static GF_Err svg_rect_add_arc(GF_Path *gp, Fixed end_x, Fixed end_y, Fixed cx, Fixed cy, Fixed rx, Fixed ry)
{
Fixed angle, start_angle, end_angle, sweep, _vx, _vy, start_x, start_y;
s32 i, num_steps;
if (!gp->n_points) return GF_BAD_PARAM;
start_x = gp->points[gp->n_points-1].x;
start_y = gp->points[gp->n_points-1].y;
//start angle and end angle
start_angle = gf_atan2(start_y-cy, start_x-cx);
end_angle = gf_atan2(end_y-cy, end_x-cx);
sweep = end_angle - start_angle;
if (sweep<0) sweep += 2*GF_PI;
num_steps = 16;
for (i=1; i<=num_steps; i++) {
angle = start_angle + sweep*i/num_steps;
_vx = cx + gf_mulfix(rx, gf_cos(angle));
_vy = cy + gf_mulfix(ry, gf_sin(angle));
gf_path_add_line_to(gp, _vx, _vy);
}
return GF_OK;
}
void camera_set_vectors(GF_Camera *cam, SFVec3f pos, SFRotation ori, Fixed fov)
{
Fixed sin_a, cos_a, icos_a, tmp;
cam->fieldOfView = fov;
cam->last_pos = cam->position;
cam->position = pos;
/*compute up & target vectors in local system*/
sin_a = gf_sin(ori.q);
cos_a = gf_cos(ori.q);
icos_a = FIX_ONE - cos_a;
tmp = gf_mulfix(icos_a, ori.z);
cam->target.x = gf_mulfix(ori.x, tmp) + gf_mulfix(sin_a, ori.y);
cam->target.y = gf_mulfix(ori.y, tmp) - gf_mulfix(sin_a, ori.x);
cam->target.z = gf_mulfix(ori.z, tmp) + cos_a;
gf_vec_norm(&cam->target);
cam->target = gf_vec_scale(cam->target, -cam->vp_dist);
gf_vec_add(cam->target, cam->target, pos);
tmp = gf_mulfix(icos_a, ori.y);
cam->up.x = gf_mulfix(ori.x, tmp) - gf_mulfix(sin_a, ori.z);
cam->up.y = gf_mulfix(ori.y, tmp) + cos_a;
cam->up.z = gf_mulfix(ori.z, tmp) + gf_mulfix(sin_a, ori.x);
gf_vec_norm(&cam->up);
cam->flags |= CAM_IS_DIRTY;
}
GF_EXPORT
GF_Err gf_path_add_arc_to(GF_Path *gp, Fixed end_x, Fixed end_y, Fixed fa_x, Fixed fa_y, Fixed fb_x, Fixed fb_y, Bool cw)
{
GF_Matrix2D mat, inv;
Fixed angle, start_angle, end_angle, sweep, axis_w, axis_h, tmp, cx, cy, _vx, _vy, start_x, start_y;
s32 i, num_steps;
if (!gp->n_points) return GF_BAD_PARAM;
start_x = gp->points[gp->n_points-1].x;
start_y = gp->points[gp->n_points-1].y;
cx = (fb_x + fa_x)/2;
cy = (fb_y + fa_y)/2;
angle = gf_atan2(fb_y-fa_y, fb_x-fa_x);
gf_mx2d_init(mat);
gf_mx2d_add_rotation(&mat, 0, 0, angle);
gf_mx2d_add_translation(&mat, cx, cy);
gf_mx2d_copy(inv, mat);
gf_mx2d_inverse(&inv);
gf_mx2d_apply_coords(&inv, &start_x, &start_y);
gf_mx2d_apply_coords(&inv, &end_x, &end_y);
gf_mx2d_apply_coords(&inv, &fa_x, &fa_y);
gf_mx2d_apply_coords(&inv, &fb_x, &fb_y);
//start angle and end angle
