?_”e ‚'rilŃRé.!Introducing 3DScheme for Windows)(c) Schemers Inc, Ft Lauderdale, FL, USAXCreateButton(`NavButton',`&Navigate',`PopupId(`3dscheme.HLP',`HyperContext147167112')'),CreateButton(`ExitButton',`&Quit',`Exit()')BrowseButtons()Z’mainOoRWmainŸšIntroduction to 3DSchemeŸm##¬O³+‡hG®’’Ÿ®Ÿ/’’’’;)z4½źh}ļŖ*ŸI½’’dd’’’’|CONTEXTŌT|CTXOMAPŻB|FONT·?|KWBTREEvD|KWDATAčB|KWMAPeD|SYSTEM|TOPIC±|TTLBTREE„L|bm0m|bm1®Ÿ|bm10ÜĢ|bm11œĪ|bm12oÕ|bm13õļ|bm14j÷|bm15qž|bm16Ē|bm17h|bm18B|bm19q |bm2M·|bm20|bm21/,|bm22œ.|bm237S|bm24d~|bm25wŽ|bm26ļ³|bm27^ß|bm28`Ž|bm29Ē¹|bm3ÕĢ|bm305|bm31ØA|bm32ęi|bm33‹|bm34œ¶|bm35źē|bm36<|bm37Ål|bm38˜|bm39„Ø|bm4į|bm40ąŌ|bm41,ź|bm42M|bm43-|bm44h%|bm45I<|bm46śS|bm47“q|bm48}™|bm49g“|bm5Æā|bm50‰Ę|bm51…Ü|bm52>|bm53Ā/|bm54}€|bm55KĒ|bm56 Ó|bm57Qē|bm589 |bm59Ķ] |bm6ˆī|bm60­| |bm61 “ |bm62MÓ |bm63Éć |bm64cś |bm65 |bm668= |bm67Ą? |bm68—D |bm69DF |bm7UQ|bm70kH |bm71ŠL |bm72-M |bm73„g |bm74Įi |bm75!u |bm76 |bm77–› |bm78ŠĄ |bm79HŪ |bm8˜y|bm80ōņ |bm81ü |bm82™E |bm83ļi |bm84g„ |bm85¾œ |bm86CĒ |bm87>ó |bm88 |bm894 |bm92Ÿ|bm90MB p:ż9’’’’ ķ¼’’’’ł1›’’’’+’’’’ł§ContentsChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext147167112')');SaveMark(`Ack');CreateButton(`Ack',`Than&ks',`PopupId(`3dscheme.HLP',`HyperContext1513142817')')2 +. ,€ €ˆ¢€†"€‚’VłBĮ#R²$$€€’T€€ē¬Ó€†"€‰€ć¬Ó€‰€‚’T€>€ē !€†"€‰€ć !€‰€‚’T€r€ē½€†"€‰€ć½€‰€‚’’’Reviewing 3DSchemeUsing 3DSchemeOrdering 3DScheme&+h# €€€‚’?B§. ,€$€€†"€€’Schemers Inc.9hą1ž’’’’’’’’’’’’ą„SunShineI§)2 4€0€€‡"€€‚’AcknowledgementŅąī@#N€ ō<4€€€ € € € € €‚’’’This Introduction to 3DScheme was produced using the Help Yourself! Integrated Help File Development System, a product of theN)<H#`€ō<€€’.€€€†"€€‚’’’Eī3#6€$ō<€€€ €‚’’’1-800-553-0400$<„" €€€ ’Õ¤z1/ž’’’’zŌReviewing 3DSchemeChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext641499894')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')1„«- *€ €†€†"€‚’dAz# €‚€€‚’A Seamlessly Integrated Programming Environment Combined With X.«g* $€\€j€€€‚’The Industry Standard ACISŅ Solid Modeler‘ų#Ņ€2d€€’D€€˜€‚ēßōՀ†"€‰€‚’€€˜’0€€’€†"€ €‚’’’¢1gšq#²€fd€€’’6€€j€†"€€€‚’6€(€j€†"€ €€‚’’’Schemers Inc.SPATIAL TECHNOLOGY INC.:ųŌ" €0€€’A Winning Combination!Cš1}’’’’’’’’’’’’QReviewing Navigate:ŌQ5 :€ €€†"€ ‚†"€ ’H™1O’’’’’’’’’’’’™  Finding Your Way Around0QÉ, (€ €€†"€ ‚’W3™ $ €f€€ ‚’There are four ways to move around in this file:•É$ o#¬€-±Ÿ0€€r€†"€€ ‚’€ €r’6€ €Trų „=€x€ƒ€ƒ€ ‚’’’·Use the Menu Boards that appear on some pages. Click on any light blue panel or any round red button to move to the corresponding page.±v Õ ; F€ī€Pų „=€x€ ƒ€ƒ€ †"€‚’·Use the Browse buttonson the main menu bar. These take you through all the pages in a predetermined sequence.]$ e 3 6€ŗ€Tų „=€x€ ƒ€ƒ€ ‚’·Use the large red buttons that appear on most pages, usually in the top right corner:˜2Õ ż f#œ€f«†•€€Pų „=€x’.€€€†"€€ ‚’€ €€€ ‚’’’Jump to the next in a sequence of pages.“@e  S#v€‚«†•.€€€†"€€ ‚’€ €€€ ‚’’’Jump to the main page in the current sequence of pages.Ōż   < F€«€Pų „=€x€ ƒ€ƒ€ †"€‚’ ·Use thebutton on the main menu bar. This brings up a diagram showing all the pages that are closely linked to the one you are reading. Click on any part of the diagram to move to the corresponding page.