円と円の交点の求め方

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1. ԁͱԁͷަ఺ͷٻΊํ !TIPSB@LVKJSB
2. w *$1$ͷϥΠϒϥϦΛ੔උ͍ͯͨ͠Β
 ʮԁͱԁͷަ఺ʯͷίʔυ͕Α͘෼͔Βͳ͔ͬͨͷ Ͱղઆ͠·͢ɻ
   w ࢀߟʹͨ͠ίʔυ͸ίϨͰ͢
3. ໰୊ͷίʔυ pair<P, P> cc_cross(const C& c1, const C& c2) { double d = abs(c1.p - c2.p); double rc = (d*d + c1.r*c1.r - c2.r*c2.r) / (2*d); double rs = sqrt(c1.r*c1.r - rc*rc); P diff = (c2.p - c1.p) / d; return make_pair(c1.p + diff * P(rc, rs), c1.p + diff * P(rc, -rs)); }
4. double d = abs(c1.p - c2.p); d c1.p c2.p
5. double rc =
 (d*d + c1.r*c1.r - c2.r*c2.r) / (2*d); cos = a2+b2 c2 2ab ༨ݭఆཧ b c a θ
6. double rc =
 (d*d + c1.r*c1.r - c2.r*c2.r) / (2*d); b bcosθ θ cos = a2 + b2 c2 2ab b cos = a2 + b2 c2 2a
7. double rs = sqrt(c1.r*c1.r - rc*rc); c1.r rc rs
8. P diff = (c2.p - c1.p) / d;
 
 => diffは c1.p→c2.p の単位ベクトル d c1.p c2.p
9. c1.p + diff * P(rc, rs)
 ௕͘ͳΔͷͰ࣍ͷϖʔδϔ rc rs c1.p
10. diff * P(rc, rs) ͱ͸ʁ
 => rc*diff + rs*rot90(diff) ͷ͜ͱ di = (x + jy) rot90(di ) = rot90(x + jy) = y + jx di P(rc, rs) = (x + jy) · (rc + jrs ) = rc(x + jy) + rs( y + jx) = rc di + rs rot90(di )
11. c1.p + diff * P(rc, -rs)
 ઌ΄Ͳͱಉ༷ rc rs c1.p
12. ײ૝ w ༨ݭఆཧศརͳΜ͚ͩͲɺΑ͘๨ΕΔ
    w KΛֻ͚ͯ›ճసͤ͞ΔςΫχοΫʹؾͮ͘ͷʹ࣌ ͕͔͔ؒͬͯ͠·ͬͨʢిؾܥͳΒ೔ৗతʹ࢖ͬͯ ͍Δ͸ͣͳͷʹʣ