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Geometric model and Algorithm

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Jian Michael
Jian Michael

The introduce of Geometric model and Applied

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Geometric Model Schema ?ﾗ採庁侏c cadcam 議PS ( Geometric model with CADCAM) ?ﾗ採庁侏議圻尖c格F (Principle and Visualization of Model) ?ﾗ採庁侏議喘I囃 (Application Field with Geometric model) ?ﾗ採庁塀初c箭 (Introduce to Geometric Model)
ﾗ採庁侏c CADCAM 議PS CAD PROCESS ON CADCAM SYSTEM ?O庁塀 In a draw :Shape,material,surface condition, dimensions,manufacturing. In a diagram:structure,system arrangement ?O庁塀 喘 Design evaluation:form, kinematic ,strength Manufacturing:Processing planning,NC program. ?揖化垢殻 Teams,fast change,short lead time,high quality Computer Aided Design
ﾗ採庁侏議圻尖c格F 親W社 g社 ﾗ採蛍裂 O古廷 ﾗ採庁侏蛍裂c秀羨 ﾗ採庁侏議喘 謡W 互吉裏e 蛍 來旗 裏蛍ﾗ 採 夛侏O 弼科W 胆W X_
ﾗ採庁侏議喘I囃 Geometric Applied I囃 圻尖 喘 Xo廁O Cad / Cam 旋喘Y室g , w參 ﾗ採Y創Ycﾗ採庁侏 Y創賤互^殻塀初中紗參 O格F 庁醤O , 垢殻uD ,PDM Mold design and Manufacturing X哺 唹駝ﾀ Animation 旋喘 3D w庁M室g , 庁M 唹岻\嘴Ec唹 唹蒙丼螺哺 Animation-Comic-Game Movie special Effect X掩R Pattern Recognition 喇唹駸O高W 瘁卆厮秀羨挫岻蛍 蛤庁塀壓耽蛤M畔 喘x協議處麻隈M佩掩R 蛍裂曳 徭啝zy , 崘斯侏C匂繁X , D侘Re Automated Optical Inspection Intelligent Robot View Pattern Recognition M廠 Virtual Reality 狼y嬬遵喇聞喘宀議嘛 邑^影寔議 3D h@ 鳥h廠a伏岷X塀議軸r 札啖K卆H樫 雁@F光N麗周 M廠垢S庁MtWO Medical Simulation Statics Analyze Virtual factory
?1959 定 P. d e C a s t e l j a u 壓 1959 定_兵Ｗ壓爆式爆中議O r麿蚪F廿垢恬 ?隈繁 P. B └ z i e r 壓跡Z廿l婢阻 Unisurf 狼y ?60 定旗 J. Ferguson 壓襖咄巷望眉肝紗秘阻O議狼y ?1974 定q麿巒議匯冩貧屎塀∂@I囃Q蕁焔Xo廁ﾗ採 O ?B-spline 議尖a伏児A麼勣轅 Mansfield 、 de Boor 才 Cox 吉 繁 ?70 定旗喇豢 W. Gor don 才 R. Riesenfeld 議冩l聞誼 B-spline 議爆式爆中_兵紗秘 CAD 議ﾗ採宰伉嶄 ?B-spline φ CAD I囃l伏阻載寄議n遙參 B-spline 児A議 凪万尖匆ma伏泌眉叔侘議爆中K (triangular patches) 才爆中蛍 護 (subdivisionsurfaces) 吉 ?除ﾗ定蹌喇豢 NURBS(Nonuniform Rotational B-spine ) 爆中頁匯 掲械挫喘議爆中庁侏侭參參 NURBS 藥A議 CAD/CAM 狼y匆_ 兵l婢欺阻 1983 定 NURBS _兵紗秘 IGES(initial graphicsexchange specification) ｸ騏弌 ﾗ採庁侏初 Geometric Model
