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ϕδΤۂઢͷ
ͳΊΒ͔͞ͷ
݄
!NBTIBCPX
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͜Μʹͪ
w !NBTIBCPX
w ιʔγϟϧ1-64ϑϩϯτΤϯυΤϯδχΞ
w લ৬ͰϑΥϯτͷΤϯδχΞΛ͍ͬͯͨ
w ࠓϕδΤۂઢʹ͍ͭͯޠΓ·͢
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w ͍Ζ͍ΖͳਤܗฤूπʔϧͰݟΔΞϨ
ϕδΤۂઢͬͯ
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w ਓؒʹͱͬͯίϯϐϡʔλʹͱͬͯѻ͍͍͢
w ϕΫλը૾ɾϑΥϯτɾඳը"1*ɾ$"%ͳͲͰར༻
w ͝ΖɺγτϩΤϯͷ1BVMEF$BTUFMKBVͱ
ϧϊʔͷ1JFSSF#É[JFS͕ಠཱʹ։ൃͨ͠Β͍͠
w ࠓճฏ໘্ͷ࣍ϕδΤۂઢΛલఏʹͯ͠͠·͢
ϕδΤۂઢ
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ֶతͳදݱ
w ࢝ɹ੍ޚऴɹͷͰఆٛ͞ΕΔ
w ύϥϝʔλΛͷൣғͰ
ಈ͔ͨ͠ͱ͖ͷي͕ɺ
ීஈΑ͘ݟΔϕδΤۂઢ
B(t) = (1 − t)3 p0
+ 3(1 − t)2t c0
+ 3(1 − t)t2 c1
+ t3 p1
p0
c0
, c1
p1
t [0,1]
p0
= B(0)
p1
= B(1)
c0
c1
B(0.6)
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༡ΔσϞ
w ϕδΤۂઢΛຊ༻ҙ͓͍ͯͨ͠ͷͰɺ৮ͬͯΈΔ
w IUUQTNBTIBCPXHJUIVCJPCF[JFSTNPPUIOFTT
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ࠓճͷςʔϚ
w ϕδΤۂઢͱϕδΤۂઢΛͳΊΒ͔ʹͭͳ͍͛ͨʂ
w ׳Ε͍ͯͳ͍ͱҙ֎ͱΉ͔͍ͣ͠
w ͳΊΒ͔ʹͱ
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·ͣͦͦ
w ͭͷϕδΤۂઢΛͭͳ͛Δඞཁ͕͋Δ
w ۂઢ"ͷऴͱɺۂઢ#ͷ࢝ΛҰகͤ͞Δʢ؆୯ʣ
w ɹ࿈ଓʢҐஔ࿈ଓʣͱ͍͏
G0
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Ͱ·ͩંΕ͍ͯΔ
w ࣍ɺͭͳ͛ͨ෦ͷ͖Λἧ͑Δඞཁ͕͋Γͦ͏
w ۂઢͷ͖ͱʁˠઢͷ͖
w ܭࢉͰٻΊΔͷͰ͋Εɺඍ͢ΕΑ͍
B′(t) = (−3t2 + 6t − 3) p0
+ (9t2 − 12t + 3) c0
+ (−9t2 + 6t) c1
+ 3t2 p1
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ઢͱϋϯυϧ
w ࣮ɺ࢝ʗऴʹ͓͚Δઢͷ͖ɺ
ϋϯυϧͷ͖ͱҰக͍ͯ͠Δ
w ɹɹΛܭࢉͯ͠ΈΔͱΘ͔Δ
B′(0) B′(1)
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͖Λἧ͑Δ
w ۂઢ"
#ͷϋϯυϧΛҰઢʹฒΕΑ͍
w ࠓճ୯७ʹɺۂઢ#ͷϋϯυϧͷ֯Λม͑ͯௐ
w ɹ࿈ଓʢઢ࿈ଓʣͱ͍͏
G1
