spiro.cpp File Reference

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Classes
struct	spiro_seg_s
struct	bandmat
Defines
#define	ORDER   12
Functions
void	integrate_spiro (const double ks[4], double xy[2])
static double	compute_ends (const double ks[4], double ends[2][4], double seg_ch)
static void	compute_pderivs (const spiro_seg *s, double ends[2][4], double derivs[4][2][4], int jinc)
static double	mod_2pi (double th)
static spiro_seg *	setup_path (const spiro_cp *src, int n)
static void	bandec11 (bandmat *m, int *perm, int n)
static void	banbks11 (const bandmat *m, const int *perm, double *v, int n)
int	compute_jinc (char ty0, char ty1)
int	count_vec (const spiro_seg *s, int nseg)
static void	add_mat_line (bandmat *m, double *v, double derivs[4], double x, double y, int j, int jj, int jinc, int nmat)
static double	spiro_iter (spiro_seg *s, bandmat *m, int *perm, double *v, int n)
int	solve_spiro (spiro_seg *s, int nseg)
static void	spiro_seg_to_bpath (const double ks[4], double x0, double y0, double x1, double y1, bezctx *bc, int depth)
spiro_seg *	run_spiro (const spiro_cp *src, int n)
void	free_spiro (spiro_seg *s)
void	spiro_to_bpath (const spiro_seg *s, int n, bezctx *bc)
double	get_knot_th (const spiro_seg *s, int i)
Variables
int	n = 4

---

Define Documentation

#define ORDER   12

Definition at line 53 of file spiro.cpp.

---

Function Documentation

static void add_mat_line	(	bandmat *	m,
		double *	v,
		double	derivs[4],
		double	x,
		double	y,
		int	j,
		int	jj,
		int	jinc,
		int	nmat
	)			[static]

Definition at line 630 of file spiro.cpp.

References org::w3c::dom::svg::a.

Referenced by spiro_iter().

{
    int k;

    if (jj >= 0) {
    int joff =  (j + 5 - jj + nmat) % nmat;
    if (nmat < 6) {
        joff = j + 5 - jj;
    } else if (nmat == 6) {
        joff = 2 + (j + 3 - jj + nmat) % nmat;
    }
#ifdef VERBOSE
    printf("add_mat_line j=%d jj=%d jinc=%d nmat=%d joff=%d\n", j, jj, jinc, nmat, joff);
#endif
    v[jj] += x;
    for (k = 0; k < jinc; k++)
        m[jj].a[joff + k] += y * derivs[k];
    }
}

static void banbks11	(	const bandmat *	m,
		const int *	perm,
		double *	v,
		int	n
	)			[static]

Definition at line 576 of file spiro.cpp.

References bandmat::a, org::w3c::dom::svg::a, Barcode::Code39Ext::i, and voronoi::x.

Referenced by spiro_iter().

{
    int i, k, l;

    /* forward substitution */
    l = 5;
    for (k = 0; k < n; k++) {
    i = perm[k];
    if (i != k) {
        double tmp = v[k];
        v[k] = v[i];
        v[i] = tmp;
    }
    if (l < n) l++;
    for (i = k + 1; i < l; i++)
        v[i] -= m[k].al[i - k - 1] * v[k];
    }

    /* back substitution */
    l = 1;
    for (i = n - 1; i >= 0; i--) {
    double x = v[i];
    for (k = 1; k < l; k++)
        x -= m[i].a[k] * v[k + i];
    v[i] = x / m[i].a[0];
    if (l < 11) l++;
    }
}

static void bandec11	(	bandmat *	m,
		int *	perm,
		int	n
	)			[static]

Definition at line 528 of file spiro.cpp.

References bandmat::a, org::w3c::dom::svg::a, bandmat::al, addnodes::e, Barcode::Code39Ext::i, and voronoi::x.

Referenced by spiro_iter().

{
    int i, j, k;
    int l;

    /* pack top triangle to the left. */
    for (i = 0; i < 5; i++) {
    for (j = 0; j < i + 6; j++)
        m[i].a[j] = m[i].a[j + 5 - i];
    for (; j < 11; j++)
        m[i].a[j] = 0.;
    }
    l = 5;
    for (k = 0; k < n; k++) {
    int pivot = k;
    double pivot_val = m[k].a[0];
    double pivot_scale;

    l = l < n ? l + 1 : n;

    for (j = k + 1; j < l; j++)
        if (fabs(m[j].a[0]) > fabs(pivot_val)) {
        pivot_val = m[j].a[0];
        pivot = j;
        }

    perm[k] = pivot;
    if (pivot != k) {
        for (j = 0; j < 11; j++) {
        double tmp = m[k].a[j];
        m[k].a[j] = m[pivot].a[j];
        m[pivot].a[j] = tmp;
        }
    }

    if (fabs(pivot_val) < 1e-12) pivot_val = 1e-12;
    pivot_scale = 1. / pivot_val;
    for (i = k + 1; i < l; i++) {
        double x = m[i].a[0] * pivot_scale;
        m[k].al[i - k - 1] = x;
        for (j = 1; j < 11; j++)
        m[i].a[j - 1] = m[i].a[j] - x * m[k].a[j];
        m[i].a[10] = 0.;
    }
    }
}

static double compute_ends	(	const double	ks[4],
		double	ends[2][4],
		double	seg_ch
	)			[static]

Definition at line 422 of file spiro.cpp.

References Geom::atan2(), integrate_spiro(), and polyhedron_3d::th.

Referenced by compute_pderivs(), and get_knot_th().

{
    double xy[2];
    double ch, th;
    double l, l2, l3;
    double th_even, th_odd;
    double k0_even, k0_odd;
    double k1_even, k1_odd;
    double k2_even, k2_odd;

    integrate_spiro(ks, xy);
    ch = hypot(xy[0], xy[1]);
    th = atan2(xy[1], xy[0]);
    l = ch / seg_ch;

    th_even = .5 * ks[0] + (1./48) * ks[2];
    th_odd = .125 * ks[1] + (1./384) * ks[3] - th;
    ends[0][0] = th_even - th_odd;
    ends[1][0] = th_even + th_odd;
    k0_even = l * (ks[0] + .125 * ks[2]);
    k0_odd = l * (.5 * ks[1] + (1./48) * ks[3]);
    ends[0][1] = k0_even - k0_odd;
    ends[1][1] = k0_even + k0_odd;
    l2 = l * l;
    k1_even = l2 * (ks[1] + .125 * ks[3]);
    k1_odd = l2 * .5 * ks[2];
    ends[0][2] = k1_even - k1_odd;
    ends[1][2] = k1_even + k1_odd;
    l3 = l2 * l;
    k2_even = l3 * ks[2];
    k2_odd = l3 * .5 * ks[3];
    ends[0][3] = k2_even - k2_odd;
    ends[1][3] = k2_even + k2_odd;

    return l;
}

int compute_jinc	(	char	ty0,
		char	ty1
	)

Definition at line 605 of file spiro.cpp.

