JAIST Repository: プレゼンテーションのための物理エンジンを搭載したアニメーションツールの開発

JAIST Repository

Type Research Paper Text version publisher

URL http://hdl.handle.net/10119/5114 Rights

Description 北陸先端科学技術大学院大学 21世紀COE プログラム 「知識科学に基づく科学技術の創造と実践」

䝥䝺䝊䞁䝔䞊䝅䝵䞁䛾䛯䜑䛾≀⌮䜶䞁䝆䞁䜢ᦚ㍕䛧䛯䜰䝙䝯䞊䝅䝵䞁䝒䞊䝹䛾㛤Ⓨ㻌

㧗ᶫ㻌 ㄔྐ䈂㻌 ୰᳃㻌 ⩏㍤䈂㻌 ᐑ⏣㻌 ୍஌䈃 䈂໭㝣ඛ➃⛉Ꮫᢏ⾡኱Ꮫ㝔኱Ꮫ㻌 ▱㆑⛉Ꮫ◊✲⛉ 䈃໭㝣ඛ➃⛉Ꮫᢏ⾡኱Ꮫ㝔኱Ꮫ㻌 ▱㆑⛉Ꮫᩍ⫱䝉䞁䝍䞊

E-mail: {masa-t, nakamori, miyata}@jaist.ac.jp

1. 䛿䛨䜑䛻 㻌 䝁䞁䝢䝳䞊䝍䜢⏝䛔䛯䝥䝺䝊䞁䝔䞊䝅䝵䞁䛻䛚䛔䛶䜰䝙 䝯䞊䝅䝵䞁䛾฼⏝䛿䠈⫈⾗䛾⌮ゎᗘ䜢㧗䜑䜛ຠᯝ䛜䛒䜛䠊 PowerPoint䛺䛹䛾䝥䝺䝊䞁䝔䞊䝅䝵䞁䝋䝣䝖䛻䛿䠈䛭䛾䛯 䜑䛾ᶵ⬟䛜ᦚ㍕䛥䜜䛶䛚䜚䠈䝥䝺䝊䞁䝔䞊䝅䝵䞁䝇䝷䜲䝗 䛻䜰䝙䝯䞊䝅䝵䞁䜢㏣ຍ䛩䜛䛣䛸䛜ฟ᮶䜛䠊䛧䛛䛧䠈䝥䝺 䝊䞁䝔䞊䝅䝵䞁䝋䝣䝖䛻௜ᒓ䛩䜛䜰䝙䝯䞊䝅䝵䞁ᶵ⬟䛿䠈 䜰䝙䝯䞊䝅䝵䞁⏕ᡂ䝒䞊䝹䛸䛧䛶䛿䠈ᶵ⬟ⓗ䛻㈋ᙅ䛷䛒 䜛䠊≉䛻䠈」㞧䛺ື䛝䛾ᐃ⩏䜔ᥥ⏬䜸䝤䝆䜵䜽䝖䛜ከ䛔 ሙྜ䛾సᴗຠ⋡䛜ᝏ䛟⾲⌧⬟ຊ䜒㧗䛔䛸䛿ゝ䛘䛺䛔䠊 