ᚻᦠ߈ࠬࠤ࠶࠴౉ജࠗࡦ࠲ࡈࠚ࡯ࠬߦ߅ߌࠆᄙ㊀⸃௝ᐲࠣ࡝࠶࠼ ࠬ࠽࠶ࡇࡦࠣߩᔅⷐᕈᰞ੗ ዁᮸ၴਅ ⾆ᒄ⷏Ꮉ ⃍Ꮉᷝ ᣽ବ૒⾐ ⡡ੱቶ⯗Ꮏᬺᄢቇ ᖱႎᎿቇ⑼E-mail: {sakurai, doushita, akira, kawazoel}@sagalab.csse.muroran-it.ac.jp 㧘saga@csse.muroran-it.ac.jp1ߪߓ߼ߦᚒ‫ߪޘ‬ᣢߦ㧘ᚻᦠ߈ᦛ✢ࠍߘߩᒻ⁁ߣឬ↹േ૞ߩ޽޿߹޿ߐߦၮߠ޿ߡ㧘✢ಽ㧘౞㧘౞ᒐ㧘ᬦ౞㧘ᬦ౞ᒐ㧘㐽⥄↱ᦛ✢㧘㐿⥄↱ᦛ✢ߩ 7 ⒳ߩၮᧄᐞ૗ᦛ✢ߩ޿ߕࠇ߆(a) ⋡ᮡ࿑ᒻߣߒߡ⹺⼂ߔࠆᚻᴺ FSCI ࠍᢥ₂ [1] ߢឭ᩺ߒߚ㧚߹ߚ㧘
ᢥ₂ [2] ߢߪ㧘FSCI ߣන⚐ߥࠣ࡝࠶࠼ ࠬ࠽࠶ࡇࡦࠣࠍ⚵(b) FSCI ߦࠃߞߡ⹺⼂ߐࠇߚᐞ૗ᦛ✢೉ߺวࠊߖࠆߎߣߢ㧘CAD ↪ߩᚻᦠ߈ࠬࠤ࠶࠴౉ജࠗࡦ࠲
ࡈࠚ࡯ࠬ SKIT ࠍ⹜૞ߒߚ㧚ߒ߆ߒߥ߇ࠄ㧘ߎߩࠃ߁ߥࠬࠤ࠶࠴౉ജࠗࡦ࠲ࡈࠚ࡯ࠬߢߪ㧘ឬ↹ߒࠃ߁ߣߔࠆᒻ⁁ߥߤߦᔕߓߡߘߩㇺᐲㆡಾߥࠣ࡝࠶࠼ ⸃௝ᐲߦ⸳ቯߒߥ޿ߣ㧘੍ᦼߒߥ޿ࠬ࠽࠶ࡇࡦࠣ⚿ᨐߣߥߞߡߒ߹߁໧(c) ૐ⸃௝ᐲߩ SGS ߢߩࠬ࠽࠶ (d) 㜞⸃௝ᐲߩ SGS ߢߩࠬ࠽࠶ࡇࡦࠣ⚿ᨐࡇࡦࠣ⚿ᨐ㗴߇޽ߞߚ㧚ߘߎߢᚒ‫ߪޘ‬㧘ឬ↹േ૞ߩ⁁ᴫߦᔕߓߡേ