Referenced by count_vec(), and spiro_iter().

{
    if (ty0 == 'o' || ty1 == 'o' ||
    ty0 == ']' || ty1 == '[')
    return 4;
    else if (ty0 == 'c' && ty1 == 'c')
    return 2;
    else if (((ty0 == '{' || ty0 == 'v' || ty0 == '[') && ty1 == 'c') ||
         (ty0 == 'c' && (ty1 == '}' || ty1 == 'v' || ty1 == ']')))
    return 1;
    else
    return 0;
}

static void compute_pderivs	(	const spiro_seg *	s,
		double	ends[2][4],
		double	derivs[4][2][4],
		int	jinc
	)			[static]

Definition at line 460 of file spiro.cpp.

References compute_ends(), CxxTest::delta(), Barcode::Code39Ext::i, spiro_seg_s::ks, and spiro_seg_s::seg_ch.

Referenced by spiro_iter().

{
    double recip_d = 2e6;
    double delta = 1./ recip_d;
    double try_ks[4];
    double try_ends[2][4];
    int i, j, k;

    compute_ends(s->ks, ends, s->seg_ch);
    for (i = 0; i < jinc; i++) {
    for (j = 0; j < 4; j++)
        try_ks[j] = s->ks[j];
    try_ks[i] += delta;
    compute_ends(try_ks, try_ends, s->seg_ch);
    for (k = 0; k < 2; k++)
        for (j = 0; j < 4; j++)
        derivs[j][k][i] = recip_d * (try_ends[k][j] - ends[k][j]);
    }
}

int count_vec	(	const spiro_seg *	s,
		int	nseg
	)

Definition at line 619 of file spiro.cpp.

References compute_jinc(), Barcode::Code39Ext::i, and n.

Referenced by solve_spiro(), and spiro_iter().

{
    int i;
    int n = 0;

    for (i = 0; i < nseg; i++)
    n += compute_jinc(s[i].ty, s[i + 1].ty);
    return n;
}

void free_spiro

(

spiro_seg *

s

)

Definition at line 889 of file spiro.cpp.

{
    free(s);
}

double get_knot_th	(	const spiro_seg *	s,
		int	i
	)

Definition at line 914 of file spiro.cpp.

References compute_ends(), and spiro_seg_s::seg_th.

{
    double ends[2][4];

    if (i == 0) {
    compute_ends(s[i].ks, ends, s[i].seg_ch);
    return s[i].seg_th - ends[0][0];
    } else {
    compute_ends(s[i - 1].ks, ends, s[i - 1].seg_ch);
    return s[i - 1].seg_th + ends[1][0];
    }
}

void integrate_spiro	(	const double	ks[4],
		double	xy[2]
	)

Definition at line 58 of file spiro.cpp.

References Geom::cos(), addnodes::e, Barcode::Code39Ext::i, n, Geom::sin(), polyhedron_3d::th, voronoi::x, and voronoi::y.

Referenced by compute_ends(), and spiro_seg_to_bpath().

{
#if 0
    int n = 1024;
#endif
    double th1 = ks[0];
    double th2 = .5 * ks[1];
    double th3 = (1./6) * ks[2];
    double th4 = (1./24) * ks[3];
    double x, y;
    double ds = 1. / n;
    double ds2 = ds * ds;
    double ds3 = ds2 * ds;
    double k0 = ks[0] * ds;
    double k1 = ks[1] * ds;
    double k2 = ks[2] * ds;
    double k3 = ks[3] * ds;
    int i;
    double s = .5 * ds - .5;

    x = 0;
    y = 0;

    for (i = 0; i < n; i++) {

#if ORDER > 2
    double u, v;
    double km0, km1, km2, km3;

    if (n == 1) {
        km0 = k0;
        km1 = k1 * ds;
        km2 = k2 * ds2;
    } else {
        km0 = (((1./6) * k3 * s + .5 * k2) * s + k1) * s + k0;
        km1 = ((.5 * k3 * s + k2) * s + k1) * ds;
        km2 = (k3 * s + k2) * ds2;
    }
    km3 = k3 * ds3;
#endif

    {

#if ORDER == 4
    double km0_2 = km0 * km0;
    u = 24 - km0_2;
    v = km1;
#endif

#if ORDER == 6
    double km0_2 = km0 * km0;
    double km0_4 = km0_2 * km0_2;
    u = 24 - km0_2 + (km0_4 - 4 * km0 * km2 - 3 * km1 * km1) * (1./80);
    v = km1 + (km3 - 6 * km0_2 * km1) * (1./80);
#endif

#if ORDER == 8
    double t1_1 = km0;
    double t1_2 = .5 * km1;
    double t1_3 = (1./6) * km2;
    double t1_4 = (1./24) * km3;
    double t2_2 = t1_1 * t1_1;
    double t2_3 = 2 * (t1_1 * t1_2);
    double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
    double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
    double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
    double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
    double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
    double t4_4 = t2_2 * t2_2;
    double t4_5 = 2 * (t2_2 * t2_3);
    double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
    double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
    double t6_6 = t4_4 * t2_2;
    u = 1;
    v = 0;
    v += (1./12) * t1_2 + (1./80) * t1_4;
    u -= (1./24) * t2_2 + (1./160) * t2_4 + (1./896) * t2_6;
    v -= (1./480) * t3_4 + (1./2688) * t3_6;
    u += (1./1920) * t4_4 + (1./10752) * t4_6;
    v += (1./53760) * t5_6;
    u -= (1./322560) * t6_6;
#endif

