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円と円の交点の求め方
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Sho Iizuka
June 13, 2014
Science
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42
円と円の交点の求め方
https://www.slideshare.net/kujira16/ss-35835784
Sho Iizuka
June 13, 2014
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Transcript
ԁͱԁͷަͷٻΊํ !TIPSB@LVKJSB
w *$1$ͷϥΠϒϥϦΛඋ͍ͯͨ͠Β ʮԁͱԁͷަʯͷίʔυ͕Α͔͘Βͳ͔ͬͨͷ Ͱղઆ͠·͢ɻ w ࢀߟʹͨ͠ίʔυίϨͰ͢
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)); }
double d = abs(c1.p - c2.p); d c1.p c2.p
double rc = (d*d + c1.r*c1.r - c2.r*c2.r) / (2*d);
cos = a2+b2 c2 2ab ༨ݭఆཧ b c a θ
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
double rs = sqrt(c1.r*c1.r - rc*rc); c1.r rc rs
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
c1.p + diff * P(rc, rs) ͘ͳΔͷͰ࣍ͷϖʔδϔ rc rs c1.p
diff * P(rc, rs) ͱʁ => 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 )
c1.p + diff * P(rc, -rs) ઌ΄Ͳͱಉ༷ rc rs c1.p
ײ w ༨ݭఆཧศརͳΜ͚ͩͲɺΑ͘ΕΔ w KΛֻ͚ͯճసͤ͞ΔςΫχοΫʹؾͮ͘ͷʹ࣌ ͕͔͔ؒͬͯ͠·ͬͨʢిؾܥͳΒৗతʹͬͯ ͍Δͣͳͷʹʣ