䛣䛖䛧䛯䛣䛸䛛䜙䠈ᙉຊ䛺ᶵ⬟䜢ᣢ䛴䜰䝙䝯䞊䝅䝵䞁〇స 䝋䝣䝖䜴䜵䜰䜢ู㏵฼⏝䛧䠈ື⏬䝣䜯䜲䝹䜢సᡂ䛧䛶䝇䝷 䜲䝗䛻㈞䜚௜䛡䜛䛣䛸䛜ከ䛔䠊䛣䛾ሙྜ䠈䝥䝺䝊䞁䝔䞊䝅 䝵䞁䝋䝣䝖䛻௜ᒓ䛩䜛䜰䝙䝯䞊䝅䝵䞁䛾⾲⌧⬟ຊ䜢㉸䛘䛯 䜒䛾䜢ᐜ᫆䛻స䜛䛣䛸䛜ྍ⬟䛷䛒䜛䠊䛧䛛䛧䠈ື⏬䝣䜯䜲 䝹䛿䝥䝺䝊䞁䝔䞊䝅䝵䞁䛾ᛶ㉁䛻䜘䛳䛶䛿ྥ䛛䛺䛔ሙྜ 䛜䛒䜛䠊䝥䝺䝊䞁䝔䞊䝅䝵䞁䛷䛿䠈ㅮ₇⪅䛾ヰ䛻ᛂ䛨䛶 䜰䝙䝯䞊䝅䝵䞁䜢䛣䜎䜑䛻䝇䝔䝑䝥䛤䛸䛻ᐇ⾜䛩䜛䜘䛖䛺 ぢ䛫᪉䜢䛩䜛ሙྜ䛜䛒䜛䠊䛣䛖䛧䛯ሙ㠃䛷䛿䠈䝥䝺䝊䞁 䝔䞊䝅䝵䞁䝋䝣䝖䛻ᦚ㍕䛥䜜䛯䜰䝙䝯䞊䝅䝵䞁ᶵ⬟䛿䠈䝬 䜴䝇䛾䜽䝸䝑䜽䛺䛹䛻ᛂ䛨䛯෌⏕䜔೵Ṇ䛺䛹䛜䜰䝙䝯䞊䝅 䝵䞁䛾䝇䝔䝑䝥䛤䛸䛻タᐃ䛜ฟ᮶䜛䛜䠈ື⏬䝣䜯䜲䝹䛿᫬ ⣔ิ䛷ᐇ⾜䛥䜜䜛䛯䜑ពᅗ䛧䛯ሙᡤ䛷ṇ☜䛻Ṇ䜑䜛䛾 䛜㞴䛧䛔䠊䛩䛺䜟䛱䠈䝥䝺䝊䞁䝔䞊䝅䝵䞁䛷⏝䛔䜛䜰䝙䝯 䞊䝅䝵䞁䛻䛿䠈᧯స䛻ྜ䜟䛫䛶ືస䜢⣽䜔䛛䛻ᣦᐃ䛷 䛝䜛ᚲせᛶ䛜䛒䜛䠊 㻌 䝥䝺䝊䞁䝔䞊䝅䝵䞁䛾䜰䝙䝯䞊䝅䝵䞁䛿䠈ື⏬䝣䜯䜲䝹 䛾⏕ᡂ䛾䜘䛖䛻ᫎീ䜢䝥䝸䝺䞁䝎䝸䞁䜾䛩䜛䛾䛷䛿䛺䛟䠈 䝡䝕䜸䝀䞊䝮䛾䜘䛖䛺䝸䜰䝹䝍䜲䝮䛻䝺䞁䝎䝸䞁䜾䛩䜛᪉ 䛜㐺ษ䛷䛒䜛䛸⪃䛘䜛䠊ᮏ䝅䝇䝔䝮䛷䛿䠈3D 䝀䞊䝮䜶䞁 䝆䞁[1]䛾タィ䜢䝰䝕䝹䛻䠈䜰䝙䝯䞊䝅䝵䞁䛾ไᚚ䛻≀⌮ 䜶䞁䝆䞁䜢ᦚ㍕䛧䛯䝒䞊䝹䜢㛤Ⓨ䛧䛯䠊3D 䝀䞊䝮䜶䞁䝆 䞁䜢䝰䝕䝹䛸䛩䜛䛣䛸䛻䜘䛳䛶䠈䜰䝙䝯䞊䝅䝵䞁䛾〇స䛻 䛚䛔䛶௚䝒䞊䝹䛸䛾㐃ᦠᛶ䠈䝣䜯䜲䝹䛾ྍᦙᛶ䜢㧗䜑䛯䠊 