#if ORDER == 10
    double t1_1 = km0;
    double t1_2 = .5 * km1;
    double t1_3 = (1./6) * km2;
    double t1_4 = (1./24) * km3;
    double t2_2 = t1_1 * t1_1;
    double t2_3 = 2 * (t1_1 * t1_2);
    double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
    double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
    double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
    double t2_7 = 2 * (t1_3 * t1_4);
    double t2_8 = t1_4 * t1_4;
    double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
    double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
    double t3_8 = t2_4 * t1_4 + t2_5 * t1_3 + t2_6 * t1_2 + t2_7 * t1_1;
    double t4_4 = t2_2 * t2_2;
    double t4_5 = 2 * (t2_2 * t2_3);
    double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
    double t4_7 = 2 * (t2_2 * t2_5 + t2_3 * t2_4);
    double t4_8 = 2 * (t2_2 * t2_6 + t2_3 * t2_5) + t2_4 * t2_4;
    double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
    double t5_8 = t4_4 * t1_4 + t4_5 * t1_3 + t4_6 * t1_2 + t4_7 * t1_1;
    double t6_6 = t4_4 * t2_2;
    double t6_7 = t4_4 * t2_3 + t4_5 * t2_2;
    double t6_8 = t4_4 * t2_4 + t4_5 * t2_3 + t4_6 * t2_2;
    double t7_8 = t6_6 * t1_2 + t6_7 * t1_1;
    double t8_8 = t6_6 * t2_2;
    u = 1;
    v = 0;
    v += (1./12) * t1_2 + (1./80) * t1_4;
    u -= (1./24) * t2_2 + (1./160) * t2_4 + (1./896) * t2_6 + (1./4608) * t2_8;
    v -= (1./480) * t3_4 + (1./2688) * t3_6 + (1./13824) * t3_8;
    u += (1./1920) * t4_4 + (1./10752) * t4_6 + (1./55296) * t4_8;
    v += (1./53760) * t5_6 + (1./276480) * t5_8;
    u -= (1./322560) * t6_6 + (1./1.65888e+06) * t6_8;
    v -= (1./1.16122e+07) * t7_8;
    u += (1./9.28973e+07) * t8_8;
#endif

#if ORDER == 12
    double t1_1 = km0;
    double t1_2 = .5 * km1;
    double t1_3 = (1./6) * km2;
    double t1_4 = (1./24) * km3;
    double t2_2 = t1_1 * t1_1;
    double t2_3 = 2 * (t1_1 * t1_2);
    double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
    double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
    double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
    double t2_7 = 2 * (t1_3 * t1_4);
    double t2_8 = t1_4 * t1_4;
    double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
    double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
    double t3_8 = t2_4 * t1_4 + t2_5 * t1_3 + t2_6 * t1_2 + t2_7 * t1_1;
    double t3_10 = t2_6 * t1_4 + t2_7 * t1_3 + t2_8 * t1_2;
    double t4_4 = t2_2 * t2_2;
    double t4_5 = 2 * (t2_2 * t2_3);
    double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
    double t4_7 = 2 * (t2_2 * t2_5 + t2_3 * t2_4);
    double t4_8 = 2 * (t2_2 * t2_6 + t2_3 * t2_5) + t2_4 * t2_4;
    double t4_9 = 2 * (t2_2 * t2_7 + t2_3 * t2_6 + t2_4 * t2_5);
    double t4_10 = 2 * (t2_2 * t2_8 + t2_3 * t2_7 + t2_4 * t2_6) + t2_5 * t2_5;
    double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
    double t5_8 = t4_4 * t1_4 + t4_5 * t1_3 + t4_6 * t1_2 + t4_7 * t1_1;
    double t5_10 = t4_6 * t1_4 + t4_7 * t1_3 + t4_8 * t1_2 + t4_9 * t1_1;
    double t6_6 = t4_4 * t2_2;
    double t6_7 = t4_4 * t2_3 + t4_5 * t2_2;
    double t6_8 = t4_4 * t2_4 + t4_5 * t2_3 + t4_6 * t2_2;
    double t6_9 = t4_4 * t2_5 + t4_5 * t2_4 + t4_6 * t2_3 + t4_7 * t2_2;
    double t6_10 = t4_4 * t2_6 + t4_5 * t2_5 + t4_6 * t2_4 + t4_7 * t2_3 + t4_8 * t2_2;
    double t7_8 = t6_6 * t1_2 + t6_7 * t1_1;
    double t7_10 = t6_6 * t1_4 + t6_7 * t1_3 + t6_8 * t1_2 + t6_9 * t1_1;
    double t8_8 = t6_6 * t2_2;
    double t8_9 = t6_6 * t2_3 + t6_7 * t2_2;
    double t8_10 = t6_6 * t2_4 + t6_7 * t2_3 + t6_8 * t2_2;
    double t9_10 = t8_8 * t1_2 + t8_9 * t1_1;
    double t10_10 = t8_8 * t2_2;
    u = 1;
    v = 0;
    v += (1./12) * t1_2 + (1./80) * t1_4;
    u -= (1./24) * t2_2 + (1./160) * t2_4 + (1./896) * t2_6 + (1./4608) * t2_8;
    v -= (1./480) * t3_4 + (1./2688) * t3_6 + (1./13824) * t3_8 + (1./67584) * t3_10;
    u += (1./1920) * t4_4 + (1./10752) * t4_6 + (1./55296) * t4_8 + (1./270336) * t4_10;
    v += (1./53760) * t5_6 + (1./276480) * t5_8 + (1./1.35168e+06) * t5_10;
    u -= (1./322560) * t6_6 + (1./1.65888e+06) * t6_8 + (1./8.11008e+06) * t6_10;
    v -= (1./1.16122e+07) * t7_8 + (1./5.67706e+07) * t7_10;
    u += (1./9.28973e+07) * t8_8 + (1./4.54164e+08) * t8_10;
    v += (1./4.08748e+09) * t9_10;
    u -= (1./4.08748e+10) * t10_10;
#endif