Ō£ t1ė+§‚’’’’t—DWhat Is 3DScheme?ChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext162261085')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')u  éY#‚€:–€€€€‚’:€*€ē¬Ó€†"€‰€‚’’’What Is 3DScheme?H%t1# €J€€‚’A Powerful Programming Environment+čéhAC T€Ó€Œ€ˆ"€€ € € € € €€ ‚’By embedding one of the most powerful high-level programming languages in an acclaimed programming environment, 3DScheme brings you the1hA  best in the software development arena. Scheme, the language taught at all levels in the world's most prestigious schools, colleges, and universities, provides a semantically simple and syntactically clean way to think about and express algorithms. And the renowned WinScheme Editor provides a program development environment second to none.J'1²A# €N€€‚’+ A Complete Geometric Solid Modelerx/hA*CI `€a€Œ€ € € € ˆ"€€ €€ € €€ ‚’With more than 450 geometric modeling procedures, 3DScheme adds a new dimension to the International Standard Scheme language. These procedures access the de facto standard ACISŅ Solid Modeler, the engine that drives so many of today's top-end solid modeling and visualization applications.m@²A—D- (€€€‚€ € € ’= A Winning Combination!Together, these elements bring computing power to educators, students, CAD users, and hobbyists that is unprecedented at such a low price. Whether your interests lie in mathematics, engineering, computer science, design, or recreational graphics, 3DScheme takes you into the next dimension!< *CÓD1v’’’’’’’’’’’’ÓD ENext page 1:—D E5 :€ €€†"€ ‚†"€’Ž­ÓDėE1nž†’’’’ėE{JThe ACIS 3D Modeling KernelChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext647174807')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Œ$ EwFh# €L‚.€€€€‚’X€4€ē¬Ó€†"€‰ēXxpĻ†"€‰€‚’’’The ACIS Solid ModeleršėE{Jj ¢€;€$ †€‡"€€€€ € €€ € ˆ"€€ € ˆ"€€€ € € ’ACIS: The StandardSPATIAL TECHNOLOGY INC. introduced the ACISŅ Geometric Modeling Kernel in 1989 as the world's first commercial, object-oriented, 3D geometric modeling toolkit. ACIS supports wireframe, 3D-surface and solid modeling using a common, unified data structure. It is developed in conjunction with the world's leading solid modeling experts, Dr. Ian Braid of Cambridge, UK, and his colleagues, and represents an investment of over $12 million. It has emerged as the de facto standard 3D modeling technology.ACIS is a proven solid modeler, being licensed by more that 200 of the world's leading 3D modeling suppliers, developers, and researchers, including such notable companies as Allied Signal, Applicon, Aries, Autodesk, Bentley Systems, CADCentre, Cognition, Ford Motor Company, Hewlett-Packard, Hitachi Zosen Systems, MICROCADAM, Mercedes, Point Control, Sharp Strässle and Toshiba.< wF·J1v’’’’’’’’’’’’·JńJNext page 2:{JńJ5 :€.€€†"€ ‚†"€"’Ń ·JĀK1š§‚‰ˆ ’’’’ĀK‹NCurve CreationChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573171307')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Œ$ńJNLh# €L„-€€€€‚’X€4€ē¬Ó€†"€‰ēęsŌō†"€‰€‚’’’The ACIS Solid Modeler“PĀKįMC T€£€€‚‡"€€ € €€ € € ‚’Curve CreationLines, arcs, circles, ellipses, conic edges, bezier curves, splines, and other types of curves are easily manipulated thanks to the powerful ACISŅ engine.In addition, you may use 3DScheme to create a curve by isolating the edge of a solid. Even parametrize it, and evaluate points along the resulting curve!