/*
* La procedure "plane_norme" calcule le vecteur norme orthogonal au plan
* defini par les 3 points.
* Entree :
* np Le vecteur norme orthogonal au plan.
* ap, bp, cp Points formant un repere du plan.
*/
void
plane_norme (Vector *np, Point3f *ap, Point3f *bp, Point3f *cp)
{
Vector u, v;
DIF_COORD3(u,*bp,*ap); /* base orthonorme (ap, u, v) */
DIF_COORD3(v,*cp,*ap);
norm_vector (&u);
norm_vector (&v);
CROSS_PRODUCT (*np,u,v);
}
/*
* La procedure "rotate_vector" transforme le vecteur
* par la rotation de sens trigonometrique d'angle et d'axe donnes.
* Entree :
* vp Vecteur a transformer.
* a Angle de rotation en degres.
* axis Vecteur directeur de l'axe de rotation.
*/
void
rotate_vector (Vector *vp, float a, Vector *axis)
{
Vector n, u, v, cross;
float f;
a *= (float)M_PI / (float)180.0; /* passage en radians */
n = *axis; /* norme le vecteur directeur */
norm_vector (&n);
/*
* Avant rotation, vp vaut :
* u + v
* Apres rotation, vp vaut :
* u + cos(a) * v + sin(a) * (n^vp)
* = u + cos(a) * v + sin(a) * (n^v)
* avec u = (vp.n) * n, v = vp-u;
* ou "u" est la projection de "vp" sur l'axe "axis",
* et "v" est la composante de "vp" perpendiculaire a "axis".
*/
f = DOT_PRODUCT(*vp, n);
u = n;
MUL_COORD3(u,f,f,f); /* (vp.n) * n */
DIF_COORD3(v,*vp,u); /* calcule "v" */
f = (float) cos ((double) a);
MUL_COORD3(v,f,f,f); /* v * cos(a) */
CROSS_PRODUCT(cross,n,*vp);
f = (float) sin ((double) a);
MUL_COORD3(cross,f,f,f); /* (n^v) * sin(a) */
SET_COORD3(*vp,
u.x + v.x + cross.x,
u.y + v.y + cross.y,
u.z + v.z + cross.z);
}
/*
* La procedure "Rotaxis_to_Matrix" initialise la matrice par la rotation
* d'angle et d'axe donnes.
* Si M est la matrice, O l'angle et N le vecteur directeur de l'axe :
*
* M = cos(O) Id3 + (1 - cosO) Nt N + sinO N~
*
* | NxNxverO+ cosO NxNyverO+NzsinO NxNzverO-NxsinO 0 |
* M = | NxNyverO-NzsinO NyNyverO+ cosO NyNzverO+NxsinO 0 |
* | NxNzverO+NysinO NyNzverO-NxsinO NzNzverO+ cosO 0 |
* | 0 0 0 1 |
*
* O angle de rotation.
* N Vecteur directeur norme de l'axe de rotation.
* Nt Vecteur transpose.
* N~ | 0 Nz -Ny|
* |-Nz 0 Nx|
* | Ny -Nx 0 |
* Entree :
* a Angle de rotation en degres.
* axis Vecteur directeur de l'axe de la rotation.
* m Matrice a initialiser.
