nr-path.cpp revision 815e3fc44098466b138092ef35137c5f71de14f9
#define __NR_PATH_C__
/*
* Pixel buffer rendering library
*
* Authors:
* Lauris Kaplinski <lauris@kaplinski.com>
*
* This code is in public domain
*/
#include <glib/gmem.h>
#include "n-art-bpath.h"
#include "nr-rect.h"
#include "nr-path.h"
static void nr_curve_bbox (NR::Coord x000, NR::Coord y000, NR::Coord x001, NR::Coord y001, NR::Coord x011, NR::Coord y011, NR::Coord x111, NR::Coord y111, NRRect *bbox);
static void nr_curve_bbox(NR::Point const p000, NR::Point const p001,
NR::Point const p011, NR::Point const p111,
NRRect *bbox);
NRBPath *nr_path_duplicate_transform(NRBPath *d, NRBPath *s, NRMatrix const *transform)
{
int i;
if (!s->path) {
d->path = NULL;
return d;
}
i = 0;
while (s->path[i].code != NR_END) i += 1;
d->path = g_new (NArtBpath, i + 1);
i = 0;
while (s->path[i].code != NR_END) {
d->path[i].code = s->path[i].code;
if (s->path[i].code == NR_CURVETO) {
d->path[i].x1 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x1, s->path[i].y1);
d->path[i].y1 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x1, s->path[i].y1);
d->path[i].x2 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x2, s->path[i].y2);
d->path[i].y2 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x2, s->path[i].y2);
}
d->path[i].x3 = NR_MATRIX_DF_TRANSFORM_X (transform, s->path[i].x3, s->path[i].y3);
d->path[i].y3 = NR_MATRIX_DF_TRANSFORM_Y (transform, s->path[i].x3, s->path[i].y3);
i += 1;
}
d->path[i].code = NR_END;
return d;
}
NRBPath *nr_path_duplicate_transform(NRBPath *d, NRBPath *s, NR::Matrix const transform) {
NRMatrix tr = transform;
return nr_path_duplicate_transform(d, s, &tr);
}
NArtBpath* nr_artpath_affine(NArtBpath *s, NR::Matrix const &aff) {
NRBPath bp, abp;
bp.path = s;
nr_path_duplicate_transform(&abp, &bp, aff);
return abp.path;
}
static void
nr_line_wind_distance (NR::Coord x0, NR::Coord y0, NR::Coord x1, NR::Coord y1, NR::Point &pt, int *wind, NR::Coord *best)
{
NR::Coord Ax, Ay, Bx, By, Dx, Dy, s;
NR::Coord dist2;
/* Find distance */
Ax = x0;
Ay = y0;
Bx = x1;
By = y1;
Dx = x1 - x0;
Dy = y1 - y0;
const NR::Coord Px = pt[NR::X];
const NR::Coord Py = pt[NR::Y];
if (best) {
s = ((Px - Ax) * Dx + (Py - Ay) * Dy) / (Dx * Dx + Dy * Dy);
if (s <= 0.0) {
dist2 = (Px - Ax) * (Px - Ax) + (Py - Ay) * (Py - Ay);
} else if (s >= 1.0) {
dist2 = (Px - Bx) * (Px - Bx) + (Py - By) * (Py - By);
} else {
NR::Coord Qx, Qy;
Qx = Ax + s * Dx;
Qy = Ay + s * Dy;
dist2 = (Px - Qx) * (Px - Qx) + (Py - Qy) * (Py - Qy);
}
if (dist2 < (*best * *best)) *best = sqrt (dist2);
}
if (wind) {
/* Find wind */
if ((Ax >= Px) && (Bx >= Px)) return;
if ((Ay >= Py) && (By >= Py)) return;
if ((Ay < Py) && (By < Py)) return;
if (Ay == By) return;
/* Ctach upper y bound */
if (Ay == Py) {
if (Ax < Px) *wind -= 1;
return;