࿑ 1: ࠣ࡝࠶࠼ ⸃௝ᐲߦࠃࠆࠬ࠽࠶ࡇࡦࠣߩ㆑޿⊛ߦࠬ࠽࠶ࡇࡦࠣߔࠆࠣ࡝࠶࠼ ⸃௝ᐲࠍㆬᛯߔࠆᚻᴺߣߒߡ㧘MFGS 㧔 Multi-resolution Fuzzy Grid Snapping 㧕
ࠍᢥ₂ [3, 4] ߢឭ᩺ߒߚ㧚ᧄ⊒⴫ߢߪ㧘MFGS ࠍታⵝߔGradeࠆ SKIT ࠍታ⃻ߒ 㧘ᚻᦠ߈ࠬࠤ࠶࠴౉ജࠗࡦ࠲ࡈࠚ࡯ࠬ1µߦ߅ߌࠆᄙ㊀⸃௝ᐲࠣ࡝࠶࠼ ࠬ࠽࠶ࡇࡦࠣߩᔅⷐᕈࠍ࠺ࡕࡦࠬ࠻࡟࡯࡚ࠪࡦߦࠃߞߡ᣿ࠄ߆ߦߔࠆ㧚2ᚻᦠ߈ࠬࠤ࠶࠴౉ജࠗࡦ࠲ࡈࠚ࡯ࠬߦ߅ߌࠆන⸃௝ᐲࠣ࡝࠶࠼ ࠬ࠽࠶ࡇࡦࠣߩ໧㗴ᓥ᧪ߩ SKIT ߢߪ㧘FSCI ߦࠃߞߡ⹺⼂ߐࠇߚᐞ૗ᦛ✢ߩ․ᓽὐࠍන⚐ߦන⸃௝ᐲࠣ࡝࠶࠼ ߦࠬ࠽࠶ࡇࡦࠣߔࠆߎߣߢࠣ࡝࠶࠼ ࠬ࠽࠶ࡇࡦࠣࠍታ⃻ߒߡ޿ߚ㧚ᧄⓂߢߪ
ߎࠇࠍ MFGS ߣ඙೎ߔࠆߚ߼ߦ SGS㧔 Single-resolution

Grid Snapping 㧕ߣ๭߱ߎߣߦߔࠆ㧚ߎߩ SGS ࠍታⵝߒߚ SKIT ߪࠣ࡝࠶࠼ ⸃௝ᐲ߇ឬ↹ߩ⁁ᴫߦㆡวߒߡ޿ࠇ߫⦟ᅢߦേ૞ߔࠆ߇㧘ߘ߁ߢߪߥ޿ߣ࡙࡯ࠩߩᗧ࿑ߣߪ

g̃2p̃

yp rpc̃ g̃1g̃3x
࿑ 2: ࡈࠔࠫࠖὐߩ ‫ ޓ‬࿑ 3: ࡈࠔࠫࠖឬ↹ὐ c̃ ߣࡈࠔࠫࠖࠣࡔࡦࡃࠪ࠶ࡊ㑐ᢙ࡝࠶࠼ ὐ g̃1 , g̃2 , g̃3 ߩ૏⟎㑐ଥߩ଀0૞ߔࠆ৻⥸⊛ߥ CAD ࠗࡦ࠲ࡈࠚ࡯ࠬߢ޽ࠇ߫㧘ߘߩㇺᐲࠣ࡝࠶࠼ ⸃௝ᐲࠍ੐೨ߦಾࠅᦧ߃ࠇ߫ࠃ޿㧚ߒ߆ߒ 㧘৻ᕷߩࠬ࠻ࡠ࡯ࠢߢⶄᢙߩᐞ૗ᦛ✢ࠍ৻ᐲߦ౉ജߔࠆߎߣߩߢ߈ࠆᚻᦠ߈ࠬࠤ࠶࠴౉ജࠗࡦ࠲ࡈࠚ࡯ࠬߩ․㐳ࠍᵴ߆ߔߚ߼ߦߪ㧘ೞ‫ߣޘ‬ᄌൻߔࠆឬ↹ߩ⁁ᴫߦᔕߓߡㆡวߔࠆࠣ࡝࠶࠼ ⸃௝ᐲࠍേ⊛ߦㆬᛯߔࠆᯏ᭴߇ᔅⷐߣߥࠆ㧚⇣ߥߞߚࠬ࠽࠶ࡇࡦࠣ⚿ᨐߣߥߞߡߒ߹߁໧㗴߇޽ߞߚ㧚