ᮏ䝅䝇䝔䝮䛷䛿䠈䝸䜰䝹䝍䜲䝮䛾䝺䞁䝎䝸䞁䜾䜶䞁䝆䞁䛸 ≀⌮䜶䞁䝆䞁䜢⤌䜏㎸䜣䛰䝡䝳䞊䝽䜢 PowerPoint 䛻⤌ 䜏㎸䜏䠈᪤Ꮡ䛾䝥䝺䝊䞁䝔䞊䝅䝵䞁䝋䝣䝖䛛䜙฼⏝ྍ⬟ 䛻䛧䠈㧗ᗘ䛺䜰䝙䝯䞊䝅䝵䞁⾲⌧䜢䝥䝺䝊䞁䝔䞊䝅䝵䞁䛻 ⤌䜏㎸䜐䛣䛸䜢ྍ⬟䛸䛧䛯䠊 2. ⫼ᬒ 2.1 䝅䝇䝔䝮䛾䛽䜙䛔 㻌 㻌 ᮏ䝅䝇䝔䝮䛿䠈ึᚰ⪅䛾䛯䜑䛾䜰䝙䝯䞊䝅䝵䞁ไస䜢 ᨭ᥼䛩䜛䝅䝇䝔䝮䛷䛿䛺䛟䠈ᢏ⾡䝥䝺䝊䞁䝔䞊䝅䝵䞁䜔䠈 ᩘᏛ䞉⌮⛉ᩍ⫱䛺䛹䛾䝝䜲䜶䞁䝗䛺せồ䛻ᑐᛂ䛩䜛䝅䝇 䝔䝮䜢┠ᣦ䛧䛶䛔䜛䠊䛣䛖䛧䛯⏝㏵䛷䛿䠈䜰䝙䝯䞊䝅䝵䞁 䜢⏝䛔䛯ㄝ᫂䛿䠈㟼Ṇ⏬䜔ᩘᘧ䜘䜚䜒⫈⾗䛾⌮ゎ䜢኱ 䛝䛟ຓ䛡䜛䠊ᩘᏛ䜔⌮⛉䛾ᩍᮦ䛾䜘䛖䛺㢟ᮦ䛷䛿䠈ᩘᘧ 䛸䛔䛖䝰䝕䝹䛜䛒䜚䛺䛜䜙䜒䠈䜰䝙䝯䞊䝅䝵䞁䛾ไస䛿ᡭ ື䛻䜘䜛䜻䞊䝣䝺䞊䝮䝧䞊䝇䛷ไస䛩䜛䛣䛸䛜ከ䛔䠊ᮏ ◊✲䛷䛿䠈≀⌮䜶䞁䝆䞁䛻ຊᏛⓗ䛺ไᚚ䜢௵䛫䜛䛣䛸 䛷䠈ᡭ௜䛡䜰䝙䝯䞊䝅䝵䞁䛾సᴗ䜢ῶ䜙䛩䛣䛸䛜ฟ᮶䜛䛸 ⪃䛘䛯䠊 䛥䜙䛻䠈3D 䜾䝷䝣䜱䝑䜽䝇䛷ᥥ⏬䛥䜜䛯䜸䝤䝆䜵䜽䝖䛻ᑐ 䛧䛶䠈ᚑ᮶䛾䝥䝺䝊䞁䝔䞊䝅䝵䞁䝋䝣䝖䛾䝇䝷䜲䝗䜘䜚䜒䜲 䞁䝍䝷䜽䝔䜱䝤䛺᧯స䜢㏣ຍ䛩䜛䛣䛸䛷䠈䜘䜚⫈⾗䜢ច䛝 䛴䛡䜛䜰䝙䝯䞊䝅䝵䞁⾲⌧䛜䛷䛝䜛䜒䛾䛸⪃䛘䜛䠊ᮏ䝅䝇 䝔䝮䛷䛿䠈䝝䜲䜶䞁䝗䛺せồ䛻ᛂ䛘䜛䛯䜑䠈䠍䠅GPU 䜢౑ 䛳䛯䝸䜰䝹䝍䜲䝮䝺䞁䝎䝸䞁䜾䠈䠎䠅䝸䜰䝹䝍䜲䝮≀⌮䝅䝭䝳 䝺䞊䝅䝵䞁䜢⾜䛖≀⌮䜶䞁䝆䞁䛾ᦚ㍕䠈䠏䠅䜰䝙䝯䞊䝅䝵䞁 䛻ᑐ䛧䛶䜲䞁䝍䝷䜽䝔䜱䝤䛺ാ䛝䛛䛡䛜䛷䛝䜛ධຊฎ⌮䠈 䛾䠏䛴䛾ᶵ⬟䜢ᐇ⿦䛧䛯䠊