#if ORDER == 14
    double t1_1 = km0;
    double t1_2 = .5 * km1;
    double t1_3 = (1./6) * km2;
    double t1_4 = (1./24) * km3;
    double t2_2 = t1_1 * t1_1;
    double t2_3 = 2 * (t1_1 * t1_2);
    double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
    double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
    double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
    double t2_7 = 2 * (t1_3 * t1_4);
    double t2_8 = t1_4 * t1_4;
    double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
    double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
    double t3_8 = t2_4 * t1_4 + t2_5 * t1_3 + t2_6 * t1_2 + t2_7 * t1_1;
    double t3_10 = t2_6 * t1_4 + t2_7 * t1_3 + t2_8 * t1_2;
    double t3_12 = t2_8 * t1_4;
    double t4_4 = t2_2 * t2_2;
    double t4_5 = 2 * (t2_2 * t2_3);
    double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
    double t4_7 = 2 * (t2_2 * t2_5 + t2_3 * t2_4);
    double t4_8 = 2 * (t2_2 * t2_6 + t2_3 * t2_5) + t2_4 * t2_4;
    double t4_9 = 2 * (t2_2 * t2_7 + t2_3 * t2_6 + t2_4 * t2_5);
    double t4_10 = 2 * (t2_2 * t2_8 + t2_3 * t2_7 + t2_4 * t2_6) + t2_5 * t2_5;
    double t4_11 = 2 * (t2_3 * t2_8 + t2_4 * t2_7 + t2_5 * t2_6);
    double t4_12 = 2 * (t2_4 * t2_8 + t2_5 * t2_7) + t2_6 * t2_6;
    double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
    double t5_8 = t4_4 * t1_4 + t4_5 * t1_3 + t4_6 * t1_2 + t4_7 * t1_1;
    double t5_10 = t4_6 * t1_4 + t4_7 * t1_3 + t4_8 * t1_2 + t4_9 * t1_1;
    double t5_12 = t4_8 * t1_4 + t4_9 * t1_3 + t4_10 * t1_2 + t4_11 * t1_1;
    double t6_6 = t4_4 * t2_2;
    double t6_7 = t4_4 * t2_3 + t4_5 * t2_2;
    double t6_8 = t4_4 * t2_4 + t4_5 * t2_3 + t4_6 * t2_2;
    double t6_9 = t4_4 * t2_5 + t4_5 * t2_4 + t4_6 * t2_3 + t4_7 * t2_2;
    double t6_10 = t4_4 * t2_6 + t4_5 * t2_5 + t4_6 * t2_4 + t4_7 * t2_3 + t4_8 * t2_2;
    double t6_11 = t4_4 * t2_7 + t4_5 * t2_6 + t4_6 * t2_5 + t4_7 * t2_4 + t4_8 * t2_3 + t4_9 * t2_2;
    double t6_12 = t4_4 * t2_8 + t4_5 * t2_7 + t4_6 * t2_6 + t4_7 * t2_5 + t4_8 * t2_4 + t4_9 * t2_3 + t4_10 * t2_2;
    double t7_8 = t6_6 * t1_2 + t6_7 * t1_1;
    double t7_10 = t6_6 * t1_4 + t6_7 * t1_3 + t6_8 * t1_2 + t6_9 * t1_1;
    double t7_12 = t6_8 * t1_4 + t6_9 * t1_3 + t6_10 * t1_2 + t6_11 * t1_1;
    double t8_8 = t6_6 * t2_2;
    double t8_9 = t6_6 * t2_3 + t6_7 * t2_2;
    double t8_10 = t6_6 * t2_4 + t6_7 * t2_3 + t6_8 * t2_2;
    double t8_11 = t6_6 * t2_5 + t6_7 * t2_4 + t6_8 * t2_3 + t6_9 * t2_2;
    double t8_12 = t6_6 * t2_6 + t6_7 * t2_5 + t6_8 * t2_4 + t6_9 * t2_3 + t6_10 * t2_2;
    double t9_10 = t8_8 * t1_2 + t8_9 * t1_1;
    double t9_12 = t8_8 * t1_4 + t8_9 * t1_3 + t8_10 * t1_2 + t8_11 * t1_1;
    double t10_10 = t8_8 * t2_2;
    double t10_11 = t8_8 * t2_3 + t8_9 * t2_2;
    double t10_12 = t8_8 * t2_4 + t8_9 * t2_3 + t8_10 * t2_2;
    double t11_12 = t10_10 * t1_2 + t10_11 * t1_1;
    double t12_12 = t10_10 * t2_2;
    u = 1;
    v = 0;
    v += (1./12) * t1_2 + (1./80) * t1_4;
    u -= (1./24) * t2_2 + (1./160) * t2_4 + (1./896) * t2_6 + (1./4608) * t2_8;
    v -= (1./480) * t3_4 + (1./2688) * t3_6 + (1./13824) * t3_8 + (1./67584) * t3_10 + (1./319488) * t3_12;
    u += (1./1920) * t4_4 + (1./10752) * t4_6 + (1./55296) * t4_8 + (1./270336) * t4_10 + (1./1.27795e+06) * t4_12;
    v += (1./53760) * t5_6 + (1./276480) * t5_8 + (1./1.35168e+06) * t5_10 + (1./6.38976e+06) * t5_12;
    u -= (1./322560) * t6_6 + (1./1.65888e+06) * t6_8 + (1./8.11008e+06) * t6_10 + (1./3.83386e+07) * t6_12;
    v -= (1./1.16122e+07) * t7_8 + (1./5.67706e+07) * t7_10 + (1./2.6837e+08) * t7_12;
    u += (1./9.28973e+07) * t8_8 + (1./4.54164e+08) * t8_10 + (1./2.14696e+09) * t8_12;
    v += (1./4.08748e+09) * t9_10 + (1./1.93226e+10) * t9_12;
    u -= (1./4.08748e+10) * t10_10 + (1./1.93226e+11) * t10_12;
    v -= (1./2.12549e+12) * t11_12;
    u += (1./2.55059e+13) * t12_12;
#endif