MFGS ߦࠃࠆࡈࠔࠫ ࠖὐߩᄙ㊀⸃௝ᐲࠣ࡝࠶࠼ ࠬ࠽࠶ࡇࡦࠣߚߣ߃߫㧘࡙࡯ࠩ߇࿑ 1(a) ߩࠃ߁ߥ࿑ᒻࠍ౉ജߒࠃ߁

ᢥ₂ [3] ߢឭ᩺ߐࠇߚ MFGS ߪࠣ࡝࠶࠼ ⸃௝ᐲߩേ⊛3ߣࠬࠤ࠶࠴౉ജࠍⴕ޿㧘FSCI ߇࿑ 1(b) ߩࠃ߁ߦᐞ૗ᦛㆬᛯࠍታ⃻ߔࠆᄙ㊀⸃௝ᐲࠬ࠽࠶ࡇࡦࠣᴺߢ޽ࠆ㧚ߎࠇ✢೉ࠍ⹺⼂ߒߚߣߔࠆ㧚ߎࠇࠍૐ⸃௝ᐲߩ SGS ߢࠬ࠽࠶ߪ㧘㔀ߥឬ↹߆ࠄ↢ᚑߐࠇࠆឬ↹ὐ߶ߤૐ⸃௝ᐲߩࠣ࡝࠶

ࡇࡦࠣߔࠆߣ࿑ 1(c) ߩࠃ߁ߦᄢ߈ߊᄌᒻߒߡߒ߹߁㧚৻࠼ ߦ㧘ৼካߥឬ↹߆ࠄ↢ᚑߐࠇࠆឬ↹ὐ߶ߤ 㜞⸃௝ᐲߩᣇ㧘㜞⸃௝ᐲߩ SGS ߢࠬ࠽࠶ࡇࡦࠣߔࠆߣ࿑ 1(d) ߩࠃࠣ࡝࠶࠼ ߦࠬ࠽࠶ࡇࡦࠣߔࠆߣ޿߁ᚢ⇛ࠍ↪޿ࠆߎߣߢ߁ߦឬ↹ߒࠃ߁ߣߒߚ߽ߩ߆ࠄᓸᅱߦߕࠇߡߒ߹߁㧚ࠣ࡝࠶࠼ ⸃௝ᐲߩേ⊛ㆬᛯࠍታ⃻ߒߡ޿ࠆ㧚ࡐࠗࡦ࠹ࠖࡦࠣ߿࠼ ࡜࠶ࠡࡦࠣߢᐞ૗ᦛ✢ࠍ୘೎ߦᠲ

MFGS ߢߪછᗧߩឬ↹ὐࠍ㧘㔀ߥឬ↹߇ⴕࠊࠇߡ޿ࠆ

Essentiality of Multi-Resolution Grid Snapping in Sketch-BasedDrawing Interface. Masaki Sakurai, Takahiro Doushita, Akira
Nishikawa, Masatoshi Kawazoe, Sato Saga, Muroran Institute ofTechnology.

ߣ߈߶ߤ ᄢ߈ߥࡈࠔࠫࡀࠬࠍ᦭ߔࠆࡈࠔࠫࠖὐ㧔 ࿑ 2 ෳᾖ㧚rp ߇ࡈࠔࠫࡀࠬ㧘ߔߥࠊߜ૏⟎⊛޽޿߹޿ߐߩᐲว޿ࠍ⴫ߔ㧚㧕ߢ㧘ㅒߦৼካߥឬ↹߇ⴕࠊࠇߡ޿ࠆߣ߈߶ߤ

