std::pair< T, T > intersection( const ray<T,2u>& ray, const circle<T>& circle )
{
// check for no intersection
const T a = dot( ray.direction(), ray.direction() );
const T b = T(2.) * sum( ray.direction() * ( ray.source() - circle.center() ) );
const T c = dot( circle.center(), circle.center() )
+ dot( ray.source(), ray.source() )
- T(2.) * dot( ray.source(), circle.center() )
- sqr( circle.radius() );
return solve_quadratic_equation(a,b,c);
}
//圆与圆切线 a[],b[],存放对应切线的切点
int gettangentcc(circle c1,circle c2,pt *a,pt *b){
int cnt=0;
if (c1.r<c2.r){swap(c1,c2);swap(a,b);}
double d2=length(c1.p-c2.p);
double rdiff=c1.r-c2.r;
double rsum=c1.r+c2.r;
if (dcmp(d2-rdiff)<0) return 0;//内含，无切线
double base=atan2(c1.p.y-c2.p.y,c1.p.x-c2.p.x);
if (dcmp(d2)==0&&c1.r==c2.r) return -1;//重合 无数条切线
if (dcmp(d2-rdiff)==0){//内切，一条切线
a[cnt]=c1.getpt(base);b[cnt]=c2.getpt(base);cnt++;
return 1;
}
//求外切线
double ang=acos((c1.r-c2.r)/d2);
a[cnt]=c1.getpt(base+ang);b[cnt]=c2.getpt(base+ang);cnt++;
a[cnt]=c1.getpt(base-ang);b[cnt]=c2.getpt(base-ang);cnt++;
if (dcmp(d2-rsum)==0){//两圆外切，一条内切线
a[cnt]=c1.getpt(base);b[cnt]=c2.getpt(pi+base);cnt++;
}
else if (dcmp(d2-rsum)>0){//两圆相离，两条内切线
ang=acos((c1.r+c2.r)/d2);
a[cnt]=c1.getpt(base+ang);b[cnt]=c2.getpt(pi+base+ang);cnt++;
a[cnt]=c1.getpt(base-ang);b[cnt]=c2.getpt(pi+base-ang);cnt++;
}
return cnt;
}
//两圆交点
int cinsc(circle c1,circle c2,vector<pt> &sol){
double d=length(c1.p-c2.p);
if (dcmp(d)==0){
if (dcmp(c1.r-c2.r)==0) return -1;//重合
return 0;//包含
}
if (dcmp(c1.r+c2.r-d)<0) return 0;
if (dcmp(fabs(c1.r-c2.r)-d)>0) return 0;
double a=atan2(c1.p.y-c2.p.y,c1.p.x-c2.p.x);
double da=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
pt p1=c1.getpt(a-da),p2=c1.getpt(a+da);
sol.push_back(p1);
if (p1==p2) return 1;
sol.push_back(p2);
return 2;
}
std::tuple<bool, float, int> line::intersect(const circle& circle) const {
std::tuple<bool, float, int> best = std::make_tuple(false, 0.0f, 0);
for(int i = 0; i < 8; ++i) {
auto res = std::tuple_cat(intersect(circle.getLineSegment(i)), std::make_tuple(i));
if (std::get<0>(best) == false) {
best = res;
} else if (std::get<1>(best) > std::get<1>(res)) {
best = res;
}
}
return best;
}
vector<pair<point, point> > tanCC(const circle &cir1, const circle &cir2) {
// `注意: 如果只有三条切线, 即 $s1 = 1, s2 = 1$, 返回的切线可能重复, 切点没有问题`
vector<pair<point, point> > list;
if (cir1.contain(cir2) || cir2.contain(cir1)) return list;
const point &c1 = cir1.o, &c2 = cir2.o;
double r1 = cir1.r, r2 = cir2.r;
point p, a1, b1, a2, b2; int s1, s2;
if (sign(r1 - r2) == 0) {
p = c2 - c1;
p = (p * (r1 / p.len())).rot90();
list.push_back(make_pair(c1 + p, c2 + p));
list.push_back(make_pair(c1 - p, c2 - p));
} else {
p = (c2 * r1 - c1 * r2) / (r1 - r2);
s1 = cir1.tanCP(p, a1, b1);
s2 = cir2.tanCP(p, a2, b2);
if (s1 >= 1 && s2 >= 1) {
list.push_back(make_pair(a1, a2));
list.push_back(make_pair(b1, b2));
}
} p = (c1 * r2 + c2 * r1) / (r1 + r2);
s1 = cir1.tanCP(p, a1, b1);