start_angle = gf_atan2(start_y, start_x);
end_angle = gf_atan2(end_y, end_x);
tmp = gf_mulfix((start_x - fa_x), (start_x - fa_x)) + gf_mulfix((start_y - fa_y), (start_y - fa_y));
axis_w = gf_sqrt(tmp);
tmp = gf_mulfix((start_x - fb_x) , (start_x - fb_x)) + gf_mulfix((start_y - fb_y), (start_y - fb_y));
axis_w += gf_sqrt(tmp);
axis_w /= 2;
axis_h = gf_sqrt(gf_mulfix(axis_w, axis_w) - gf_mulfix(fa_x,fa_x));
sweep = end_angle - start_angle;
if (cw) {
if (sweep>0) sweep -= 2*GF_PI;
} else {
if (sweep<0) sweep += 2*GF_PI;
}
num_steps = GF_2D_DEFAULT_RES/2;
for (i=1; i<=num_steps; i++) {
angle = start_angle + sweep*i/num_steps;
_vx = gf_mulfix(axis_w, gf_cos(angle));
_vy = gf_mulfix(axis_h, gf_sin(angle));
/*re-invert*/
gf_mx2d_apply_coords(&mat, &_vx, &_vy);
gf_path_add_line_to(gp, _vx, _vy);
}
return GF_OK;
}
GF_EXPORT
GF_Err gf_path_add_ellipse(GF_Path *gp, Fixed cx, Fixed cy, Fixed a_axis, Fixed b_axis)
{
GF_Err e;
Fixed _vx, _vy, cur;
u32 i;
a_axis /= 2;
b_axis /= 2;
e = gf_path_add_move_to(gp, cx+a_axis, cy);
if (e) return e;
for (i=1; i<GF_2D_DEFAULT_RES; i++) {
cur = GF_2PI*i/GF_2D_DEFAULT_RES;
_vx = gf_mulfix(a_axis, gf_cos(cur) );
_vy = gf_mulfix(b_axis, gf_sin(cur) );
e = gf_path_add_line_to(gp, _vx + cx, _vy + cy);
if (e) return e;
}
return gf_path_close(gp);
}
GF_EXPORT
GF_Err gf_path_add_arc(GF_Path *gp, Fixed radius, Fixed start_angle, Fixed end_angle, u32 close_type)
{
GF_Err e;
Fixed _vx, _vy, step, cur;
s32 i, do_run;
step = (end_angle - start_angle) / (GF_2D_DEFAULT_RES);
radius *= 2;
/*pie*/
i=0;
if (close_type==2) {
gf_path_add_move_to(gp, 0, 0);
i=1;
}
do_run = 1;
cur=start_angle;
while (do_run) {
if (cur>=end_angle) {
do_run = 0;
cur = end_angle;
}
_vx = gf_mulfix(radius, gf_cos(cur));
_vy = gf_mulfix(radius, gf_sin(cur));
if (!i) {
e = gf_path_add_move_to(gp, _vx, _vy);
i = 1;
} else {
e = gf_path_add_line_to(gp, _vx, _vy);
}
if (e) return e;
cur+=step;
}
if (close_type) e = gf_path_close(gp);
return e;
}
static void NLD_Apply(M_NonLinearDeformer *nld, GF_Mesh *mesh)
{
u32 i;
GF_Matrix mx;
SFVec3f n;
Fixed param, z_min, z_max, v_min, v_max, f_min, f_max, frac, val, a_cos, a_sin;
Bool needs_transform = NLD_GetMatrix(nld, &mx);
param = nld->param;
if (!param) param = 1;
if (mesh->bounds.min_edge.z == mesh->bounds.max_edge.z) return;
z_min = FIX_MAX;
z_max = -FIX_MAX;
if (needs_transform) {
for (i=0; i<mesh->v_count; i++) {
gf_mx_apply_vec(&mx, &mesh->vertices[i].pos);