ŖyNL‹N1 2€ō€$˜†€ ˆ"€’Moreover, curves may be extruded along vectors to form prisms, or rotated about axes to form solids of revolution.< įMĒN1v’’’’’’’’ ’’’’ĒNONext page 3:‹NO5 :€.€€†"€ ‚†"€"’Ń ĒNŅO1† ’’’’ŅOSolid CreationChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573214205')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Œ$Oj€h# €L…+€€€ŅOj€O€‚’X€4€ē¬Ó€†"€‰ēĢ‹;õ†"€‰€‚’’’The ACIS Solid Modeler3łŅO: B€õ€€‚‡"€€ €€ ’Solid CreationIf you've ever enjoyed playing with LegoŌ, then you're about to experience the ultimate in building satisfaction. Choose your bricks, blocks, cylinders, cones, toruses, extruded curves, solids of rotation. And away you go!< j€Ł1v’’’’’’’’ ’’’’Ł‚Next page 4:‚5 :€.€€†"€ ‚†"€"’ȗŁŪ‚1䉈Œ ’’’’Ū‚÷„ViewsChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573287621')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Œ$‚gƒh# €L5€€€€‚’X€4€ē¬Ó€†"€‰ēłÓžō†"€‰€‚’’’The ACIS Solid Modeler=Ū‚÷„S t€}€€‚ˆ"€€ € €€ €€ €€ €€ ’ViewsYou may never have the opportunity to hold your creations in your hand ... even so you can use the ACISŅ engine to put your models through their paces.Perspective view? No problem. From the inside out? A snap. That is, as long as you know where you are, where it is, and which way is up!< gƒ3…1v’’’’’’’’’’’’3…m…Next page 5:÷„m…5 :€.€€†"€ ‚†"€"’Ņ”3…?†1xx’’’’?†åˆTransformationsChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573339944')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Œ$m…Ė†h# €L‚)€€€€‚’X€4€ē¬Ó€†"€‰ē€Hõ†"€‰€‚’’’The ACIS Solid Modelerā©?†­ˆ9 @€S€€‚€ € €€ ‚‚€ € ‚’TransformationsOnce created, solid and wireframe entities may, individually or in groups, be translated, rotated, scaled, and reflected. In fact, ACISŅ provides comprehensive facilities for defining and manipulating transform entities, including composing them and inverting them.You may even use 3DScheme to define transforms in terms of the transformation required to move between different coordinate systems.8Ė†åˆ4 8€ €€ †"€†"€ ’< ­ˆ!‰1v’’’’’’’’’’’’!‰[‰Next page 6:åˆ[‰5 :€.€€†"€ ‚†"€"!’Õ¤!‰0Š1‡Œ’’’’0ŠāBoolean OperationsChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573363889')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Œ$[‰¼Šh# €L2€€€€‚’X€4€ē¬Ó€†"€‰ē¼¼õ†"€‰€‚’’’The ACIS Solid Modeler&Ė0Šā[ „€™€€ˆ"€"€€ € €€ €€ € € €€ €€ ’Boolean Operations3DScheme allows you to create various types of regular solids¾ blocks, cylinders, cones, spheres, and toruses, for example. But often, the more interesting solids are those, like the one whose construction is shown on the right, that are formed by combining regular solids using Boolean operations to form unions, intersections, and differences.Mass PropertiesWant to know more about the solid you have created? No problem. The 3DScheme procedure solid:massprop tells you much of what you might need, starting with its volume, and including its center of mass and principal axes and moments of inertia.In addition, the procedure solid:area tells you the surface area. < ¼ŠŽ1v’’’’’’’’’’’’ŽXŽNext page 7:āXŽ5 :€.