2.2 㛵㐃◊✲ 㻌 3D 䜾䝷䝣䜱䝑䜽䝇䜢⏝䛔䛯䝥䝺䝊䞁䝔䞊䝅䝵䞁ྥ䛡䛾ど ぬ⾲♧ᡭἲ䛾◊✲䛷䛿䠈➉ᮧ䜙[2]䛾◊✲䛜䛒䜛䠊➉ᮧ 䜙䛿䠈䝇䝷䜲䝗䜢䜎䛯䛠䜸䝤䝆䜵䜽䝖䜢 ID 䛷⟶⌮䛧䠈ྠ୍ 䛛䛹䛖䛛䜢ุู䛧䠈䝇䝷䜲䝗㛫䛾఩⨨䛾㑄⛣䜢⿵㛫䛩䜛 䝅䞊䝮䝺䝇䝖䝷䞁䝆䝅䝵䞁䛸䛔䛖ᡭἲ䜢ᥦ᱌䛧䛶䛔䜛䠊➉ ᮧ䜙䛾ᡭἲ䛿䠈prezvision[3]䛸䛔䛖䝥䝺䝊䞁䝔䞊䝅䝵䞁䝋 䝣䝖䛷฼⏝䛥䜜䛶䛔䜛䠊䛣䛾ᡭἲ䛷䛿䠈䝇䝷䜲䝗ไస⪅䛿 䜸䝤䝆䜵䜽䝖䛾ື䛝䜢⪃䛘䜛ୖ䛷䠈㑄⛣䛾๓ᚋ䜢⪃䛘䜜 䜀䜘䛔䠊䛣䛾ᡭἲ䛿䠈䜻䞊䝣䝺䞊䝮䝧䞊䝇䛾ᡭἲ䛷䛒䜛 䛜䠈⤒㦂๎䛻ᇶ䛵䛔䛯⊂⮬䛾䜸䝤䝆䜵䜽䝖䛾㆑ู䝹䞊 䝹䛷䠈ᣑᙇ䛥䜜䛯ᡭἲ䛷䛒䜛䠊ᮏᡭἲ䛷䛿䠈䛣䛾ᡭἲ䛸 ྠ䛨䛟 3D 䜾䝷䝣䜱䝑䜽䝇䜢⏝䛔䜛䛜䠈䜻䞊䝣䝺䞊䝮䝧䞊䝇 䛷䜸䝤䝆䜵䜽䝖䛾ື䛝䜢⪃䛘䜛䛾䛷䛿䠈ຊᏛ䝧䞊䝇䛷⪃ 䛘䜛䛾䛜␗䛺䜛䠊 㻌 ᩘᏛ䜔≀⌮ᩍ⫱䜢ຓ䛡䜛䜰䝙䝯䞊䝅䝵䞁䝒䞊䝹䛾◊✲ 䛸䛧䛶䠈Laviola 䜙䛾 MathPad2[4]䛜䛒䜛䠊䛣䛾◊✲䛷䛿䠈 䝨䞁䝍䝤䝺䝑䝖䜢⏝䛔䛶⏬㠃䛻グ㏙䛧䛯ᩘᏛ䜔≀⌮䛺䛹 䛾ᩘᘧ䜢ᡭ᭩䛝䛾ᅗ䜔⤮䛻㛵㐃௜䛡䛶䠈䜰䝙䝯䞊䝅䝵䞁 䛥䛫䜛䛣䛸䛜ฟ᮶䜛䠊䛣䜜䛻䜘䜚䠈⏕ᚐ䛿ᤵᴗ䛷⩦䛳䛯ᩘ ᘧ䛜䛹䛾䜘䛖䛺㐠ື䜢ᐃ⩏䛧䛶䛔䜛䛛䜢䠈どぬⓗ䛻▱䜛 䛣䛸䛜䛷䛝䜛䠊䛣䛾◊✲䛷䛿䠈䜲䞁䝍䝷䜽䝔䜱䝤䛺䜰䝙䝯䞊 䝅䝵䞁䛾฼⏝䛜ே䚻䛾⌮ゎ䜢኱䛝䛟ຓ䛡䜛䛣䛸䜢♧䛧䛶 䛔䜛䠊䛧䛛䛧䛺䛜䜙䠈MathPad2 䛿⏕ᚐ䛜⣬䛾䝜䞊䝖䛸ྠ 䛨䜘䛖䛻฼⏝䛩䜛䛣䛸䛷⮬ศ䛾Ꮫ⩦䛾⿵ຓⓗ䛻⏝䛔䜛≀ 䛷䛒䛳䛶䠈䝥䝺䝊䞁䝔䞊䝅䝵䞁䛾䜘䛖䛺ከᩘ䛻ぢ䛫䜛䛴䛟 䜚䛻䛿䛺䛳䛶䛔䛺䛔䠊 㻌 ୍᪉䠈䝡䝆䝛䝇䜔Ꮫ⾡ⓗ䛺⌧ሙ䛷䛾䝗䜻䝳䝯䞁䝖䛾䜔䜚 䛸䜚䛷䛿 PDF 䛜⏝䛔䜙䜜䛶䛔䜛䠊Adobe 䛿 Acrobat3D[5] 䛸ゝ䛖ᢏ⾡䛷䠈3D 䝰䝕䝹䛸䜰䝙䝯䞊䝅䝵䞁䜢 PDF 䛻ᇙ䜑 ㎸䜐ᢏ⾡䜢ᥦ᱌䛧䛶䛔䜛䠊䛣䛖䛧䛯ᢏ⾡䛿䠈CAD 䜢౑䛖 〇㐀ᴗ䛺䛹䛾௻ᴗ䛜䠈సᡂ䛧䛯ᅗ㠃䜔䝰䝕䝹䜢㢳ᐈ䛻 䜲䞁䝍䝷䜽䝔䜱䝤䛻ぢ䛫䜛䛣䛸䛜ྍ⬟䛻䛺䜛䠊䛣䛾䜘䛖䛻䠈 䝥䝺䝊䞁䝔䞊䝅䝵䞁䛻䛚䛔䛶䜒䠈䜲䞁䝍䝷䜽䝔䜱䝤䛻 3D 䜾 䝷䝣䜱䝑䜽䝇䛷ぢ䛫䜛䛾䛿᭷ຠ䛷䛒䜛䛸⪃䛘䜛䠊 3. 