MESH_GET_NORMAL(n, mesh->vertices[i]);
gf_mx_rotate_vector(&mx, &n);
MESH_SET_NORMAL(mesh->vertices[i], n);
if (mesh->vertices[i].pos.z<z_min) z_min = mesh->vertices[i].pos.z;
if (mesh->vertices[i].pos.z>z_max) z_max = mesh->vertices[i].pos.z;
}
} else {
z_min = mesh->bounds.min_edge.z;
z_max = mesh->bounds.max_edge.z;
}
for (i=0; i<mesh->v_count; i++) {
SFVec3f old = mesh->vertices[i].pos;
frac = gf_divfix(old.z - z_min, z_max - z_min);
NLD_GetKey(nld, frac, &f_min, &v_min, &f_max, &v_max);
if (f_max == f_min) {
val = v_min;
} else {
frac = gf_divfix(frac-f_min, f_max - f_min);
val = gf_mulfix(v_max - v_min, frac) + v_min;
}
val = gf_mulfix(val, param);
switch (nld->type) {
/*taper*/
case 0:
mesh->vertices[i].pos.x = gf_mulfix(mesh->vertices[i].pos.x, val);
mesh->vertices[i].pos.y = gf_mulfix(mesh->vertices[i].pos.y, val);
MESH_GET_NORMAL(old, mesh->vertices[i]);
n=old;
n.x = gf_mulfix(n.x, val);
n.y = gf_mulfix(n.y, val);
gf_vec_norm(&n);
MESH_SET_NORMAL(mesh->vertices[i], n);
break;
/*twist*/
case 1:
a_cos = gf_cos(val);
a_sin = gf_sin(val);
mesh->vertices[i].pos.x = gf_mulfix(a_cos, old.x) - gf_mulfix(a_sin, old.y);
mesh->vertices[i].pos.y = gf_mulfix(a_sin, old.x) + gf_mulfix(a_cos, old.y);
MESH_GET_NORMAL(old, mesh->vertices[i]);
n=old;
n.x = gf_mulfix(a_cos, old.x) - gf_mulfix(a_sin, old.y);
n.y = gf_mulfix(a_sin, old.x) + gf_mulfix(a_cos, old.y);
gf_vec_norm(&n);
MESH_SET_NORMAL(mesh->vertices[i], n);
break;
/*bend*/
case 2:
a_cos = gf_cos(val);
a_sin = gf_sin(val);
mesh->vertices[i].pos.x = gf_mulfix(a_sin, old.z) + gf_mulfix(a_cos, old.x);
mesh->vertices[i].pos.z = gf_mulfix(a_cos, old.z) - gf_mulfix(a_sin, old.x);
MESH_GET_NORMAL(old, mesh->vertices[i]);
n=old;
n.x = gf_mulfix(a_sin, old.z) + gf_mulfix(a_cos, old.x);
n.z = gf_mulfix(a_cos, old.z) - gf_mulfix(a_sin, old.x);
gf_vec_norm(&n);
MESH_SET_NORMAL(mesh->vertices[i], n);
break;
/*pinch, not standard (taper on X dim only)*/
case 3:
mesh->vertices[i].pos.x = gf_mulfix(mesh->vertices[i].pos.x, val);
MESH_GET_NORMAL(old, mesh->vertices[i]);
n=old;
n.x = gf_mulfix(n.x, val);
gf_vec_norm(&n);
MESH_SET_NORMAL(mesh->vertices[i], n);
break;
}
}
if (needs_transform) {
gf_mx_inverse(&mx);
for (i=0; i<mesh->v_count; i++) {
gf_mx_apply_vec(&mx, &mesh->vertices[i].pos);
MESH_GET_NORMAL(n, mesh->vertices[i]);
gf_mx_rotate_vector(&mx, &n);
MESH_SET_NORMAL(mesh->vertices[i], n);
}
}
mesh_update_bounds(mesh);
gf_mesh_build_aabbtree(mesh);
}
