円と円の交点の求め方

https://www.slideshare.net/kujira16/ss-35835784

Transcript

1. ԁͱԁͷަ఺ͷٻΊํ
   !TIPSB@LVKJSB
   

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2. w *$1$ͷϥΠϒϥϦΛ੔උ͍ͯͨ͠Β

   ʮԁͱԁͷަ఺ʯͷίʔυ͕Α͘෼͔Βͳ͔ͬͨͷ
   Ͱղઆ͠·͢ɻ
   w ࢀߟʹͨ͠ίʔυ͸ίϨͰ͢
   

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3. ໰୊ͷίʔυ
   pair 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));
   }
   

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4. double d = abs(c1.p - c2.p);
   d
   c1.p
   c2.p
   

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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
   

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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
   

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7. double rs = sqrt(c1.r*c1.r - rc*rc);
   c1.r
   rc
   rs
   

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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
   

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9. c1.p + diff * P(rc, rs)

   ௕͘ͳΔͷͰ࣍ͷϖʔδϔ
   rc
   rs
   c1.p
   

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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 )
    

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11. c1.p + diff * P(rc, -rs)

    ઌ΄Ͳͱಉ༷
    rc
    rs
    c1.p
    

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12. ײ૝
    w ༨ݭఆཧศརͳΜ͚ͩͲɺΑ͘๨ΕΔ
    w KΛֻ͚ͯ›ճసͤ͞ΔςΫχοΫʹؾͮ͘ͷʹ࣌
    ͕͔͔ؒͬͯ͠·ͬͨʢిؾܥͳΒ೔ৗతʹ࢖ͬͯ
    ͍Δ͸ͣͳͷʹʣ
    

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