s2 = cir2.tanCP(p, a2, b2);
if (s1 >= 1 && s2 >= 1) {
list.push_back(make_pair(a1, a2));
list.push_back(make_pair(b1, b2));
} return list;
}
void draw_indicator(canvas& cnv, circle cp, float val, color c)
{
constexpr float w_factor = 0.05; // relative width of the indicator
constexpr float h_factor = 0.2; // relative height of the indicator
using namespace radial_consts;
auto state = cnv.new_state();
auto center = cp.center();
cnv.translate({ center.x, center.y });
cnv.rotate(offset + (val * range));
float r = cp.radius * 0.85;
float ind_w = r * w_factor;
float ind_h = r * h_factor;
rect ind_r = { -ind_w, -ind_h, ind_w, ind_h };
ind_r = ind_r.move(0, r*0.6);
draw_indicator(cnv, ind_r, c);
}
/* static */ void compact::rotate_branch(
iterator it,
circle c,
double alpha)
{
assert(!rna_tree::is_leaf(it));
for (pre_post_order_iterator ch = pre_post_order_iterator(it, true); id(ch) <= id(it); ++ch)
{
if (!ch->inited_points())
continue;
double dist = distance(c.centre, ch->at(ch.label_index()).p);
c.p1 = ch->at(ch.label_index()).p;
c.p2 = move_point(c.centre, c.p2, dist);
ch->at(ch.label_index()).p = c.rotate(alpha);
}
}
void draw_radial_marks(canvas& cnv, circle cp, float size, color c)
{
using namespace radial_consts;
auto state = cnv.new_state();
auto center = cp.center();
constexpr auto num_divs = 50;
float div = range / num_divs;
auto const& theme = get_theme();
cnv.translate({ center.x, center.y });
cnv.stroke_style(theme.ticks_color);
for (int i = 0; i != num_divs+1; ++i)
{
float from = cp.radius;
if (i % (num_divs / 10))
{
// Minor ticks
from -= size / 4;
cnv.line_width(theme.minor_ticks_width);
cnv.stroke_style(c.level(theme.minor_ticks_level));
}
else
{
// Major ticks
cnv.line_width(theme.major_ticks_width);
cnv.stroke_style(c.level(theme.major_ticks_level));
}
float angle = offset + (M_PI / 2) + (i * div);
float sin_ = std::sin(angle);
float cos_ = std::cos(angle);
float to = cp.radius - (size / 2);
cnv.move_to({ from * cos_, from * sin_ });
cnv.line_to({ to * cos_, to * sin_ });
cnv.stroke();
}
}
void draw_radial_labels(
canvas& cnv
, circle cp
, float size
, float font_size
, std::string const labels[]
, std::size_t num_labels
)
{
if (num_labels < 2)
return; // Nothing to do
using namespace radial_consts;
auto state = cnv.new_state();
auto center = cp.center();
float div = range / (num_labels-1);
auto const& theme = get_theme();
cnv.translate({ center.x, center.y });
cnv.text_align(cnv.middle | cnv.center);
cnv.fill_style(theme.label_font_color);
cnv.font(
theme.label_font,
theme.label_font_size * font_size,
theme.label_style
);
for (int i = 0; i != num_labels; ++i)
{
float angle = offset + (M_PI / 2) + (i * div);
float sin_ = std::sin(angle);
float cos_ = std::cos(angle);
cnv.fill_text({ cp.radius * cos_, cp.radius * sin_ }, labels[i].c_str());
}
}
circle::circle(circle &old)
{
radius = old.getRadius();
color = old.getColor();
circle(radius, color);
}