GF_EXPORT
GF_Err gf_path_add_svg_arc_to(GF_Path *gp, Fixed end_x, Fixed end_y, Fixed r_x, Fixed r_y, Fixed x_axis_rotation, Bool large_arc_flag, Bool sweep_flag)
{
Fixed start_x, start_y;
Fixed xmid,ymid;
Fixed xmidp,ymidp;
Fixed xmidpsq,ymidpsq;
Fixed phi, cos_phi, sin_phi;
Fixed c_x, c_y;
Fixed cxp, cyp;
Fixed scale;
Fixed rxsq, rysq;
Fixed start_angle, sweep_angle;
Fixed radius_scale;
Fixed vx, vy, normv;
Fixed ux, uy, normu;
Fixed sign;
u32 i, num_steps;
if (!gp->n_points) return GF_BAD_PARAM;
if (!r_x || !r_y) {
gf_path_add_line_to(gp, end_x, end_y);
return GF_OK;
}
if (r_x < 0) r_x = -r_x;
if (r_y < 0) r_y = -r_y;
start_x = gp->points[gp->n_points-1].x;
start_y = gp->points[gp->n_points-1].y;
phi = gf_mulfix(gf_divfix(x_axis_rotation, 180), GF_PI);
cos_phi = gf_cos(phi);
sin_phi = gf_sin(phi);
xmid = (start_x - end_x)/2;
ymid = (start_y - end_y)/2;
if (!xmid && !ymid) {
gf_path_add_line_to(gp, end_x, end_y);
return GF_OK;
}
xmidp = gf_mulfix(cos_phi, xmid) + gf_mulfix(sin_phi, ymid);
ymidp = gf_mulfix(-sin_phi, xmid) + gf_mulfix(cos_phi, ymid);
xmidpsq = gf_mulfix(xmidp, xmidp);
ymidpsq = gf_mulfix(ymidp, ymidp);
rxsq = gf_mulfix(r_x, r_x);
rysq = gf_mulfix(r_y, r_y);
assert(rxsq && rxsq);
radius_scale = gf_divfix(xmidpsq, rxsq) + gf_divfix(ymidpsq, rysq);
if (radius_scale > FIX_ONE) {
r_x = gf_mulfix(gf_sqrt(radius_scale), r_x);
r_y = gf_mulfix(gf_sqrt(radius_scale), r_y);
rxsq = gf_mulfix(r_x, r_x);
rysq = gf_mulfix(r_y, r_y);
}
#if 0
/* Old code with overflow problems in fixed point,
sign was sometimes negative (cf tango SVG icons appointment-new.svg)*/
sign = gf_mulfix(rxsq,ymidpsq) + gf_mulfix(rysq, xmidpsq);
scale = FIX_ONE;
/*FIXME - what if scale is 0 ??*/
if (sign) scale = gf_divfix(
(gf_mulfix(rxsq,rysq) - gf_mulfix(rxsq, ymidpsq) - gf_mulfix(rysq,xmidpsq)),
sign
);
#else
/* New code: the sign variable computation is split into simpler cases and
the expression is divided by rxsq to reduce the range */
if ((rxsq == 0 || ymidpsq ==0) && (rysq == 0 || xmidpsq == 0)) {
scale = FIX_ONE;
} else if (rxsq == 0 || ymidpsq ==0) {
scale = gf_divfix(rxsq,xmidpsq) - FIX_ONE;
} else if (rysq == 0 || xmidpsq == 0) {
scale = gf_divfix(rysq,ymidpsq) - FIX_ONE;
} else {
Fixed tmp;
tmp = gf_mulfix(gf_divfix(rysq, rxsq), xmidpsq);
sign = ymidpsq + tmp;
scale = gf_divfix((rysq - ymidpsq - tmp),sign);
}
#endif
/* precision problem may lead to negative value around zero, we need to take care of it before sqrt */