*/
void
Rotaxis_to_Matrix (float a, Vector *axis, Matrix m)
{
float cosa;
float sina;
float vera; /* 1 - cosa */
Vector n; /* vecteur norme*/
Vector conv; /* verO n */
Vector tilde; /* sinO n */
a *= (float)M_PI / (float)180.0; /* passage en radians */
cosa = (float) cos ((double) a);
sina = (float) sin ((double) a);
vera = (float)1.0 - cosa;
n = *axis; /* norme le vecteur directeur */
norm_vector (&n);
tilde = conv = n;
MUL_COORD3(conv,vera,vera,vera);
MUL_COORD3(tilde,sina,sina,sina);
m[0][0] = conv.x * n.x + cosa;
m[0][1] = conv.x * n.y + tilde.z;
m[0][2] = conv.x * n.z - tilde.y;
m[1][0] = conv.y * n.x - tilde.z;
m[1][1] = conv.y * n.y + cosa;
m[1][2] = conv.y * n.z + tilde.x;
m[2][0] = conv.z * n.x + tilde.y;
m[2][1] = conv.z * n.y - tilde.x;
m[2][2] = conv.z * n.z + cosa;
m[0][3] = m[2][3] = m[1][3] = 0.0;
m[3][0] = m[3][1] = m[3][2] = 0.0;
m[3][3] = 1.0;
}
/* input line must be looped */
static void convolution_line(struct line_pnts *Points, double da, double db,
double dalpha, int side, int round, int caps,
double tol, struct line_pnts *nPoints)
{
int i, j, res, np;
double *x, *y;
double tx, ty, vx, vy, wx, wy, nx, ny, mx, my, rx, ry;
double vx1, vy1, wx1, wy1;
double a0, b0, c0, a1, b1, c1;
double phi1, phi2, delta_phi;
double nsegments, angular_tol, angular_step;
double angle0, angle1;
int inner_corner, turns360;
G_debug(3, "convolution_line() side = %d", side);
np = Points->n_points;
x = Points->x;
y = Points->y;
if ((np == 0) || (np == 1))
return;
if ((x[0] != x[np - 1]) || (y[0] != y[np - 1])) {
G_fatal_error(_("Line is not looped"));
return;
}
Vect_reset_line(nPoints);
if ((da == 0) || (db == 0)) {
Vect_copy_xyz_to_pnts(nPoints, x, y, NULL, np);
return;
}
side = (side >= 0) ? (1) : (-1); /* normalize variable */
dalpha *= PI / 180; /* convert dalpha from degrees to radians */
angular_tol = angular_tolerance(tol, da, db);
i = np - 2;
norm_vector(x[i], y[i], x[i + 1], y[i + 1], &tx, &ty);
elliptic_tangent(side * tx, side * ty, da, db, dalpha, &vx, &vy);
angle1 = atan2(ty, tx);
nx = x[i] + vx;
ny = y[i] + vy;
mx = x[i + 1] + vx;
my = y[i + 1] + vy;
if (!round)
line_coefficients(nx, ny, mx, my, &a1, &b1, &c1);
for (i = 0; i <= np - 2; i++) {
G_debug(4, "point %d, segment %d-%d", i, i, i + 1);
/* save the old values */
if (!round) {
a0 = a1;
b0 = b1;
c0 = c1;
}
wx = vx;
wy = vy;
angle0 = angle1;
norm_vector(x[i], y[i], x[i + 1], y[i + 1], &tx, &ty);
if ((tx == 0) && (ty == 0))
continue;
elliptic_tangent(side * tx, side * ty, da, db, dalpha, &vx, &vy);
angle1 = atan2(ty, tx);
nx = x[i] + vx;
ny = y[i] + vy;
mx = x[i + 1] + vx;
my = y[i + 1] + vy;
if (!round)
line_coefficients(nx, ny, mx, my, &a1, &b1, &c1);
delta_phi = angle1 - angle0;
if (delta_phi > PI)
delta_phi -= 2 * PI;
else if (delta_phi <= -PI)
delta_phi += 2 * PI;
/* now delta_phi is in [-pi;pi] */
turns360 = (fabs(fabs(delta_phi) - PI) < 1e-15);
inner_corner = (side * delta_phi <= 0) && (!turns360);
/* if <line turns 360> and (<caps> and <not round>) */
if (turns360 && caps && (!round)) {