䝅䝇䝔䝮䛾ᴫせ 㻌 ᮏ䝅䝇䝔䝮䛷䛿䠈⊂❧䛧䛯䝥䝺䝊䞁䝔䞊䝅䝵䞁䝋䝣䝖䛸䛧 䛶㛤Ⓨ䛩䜛䛾䛷䛿䛺䛟䠈PowerPoint 䜈⤌䜏㎸䜣䛷฼⏝ 䛩䜛䠊 ᅗ 1 䛜䛭䛾౛䛷䛒䜛䠊 䝅䝇䝔䝮䛾㛤Ⓨ䛻䛿䠈ᢏ⾡ⓗ䛻 3 䛴䛾኱䛝䛺ᵓᡂせ⣲ 䛜䛒䜛䠊1 䛴䛿䠈䜰䝙䝯䞊䝅䝵䞁䛾ไᚚ䜢⾜䛖≀⌮䜶䞁䝆 䞁䠈2 䛴┠䛿䠈䜹䝇䝍䝬䜲䝈䛷䛝䜛䝅䜵䞊䝎䜶䝣䜵䜽䝖䠈3 䛴┠䛿䝡䝳䞊䝽䛻䜲䞁䝍䝷䜽䝔䜱䝤䛺᧯స䛜䛷䛝䜛䜘䛖䛻 䛩䜛䛯䜑䛾ධຊ䜢ฎ⌮䛩䜛ᶵ⬟䛷䛒䜛䠊 ᅗ 1䠊PowerPoint 䜈䛾䝡䝳䞊䝽䞊䛾⤌䜏㎸䜏 3.1 ≀⌮䜶䞁䝆䞁 ᮏ䝅䝇䝔䝮䛷䛿䠈䜰䝙䝯䞊䝅䝵䞁䛾ไᚚ䛻≀⌮䜶䞁䝆䞁 䜢ྲྀ䜚ධ䜜䛯䠊⾪✺䛾౛䛿ᅗ 2 䛻♧䛩䠊 䜰䝙䝯䞊䝅䝵䞁䛾ไᚚ䛻≀⌮䜶䞁䝆䞁䜢ྲྀ䜚ධ䜜䛯䛾 䛿䠈௨ୗ䛾 2 䛴䛾⌮⏤䛻䜘䜛䠊䠍䠅ຊᏛ䜢䝧䞊䝇䛻䛩䜛䛯 䜑䠈䜰䝙䝯䞊䝅䝵䞁ไస⪅䛻䛸䛳䛶≀య䛾ᣲື䜢䜲䝯䞊䝆 䛧䜔䛩䛔䠈䠎䠅⾪✺ฎ⌮䛺䛹䛾」㞧䛺䜰䝙䝯䞊䝅䝵䞁䛻ᑐ 䛩䜛ไసຠ⋡䛜㧗䛔䛯䜑䛷䛒䜛䠊 ≀⌮䜶䞁䝆䞁䛻䜘䛳䛶ᣲື䛜䜲䝯䞊䝆䛧䜔䛩䛔䛸䛔䛖 䛾䛿䠈䜸䝤䝆䜵䜽䝖䛾ᣲື䜢㔜ຊ䛾స⏝䜔㐠ື䛾័ᛶ䠈 ≀య䛾⾪✺䛸䛔䛖⌧ᐇ䛾ୡ⏺䛷㉳䛝䛶䛔䜛⌧㇟䛸ྠ䛨䜘 䛖䛻䛸䜙䛘䜜䜀Ⰻ䛔䛛䜙䛷䛒䜛䠊 3.2 䝺䞁䝎䝸䞁䜾䜶䞁䝆䞁 ᮏ䝅䝇䝔䝮䛷䛿䠈䝺䞁䝎䝸䞁䜾䛻 Direct3D 䜢⏝䛔䜛䠊 䝺䞁䝎䝸䞁䜾䛻 3D 䜾䝷䝣䜱䝑䜽⏝ API 䜢⏝䛔䜛䛾䛿䠈 GPU䛾⬟ຊ䛜ά⏝䛷䛝䜛䛯䜑䛷䛒䜛䠊GPU 䜢౑䛖䛣䛸䛷 ᚑ᮶䛾䝒䞊䝹䛻ẚ㍑䛧䛶䠈䝸䜰䝹䝍䜲䝮 3DCG 䛾ᵝ䚻䛺 ᫎീຠᯝ䛾ᡭἲ䜢⏝䛔䜛䛣䛸䛜䛷䛝䜛䠊䛣䜜䛻䜘䛳䛶䠈䜰 䝙䝯䞊䝅䝵䞁ෆ䛷⏝䛔䜛 3D 䜾䝷䝣䜱䝑䜽䝇䛾㉁ឤ䜢㧗䜑 䜛䛣䛸䛜䛷䛝䠈䝥䝺䝊䞁䝔䞊䝅䝵䞁䜢ほ䜛ே䛾ぢ䜔䛩䛥䛾