} else if (By == Py) {
if (Bx < Px) *wind += 1;
return;
} else {
NR::Coord Qx;
/* Have to calculate intersection */
Qx = Ax + Dx * (Py - Ay) / Dy;
if (Qx < Px) {
*wind += (Dy > 0.0) ? 1 : -1;
}
}
}
}
static void
nr_curve_bbox_wind_distance (NR::Coord x000, NR::Coord y000,
NR::Coord x001, NR::Coord y001,
NR::Coord x011, NR::Coord y011,
NR::Coord x111, NR::Coord y111,
NR::Point &pt,
NRRect *bbox, int *wind, NR::Coord *best,
NR::Coord tolerance)
{
NR::Coord x0, y0, x1, y1, len2;
int needdist, needwind, needline;
const NR::Coord Px = pt[NR::X];
const NR::Coord Py = pt[NR::Y];
needdist = 0;
needwind = 0;
needline = 0;
if (bbox) nr_curve_bbox (x000, y000, x001, y001, x011, y011, x111, y111, bbox);
x0 = MIN (x000, x001);
x0 = MIN (x0, x011);
x0 = MIN (x0, x111);
y0 = MIN (y000, y001);
y0 = MIN (y0, y011);
y0 = MIN (y0, y111);
x1 = MAX (x000, x001);
x1 = MAX (x1, x011);
x1 = MAX (x1, x111);
y1 = MAX (y000, y001);
y1 = MAX (y1, y011);
y1 = MAX (y1, y111);
if (best) {
/* Quicly adjust to endpoints */
len2 = (x000 - Px) * (x000 - Px) + (y000 - Py) * (y000 - Py);
if (len2 < (*best * *best)) *best = (NR::Coord) sqrt (len2);
len2 = (x111 - Px) * (x111 - Px) + (y111 - Py) * (y111 - Py);
if (len2 < (*best * *best)) *best = (NR::Coord) sqrt (len2);
if (((x0 - Px) < *best) && ((y0 - Py) < *best) && ((Px - x1) < *best) && ((Py - y1) < *best)) {
/* Point is inside sloppy bbox */
/* Now we have to decide, whether subdivide */
/* fixme: (Lauris) */
if (((y1 - y0) > 5.0) || ((x1 - x0) > 5.0)) {
needdist = 1;
} else {
needline = 1;
}
}
}
if (!needdist && wind) {
if ((y1 >= Py) && (y0 < Py) && (x0 < Px)) {
/* Possible intersection at the left */
/* Now we have to decide, whether subdivide */
/* fixme: (Lauris) */
if (((y1 - y0) > 5.0) || ((x1 - x0) > 5.0)) {
needwind = 1;
} else {
needline = 1;
}
}
}
if (needdist || needwind) {
NR::Coord x00t, x0tt, xttt, x1tt, x11t, x01t;
NR::Coord y00t, y0tt, yttt, y1tt, y11t, y01t;
NR::Coord s, t;
t = 0.5;
s = 1 - t;
x00t = s * x000 + t * x001;
x01t = s * x001 + t * x011;
x11t = s * x011 + t * x111;
x0tt = s * x00t + t * x01t;
x1tt = s * x01t + t * x11t;
xttt = s * x0tt + t * x1tt;
y00t = s * y000 + t * y001;
y01t = s * y001 + t * y011;
y11t = s * y011 + t * y111;
y0tt = s * y00t + t * y01t;
y1tt = s * y01t + t * y11t;
yttt = s * y0tt + t * y1tt;
nr_curve_bbox_wind_distance (x000, y000, x00t, y00t, x0tt, y0tt, xttt, yttt, pt, NULL, wind, best, tolerance);
nr_curve_bbox_wind_distance (xttt, yttt, x1tt, y1tt, x11t, y11t, x111, y111, pt, NULL, wind, best, tolerance);
} else if (1 || needline) {
nr_line_wind_distance (x000, y000, x111, y111, pt, wind, best);
}
}
void
nr_path_matrix_point_bbox_wind_distance (NRBPath *bpath, NR::Matrix const &m, NR::Point &pt,
NRRect *bbox, int *wind, NR::Coord *dist,
NR::Coord tolerance)
{
NR::Coord x0, y0, x3, y3;