#if ORDER == 16
    double t1_1 = km0;
    double t1_2 = .5 * km1;
    double t1_3 = (1./6) * km2;
    double t1_4 = (1./24) * km3;
    double t2_2 = t1_1 * t1_1;
    double t2_3 = 2 * (t1_1 * t1_2);
    double t2_4 = 2 * (t1_1 * t1_3) + t1_2 * t1_2;
    double t2_5 = 2 * (t1_1 * t1_4 + t1_2 * t1_3);
    double t2_6 = 2 * (t1_2 * t1_4) + t1_3 * t1_3;
    double t2_7 = 2 * (t1_3 * t1_4);
    double t2_8 = t1_4 * t1_4;
    double t3_4 = t2_2 * t1_2 + t2_3 * t1_1;
    double t3_6 = t2_2 * t1_4 + t2_3 * t1_3 + t2_4 * t1_2 + t2_5 * t1_1;
    double t3_8 = t2_4 * t1_4 + t2_5 * t1_3 + t2_6 * t1_2 + t2_7 * t1_1;
    double t3_10 = t2_6 * t1_4 + t2_7 * t1_3 + t2_8 * t1_2;
    double t3_12 = t2_8 * t1_4;
    double t4_4 = t2_2 * t2_2;
    double t4_5 = 2 * (t2_2 * t2_3);
    double t4_6 = 2 * (t2_2 * t2_4) + t2_3 * t2_3;
    double t4_7 = 2 * (t2_2 * t2_5 + t2_3 * t2_4);
    double t4_8 = 2 * (t2_2 * t2_6 + t2_3 * t2_5) + t2_4 * t2_4;
    double t4_9 = 2 * (t2_2 * t2_7 + t2_3 * t2_6 + t2_4 * t2_5);
    double t4_10 = 2 * (t2_2 * t2_8 + t2_3 * t2_7 + t2_4 * t2_6) + t2_5 * t2_5;
    double t4_11 = 2 * (t2_3 * t2_8 + t2_4 * t2_7 + t2_5 * t2_6);
    double t4_12 = 2 * (t2_4 * t2_8 + t2_5 * t2_7) + t2_6 * t2_6;
    double t4_13 = 2 * (t2_5 * t2_8 + t2_6 * t2_7);
    double t4_14 = 2 * (t2_6 * t2_8) + t2_7 * t2_7;
    double t5_6 = t4_4 * t1_2 + t4_5 * t1_1;
    double t5_8 = t4_4 * t1_4 + t4_5 * t1_3 + t4_6 * t1_2 + t4_7 * t1_1;
    double t5_10 = t4_6 * t1_4 + t4_7 * t1_3 + t4_8 * t1_2 + t4_9 * t1_1;
    double t5_12 = t4_8 * t1_4 + t4_9 * t1_3 + t4_10 * t1_2 + t4_11 * t1_1;
    double t5_14 = t4_10 * t1_4 + t4_11 * t1_3 + t4_12 * t1_2 + t4_13 * t1_1;
    double t6_6 = t4_4 * t2_2;
    double t6_7 = t4_4 * t2_3 + t4_5 * t2_2;
    double t6_8 = t4_4 * t2_4 + t4_5 * t2_3 + t4_6 * t2_2;
    double t6_9 = t4_4 * t2_5 + t4_5 * t2_4 + t4_6 * t2_3 + t4_7 * t2_2;
    double t6_10 = t4_4 * t2_6 + t4_5 * t2_5 + t4_6 * t2_4 + t4_7 * t2_3 + t4_8 * t2_2;
    double t6_11 = t4_4 * t2_7 + t4_5 * t2_6 + t4_6 * t2_5 + t4_7 * t2_4 + t4_8 * t2_3 + t4_9 * t2_2;
    double t6_12 = t4_4 * t2_8 + t4_5 * t2_7 + t4_6 * t2_6 + t4_7 * t2_5 + t4_8 * t2_4 + t4_9 * t2_3 + t4_10 * t2_2;
    double t6_13 = t4_5 * t2_8 + t4_6 * t2_7 + t4_7 * t2_6 + t4_8 * t2_5 + t4_9 * t2_4 + t4_10 * t2_3 + t4_11 * t2_2;
    double t6_14 = t4_6 * t2_8 + t4_7 * t2_7 + t4_8 * t2_6 + t4_9 * t2_5 + t4_10 * t2_4 + t4_11 * t2_3 + t4_12 * t2_2;
    double t7_8 = t6_6 * t1_2 + t6_7 * t1_1;
    double t7_10 = t6_6 * t1_4 + t6_7 * t1_3 + t6_8 * t1_2 + t6_9 * t1_1;
    double t7_12 = t6_8 * t1_4 + t6_9 * t1_3 + t6_10 * t1_2 + t6_11 * t1_1;
    double t7_14 = t6_10 * t1_4 + t6_11 * t1_3 + t6_12 * t1_2 + t6_13 * t1_1;
    double t8_8 = t6_6 * t2_2;
    double t8_9 = t6_6 * t2_3 + t6_7 * t2_2;
    double t8_10 = t6_6 * t2_4 + t6_7 * t2_3 + t6_8 * t2_2;
    double t8_11 = t6_6 * t2_5 + t6_7 * t2_4 + t6_8 * t2_3 + t6_9 * t2_2;
    double t8_12 = t6_6 * t2_6 + t6_7 * t2_5 + t6_8 * t2_4 + t6_9 * t2_3 + t6_10 * t2_2;
    double t8_13 = t6_6 * t2_7 + t6_7 * t2_6 + t6_8 * t2_5 + t6_9 * t2_4 + t6_10 * t2_3 + t6_11 * t2_2;
    double t8_14 = t6_6 * t2_8 + t6_7 * t2_7 + t6_8 * t2_6 + t6_9 * t2_5 + t6_10 * t2_4 + t6_11 * t2_3 + t6_12 * t2_2;
    double t9_10 = t8_8 * t1_2 + t8_9 * t1_1;
    double t9_12 = t8_8 * t1_4 + t8_9 * t1_3 + t8_10 * t1_2 + t8_11 * t1_1;
    double t9_14 = t8_10 * t1_4 + t8_11 * t1_3 + t8_12 * t1_2 + t8_13 * t1_1;
    double t10_10 = t8_8 * t2_2;
    double t10_11 = t8_8 * t2_3 + t8_9 * t2_2;
    double t10_12 = t8_8 * t2_4 + t8_9 * t2_3 + t8_10 * t2_2;
    double t10_13 = t8_8 * t2_5 + t8_9 * t2_4 + t8_10 * t2_3 + t8_11 * t2_2;
    double t10_14 = t8_8 * t2_6 + t8_9 * t2_5 + t8_10 * t2_4 + t8_11 * t2_3 + t8_12 * t2_2;
    double t11_12 = t10_10 * t1_2 + t10_11 * t1_1;
    double t11_14 = t10_10 * t1_4 + t10_11 * t1_3 + t10_12 * t1_2 + t10_13 * t1_1;
    double t12_12 = t10_10 * t2_2;
    double t12_13 = t10_10 * t2_3 + t10_11 * t2_2;
    double t12_14 = t10_10 * t2_4 + t10_11 * t2_3 + t10_12 * t2_2;
    double t13_14 = t12_12 * t1_2 + t12_13 * t1_1;
    double t14_14 = t12_12 * t2_2;
    u = 1;
    u -= 1./24 * t2_2 + 1./160 * t2_4 + 1./896 * t2_6 + 1./4608 * t2_8;
    u += 1./1920 * t4_4 + 1./10752 * t4_6 + 1./55296 * t4_8 + 1./270336 * t4_10 + 1./1277952 * t4_12 + 1./5898240 * t4_14;
    u -= 1./322560 * t6_6 + 1./1658880 * t6_8 + 1./8110080 * t6_10 + 1./38338560 * t6_12 + 1./176947200 * t6_14;
    u += 1./92897280 * t8_8 + 1./454164480 * t8_10 + 4.6577500191e-10 * t8_12 + 1.0091791708e-10 * t8_14;
    u -= 2.4464949595e-11 * t10_10 + 5.1752777990e-12 * t10_12 + 1.1213101898e-12 * t10_14;
    u += 3.9206649992e-14 * t12_12 + 8.4947741650e-15 * t12_14;
    u -= 4.6674583324e-17 * t14_14;
    v = 0;
    v += 1./12 * t1_2 + 1./80 * t1_4;
    v -= 1./480 * t3_4 + 1./2688 * t3_6 + 1./13824 * t3_8 + 1./67584 * t3_10 + 1./319488 * t3_12;
    v += 1./53760 * t5_6 + 1./276480 * t5_8 + 1./1351680 * t5_10 + 1./6389760 * t5_12 + 1./29491200 * t5_14;
    v -= 1./11612160 * t7_8 + 1./56770560 * t7_10 + 1./268369920 * t7_12 + 8.0734333664e-10 * t7_14;
    v += 2.4464949595e-10 * t9_10 + 5.1752777990e-11 * t9_12 + 1.1213101898e-11 * t9_14;
    v -= 4.7047979991e-13 * t11_12 + 1.0193728998e-13 * t11_14;
    v += 6.5344416654e-16 * t13_14;
#endif