ﾗ採庁侏初 PitBtP n i n i ?= ‘= )()( 0 ]1,0[（ t1)( 0 =‘= tB n i n i ),...,( 10 nxxxx 《 ),...,( 10 nyyyy 《 inin i tt ini n tB ? ? ? 《 )1( )!(! ! )( 協x 凪嶄 ? B └ z i e r CURVE Q岻 Bernstein 謹塀児久 }0|),{( niyxP iii <<= 爆頁喇隈 垢殻 Pierre Bezier 阻盾Q廿 議LD} 侭戻竃議圭隈 . 凪 豢匯爆議宙峰 圭隈 . 戻竃議圭隈 , 淫凄 cubic spline , 麗∈老 (parabolic blending), B-spline 吉 , @乂爆 燕幣隈寄脅鞭 溲怯罹宥^侭嗤 c , 咀緩搆暁 M栽 (curve fitting)
?D侘 陣崙c鹿 n =5 r 2 3 4 5 6 7 8 9 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 ?D侘 陣崙c鹿 n =100 r
ﾗ採庁侏初 ?B └ z i e r Surface ij n j n j m i m i QvBuBvuS ‘‘ == = 00 )()(),( 3 RQij （ }0,0|),,{( njmizyxQ ijijijij <<<<= imim i uu imi m uB ? ? ? 《 )1( )!(! ! )( ?邪O ?協x jnjn j vv jnj n vB ? ? ? 《 )1( )!(! ! )( ]1,0[（u ]1,0[（v (m+1)*(n+1) 陣崙c鹿
?D侘 陣崙c鹿 m=5 n=5
?D侘 陣崙c鹿 m=100 n=80
ﾗ採庁侏初 ?哩侘 (fractals) ?哩侘頁徭隼議ﾗ採 ; 哩侘c詞竍畜音辛蛍 ; 哩侘辛參喘 躱ｴa鎖sY創 ; 哩侘辛參冩梢脅偏議w ; 哩侘辛參 庁M紘偏議軟懸 ; 哩侘咄渓 夐。F ?蟻W社須砕 (Koch) 祥戻竃秀D爆議o FB旗議圭塀 ?槐如畢棒瘁l燕 (1961 ) 議猟嫗冥今斡議L 業。lF今斡L業 L cy楚樫業議PS ?凧誼隠 (Benoit B. Mandelbrot ) 豢 1967 定 竃槐遥 如畢議猟嫗遍哩侘古廷l燕豢仝徭隼々豚侵 ?須砕爆壓販匯c貧協x音竃俳徽須砕爆 K掲痕機v雰貧及匯哩侘痕脚附f房堪 (Karl Weierstrass ) 侭戻竃
?遍枠函匯屎眉叔侘眉叔侘議耽匯眉吉芸函嶄 g椎匯吉芸恂匯吏翌郵軟議屎眉叔侘隼瘁価肇圻輹 g匯吉芸耽l粁嶷疙亙議嘛泌緩B旗oF謹 肝侭誼欺議爆Q恂須砕爆 ?哩侘議帆秀羨壓凪蒙嗤議來| : oF議Yc 徭厘猖鳶圈 ﾗ採庁侏初 ?哩侘 (fractals)
ﾗ採庁侏初 ?哩侘 (fractals) 幀旋鹿 Julia set D侘 ?橲栓壓 1918 定l燕阻 199 議榕遇兆夐匯r 凪r定H 25 q 凧誼隠D侘
Definition of geometric modelDefinition of geometric model Definition translatorDefinition translator Geometric modelGeometric model Interface algorithmsInterface algorithms Design and analysis algorithmsDesign and analysis algorithms Drafting and detailingDrafting and detailing DocumentationDocumentation To CAM processTo CAM process Design change

