SPShapeClass *shape_class = reinterpret_cast<SPShapeClass *>(klass);

    parent_class = reinterpret_cast<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;

    //lpe_item_class->update_patheffect = sp_spiral_update_patheffect;

    //shape_class->set_shape = sp_spiral_set_shape;
}

CSpiral::CSpiral(SPSpiral* spiral) : CShape(spiral) {
    this->spspiral = spiral;
}

CSpiral::~CSpiral() {
}

/**
 * Callback for SPSpiral object initialization.
 */
static void
sp_spiral_init (SPSpiral * spiral)
{
    spiral->cspiral = new CSpiral(spiral);
    spiral->cshape = spiral->cspiral;
    spiral->clpeitem = spiral->cspiral;
    spiral->citem = spiral->cspiral;
    spiral->cobject = spiral->cspiral;

    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;
}

void CSpiral::onBuild(SPDocument * document, Inkscape::XML::Node * repr) {
    SPSpiral* object = this->spspiral;

    CShape::onBuild(document, repr);

    object->readAttr( "sodipodi:cx" );
    object->readAttr( "sodipodi:cy" );
    object->readAttr( "sodipodi:expansion" );
    object->readAttr( "sodipodi:revolution" );
    object->readAttr( "sodipodi:radius" );
    object->readAttr( "sodipodi:argument" );
    object->readAttr( "sodipodi:t0" );
}

// CPPIFY: remove
/**
 * Virtual build: set spiral properties from corresponding repr.
 */
static void sp_spiral_build(SPObject * object, SPDocument * document, Inkscape::XML::Node * repr)
{
    ((SPSpiral*)object)->cspiral->onBuild(document, repr);
}

Inkscape::XML::Node* CSpiral::onWrite(Inkscape::XML::Document *xml_doc, Inkscape::XML::Node *repr, guint flags) {
    SPSpiral *spiral = this->spspiral;

    if ((flags & SP_OBJECT_WRITE_BUILD) && !repr) {
        repr = xml_doc->createElement("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);
    }

     // make sure the curve is rebuilt with all up-to-date parameters
     sp_spiral_set_shape(spiral);

    //Nulls might be possible if this called iteratively
    if ( !spiral->_curve ) {
            //g_warning("sp_spiral_write(): No path to copy\n");
            return NULL;
    }
    char *d = sp_svg_write_path ( spiral->_curve->get_pathvector() );
    repr->setAttribute("d", d);
    g_free (d);

    CShape::onWrite(xml_doc, repr, flags | SP_SHAPE_WRITE_PATH);

    return repr;
}

// CPPIFY: remove
/**
 * Virtual write: write spiral attributes to corresponding repr.
 */
static Inkscape::XML::Node *
sp_spiral_write (SPObject *object, Inkscape::XML::Document *xml_doc, Inkscape::XML::Node *repr, guint flags)
{
    return ((SPSpiral*)object)->cspiral->onWrite(xml_doc, repr, flags);
}

void CSpiral::onSet(unsigned int key, gchar const* value) {
    SPSpiral *spiral = this->spspiral;
    SPSpiral* object = spiral;

    /// \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:
        CShape::onSet(key, value);
        break;
    }
}

// CPPIFY: remove
/**
 * Virtual set: change spiral object attribute.
 */
static void sp_spiral_set(SPObject *object, unsigned int key, const gchar *value)
{
    ((SPSpiral*)object)->cspiral->onSet(key, value);
}

void CSpiral::onUpdate(SPCtx *ctx, guint flags) {
    SPSpiral* object = this->spspiral;

    if (flags & (SP_OBJECT_MODIFIED_FLAG | SP_OBJECT_STYLE_MODIFIED_FLAG | SP_OBJECT_VIEWPORT_MODIFIED_FLAG)) {
        reinterpret_cast<SPShape *>(object)->setShape();
    }

    CShape::onUpdate(ctx, flags);
}

// CPPIFY: remove
/**
 * Virtual update callback.
 */
static void sp_spiral_update(SPObject *object, SPCtx *ctx, guint flags)
{
    ((SPSpiral*)object)->cspiral->onUpdate(ctx, flags);
}

void CSpiral::onUpdatePatheffect(bool write) {
    SPSpiral* shape = this->spspiral;

    sp_spiral_set_shape(shape);

    if (write) {
        Inkscape::XML::Node *repr = shape->getRepr();
        if ( shape->_curve != NULL ) {
            gchar *str = sp_svg_write_path(shape->_curve->get_pathvector());
            repr->setAttribute("d", str);
            g_free(str);
        } else {
            repr->setAttribute("d", NULL);
        }
    }

    shape->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
}

// CPPIFY: remove
static void sp_spiral_update_patheffect(SPLPEItem *lpeitem, bool write)
{
    ((SPSpiral*)lpeitem)->cspiral->onUpdatePatheffect(write);
}

gchar* CSpiral::onDescription() {
    SPSpiral* item = this->spspiral;

    // 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);
}

// CPPIFY: remove
/**
 * Return textual description of spiral.
 */
static gchar *sp_spiral_description(SPItem * item)
{
    return ((SPSpiral*)item)->cspiral->onDescription();
}