    }

    if (n == 1) {
#if ORDER == 2
        x = 1;
        y = 0;
#else
        x = u;
        y = v;
#endif
    } else {
        double th = (((th4 * s + th3) * s + th2) * s + th1) * s;
        double cth = cos(th);
        double sth = sin(th);

#if ORDER == 2
        x += cth;
        y += sth;
#else
        x += cth * u - sth * v;
        y += cth * v + sth * u;
#endif
        s += ds;
    }
    }

#if ORDER == 4 || ORDER == 6
    xy[0] = x * (1./24 * ds);
    xy[1] = y * (1./24 * ds);
#else
    xy[0] = x * ds;
    xy[1] = y * ds;
#endif
}

static double mod_2pi

(

double

th

)

[static]

Definition at line 482 of file spiro.cpp.

References M_PI.

Referenced by setup_path(), and spiro_iter().

{
    double u = th / (2 * M_PI);
    return 2 * M_PI * (u - floor(u + 0.5));
}

spiro_seg* run_spiro	(	const spiro_cp *	src,
		int	n
	)

Definition at line 879 of file spiro.cpp.

References setup_path(), solve_spiro(), and spiro_cp::ty.

Referenced by Inkscape::LivePathEffect::LPESpiro::doEffect().

{
    int nseg = src[0].ty == '{' ? n - 1 : n;
    spiro_seg *s = setup_path(src, n);
    if (nseg > 1)
    solve_spiro(s, nseg);
    return s;
}

static spiro_seg* setup_path	(	const spiro_cp *	src,
		int	n
	)			[static]

Definition at line 489 of file spiro.cpp.

References Geom::atan2(), spiro_seg_s::bend_th, Barcode::Code39Ext::i, spiro_seg_s::ks, mod_2pi(), polyhedron_3d::r, spiro_seg_s::seg_ch, spiro_seg_s::seg_th, spiro_seg_s::ty, spiro_cp::ty, spiro_cp::x, spiro_seg_s::x, spiro_cp::y, and spiro_seg_s::y.

Referenced by run_spiro().

{
    int n_seg = src[0].ty == '{' ? n - 1 : n;
    spiro_seg *r = (spiro_seg *)malloc((n_seg + 1) * sizeof(spiro_seg));
    int i;
    int ilast;

    for (i = 0; i < n_seg; i++) {
    r[i].x = src[i].x;
    r[i].y = src[i].y;
    r[i].ty = src[i].ty;
    r[i].ks[0] = 0.;
    r[i].ks[1] = 0.;
    r[i].ks[2] = 0.;
    r[i].ks[3] = 0.;
    }
    r[n_seg].x = src[n_seg % n].x;
    r[n_seg].y = src[n_seg % n].y;
    r[n_seg].ty = src[n_seg % n].ty;

    for (i = 0; i < n_seg; i++) {
    double dx = r[i + 1].x - r[i].x;
    double dy = r[i + 1].y - r[i].y;
    r[i].seg_ch = hypot(dx, dy);
    r[i].seg_th = atan2(dy, dx);
    }

    ilast = n_seg - 1;
    for (i = 0; i < n_seg; i++) {
    if (r[i].ty == '{' || r[i].ty == '}' || r[i].ty == 'v')
        r[i].bend_th = 0.;
    else
        r[i].bend_th = mod_2pi(r[i].seg_th - r[ilast].seg_th);
    ilast = i;
    }
    return r;
}

int solve_spiro	(	spiro_seg *	s,
		int	nseg
	)

Definition at line 784 of file spiro.cpp.

References count_vec(), addnodes::e, Barcode::Code39Ext::i, cubicsuperpath::norm(), and spiro_iter().

Referenced by run_spiro().

{
    bandmat *m;
    double *v;
    int *perm;
    int nmat = count_vec(s, nseg);
    int n_alloc = nmat;
    double norm;
    int i;

    if (nmat == 0)
    return 0;
    if (s[0].ty != '{' && s[0].ty != 'v')
    n_alloc *= 3;
    if (n_alloc < 5)
    n_alloc = 5;
    m = (bandmat *)malloc(sizeof(bandmat) * n_alloc);
    v = (double *)malloc(sizeof(double) * n_alloc);
    perm = (int *)malloc(sizeof(int) * n_alloc);

    for (i = 0; i < 10; i++) {
    norm = spiro_iter(s, m, perm, v, nseg);
#ifdef VERBOSE
    printf("%% norm = %g\n", norm);
#endif
    if (norm < 1e-12) break;
    }

    free(m);
    free(v);
    free(perm);
    return 0;
}

static double spiro_iter	(	spiro_seg *	s,
		bandmat *	m,
		int *	perm,
		double *	v,
		int	n
	)			[static]

Definition at line 653 of file spiro.cpp.

References org::w3c::dom::svg::a, add_mat_line(), banbks11(), bandec11(), spiro_seg_s::bend_th, compute_jinc(), compute_pderivs(), count_vec(), cyclic(), Barcode::Code39Ext::i, spiro_seg_s::ks, mod_2pi(), cubicsuperpath::norm(), polyhedron_3d::th, and spiro_seg_s::ty.

Referenced by solve_spiro().

{
    int cyclic = s[0].ty != '{' && s[0].ty != 'v';
    int i, j, jj;
    int nmat = count_vec(s, n);
    double norm;
    int n_invert;

    for (i = 0; i < nmat; i++) {
    v[i] = 0.;
    for (j = 0; j < 11; j++)
        m[i].a[j] = 0.;
    for (j = 0; j < 5; j++)
        m[i].al[j] = 0.;
    }

    j = 0;
    if (s[0].ty == 'o')
    jj = nmat - 2;
    else if (s[0].ty == 'c')
    jj = nmat - 1;
    else
    jj = 0;
    for (i = 0; i < n; i++) {
    char ty0 = s[i].ty;
    char ty1 = s[i + 1].ty;
    int jinc = compute_jinc(ty0, ty1);
    double th = s[i].bend_th;
    double ends[2][4];
    double derivs[4][2][4];
    int jthl = -1, jk0l = -1, jk1l = -1, jk2l = -1;
    int jthr = -1, jk0r = -1, jk1r = -1, jk2r = -1;

    compute_pderivs(&s[i], ends, derivs, jinc);

    /* constraints crossing left */
    if (ty0 == 'o' || ty0 == 'c' || ty0 == '[' || ty0 == ']') {
        jthl = jj++;
        jj %= nmat;
        jk0l = jj++;
    }
    if (ty0 == 'o') {
        jj %= nmat;
        jk1l = jj++;
        jk2l = jj++;
    }