ྥୖ䛻ᐤ୚䛩䜛≀䛸⪃䛘䜛䠊 㻌 䜰䝙䝯䞊䝅䝵䞁䜢ຠᯝⓗ䛻ぢ䛫䜛䛯䜑䛻䛿䠈䜰䝙䝯䞊䝅 䝵䞁䛾ᣲື䛰䛡䛷䛺䛟䝅䜵䞊䝕䜱䞁䜾䛾ᙳ㡪䜒䛒䜛䛸⪃䛘 䜛䠊୍⯡ⓗ䛺䝸䜰䝹䝍䜲䝮 3DCG 䜢౑䛳䛯䜰䝥䝸䜿䞊䝅䝵 䞁䛷䛿䠈Lambert 䛾ᣑᩓ཯ᑕ䛸 Blinn 䛾㙾㠃཯ᑕ䝰䝕䝹 䛜⏝䛔䜙䜜䜛䠊䛧䛛䛧䠈䝥䝺䝊䞁䝔䞊䝅䝵䞁䛷౑䛖䜰䝙䝯 䞊䝅䝵䞁䛻䛿䠈䛣䛾䝅䜵䞊䝕䜱䞁䜾䝰䝕䝹䛜᭷ຠ䛷䛿䛺 䛔䛸⪃䛘䜛䠊䝥䝺䝊䞁䝔䞊䝅䝵䞁䛷౑䛖䜰䝙䝯䞊䝅䝵䞁䛾 䝅䜵䞊䝕䜱䞁䜾䛷䛿䠈෗ᐇⓗ䛺䝺䞁䝎䝸䞁䜾ᡭἲ䛾䝷䜲䝖 䜔䝬䝔䝸䜰䝹䛺䛹䛾ᴫᛕ䜢ᣢ䛱㎸䜐䜘䜚䜒䠈䝔䜽䝙䜹䝹䜲 䝷䝇䝖䝺䞊䝅䝵䞁䛺䛹䝜䞁䝣䜷䝖䝸䜰䝸䝇䝔䜱䝑䜽䝺䞁䝎䝸䞁䜾 䛾ᥥ⏬ᡭἲ䛾᪉䛜᭷ຠ䛺䛾䛷䛿䛺䛔䛛䛸⪃䛘䜛䠊ᮏ䝅 䝇䝔䝮䛷䛿䠈䝕䝣䜷䝹䝖䛾䝅䜵䞊䝕䜱䞁䜾䜢 Gooch 䜙䛾䝔 䜽䝙䜹䝹䜲䝷䝇䝖䝺䞊䝅䝵䞁䛾䛯䜑䛾ᡭἲ[6]䜢ᛂ⏝䛧䛯䠊 3D API䛾ᅛᐃᶵ⬟䝺䞁䝎䝸䞁䜾䛸⥺⏬䛾ẚ㍑䜢ᅗ 3 䛷 ♧䛩䠊 3.3 ධຊฎ⌮ 㻌 ௦⾲ⓗ䛺䝥䝺䝊䞁䝔䞊䝅䝵䞁䝋䝣䝖䛷䛒䜛 PowerPoint 䛷䛿䠈ㅮ₇⪅䛛䜙䛾᧯సධຊ䛿䝬䜴䝇䜽䝸䝑䜽䛷䛒䜛䠊䝬 䜴䝇䜽䝸䝑䜽䜢䝖䝸䜺䞊䛻 1 䛴䛾䜰䝙䝯䞊䝅䝵䞁䛾䝉䝑䝖䛜 ㉳ື䛧䠈⤊䛳䛯䜙䜎䛯ḟ䛾䝅䞊䜿䞁䝇䜢෌⏕䛩䜛䠊ື⏬ 䝣䜯䜲䝹䛾ሙྜ䛷䛿䠈䜽䝸䝑䜽䛷෌⏕䛸೵Ṇ䜢⾜䛖䠊୍ᗘ䠈 ೵Ṇ䛧䛯ሙྜ䛻䛿෌ᗘ䛭䛾㒊ศ䛛䜙䛾෌⏕䛜⾜䛘䜛䠊 ᮏ䝅䝇䝔䝮䛷䜒䠈䝬䜴䝇䛻䜘䜛䜰䝙䝯䞊䝅䝵䞁䛾෌⏕䛸 ೵Ṇ䛿ྍ⬟䛷䛒䜛䠊≀⌮䜶䞁䝆䞁䛜䝸䜰䝹䝍䜲䝮䛻≀య 䛾ᣲື䜢ィ⟬䛩䜛䛣䛸䛛䜙䠈ື⏬䝣䜯䜲䝹䜔஦๓䛻ື䛝 