scale = gf_sqrt(ABS(scale));
cxp = gf_mulfix(scale, gf_divfix(gf_mulfix(r_x, ymidp),r_y));
cyp = gf_mulfix(scale, -gf_divfix(gf_mulfix(r_y, xmidp),r_x));
cxp = (large_arc_flag == sweep_flag ? - cxp : cxp);
cyp = (large_arc_flag == sweep_flag ? - cyp : cyp);
c_x = gf_mulfix(cos_phi, cxp) - gf_mulfix(sin_phi, cyp) + (start_x + end_x)/2;
c_y = gf_mulfix(sin_phi, cxp) + gf_mulfix(cos_phi, cyp) + (start_y + end_y)/2;
ux = FIX_ONE;
uy = 0;
normu = FIX_ONE;
vx = gf_divfix(xmidp-cxp,r_x);
vy = gf_divfix(ymidp-cyp,r_y);
normv = gf_sqrt(gf_mulfix(vx, vx) + gf_mulfix(vy,vy));
sign = vy;
start_angle = gf_acos(gf_divfix(vx,normv));
start_angle = (sign > 0 ? start_angle: -start_angle);
ux = vx;
uy = vy;
normu = normv;
vx = gf_divfix(-xmidp-cxp,r_x);
vy = gf_divfix(-ymidp-cyp,r_y);
normu = gf_sqrt(gf_mulfix(ux, ux) + gf_mulfix(uy,uy));
sign = gf_mulfix(ux, vy) - gf_mulfix(uy, vx);
sweep_angle = gf_divfix( gf_mulfix(ux,vx) + gf_mulfix(uy, vy), gf_mulfix(normu, normv) );
/*numerical stability safety*/
sweep_angle = MAX(-FIX_ONE, MIN(sweep_angle, FIX_ONE));
sweep_angle = gf_acos(sweep_angle);
sweep_angle = (sign > 0 ? sweep_angle: -sweep_angle);
if (sweep_flag == 0) {
if (sweep_angle > 0) sweep_angle -= GF_2PI;
} else {
if (sweep_angle < 0) sweep_angle += GF_2PI;
}
num_steps = GF_2D_DEFAULT_RES/2;
for (i=1; i<=num_steps; i++) {
Fixed _vx, _vy;
Fixed _vxp, _vyp;
Fixed angle = start_angle + sweep_angle*i/num_steps;
_vx = gf_mulfix(r_x, gf_cos(angle));
_vy = gf_mulfix(r_y, gf_sin(angle));
_vxp = gf_mulfix(cos_phi, _vx) - gf_mulfix(sin_phi, _vy) + c_x;
_vyp = gf_mulfix(sin_phi, _vx) + gf_mulfix(cos_phi, _vy) + c_y;
gf_path_add_line_to(gp, _vxp, _vyp);
}
return GF_OK;
}
static void back_build_dome(GF_Mesh *mesh, MFFloat *angles, MFColor *color, Bool ground_dome)
{
u32 i, j, last_idx, ang_idx, new_idx;
Bool pad;
u32 step_div_h;
GF_Vertex vx;
SFColorRGBA start_col, end_col, fcol;
Fixed start_angle, next_angle, angle, r, frac, first_angle;
start_angle = 0;
mesh_reset(mesh);
start_col.red = start_col.green = start_col.blue = 0;
end_col = start_col;
if (color->count) {
COL_TO_RGBA(start_col, color->vals[0]);
end_col = start_col;
if (color->count>1) COL_TO_RGBA(end_col, color->vals[1]);
}
start_col.alpha = end_col.alpha = FIX_ONE;
vx.texcoords.x = vx.texcoords.y = 0;
vx.color = MESH_MAKE_COL(start_col);
vx.pos.x = vx.pos.z = 0;
vx.pos.y = FIX_ONE;
vx.normal.x = vx.normal.z = 0;
vx.normal.y = -MESH_NORMAL_UNIT;