    /* constraints on left */
    if ((ty0 == '[' || ty0 == 'v' || ty0 == '{' || ty0 == 'c') &&
        jinc == 4) {
        if (ty0 != 'c')
        jk1l = jj++;
        jk2l = jj++;
    }

    /* constraints on right */
    if ((ty1 == ']' || ty1 == 'v' || ty1 == '}' || ty1 == 'c') &&
        jinc == 4) {
        if (ty1 != 'c')
        jk1r = jj++;
        jk2r = jj++;
    }

    /* constraints crossing right */
    if (ty1 == 'o' || ty1 == 'c' || ty1 == '[' || ty1 == ']') {
        jthr = jj;
        jk0r = (jj + 1) % nmat;
    }
    if (ty1 == 'o') {
        jk1r = (jj + 2) % nmat;
        jk2r = (jj + 3) % nmat;
    }

    add_mat_line(m, v, derivs[0][0], th - ends[0][0], 1, j, jthl, jinc, nmat);
    add_mat_line(m, v, derivs[1][0], ends[0][1], -1, j, jk0l, jinc, nmat);
    add_mat_line(m, v, derivs[2][0], ends[0][2], -1, j, jk1l, jinc, nmat);
    add_mat_line(m, v, derivs[3][0], ends[0][3], -1, j, jk2l, jinc, nmat);
    add_mat_line(m, v, derivs[0][1], -ends[1][0], 1, j, jthr, jinc, nmat);
    add_mat_line(m, v, derivs[1][1], -ends[1][1], 1, j, jk0r, jinc, nmat);
    add_mat_line(m, v, derivs[2][1], -ends[1][2], 1, j, jk1r, jinc, nmat);
    add_mat_line(m, v, derivs[3][1], -ends[1][3], 1, j, jk2r, jinc, nmat);
    if (jthl >= 0)
        v[jthl] = mod_2pi(v[jthl]);
    if (jthr >= 0)
        v[jthr] = mod_2pi(v[jthr]);
    j += jinc;
    }
    if (cyclic) {
    memcpy(m + nmat, m, sizeof(bandmat) * nmat);
    memcpy(m + 2 * nmat, m, sizeof(bandmat) * nmat);
    memcpy(v + nmat, v, sizeof(double) * nmat);
    memcpy(v + 2 * nmat, v, sizeof(double) * nmat);
    n_invert = 3 * nmat;
    j = nmat;
    } else {
    n_invert = nmat;
    j = 0;
    }
#ifdef VERBOSE
    for (i = 0; i < n; i++) {
    int k;
    for (k = 0; k < 11; k++)
        printf(" %2.4f", m[i].a[k]);
    printf(": %2.4f\n", v[i]);
    }
    printf("---\n");
#endif
    bandec11(m, perm, n_invert);
    banbks11(m, perm, v, n_invert);
    norm = 0.;
    for (i = 0; i < n; i++) {
    char ty0 = s[i].ty;
    char ty1 = s[i + 1].ty;
    int jinc = compute_jinc(ty0, ty1);
    int k;

    for (k = 0; k < jinc; k++) {
        double dk = v[j++];

#ifdef VERBOSE
        printf("s[%d].ks[%d] += %f\n", i, k, dk);
#endif
        s[i].ks[k] += dk;
        norm += dk * dk;
    }
        s[i].ks[0] = 2.0*mod_2pi(s[i].ks[0]/2.0);
    }
    return norm;
}

static void spiro_seg_to_bpath	(	const double	ks[4],
		double	x0,
		double	y0,
		double	x1,
		double	y1,
		bezctx *	bc,
		int	depth
	)			[static]

Definition at line 819 of file spiro.cpp.

References Geom::atan2(), Inkscape::LivePathEffect::bend(), bezctx_curveto(), bezctx_lineto(), Geom::cos(), addnodes::e, integrate_spiro(), dxf_input::scale, Geom::sin(), and polyhedron_3d::th.

Referenced by spiro_to_bpath().

{
    double bend = fabs(ks[0]) + fabs(.5 * ks[1]) + fabs(.125 * ks[2]) +
    fabs((1./48) * ks[3]);

    if (!bend > 1e-8) {
    bezctx_lineto(bc, x1, y1);
    } else {
    double seg_ch = hypot(x1 - x0, y1 - y0);
    double seg_th = atan2(y1 - y0, x1 - x0);
    double xy[2];
    double ch, th;
    double scale, rot;
    double th_even, th_odd;
    double ul, vl;
    double ur, vr;

    integrate_spiro(ks, xy);
    ch = hypot(xy[0], xy[1]);
    th = atan2(xy[1], xy[0]);
    scale = seg_ch / ch;
    rot = seg_th - th;
    if (depth > 5 || bend < 1.) {
        th_even = (1./384) * ks[3] + (1./8) * ks[1] + rot;
        th_odd = (1./48) * ks[2] + .5 * ks[0];
        ul = (scale * (1./3)) * cos(th_even - th_odd);
        vl = (scale * (1./3)) * sin(th_even - th_odd);
        ur = (scale * (1./3)) * cos(th_even + th_odd);
        vr = (scale * (1./3)) * sin(th_even + th_odd);
        bezctx_curveto(bc, x0 + ul, y0 + vl, x1 - ur, y1 - vr, x1, y1);
    } else {
        /* subdivide */
        double ksub[4];
        double thsub;
        double xysub[2];
        double xmid, ymid;
        double cth, sth;

        ksub[0] = .5 * ks[0] - .125 * ks[1] + (1./64) * ks[2] - (1./768) * ks[3];
        ksub[1] = .25 * ks[1] - (1./16) * ks[2] + (1./128) * ks[3];
        ksub[2] = .125 * ks[2] - (1./32) * ks[3];
        ksub[3] = (1./16) * ks[3];
        thsub = rot - .25 * ks[0] + (1./32) * ks[1] - (1./384) * ks[2] + (1./6144) * ks[3];
        cth = .5 * scale * cos(thsub);
        sth = .5 * scale * sin(thsub);
        integrate_spiro(ksub, xysub);
        xmid = x0 + cth * xysub[0] - sth * xysub[1];
        ymid = y0 + cth * xysub[1] + sth * xysub[0];
        spiro_seg_to_bpath(ksub, x0, y0, xmid, ymid, bc, depth + 1);
        ksub[0] += .25 * ks[1] + (1./384) * ks[3];
        ksub[1] += .125 * ks[2];
        ksub[2] += (1./16) * ks[3];
        spiro_seg_to_bpath(ksub, xmid, ymid, x1, y1, bc, depth + 1);
    }
    }
}

void spiro_to_bpath	(	const spiro_seg *	s,
		int	n,
		bezctx *	bc
	)

Definition at line 895 of file spiro.cpp.