䛜ᐃ⩏䛥䜜䛯䜰䝙䝯䞊䝅䝵䞁䛸␗䛺䜚䜲䞁䝍䝷䜽䝔䜱䝤䛺 ᧯స䜢ྍ⬟䛸䛧䛯䠊䛣䛣䛷䠈䜲䞁䝍䝷䜽䝔䜱䝤䛺᧯స䛸䛿䠈 䜰䝙䝯䞊䝅䝵䞁䝅䞊䞁୰䛾ᥥ⏬䜸䝤䝆䜵䜽䝖䜢䝗䝷䝑䜾䛧 䛶᧯స䛩䜛䛣䛸䛜ฟ᮶䜛䛣䛸䛷䛒䜛䠊 䛣䜜䛻䜘䜚䠈᪤Ꮡ䛾 䝥䝺䝊䞁䝔䞊䝅䝵䞁䝋䝣䝖䛾䜘䛖䛻䝬䜴䝇䜽䝸䝑䜽䛻䜘䛳䛶 䜰䝙䝯䞊䝅䝵䞁䛜㛤ጞ䛥䜜䜛䛾䛷䛿䛺䛟䠈䝅䞊䞁ෆ䛾䜸䝤 䝆䜵䜽䝖䜢᧯స䛩䜛䛣䛸䛷䜰䝙䝯䞊䝅䝵䞁䜢㛤ጞ䛩䜛䛣䛸䛜 䛷䛝䠈䝥䝺䝊䞁䝔䞊䝅䝵䞁䛾䝷䜲䝤ឤ䛜ฟ䜛䜒䛾䛸⪃䛘䜛䠊 䛥䜙䛻䠈䜲䞁䝍䝷䜽䝔䜱䝤䛻䝅䞊䞁䛾䜹䝯䝷䛾ᅇ㌿䛸䝈䞊䝮 ᧯స䛜⾜䛘䜛䠊ᅗ 4 䛻౛䜢♧䛩䠊 4. 䛚䜟䜚䛻 㻌 ᮏ䝅䝇䝔䝮䛷䛿䠈䝥䝺䝊䞁䝔䞊䝅䝵䞁䛷౑䛖䜰䝙䝯䞊䝅 䝵䞁䛻≀⌮䜶䞁䝆䞁䜢ᦚ㍕䛧䛶䜲䞁䝍䝷䜽䝔䜱䝤䛻䛩䜛䛣 䛸䜢ᥦ᱌䛧䛯䠊ᚑ᮶䛾䜰䝙䝯䞊䝅䝵䞁ᥥ⏬䝒䞊䝹䛷䛿䠈 ஦๓䛻సᡂ䛧䛯ື⏬䜔䜰䝙䝯䞊䝅䝵䞁䛾䝅䞊䜿䞁䝇䜢෌ ⏕䛩䜛䛰䛡䛷䛒䛳䛯䛜䠈ᮏ䝅䝇䝔䝮䜢⏝䛔䜛䛣䛸䛷䠈䜲䞁 䝍䝷䜽䝔䜱䝤䛺᧯స䛜ྍ⬟䛻䛺䛳䛯䠊䛣䜜䛻䜘䜚䠈䝃䜲䜶 䞁䝇䝅䝵䞊䜔䝬䝆䝑䜽䝅䝵䞊䛾䜘䛖䛺䝷䜲䝤ᛶ䛾䛒䜛ぢ䛫 ᪉䛜䠈䝥䝺䝊䞁䝔䞊䝅䝵䞁䛾䜰䝙䝯䞊䝅䝵䞁䛷䜒ྍ⬟䛻䛺 䜚䠈⫈⾗䜢䜘䜚ច䛝䛴䛡䜛䜒䛾䜈䛸᪼⳹䛷䛝䜛䠊 䛥䜙䛻䠈≀⌮䜶䞁䝆䞁䛜䜸䝤䝆䜵䜽䝖䛾ᣲືィ⟬䜢䛩䜛䛣 䛸䛷䠈ᢏ⾡ㄝ᫂䜔ᩍ⫱⏝㏵䛾䜰䝙䝯䞊䝅䝵䞁䜢సᡂ䛧䜔 䛩䛟䛺䜛䠊 5. ㅰ㎡ 㻌 ᮏ◊✲䛿䠈໭㝣ඛ➃⛉Ꮫᢏ⾡኱Ꮫ㝔኱Ꮫ䛾 21 ୡ⣖ COE 䝥䝻䜾䝷䝮䛂▱㆑⛉Ꮫ䛻ᇶ䛵䛟⛉Ꮫᢏ⾡䛾๰㐀䛸 ᐇ㊶䛃䛾ຓᡂ䛾䜒䛸⾜䜟䜜䛯䠊 6. ཧ⪃ᩥ⊩