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Ͱ·ͩෆࣗવ
w ۂ͕Γ۩߹͕ҧ͏Α͏ͳʜʁ
w ۂ͕Γ۩߹ͱ
͜͜ΒΜͰٸʹ
ઢͬΆ͘ͳͬͯ
ϋϦ͕ͳ͘ͳͬͨΑ͏ͳ
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৮ԁ
w ۂઢҰൠͩͱΑ͘Θ͔Βͳ͍ͷͰɺۙͳԁͰߟ͑ͯΈΔ
w ۂઢͷ͘͝Ұ෦͚ͩʹͯ͠ɺԁހͰۙࣅ͢Δ
w ͦͷۃݶͷԁΛ৮ԁͱ͍͏
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R
w ৮ԁͷେ͖͞Ͱۂ͕Γ۩߹͕දݱͰ͖ͦ͏
w ৮ԁͷܘΛۂܘͱݺͿ
w ۂܘ͕େ͖͍˱Χʔϒ͕ΏΔ͍
w ۂܘ͕খ͍͞˱Χʔϒ͕͖͍ͭ
w ٸΧʔϒҙͷඪࣝʹ
ॻ͍ͯ͋ͬͨΓ͢Δ
ۂܘ
R
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ۂܘͷܭࢉ
w Ұൠͷύϥϝʔλۂઢͷۂܘɺ࣍ࣜͰܭࢉͰ͖Δ
w ͨͩ͠ɺμογϡύϥϝʔλɹʹΑΔඍΛද͢
w ͜ͷࣜͰग़ͯ͘Δۂܘූ߸͖
w ਖ਼ͳΒࠨճΓɺෛͳΒӈճΓ
R =
(x′2 + y′2
)
3
2
x′y′′− y′x′′
t
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෦ͷۂܘ
w ۂܘ͕ͥΜͥΜҧ͏
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ۂ
w ۂܘͷٯɹɹΛۂɹͱ͍͏
w ۂܘ͕େ͖͍˱ۂ͕খ͍͞˱Χʔϒ͕ΏΔ͍
w ۂܘ͕খ͍͞˱ۂ͕େ͖͍˱Χʔϒ͕͖͍ͭ
w ͬͪ͜ͷํ͕Θ͔Γ͍͢ʁ
1/R κ
ۂେ
ۂখ
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ۂͷࢹ֮Խ
w DVSWBUVSFDPNCʢۂͷᷱʁʣ
w ֤ʹ͓͚ΔۂΛɺ๏ઢํʹදࣔͨ͠ͷ
w $"%ιϑτϑΥϯτΤσΟλʹࡌ͞Ε͍ͯΔ
ۂେ
ۂখ
มۂ
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෦ͷۂͷᷱ
w ۂͷҧ͍͕Ұྎવ
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ۂΛἧ͑Δ
w ΄Ͳ୯७Ͱͳ͍͕ɺܭࢉͰͳΜͱ͔Ͱ͖Δ
w ࠓճɺۂઢ#ͷϋϯυϧͷ͞Λม͑ͯௐ
w ɹ࿈ଓʢۂ࿈ଓʣͱ͍͏
G2
G0, G1
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ϏϑΥʔΞϑλʔ
w ͗ͪ͜ͳ͕͞ݮͬͯɺΑΓͳΊΒ͔ʹͳͬͨ
☺
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·ͱΊ
w ϕδΤۂઢɾઢɾۂ͋ͨΓΛͬ͘͟Γઆ໌ͨ͠
w ɹɹɹɹɹ࿈ଓੑΛຬͨ͢Α͏ʹௐ͢Δ͜ͱͰɺ
ϕδΤۂઢ͕ͳΊΒ͔ʹͳͬͨ
w Ϣʔβʔʹͱͬͯɺ
ࢹ֮Խ͕େ͖ͳख͕͔ΓʹͳΔ
G0, G1, G2
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͜ͷઌͷτϐοΫ
w ɹ࿈ଓɺ͋Δ͍ͦΕҎ্ʁ
w ɹ࿈ଓͳΒͯ͢ਓؒͷݟͨʹඒ͍͠ʁ
w ࢥ͍ඳ͍͍ͯΔܗΛͳΔ่ͣ͘͞ʹௐ͢Δʹʁ
w ΫϩιΠυۂઢʢผ໊ɿΦΠϥʔཐટɺ4QJSPʣ
G3
Gn