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Geometric model and Algorithm

  • 1. Geometric Model Schema ?ﾗ採庁侏c cadcam 議PS ( Geometric model with CADCAM) ?ﾗ採庁侏議圻尖c格F (Principle and Visualization of Model) ?ﾗ採庁侏議喘I囃 (Application Field with Geometric model) ?ﾗ採庁塀初c箭 (Introduce to Geometric Model)
  • 2. ﾗ採庁侏c CADCAM 議PS CAD PROCESS ON CADCAM SYSTEM ?O庁塀 In a draw :Shape,material,surface condition, dimensions,manufacturing. In a diagram:structure,system arrangement ?O庁塀 喘 Design evaluation:form, kinematic ,strength Manufacturing:Processing planning,NC program. ?揖化垢殻 Teams,fast change,short lead time,high quality Computer Aided Design
  • 4. ﾗ採庁侏議喘I囃 Geometric Applied I囃 圻尖 喘 Xo廁O Cad / Cam 旋喘Y室g , w參 ﾗ採Y創Ycﾗ採庁侏 Y創賤互^殻塀初中紗參 O格F 庁醤O , 垢殻uD ,PDM Mold design and Manufacturing X哺 唹駝ﾀ Animation 旋喘 3D w庁M室g , 庁M 唹岻\嘴Ec唹 唹蒙丼螺哺 Animation-Comic-Game Movie special Effect X掩R Pattern Recognition 喇唹駸O高W 瘁卆厮秀羨挫岻蛍 蛤庁塀壓耽蛤M畔 喘x協議處麻隈M佩掩R 蛍裂曳 徭啝zy , 崘斯侏C匂繁X , D侘Re Automated Optical Inspection Intelligent Robot View Pattern Recognition M廠 Virtual Reality 狼y嬬遵喇聞喘宀議嘛 邑^影寔議 3D h@ 鳥h廠a伏岷X塀議軸r 札啖K卆H樫 雁@F光N麗周 M廠垢S庁MtWO Medical Simulation Statics Analyze Virtual factory
  • 5. ?1959 定 P. d e C a s t e l j a u 壓 1959 定_兵Ｗ壓爆式爆中議O r麿蚪F廿垢恬 ?隈繁 P. B └ z i e r 壓跡Z廿l婢阻 Unisurf 狼y ?60 定旗 J. Ferguson 壓襖咄巷望眉肝紗秘阻O議狼y ?1974 定q麿巒議匯冩貧屎塀∂@I囃Q蕁焔Xo廁ﾗ採 O ?B-spline 議尖a伏児A麼勣轅 Mansfield 、 de Boor 才 Cox 吉 繁 ?70 定旗喇豢 W. Gor don 才 R. Riesenfeld 議冩l聞誼 B-spline 議爆式爆中_兵紗秘 CAD 議ﾗ採宰伉嶄 ?B-spline φ CAD I囃l伏阻載寄議n遙參 B-spline 児A議 凪万尖匆ma伏泌眉叔侘議爆中K (triangular patches) 才爆中蛍 護 (subdivisionsurfaces) 吉 ?除ﾗ定蹌喇豢 NURBS(Nonuniform Rotational B-spine ) 爆中頁匯 掲械挫喘議爆中庁侏侭參參 NURBS 藥A議 CAD/CAM 狼y匆_ 兵l婢欺阻 1983 定 NURBS _兵紗秘 IGES(initial graphicsexchange specification) ｸ騏弌 ﾗ採庁侏初 Geometric Model
  • 6. ﾗ採庁侏初 PitBtP n i n i ?= ‘= )()( 0 ]1,0[（ t1)( 0 =‘= tB n i n i ),...,( 10 nxxxx 《 ),...,( 10 nyyyy 《 inin i tt ini n tB ? ? ? 《 )1( )!(! ! )( 協x 凪嶄 ? B └ z i e r CURVE Q岻 Bernstein 謹塀児久 }0|),{( niyxP iii <<= 爆頁喇隈 垢殻 Pierre Bezier 阻盾Q廿 議LD} 侭戻竃議圭隈 . 凪 豢匯爆議宙峰 圭隈 . 戻竃議圭隈 , 淫凄 cubic spline , 麗∈老 (parabolic blending), B-spline 吉 , @乂爆 燕幣隈寄脅鞭 溲怯罹宥^侭嗤 c , 咀緩搆暁 M栽 (curve fitting)
  • 7. ?D侘 陣崙c鹿 n =5 r 2 3 4 5 6 7 8 9 3 4 5 6 7 8 9
  • 8. 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 ?D侘 陣崙c鹿 n =100 r
  • 9. ﾗ採庁侏初 ?B └ z i e r Surface ij n j n j m i m i QvBuBvuS ‘‘ == = 00 )()(),( 3 RQij （ }0,0|),,{( njmizyxQ ijijijij <<<<= imim i uu imi m uB ? ? ? 《 )1( )!(! ! )( ?邪O ?協x jnjn j vv jnj n vB ? ? ? 《 )1( )!(! ! )( ]1,0[（u ]1,0[（v (m+1)*(n+1) 陣崙c鹿
  • 12. ﾗ採庁侏初 ?哩侘 (fractals) ?哩侘頁徭隼議ﾗ採 ; 哩侘c詞竍畜音辛蛍 ; 哩侘辛參喘 躱ｴa鎖sY創 ; 哩侘辛參冩梢脅偏議w ; 哩侘辛參 庁M紘偏議軟懸 ; 哩侘咄渓 夐。F ?蟻W社須砕 (Koch) 祥戻竃秀D爆議o FB旗議圭塀 ?槐如畢棒瘁l燕 (1961 ) 議猟嫗冥今斡議L 業。lF今斡L業 L cy楚樫業議PS ?凧誼隠 (Benoit B. Mandelbrot ) 豢 1967 定 竃槐遥 如畢議猟嫗遍哩侘古廷l燕豢仝徭隼々豚侵 ?須砕爆壓販匯c貧協x音竃俳徽須砕爆 K掲痕機v雰貧及匯哩侘痕脚附f房堪 (Karl Weierstrass ) 侭戻竃
  • 14. ﾗ採庁侏初 ?哩侘 (fractals) 幀旋鹿 Julia set D侘 ?橲栓壓 1918 定l燕阻 199 議榕遇兆夐匯r 凪r定H 25 q 凧誼隠D侘
  • 15. Definition of geometric modelDefinition of geometric model Definition translatorDefinition translator Geometric modelGeometric model Interface algorithmsInterface algorithms Design and analysis algorithmsDesign and analysis algorithms Drafting and detailingDrafting and detailing DocumentationDocumentation To CAM processTo CAM process Design change