References bezctx_mark_knot(), bezctx_moveto(), Barcode::Code39Ext::i, spiro_seg_to_bpath(), spiro_seg_s::ty, spiro_seg_s::x, and spiro_seg_s::y.

Referenced by Inkscape::LivePathEffect::LPESpiro::doEffect().

{
    int i;
    int nsegs = s[n - 1].ty == '}' ? n - 1 : n;

    for (i = 0; i < nsegs; i++) {
    double x0 = s[i].x;
    double y0 = s[i].y;
    double x1 = s[i + 1].x;
    double y1 = s[i + 1].y;

    if (i == 0)
        bezctx_moveto(bc, x0, y0, s[0].ty == '{');
    bezctx_mark_knot(bc, i);
    spiro_seg_to_bpath(s[i].ks, x0, y0, x1, y1, bc, 0);
    }
}

---

Variable Documentation

int n = 4

Definition at line 50 of file spiro.cpp.

Referenced by Inkscape::UI::Node::_linearGrow(), Inkscape::UI::Dialogs::_loadPaletteFile(), Inkscape::UI::Node::_next(), SweepTreeList::add(), SweepEventQueue::add(), IntLigne::AddBord(), FloatLigne::AddBord(), FloatLigne::AddBordR(), Shape::AddEdge(), Path::AddForcedPoint(), Shape::AddPoint(), Path::AddPoint(), IntLigne::AddRun(), FloatLigne::AddRun(), adjust_vertices(), Geom::detail::bezier_clipping::angle(), FloatLigne::AppendBord(), bestpolygon(), Inkscape::UI::PathManipulator::breakNodes(), calc_lon(), calc_sums(), Inkscape::Extension::Internal::SingularValueDecomposition::calculate(), Geom::ConvexHull::centroid_and_area(), char_index_of_iterator(), Shape::CheckAdjacencies(), Geom::detail::bezier_clipping::clip_interval(), clonetiler_change_selection(), clonetiler_number_of_clones(), Inkscape::IO::GzipOutputStream::close(), UStringPrivate::Composition::Composition(), StringPrivate::Composition::Composition(), cola::connectedComponents(), cola::ConstrainedMajorizationLayout::ConstrainedMajorizationLayout(), Path::ConvertWithBackData(), Geom::detail::bezier_clipping::convex_hull(), count_vec(), Inkscape::Whiteboard::SessionManager::createSessionId(), Inkscape::LivePathEffect::LPEKnotNS::CrossingPoints::CrossingPoints(), Geom::MonoCrosser::crossings(), Geom::Crosser< Path >::crossings(), Path::DashSubPath(), Geom::detail::bezier_clipping::derivative(), Geom::detail::bezier_clipping::distance_control_points(), Inkscape::LivePathEffect::LPETextLabel::doEffect_pwd2(), Inkscape::LivePathEffect::LPERuler::doEffect_pwd2(), Inkscape::LivePathEffect::LPERecursiveSkeleton::doEffect_pwd2(), Inkscape::LivePathEffect::LPEPatternAlongPath::doEffect_pwd2(), Inkscape::LivePathEffect::LPEOffset::doEffect_pwd2(), Inkscape::LivePathEffect::LPEDynastroke::doEffect_pwd2(), Path::DoJoin(), doXmlTest(), Inkscape::UI::Node::dragged(), dxf_get_sections(), filter_onefield(), Inkscape::UI::Dialog::Find::filter_types(), filter_types(), Geom::Bernsteins::find_bernstein_roots(), Inkscape::ObjectSnapper::freeSnap(), Inkscape::LivePathEffect::LPERoughHatches::generateLevels(), Geom::detail::bezier_clipping::get_precision(), Inkscape::XML::get_prev(), org::w3c::dom::NodeImpl::getTextContent(), gm_readbody_bmp(), graphlayout(), Geom::Bernsteins::horner(), Inkscape::LivePathEffect::LPEKnotNS::CrossingPoints::inherit_signs(), inkscape_crash_handler(), org::w3c::dom::NodeImpl::insertBefore(), integrate_spiro(), Geom::intersect_polish_root(), Geom::detail::bezier_clipping::left_portion(), Inkscape::LivePathEffect::LPERoughHatches::linearSnake(), Geom::detail::bezier_clipping::make_focus(), makeCrcTable(), SweepEvent::MakeDelete(), matrix_times_vector(), Geom::ConvexHull::narrowest_diameter(), Geom::detail::ellipse_equation::normal(), Inkscape::Preferences::PrefNodeObserver::notifyAttributeChanged(), octreePrune(), Inkscape::UI::Dialog::Find::onFind(), Geom::OldBezier::operator()(), font_style_hash::operator()(), operator<<(), Pedro::Parser::parse(), buildtool::Parser::parse(), org::w3c::dom::svg::SVGReader::parseElement(), Pedro::Parser::parseElement(), buildtool::Parser::parseElement(), Pedro::Parser::parseFile(), buildtool::Parser::parseFile(), penalty3(), pointslope(), Shape::PushIncidence(), Shape::ReFormeBezierTo(), SweepEventQueue::remove(), org::w3c::dom::NodeImpl::removeChild(), org::w3c::dom::NodeImpl::replaceChild(), Path::ReplacePoint(), Geom::detail::bezier_clipping::right_portion(), sel_matches_node_real(), cola::separateComponents(), Inkscape::UI::Dialog::DualSpinButton::set_from_attribute(), set_pos_and_anchor(), Inkscape::LivePathEffect::TextParam::setPosAndAnchor(), Inkscape::UI::PathManipulator::shiftSelection(), Shape::SortEdges(), sp_dyna_draw_apply(), sp_eraser_apply(), sp_export_export_clicked(), sp_find_dialog_find(), sp_font_selector_init(), sp_guide_create(), sp_key_name(), sp_png_write_rgba_striped(), sp_selection_apply_affine(), sp_shape_number_of_markers(), sp_text_description(), Inkscape::UI::PathManipulator::subdivideSegment(), SVGColorTest::testReadColor(), SvgAffineTest::testReadIdentity(), Inkscape::LivePathEffect::LPEKnotNS::CrossingPoints::to_vector(), buildtool::trex_charclass(), buildtool::trex_matchnode(), buildtool::trex_newnode(), unclump_average(), Geom::Curve::unitTangentAt(), Geom::Piecewise< Geom::D2< Geom::SBasis > >::valueAndDerivatives(), Geom::Piecewise< Geom::D2< Geom::SBasis > >::valueAt(), Geom::Bezier::valueAt(), and CycleDetector::visit().