geometry/old/gmtr_005_circle_crossp.cpp

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• Last update: 2019-11-24 02:02:41+09:00

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// 直線 a1, a2 と円 C との交点

// Verified: AOJ CGL_7_D: Cross Points of a Circle and a Line

vector<Point> crossp_lc(Point a1, Point a2, Circle c) {
    vector<Point> ps;
    double r = c.second;
    Point ft = projection(a1, a2, c.first);
    if(!GEQ(r*r, norm(ft-c.first))) return ps;

    Point dir = sqrt(max(r*r - norm(ft-c.first), 0.0)) / abs(a2-a1) * (a2-a1);
    ps.push_back(ft + dir);
    if(!EQ(r*r, norm(ft-c.first))) ps.push_back(ft - dir);
    return ps;
}

// 円 x と円 y の交点

// Verified: AOJ CGL_7_E: Cross Points of Circles

vector<Point> crossp_cc(Circle x, Circle y) {
    vector<Point> ps;
    Point a = x.first, b = y.first;
    double ar = x.second, br = y.second;

    Point ab = b-a;
    double d = abs(ab);
    double crL = (norm(ab) + ar * ar - br * br) / (2 * d);
    if(EQ(d,0) || ar < abs(crL)) return ps;

    Point abN = ab * Point(0, sqrt(ar*ar - crL*crL) / d);
    Point cp = a + crL/d * ab;
    ps.push_back(cp + abN);
    if(!EQ(norm(abN), 0)) ps.push_back(cp - abN);
    return ps;
}

#line 1 "geometry/old/gmtr_005_circle_crossp.cpp"
// 直線 a1, a2 と円 C との交点

// Verified: AOJ CGL_7_D: Cross Points of a Circle and a Line

vector<Point> crossp_lc(Point a1, Point a2, Circle c) {
    vector<Point> ps;
    double r = c.second;
    Point ft = projection(a1, a2, c.first);
    if(!GEQ(r*r, norm(ft-c.first))) return ps;

    Point dir = sqrt(max(r*r - norm(ft-c.first), 0.0)) / abs(a2-a1) * (a2-a1);
    ps.push_back(ft + dir);
    if(!EQ(r*r, norm(ft-c.first))) ps.push_back(ft - dir);
    return ps;
}

// 円 x と円 y の交点

// Verified: AOJ CGL_7_E: Cross Points of Circles

vector<Point> crossp_cc(Circle x, Circle y) {
    vector<Point> ps;
    Point a = x.first, b = y.first;
    double ar = x.second, br = y.second;

    Point ab = b-a;
    double d = abs(ab);
    double crL = (norm(ab) + ar * ar - br * br) / (2 * d);
    if(EQ(d,0) || ar < abs(crL)) return ps;

    Point abN = ab * Point(0, sqrt(ar*ar - crL*crL) / d);
    Point cp = a + crL/d * ab;
    ps.push_back(cp + abN);
    if(!EQ(norm(abN), 0)) ps.push_back(cp - abN);
    return ps;
}

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