[1]Michael Lewis , Jeffrey Jacobson, Introduction, Communications of the ACM, v.45 n.1, January 2002

[2] ➉ᮧ ఙኴ㑻, Ⳣཎ ர䠈䝇䝷䜲䝗㛫䛾┦㛵᝟ሗ䜢⏝

䛔䛯䛸䛞䜜䛾䛺䛔䝥䝺䝊䞁䝔䞊䝅䝵䞁, 14 ᅇ䜲䞁䝍䝷䜽䝔 䜱䝤䝅䝇䝔䝮䛸䝋䝣䝖䜴䜵䜰䛻㛵䛩䜛䝽䞊䜽䝅䝵䝑䝥(WISS 2006),pp.113-114, 2006

[3]prezvision, http://www.prezvision.com/

[4]LaViola, J. and Zeleznik, R. "MathPad2: A System for the Creation and Exploration of Mathematical Sketches", ACM Transactions on Graphics (Proceedings of SIGGRAPH 2004), 23(3):432-440, August 2004. [5] Adobe Acrobat3D,

http://www.adobe.com/jp/products/acrobat3d/

[6] Bruce Gooch , Peter-Pike J. Sloan , Amy Gooch , Peter Shirley , Richard Riesenfeld, Interactive technical illustration, Proceedings of the 1999 symposium on Interactive 3D graphics, p.31-38, April 26-29, 1999, Atlanta, Georgia, United States

ᅗ 2䠊⾪✺ฎ⌮䜢ྲྀ䜚ධ䜜䛯䜰䝙䝯䞊䝅䝵䞁䛾౛ 㻌 ᅗ 3䠊䜹䝇䝍䝬䜲䝈ྍ⬟䛺䝅䜵䞊䝕䜱䞁䜾䛾౛䠊

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