const NArtBpath *p;
if (!bpath->path) {
if (wind) *wind = 0;
if (dist) *dist = NR_HUGE;
return;
}
x0 = y0 = 0.0;
x3 = y3 = 0.0;
for (p = bpath->path; p->code != NR_END; p+= 1) {
switch (p->code) {
case NR_MOVETO_OPEN:
case NR_MOVETO:
x0 = m[0] * p->x3 + m[2] * p->y3 + m[4];
y0 = m[1] * p->x3 + m[3] * p->y3 + m[5];
if (bbox) {
bbox->x0 = (NR::Coord) MIN (bbox->x0, x0);
bbox->y0 = (NR::Coord) MIN (bbox->y0, y0);
bbox->x1 = (NR::Coord) MAX (bbox->x1, x0);
bbox->y1 = (NR::Coord) MAX (bbox->y1, y0);
}
break;
case NR_LINETO:
x3 = m[0] * p->x3 + m[2] * p->y3 + m[4];
y3 = m[1] * p->x3 + m[3] * p->y3 + m[5];
if (bbox) {
bbox->x0 = (NR::Coord) MIN (bbox->x0, x3);
bbox->y0 = (NR::Coord) MIN (bbox->y0, y3);
bbox->x1 = (NR::Coord) MAX (bbox->x1, x3);
bbox->y1 = (NR::Coord) MAX (bbox->y1, y3);
}
if (dist || wind) {
nr_line_wind_distance (x0, y0, x3, y3, pt, wind, dist);
}
x0 = x3;
y0 = y3;
break;
case NR_CURVETO:
x3 = m[0] * p->x3 + m[2] * p->y3 + m[4];
y3 = m[1] * p->x3 + m[3] * p->y3 + m[5];
nr_curve_bbox_wind_distance (x0, y0,
m[0] * p->x1 + m[2] * p->y1 + m[4],
m[1] * p->x1 + m[3] * p->y1 + m[5],
m[0] * p->x2 + m[2] * p->y2 + m[4],
m[1] * p->x2 + m[3] * p->y2 + m[5],
x3, y3,
pt,
bbox, wind, dist, tolerance);
x0 = x3;
y0 = y3;
break;
default:
break;
}
}
}
static void
nr_curve_bbox(NR::Point const p000, NR::Point const p001,
NR::Point const p011, NR::Point const p111,
NRRect *bbox)
{
using NR::X;
using NR::Y;
nr_curve_bbox(p000[X], p000[Y],
p001[X], p001[Y],
p011[X], p011[Y],
p111[X], p111[Y],
bbox);
}
/* Fast bbox calculation */
/* Thanks to Nathan Hurst for suggesting it */
static void
nr_curve_bbox (NR::Coord x000, NR::Coord y000, NR::Coord x001, NR::Coord y001, NR::Coord x011, NR::Coord y011, NR::Coord x111, NR::Coord y111, NRRect *bbox)
{
NR::Coord a, b, c, D;
bbox->x0 = (NR::Coord) MIN (bbox->x0, x111);
bbox->y0 = (NR::Coord) MIN (bbox->y0, y111);
bbox->x1 = (NR::Coord) MAX (bbox->x1, x111);
bbox->y1 = (NR::Coord) MAX (bbox->y1, y111);
/*
* xttt = s * (s * (s * x000 + t * x001) + t * (s * x001 + t * x011)) + t * (s * (s * x001 + t * x011) + t * (s * x011 + t * x111))
* xttt = s * (s2 * x000 + s * t * x001 + t * s * x001 + t2 * x011) + t * (s2 * x001 + s * t * x011 + t * s * x011 + t2 * x111)
* xttt = s * (s2 * x000 + 2 * st * x001 + t2 * x011) + t * (s2 * x001 + 2 * st * x011 + t2 * x111)
* xttt = s3 * x000 + 2 * s2t * x001 + st2 * x011 + s2t * x001 + 2st2 * x011 + t3 * x111
* xttt = s3 * x000 + 3s2t * x001 + 3st2 * x011 + t3 * x111
* xttt = s3 * x000 + (1 - s) 3s2 * x001 + (1 - s) * (1 - s) * 3s * x011 + (1 - s) * (1 - s) * (1 - s) * x111
* xttt = s3 * x000 + (3s2 - 3s3) * x001 + (3s - 6s2 + 3s3) * x011 + (1 - 2s + s2 - s + 2s2 - s3) * x111
* xttt = (x000 - 3 * x001 + 3 * x011 - x111) * s3 +
* ( 3 * x001 - 6 * x011 + 3 * x111) * s2 +
* ( 3 * x011 - 3 * x111) * s +