inline bool operator() (const circle &a, const circle &b)
{
return a.highest(curt) < b.highest(curt);
}
double intersect(circle c, point a, point b){
if ( a == c.o || b == c.o ) {
// cout << "point same as center" << endl;
return 0.0;
}
if( signum( det(a,b) ) == 0 ) {
// cout << "area 0" << endl;
return 0.0;
}
a.x -= c.o.x, a.y -= c.o.y;
b.x -= c.o.x , b.y -= c.o.y;
c.o = point();
if (c.contains(b)) swap(a, b);
if (c.contains(a) && c.contains(b)) {
// cout << "sec1 ans : " << 0.5 * fabs(det(a, b)) << endl;
return 0.5 * fabs(det(a, b)); // 1. the area of the triangle
}
if (c.contains(a)) {
point p = intersect_cir_line(c, b, a);
// cout << "1 pt " << p.x << " " << p.y << endl;
//cout << "sec1 ans : " << 0.5 * ( fabs(det(a, p)) + fabs( c.r*c.r * angle(p, b) ) ) << endl;
return 0.5 * ( fabs(det(a, p)) + fabs( c.r*c.r * angle(p, b) ) ); // 2. one point inside
}
if ( point_to(c.o,a, b) >= c.r - EPS){
// cout << "section " << 3 << endl;
//cout << "sec3 ans : " << 0.5 * fabs(c.r*c.r * angle(a, b)) << endl;
return 0.5 * fabs(c.r*c.r * angle(a, b)); // 3. Both outside and line doesnt intersect
}
// 4. Both Outside & Line Intersects circle at 2 points
point p = intersect_cir_line(c, a, b);
point q = intersect_cir_line(c, b, a);
point prj = project( point(0,0) , a, b );
double totSector = fabs( c.r * c.r * angle(a,b) ) / 2;
double triangle = fabs( det(p,q) ) / 2;
double smallSector = fabs( c.r * c.r * angle(p,q) ) / 2;
if( onSegment( prj , a, b ) ) {
// cout << "sec4 ans: " << totSector - ( smallSector - triangle ) << endl;
// cout << "sec4 ans: " << totSector << endl;
return totSector - ( smallSector - triangle ) ;
}
// cout << "2 pts " << " (" << p.x << " " <<p.y << ") (" << q.x << " " << q.y <<")"<< endl;
// cout << p.x << " " << p.y << " " << q.x << " " << q.y << endl;
// cout << withA.x << " " << withA.y << " " << withB.x << " " << withB.y << endl;
// cout << "section " << 4 << endl;
// cout << "2 pts " << " (" << p.x << " " <<p.y << ") (" << q.x << " " << q.y <<")"<< endl;
// cout << angle(p,q) << endl;
// if( p == q ) {
//// cout << "here1" << endl;
// return 0.5 * fabs(c.r*c.r * angle(a, b));
// }
// cout << "here2" << endl;
// swap(p,q);
// cout << "2 pts " << " (" << p.x << " " <<p.y << ") (" << q.x << " " << q.y <<")"<< endl;
// cout << "angles: " << angle( a, p ) << " " << angle(q,b) << endl;
//cout << "sec4 ans : " << 0.5 * ( fabs(c.r*c.r*angle(a,p)) + fabs( det(p,q) ) + fabs(c.r*c.r*angle(q,b)) ) << endl;
// return 0.5 * ( fabs(c.r*c.r*angle(a,p)) + fabs( det(p,q) ) + fabs(c.r*c.r*angle(q,b)) ); // seems fine
// double totSector = fabs( c.r * c.r * angle(a,b) ) / 2;
// double triangle = fabs( det(p,q) ) / 2;
// double smallSector = fabs( c.r * c.r * angle(p,q) ) / 2;
//// cout << "sec4 ans: " << totSector - ( smallSector - triangle ) << endl;
// cout << "sec4 ans: " << totSector << endl;
return totSector ;
}
// Area
template<class T> inline pure T area(const circle<T>& a) { return M_PI * std::sqr(a.r()); }