€€†"€ ‚†"€"#’Ģ›Ž$1mx€’’’’$ŃĀRenderingChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573484488')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Œ$XŽ°h# €L~/€€€€‚’X€4€ē¬Ó€†"€‰ē-ģ×ų†"€‰€‚’’’The ACIS Solid ModelerÄ$ŃĀQ p€‹€€‚€ €€ ‚‚‡"€$€€ € € €€ €°ŃĀXŽ’RenderingACISŅ provides the very latest in visualization technology, allowing you to depict your creations in a variety of ways. Solids may be covered with any of a range of provided materials, each of which has various properties¾such as its color, displacement, transparency, and reflectivity.Specify the material for each of the solids in your "part". Tell ACIS what types of render lights to use and where to place them. Adjust their properties, if desired. And don't forget to mention where you are in relation to the part you are viewing!Choose the rendering algorithm from the list of available modes including flat and Gouraud. Finally choose a suitable background, and Presto!< ° Ć1v’’’’’’’’’’’’ ĆGĆNext page 8:ŃĀGĆ5 :€.€€†"€ ‚†"€"%’Ų§ ĆÄ1FŁƒ’’’’čČGraphical InteractionChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573514687')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')z!GƙÄY#‚€D™€€€€‚’:€4€ē¬Ó€†"€‰€‚’’’The ACIS Solid Modelerh5ÄĒ3 4€m€€ˆ"€&€ ‚’Graphical InteractionOne of the common needs in solid modeling programs is for "rubber banding" and "dragging" procedures.In rubber banding, the graphical image modifies itself dynamically as the mouse moves. On the right, for example, the height of a rectangular block shrinks and grows in response to the up and down movement of the mouse. Depending on which rubber banding method you are using, one or more defining characteristics of the geometrical object you are building are registered in response to mouse clicks while rubber banding is in progress.ŒS™ÄČ9 @€§€€ ‚€ €€ € € € € ’Rubber banding and dragging are supported by the ACISŅ Solid Modeler and accessed directly through 3DScheme. In fact, 3DScheme lets you tap directly into the underlying Microsoft Windows messaging system to write event-based programs that make use of dynamic interaction with the program by means of events such as mouse clicks.< ĒÉČ1v’’’’’’’’’’’’ÉČÉNext page 9:ČÉ5 :€.€€†"€ ‚†"€"'’ā±ÉČåÉ1r€Š‡’’’’åÉuĪThe Scheme Programming LanguageChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573676469')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')•-ÉzŹh# €^…+€€€€‚’X€F€ē¬Ó€†"€‰ēØ·@ļ†"€‰€‚’’’The Scheme Programming Language< åɶĢ1 0€€€‚€ ‡"€‚’Scheme: A Modern Programming LanguageScheme is a dialect of the Lisp programming language that was invented by Guy Lewis Steele Jr. and Gerald Jay Sussman of the Artificial Intelligence Laboratory at the Massachusetts Institute of Technology. It demonstrates that a clear and simple language with few syntactic rules is sufficient to form the basis of a practical, efficient, and extremely powerful programming language, flexible enough to support the major programming paradigms such as object-oriented programming.&zŹÜĢ# €€€ ‚’™a¶ĢuĪ8 >€Å€ ˜€ ˆ"€(€ €€ ’The Scheme programming language is powerful enough for the professional, yet its structure is so consistent and conceptually simple that even computer novices can pick up the language and write significant programs.Best of all, Scheme is easily extended to give you access to powerful underlying technology . . . such as the ACISŅ Solid Modeler!