* ( x111)
* xttt' = (3 * x000 - 9 * x001 + 9 * x011 - 3 * x111) * s2 +
* ( 6 * x001 - 12 * x011 + 6 * x111) * s +
* ( 3 * x011 - 3 * x111)
*/
a = 3 * x000 - 9 * x001 + 9 * x011 - 3 * x111;
b = 6 * x001 - 12 * x011 + 6 * x111;
c = 3 * x011 - 3 * x111;
/*
* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a;
*/
if (fabs (a) < NR_EPSILON) {
/* s = -c / b */
if (fabs (b) > NR_EPSILON) {
double s, t, xttt;
s = -c / b;
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
bbox->x0 = (float) MIN (bbox->x0, xttt);
bbox->x1 = (float) MAX (bbox->x1, xttt);
}
}
} else {
/* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a; */
D = b * b - 4 * a * c;
if (D >= 0.0) {
NR::Coord d, s, t, xttt;
/* Have solution */
d = sqrt (D);
s = (-b + d) / (2 * a);
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
bbox->x0 = (NR::Coord) MIN (bbox->x0, xttt);
bbox->x1 = (NR::Coord) MAX (bbox->x1, xttt);
}
s = (-b - d) / (2 * a);
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
bbox->x0 = (NR::Coord) MIN (bbox->x0, xttt);
bbox->x1 = (NR::Coord) MAX (bbox->x1, xttt);
}
}
}
a = 3 * y000 - 9 * y001 + 9 * y011 - 3 * y111;
b = 6 * y001 - 12 * y011 + 6 * y111;
c = 3 * y011 - 3 * y111;
if (fabs (a) < NR_EPSILON) {
/* s = -c / b */
if (fabs (b) > NR_EPSILON) {
double s, t, yttt;
s = -c / b;
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
bbox->y0 = (float) MIN (bbox->y0, yttt);
bbox->y1 = (float) MAX (bbox->y1, yttt);
}
}
} else {
/* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a; */
D = b * b - 4 * a * c;
if (D >= 0.0) {
NR::Coord d, s, t, yttt;
/* Have solution */
d = sqrt (D);
s = (-b + d) / (2 * a);
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
bbox->y0 = (NR::Coord) MIN (bbox->y0, yttt);
bbox->y1 = (NR::Coord) MAX (bbox->y1, yttt);
}
s = (-b - d) / (2 * a);
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
yttt = s * s * s * y000 + 3 * s * s * t * y001 + 3 * s * t * t * y011 + t * t * t * y111;
bbox->y0 = (NR::Coord) MIN (bbox->y0, yttt);
bbox->y1 = (NR::Coord) MAX (bbox->y1, yttt);
}
}
}
}
void
nr_path_matrix_bbox_union(NRBPath const *bpath, NR::Matrix const &m,
NRRect *bbox)
{
using NR::X;
using NR::Y;
if (!bpath->path) {
return;
}
NR::Point prev0(0, 0);
for (NArtBpath const *p = bpath->path; p->code != NR_END; ++p) {
switch (p->code) {
case NR_MOVETO_OPEN:
case NR_MOVETO: {
NR::Point const c3(p->x3,
p->y3);
prev0 = c3 * m;
nr_rect_union_pt(bbox, prev0);
break;
}
case NR_LINETO: {
NR::Point const c3(p->x3,
p->y3);
NR::Point const endPt( c3 * m );
nr_rect_union_pt(bbox, endPt);
prev0 = endPt;
break;
}
case NR_CURVETO: {
NR::Point const c1(p->x1, p->y1);
NR::Point const c2(p->x2, p->y2);
NR::Point const c3(p->x3, p->y3);
NR::Point const endPt( c3 * m );
nr_curve_bbox(prev0,
c1 * m,
c2 * m,
endPt,
bbox);
prev0 = endPt;
break;
}
default:
break;
}
}
}