(a) ✢ಽ(b) ౞ᒐ(c) ᬦ౞ᒐ(d) ⥄↱ᦛ✢

࿑ 4: ઒⺑ࡈࠔࠫࠖࡕ࠺࡞ߣߘߩ․ᓽࡈࠔࠫࠖὐߩ଀
ዊߐߥࡈࠔࠫࡀࠬࠍ᦭ߔࠆࡈࠔࠫࠖὐߢ⴫⃻ߔࠆ㧔 ࿑ 3(a) ౉ജࠬ࠻ࡠ࡯ࠢ⟲(b) FSCI ߦࠃߞߡ⹺⼂ߐࠇߚᐞ૗ᦛ✢೉(c) ૐ⸃௝ᐲߩ SGS ߢߩࠬ࠽࠶ࡇࡦࠣ⚿ᨐ(d) 㜞⸃௝ᐲߩ SGS ߢߩࠬ࠽࠶ࡇࡦࠣ⚿ᨐߩ c̃ ෳᾖ㧕㧚৻ᣇ㧘ᄙ㊀⸃௝ᐲࠣ࡝࠶࠼ߩࠣ࡝࠶࠼ ὐߦߟ޿ߡߪ㧘ૐ⸃௝ᐲߢ޽ࠆ߶ߤ ᄢ߈ߥࡈࠔࠫࡀࠬࠍ᦭ߔࠆࡈࠔࠫࠖὐ㧘㜞⸃௝ᐲߩࠣ࡝࠶࠼ߢ޽ࠆ߶ߤዊߐߥࡈࠔࠫ
ࡀࠬࠍ᦭ߔࠆࡈࠔࠫࠖὐߢ᭴ᚑߔࠆ㧔࿑ 3 ߩ g̃1 , g̃2 , g̃3 ෳᾖ㧕㧚ߘߩ਄ߢ㧘MFGS ߪ‫ ࠼࠶࡝ࠣࠖࠫࠔࡈޟ‬ὐ g̃1 , g̃2 , g̃3ߩਛߢ㧘ࡈࠔࠫࠖឬ↹ὐ c̃ ߦ฽߹ࠇࠆᔅὼᕈ߇ߥࠆߴߊ㜞ߊ㧘߆ߟࠣ ࡝࠶࠼ ⸃௝ᐲߩߥࠆߴߊૐ޿߽ߩࠍࠬ࠽࠶ࡇࡦࠣవߣߒߡㆬᛯߔࠆ‫ࠖࠫࠔࡈ߁޿ߣޠ‬ផ⺰ࠍⴕ߁ߎߣߢ㧘਄ㅀߩᚢ⇛ߦၮߠߊࠬ࠽࠶ࡇࡦࠣࠣ࡝࠶࠼ ⸃௝ᐲߩേ⊛ㆬᛯࠍታ⃻ߒߡ޿ࠆ㧚4(e) MFGS ߢߩࠬ࠽࠶ࡇࡦࠣ⚿ᨐ࿑ 5: MFGS ࠍታⵝߒߚ SKIT ߢߩ૞࿑଀

MFGS ࠍታⵝߔࠆ SKIT ߩታ⃻
2 ▵ߢㅀߴߚ SGS ߩ໧㗴ὐࠍ⸃᳿ߔࠆߚ߼ߦ㧘SKIT ߦߓߡߒ߹߁㧚ߒ߆ߒ 㧘࿑ 5(e) ߦ␜ߔࠃ߁ߦ MFGS ࠍ↪

߅ߌࠆᐞ૗ᦛ✢ࠬ࠽࠶ࡇࡦࠣߦ MFGS ࠍㆡ↪ߔࠆ㧚FSCI޿ࠆߎߣߢ㧘ᐞ૗ᦛ✢೉߇ឬ↹ߩ⁁ᴫߦᔕߓߡㆡಾߥࠣౝㇱߢߪᚻᦠ߈ᦛ✢ߪ࿑ 4 ߩࠃ߁ߥࡈࠔࠫࠖὐ߆ࠄ᭴ᚑ࡝࠶࠼ ⸃௝ᐲߦࠬ࠽࠶ࡇࡦࠣߐࠇࠆ㧚ߐࠇࠆᐞ૗ᦛ✢ߣߒߡ⹺⼂ߐࠇ㧘ߘࠇࠄߩ․ᓽὐ㧔 ࿑ 46✂ដߌㇱ㧕߽ࡈࠔࠫࠖὐߣߒߡᓧࠄࠇࠆ㧚ߎߎߢ㧘ߎࠇࠄߩࡈࠔࠫࠖὐߪឬ↹േ૞ߩৼካߐߩ⒟ᐲߦᔕߓߡ㔀ߥ߶ߤ ᄢ߈ߥࡈࠔࠫࡀࠬ㧘ৼካߥ߶ߤ ዊߐߥࡈࠔࠫࡀࠬ߇ਈ߃ࠄࠇࠆ㧚ߒߚ߇ߞߡ㧘ߎࠇࠄߩ․ᓽࡈࠔࠫࠖὐߦ 3▵ߩ MFGS ࠍㆡ↪ߔࠆߎߣߢ SKIT ߦ߅ߌࠆ MFGS ߦ߹ߣ߼MFGS ࠍታⵝߒߚ SKIT ࠗࡦ࠲ࡈࠚ࡯ࠬࠍታ⃻ߒ㧘ᚻᦠ߈ࠬࠤ࠶࠴౉ജࠗࡦ࠲ࡈࠚ࡯ࠬߦ߅ߌࠆᄙ㊀⸃௝ᐲࠣ࡝࠶࠼ ࠬ࠽࠶ࡇࡦࠣߩᔅⷐᕈࠍ᣿ࠄ߆ߦߒߚ㧚⻢ㄉࠃࠆᐞ૗ᦛ✢ࠬ࠽࠶ࡇࡦࠣࠍታ⃻ߔࠆ㧚ߎߩߎߣߦࠃࠅ㧘ᧄ⎇ⓥߪ⑼ቇ⎇ⓥ⾌⵬ഥ㊄㧔 ⺖㗴⇟ภ 18500095 㧕ߦࠃࠆ⎇ⓥᚑᨐߩ৻ㇱߢ޽ࠆ㧚৻ᕷߩࠬ࠻ࡠ࡯ࠢਛߢ߽㧘㔀ߥឬ↹ㇱಽ߆ࠄ⹺⼂ߐࠇߚෳ⠨ᢥ₂ᐞ૗ᦛ✢ߪૐ⸃௝ᐲࠣ࡝࠶࠼ ߦ㧘ৼካߥឬ↹ㇱಽ߆ࠄ⹺[1] ૒⾐⡡ੱ㧘’㊁ብ⟤㧘૒‫ᧁޘ‬ᷕ৻㧦ࡈࠔࠫ࡯ࠬࡊ࡜ࠗࡦᦛ✢หቯᴺ㧘
㔚ሶᖱႎㅢାቇળ⺰ᢥ⹹㧘 Vol. J77-D-II, No. 8, pp. 1620–1629(1994).