/**
 * 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,
            Geom::Point darray[],
            Geom::Point const &hat1,
            Geom::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));

    Geom::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 = Geom::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) {
            c->curveto(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++)
            c->lineto(darray[i]);
    }
    *t = next_t;
    g_assert (is_unit_vector (hat2));
}

void CSpiral::onSetShape() {
    SPSpiral *spiral = this->spspiral;
    SPSpiral* shape = spiral;

    if (sp_lpe_item_has_broken_path_effect(SP_LPE_ITEM(shape))) {
        g_warning ("The spiral shape has unknown LPE on it! Convert to path to make it editable preserving the appearance; editing it as spiral will remove the bad LPE");
        if (shape->getRepr()->attribute("d")) {
            // unconditionally read the curve from d, if any, to preserve appearance
            Geom::PathVector pv = sp_svg_read_pathv(shape->getRepr()->attribute("d"));
            SPCurve *cold = new SPCurve(pv);
            shape->setCurveInsync( cold, TRUE);
            shape->setCurveBeforeLPE( cold );
            cold->unref();
        }
        return;
    }

    Geom::Point darray[SAMPLE_SIZE + 1];
    double t;

    spiral->requestModified(SP_OBJECT_MODIFIED_FLAG);

    SPCurve *c = new SPCurve ();

#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. */
    c->moveto(sp_spiral_get_xy(spiral, spiral->t0));

    double const tstep = SAMPLE_STEP / spiral->revo;
    double const dstep = tstep / (SAMPLE_SIZE - 1);

    Geom::Point hat1 = sp_spiral_get_tangent (spiral, spiral->t0);
    Geom::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);

    /* Reset the shape'scurve to the "original_curve"
     * This is very important for LPEs to work properly! (the bbox might be recalculated depending on the curve in shape)*/
    shape->setCurveInsync( c, TRUE);
    shape->setCurveBeforeLPE( c );
    if (sp_lpe_item_has_path_effect(SP_LPE_ITEM(shape)) && sp_lpe_item_path_effects_enabled(SP_LPE_ITEM(shape))) {
        SPCurve *c_lpe = c->copy();
        bool success = sp_lpe_item_perform_path_effect(SP_LPE_ITEM (shape), c_lpe);
        if (success) {
            shape->setCurveInsync( c_lpe, TRUE);
        }
        c_lpe->unref();
    }
    c->unref();
}

// CPPIFY: remove
static void
sp_spiral_set_shape (SPShape *shape)
{
    ((SPSpiral*)shape)->cspiral->onSetShape();
}

/**
 * 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, 0.0);
    spiral->arg        = arg;
    spiral->t0         = CLAMP(t0, 0.0, 0.999);

    (static_cast<SPObject *>(spiral))->requestDisplayUpdate(SP_OBJECT_MODIFIED_FLAG);
}

void CSpiral::onSnappoints(std::vector<Inkscape::SnapCandidatePoint> &p, Inkscape::SnapPreferences const *snapprefs) {
    SPSpiral* item = this->spspiral;

    // We will determine the spiral's midpoint ourselves, instead of trusting on the base class
    // Therefore snapping to object midpoints is temporarily disabled
    Inkscape::SnapPreferences local_snapprefs = *snapprefs;
    local_snapprefs.setTargetSnappable(Inkscape::SNAPTARGET_OBJECT_MIDPOINT, false);

    CShape::onSnappoints(p, &local_snapprefs);

    if (snapprefs->isTargetSnappable(Inkscape::SNAPTARGET_OBJECT_MIDPOINT)) {
        Geom::Affine const i2dt (item->i2dt_affine ());
        SPSpiral *spiral = SP_SPIRAL(item);
        p.push_back(Inkscape::SnapCandidatePoint(Geom::Point(spiral->cx, spiral->cy) * i2dt, Inkscape::SNAPSOURCE_OBJECT_MIDPOINT, Inkscape::SNAPTARGET_OBJECT_MIDPOINT));
        // This point is the start-point of the spiral, which is also returned when _snap_to_itemnode has been set
        // in the object snapper. In that case we will get a duplicate!
    }
}

// CPPIFY: remove
/**
 * Virtual snappoints callback.
 */
static void sp_spiral_snappoints(SPItem const *item, std::vector<Inkscape::SnapCandidatePoint> &p, Inkscape::SnapPreferences const *snapprefs)
{
    ((SPSpiral*)item)->cspiral->onSnappoints(p, snapprefs);
}

/**
 * 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.)
 */
Geom::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 Geom::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 Geom::Point
sp_spiral_get_tangent (SPSpiral const *spiral, gdouble t)
{
    Geom::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 = Geom::Point(-s, c);
    } else if (t_scaled == 0.0) {
        ret = Geom::Point(c, s);
    } else {
        Geom::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 = Geom::Point(dot(unrotated, Geom::Point(c, -s)),
                                  dot(unrotated, Geom::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:fileencoding=utf-8:textwidth=99 :