norm_vector(0, 0, vx, vy, &tx, &ty);
elliptic_tangent(side * tx, side * ty, da, db, dalpha, &tx, &ty);
Vect_append_point(nPoints, x[i] + wx + tx, y[i] + wy + ty, 0);
G_debug(4, " append point (c) x=%.16f y=%.16f", x[i] + wx + tx,
y[i] + wy + ty);
Vect_append_point(nPoints, nx + tx, ny + ty, 0); /* nx == x[i] + vx, ny == y[i] + vy */
G_debug(4, " append point (c) x=%.16f y=%.16f", nx + tx, ny + ty);
}
if ((!turns360) && (!round) && (!inner_corner)) {
res = line_intersection(a0, b0, c0, a1, b1, c1, &rx, &ry);
if (res == 1) {
Vect_append_point(nPoints, rx, ry, 0);
G_debug(4, " append point (o) x=%.16f y=%.16f", rx, ry);
}
else if (res == 2) {
/* no need to append point in this case */
}
else
G_fatal_error
("unexpected result of line_intersection() res = %d",
res);
}
if (round && (!inner_corner) && (!turns360 || caps)) {
/* we should draw elliptical arc for outside corner */
/* inverse transforms */
elliptic_transform(wx, wy, 1 / da, 1 / db, dalpha, &wx1, &wy1);
elliptic_transform(vx, vy, 1 / da, 1 / db, dalpha, &vx1, &vy1);
phi1 = atan2(wy1, wx1);
phi2 = atan2(vy1, vx1);
delta_phi = side * (phi2 - phi1);
/* make delta_phi in [0, 2pi] */
if (delta_phi < 0)
delta_phi += 2 * PI;
nsegments = (int)(delta_phi / angular_tol) + 1;
angular_step = side * (delta_phi / nsegments);
phi1 += angular_step;
for (j = 1; j <= nsegments - 1; j++) {
elliptic_transform(cos(phi1), sin(phi1), da, db, dalpha, &tx,
&ty);
Vect_append_point(nPoints, x[i] + tx, y[i] + ty, 0);
G_debug(4, " append point (r) x=%.16f y=%.16f", x[i] + tx,
y[i] + ty);
phi1 += angular_step;
}
}
Vect_append_point(nPoints, nx, ny, 0);
G_debug(4, " append point (s) x=%.16f y=%.16f", nx, ny);
Vect_append_point(nPoints, mx, my, 0);
G_debug(4, " append point (s) x=%.16f y=%.16f", mx, my);
}
/* close the output line */
Vect_append_point(nPoints, nPoints->x[0], nPoints->y[0], nPoints->z[0]);
Vect_line_prune ( nPoints );
}
/*
* This function generates parallel line (with loops, but not like the old ones).
* It is not to be used directly for creating buffers.
* + added elliptical buffers/par.lines support
*
* dalpha - direction of elliptical buffer major axis in degrees
* da - distance along major axis
* db: distance along minor (perp.) axis
* side: side >= 0 - right side, side < 0 - left side
* when (da == db) we have plain distances (old case)
* round - 1 for round corners, 0 for sharp corners. (tol is used only if round == 1)
*/
static void parallel_line(struct line_pnts *Points, double da, double db,
double dalpha, int side, int round, int caps, int looped,
double tol, struct line_pnts *nPoints)
{
int i, j, res, np;
double *x, *y;
double tx, ty, vx, vy, wx, wy, nx, ny, mx, my, rx, ry;
double vx1, vy1, wx1, wy1;
double a0, b0, c0, a1, b1, c1;
double phi1, phi2, delta_phi;
double nsegments, angular_tol, angular_step;
int inner_corner, turns360;
G_debug(3, "parallel_line()");
if (looped && 0) {
/* start point != end point */
return;
}
Vect_reset_line(nPoints);
if (looped) {