mesh_set_vertex_vx(mesh, &vx);
last_idx = 0;
ang_idx = 0;
pad = 1;
next_angle = first_angle = 0;
if (angles->count) {
next_angle = angles->vals[0];
first_angle = 7*next_angle/8;
pad = 0;
}
step_div_h = DOME_STEP_H;
i=0;
if (ground_dome) {
step_div_h *= 2;
i=1;
}
for (; i<DOME_STEP_V; i++) {
if (ground_dome) {
angle = first_angle + (i * (GF_PI2-first_angle) / DOME_STEP_V);
} else {
angle = (i * GF_PI / DOME_STEP_V);
}
/*switch cols*/
if (angle >= next_angle) {
if (ang_idx+1<=angles->count) {
start_angle = next_angle;
next_angle = angles->vals[ang_idx+1];
if (next_angle>GF_PI) next_angle=GF_PI;
start_col = end_col;
ang_idx++;
if (ang_idx+1<color->count) {
COL_TO_RGBA(end_col, color->vals[ang_idx+1]);
} else {
pad = 1;
}
} else {
if (ground_dome) break;
pad = 1;
}
}
if (pad) {
fcol = end_col;
} else {
frac = gf_divfix(angle - start_angle, next_angle - start_angle) ;
fcol.red = gf_mulfix(end_col.red - start_col.red, frac) + start_col.red;
fcol.green = gf_mulfix(end_col.green - start_col.green, frac) + start_col.green;
fcol.blue = gf_mulfix(end_col.blue - start_col.blue, frac) + start_col.blue;
fcol.alpha = FIX_ONE;
}
vx.color = MESH_MAKE_COL(fcol);
vx.pos.y = gf_sin(GF_PI2 - angle);
r = gf_sqrt(FIX_ONE - gf_mulfix(vx.pos.y, vx.pos.y));
new_idx = mesh->v_count;
for (j = 0; j < step_div_h; j++) {
SFVec3f n;
Fixed lon = 2 * GF_PI * j / step_div_h;
vx.pos.x = gf_mulfix(gf_sin(lon), r);
vx.pos.z = gf_mulfix(gf_cos(lon), r);
n = gf_vec_scale(vx.pos, FIX_ONE /*-FIX_ONE*/);
gf_vec_norm(&n);
MESH_SET_NORMAL(vx, n);
mesh_set_vertex_vx(mesh, &vx);
if (j) {
if (i>1) {
mesh_set_triangle(mesh, last_idx+j, new_idx+j, new_idx+j-1);
mesh_set_triangle(mesh, last_idx+j, new_idx+j-1, last_idx+j-1);
} else {
mesh_set_triangle(mesh, 0, new_idx+j, new_idx+j-1);
}
}
}
if (i>1) {
mesh_set_triangle(mesh, last_idx, new_idx, new_idx+step_div_h-1);
mesh_set_triangle(mesh, last_idx, new_idx+step_div_h-1, last_idx+step_div_h-1);
} else {
mesh_set_triangle(mesh, 0, new_idx, new_idx+step_div_h-1);
}
last_idx = new_idx;
}
if (!ground_dome) {
new_idx = mesh->v_count;
vx.pos.x = vx.pos.z = 0;
vx.pos.y = -FIX_ONE;
vx.normal.x = vx.normal.z = 0;
vx.normal.y = MESH_NORMAL_UNIT;
mesh_set_vertex_vx(mesh, &vx);
for (j=1; j < step_div_h; j++) {
mesh_set_triangle(mesh, last_idx+j-1, last_idx+j, new_idx);
}
mesh_set_triangle(mesh, last_idx+step_div_h-1, last_idx, new_idx);
}
mesh->flags |= MESH_HAS_COLOR | MESH_NO_TEXTURE;
mesh_update_bounds(mesh);
}