⼂ߐࠇߚᐞ૗ᦛ✢ߪ㜞⸃௝ᐲࠣ࡝࠶࠼ ߦࠬ࠽࠶ࡇࡦࠣߐࠇࠆߣ޿߁㧘ࠣ࡝࠶࠼ ⸃௝ᐲߩേ⊛ㆬᛯ߇ታ⃻ߐࠇࠆ㧚5േ૞ታ㛎

MFGS ࠍታⵝߒߚ SKIT ߢ૞࿑ࠍⴕߞߚ଀ࠍ࿑ 5 ߦ␜ߔ㧚࿑ 5(a) ߇࡙࡯ࠩߩᚻᦠ߈౉ജࠬ࠻ࡠ࡯ࠢ⟲㧘࿑
5(b) ߇ FSCI ߦࠃࠆᐞ૗ᦛ✢⹺⼂ߩ⚿ᨐߢ޽ࠆ㧚SGS ߢߪ㧘࿑ 5(c)㧘࿑ 5(d) ߦ␜ߔࠃ߁ߦ㧘ឬ↹ߩ⁁ᴫߦࠣ࡝࠶࠼ ⸃௝ᐲ߇ㆡวߒߡ޿ߥ޿ㇱಽߢᄌᒻ߿ᓸᅱߥߕࠇ߇↢[2] ᴡว⦟ᄥ㧘⷏Ꮉ ‫⃍ޓ‬㧘૒⾐⡡ੱ㧦ᚻᦠ߈ࠬࠤ࠶࠴౉ജࡈࡠࡦ࠻ࠛࡦ
࠼ࡊࡠ࠮࠶ࠨ:SKIT㧘㔚ሶᖱႎㅢାቇળ⺰ᢥ⹹㧘 Vol. J88-D-II,
No. 5, pp. 897–905 (2005).
[3] Khand, Q. U., Saga, S. and Maeda, J.: Automatic Cursor
Snapping into Multi-Resolution Grid Systems Based on Fuzzy
Model, Transactions of the Information Processing Society ofJapan, Vol. 45, No. 10, pp. 2439–2442 (2004).
[4] Dematapitiya, S., Kawazoe, M., Khand, Q. U. and Saga,
S.: Object Snapping Method using Multi-Resolution Fuzzy
Grid Snapping Technique, Eurographics Workshop on SketchBased Interfaces and Modeling, pp. 9–18 (2005).