Vect_append_point(Points, Points->x[1], Points->y[1], Points->z[1]);
}
np = Points->n_points;
x = Points->x;
y = Points->y;
if ((np == 0) || (np == 1))
return;
if ((da == 0) || (db == 0)) {
Vect_copy_xyz_to_pnts(nPoints, x, y, NULL, np);
return;
}
side = (side >= 0) ? (1) : (-1); /* normalize variable */
dalpha *= PI / 180; /* convert dalpha from degrees to radians */
angular_tol = angular_tolerance(tol, da, db);
for (i = 0; i < np - 1; i++) {
/* save the old values */
a0 = a1;
b0 = b1;
c0 = c1;
wx = vx;
wy = vy;
norm_vector(x[i], y[i], x[i + 1], y[i + 1], &tx, &ty);
if ((tx == 0) && (ty == 0))
continue;
elliptic_tangent(side * tx, side * ty, da, db, dalpha, &vx, &vy);
nx = x[i] + vx;
ny = y[i] + vy;
mx = x[i + 1] + vx;
my = y[i + 1] + vy;
line_coefficients(nx, ny, mx, my, &a1, &b1, &c1);
if (i == 0) {
if (!looped)
Vect_append_point(nPoints, nx, ny, 0);
continue;
}
delta_phi = atan2(ty, tx) - atan2(y[i] - y[i - 1], x[i] - x[i - 1]);
if (delta_phi > PI)
delta_phi -= 2 * PI;
else if (delta_phi <= -PI)
delta_phi += 2 * PI;
/* now delta_phi is in [-pi;pi] */
turns360 = (fabs(fabs(delta_phi) - PI) < 1e-15);
inner_corner = (side * delta_phi <= 0) && (!turns360);
if ((turns360) && (!(caps && round))) {
if (caps) {
norm_vector(0, 0, vx, vy, &tx, &ty);
elliptic_tangent(side * tx, side * ty, da, db, dalpha, &tx,
&ty);
}
else {
tx = 0;
ty = 0;
}
Vect_append_point(nPoints, x[i] + wx + tx, y[i] + wy + ty, 0);
Vect_append_point(nPoints, nx + tx, ny + ty, 0); /* nx == x[i] + vx, ny == y[i] + vy */
}
else if ((!round) || inner_corner) {
res = line_intersection(a0, b0, c0, a1, b1, c1, &rx, &ry);
/* if (res == 0) {
G_debug(4, "a0=%.18f, b0=%.18f, c0=%.18f, a1=%.18f, b1=%.18f, c1=%.18f", a0, b0, c0, a1, b1, c1);
G_fatal_error("Two consequtive line segments are parallel, but not on one straight line! This should never happen.");
return;
} */
if (res == 1) {
if (!round)
Vect_append_point(nPoints, rx, ry, 0);
else {
/* d = dig_distance2_point_to_line(rx, ry, 0, x[i-1], y[i-1], 0, x[i], y[i], 0,
0, NULL, NULL, NULL, NULL, NULL);
if ( */
Vect_append_point(nPoints, rx, ry, 0);
}
}
}
else {
/* we should draw elliptical arc for outside corner */
/* inverse transforms */
elliptic_transform(wx, wy, 1 / da, 1 / db, dalpha, &wx1, &wy1);
elliptic_transform(vx, vy, 1 / da, 1 / db, dalpha, &vx1, &vy1);
phi1 = atan2(wy1, wx1);
phi2 = atan2(vy1, vx1);
delta_phi = side * (phi2 - phi1);
/* make delta_phi in [0, 2pi] */
if (delta_phi < 0)
delta_phi += 2 * PI;
nsegments = (int)(delta_phi / angular_tol) + 1;
angular_step = side * (delta_phi / nsegments);
for (j = 0; j <= nsegments; j++) {
elliptic_transform(cos(phi1), sin(phi1), da, db, dalpha, &tx,
&ty);
Vect_append_point(nPoints, x[i] + tx, y[i] + ty, 0);
phi1 += angular_step;
}
}
if ((!looped) && (i == np - 2)) {
Vect_append_point(nPoints, mx, my, 0);
}
}
if (looped) {
Vect_append_point(nPoints, nPoints->x[0], nPoints->y[0],
nPoints->z[0]);
}
Vect_line_prune(nPoints);
if (looped) {
Vect_line_delete_point(Points, Points->n_points - 1);
}
}