= ÜĢ²Ī1w’’’’’’’’’’’’²ĪģĪNext page 10:uĪģĪ5 :€"€€†"€ ‚†"€)’Ö„²ĪĀĻ1{ŁƒŠĀĻwĮScheme code exampleChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext573681639')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ƒ*ģĪQY#‚€V˜€€€€‚’:€F€ĀĻQģĪē¬Ó€†"€‰€‚’’’The Scheme Programming Language&ĀĻw# €€€ ‚’HQæ9 @€€€‚€ ‚‚€ € € €€ ‚’A Solid Modeling Scheme ExampleScheme's functional basis is perfect for "capturing" solid and wire-body entities, while its tolerance for imperative programming allows for in-place manipulation of top-level entities and their dependent entities.Here is an example of some actual 3DScheme code as it puts the ACISŅ Solid Modeler through its paces. On the left is the Scheme code that creates the abstract solids, and on the right is the Scheme code that causes these solids to be visualized as shown in the figures.XŽwŹ#bSĢ€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ ‚’8€ŗ‚€€€€€€‚’(€ƒ†"€*€ ‚’’’;; create an equilateral triangular prism;;(define wedge (solid:sweep-wire (wire-body (list (linear-edge (position 0 0 -20) (position 30 0 -20)) (linear-edge (position 30 0 -20) (position 30 60 -20 "polar")) (linear-edge (position 30 60 -20 "polar") (position 0 0 -20)))) 40))(entity:paint wedge YELLOW)(render)6/æM#܁aS€€’ €„„Ü€€€€€€ƒ€ƒ€ƒƒƒƒƒ€€ƒƒ€ƒƒ€€€ƒƒ€ƒƒ€€€€€€ƒƒ€€€€€€€€€ ‚’€īƒ„„Ü’8€šƒ€€€€‚€€‚’,€R„‚‚†"€+€ ‚’’’;; create a hexagonal collar by uniting six copies of the equilateral;; triangular prism and drilling a large cylindrical hole along the axis.;;(define hex-collar (solid:subtract (applysolid:unite(conswedge(map (lambda (angle) (entity:transform (entity:copy wedge) (transform:rotation (position 0 0 0) (gvector 0 0 1) angle)) '(60 120 180 240 300)))) (solid:cylinder (position 0 0 -20) (position 0 0 20) 20)))(entity:paint hex-collar GREEN)(render)Ńō Ż#ˆėS€€’耀€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ ‚’*€Āƒ€€€€‚’(€ąƒ†"€,€ ‚’’’;; turn the collar through 90 degrees and punch six holes in it.;;(entity:transform (solid:subtract hex-collar (solid:cylinder (position 30 -30 0 "polar") (position 30 150 0 "polar") 10) (solid:cylinder (position 35 -90 7.5 "polar") (position 35 90 7.5 "polar") 10) (solid:cylinder (position 35 30 -7.5 "polar") (position 35 210 -7.5 "polar") 10)) (transform:rotation (position 0 0 0) (gvector 1 0 0) 90))(render)vM #ąļS€€’€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ ‚’T€„€€€€€€€€‚€€‚’*€ā„†"€-‚€ ‚’’’;; create a ball in the center of the hexagonal collar.;;(define ball (solid:sphere (position 0 0 0) 10));; create a cone lying on its side at one end of the collar's axis.;;(define cone (solid:cone (position 0 60 0) (position 0 30 0) 10 0));; create a tilted cube at the other end of the collar's axis.;;(define block (entity:transform (solid:block (position 10 -40 -10) (position -10 -60 10)) (transform:rotation (position -10 -40 10) (gvector 1 1 1) 60)))(entity:paint ball RED)(entity:paint cone YELLOW)(entity:paint block MAGENTA)(render)$ Į" €€€ ’= ž1w’’’’’’’’’’’’ž8Next page 11:Į85 :€"€€†"€ ‚†"€.’צž@1@€ȉ’’’’@ƒBThe WinScheme EditorChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext959975814')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):Dele8@8teMark(`Ack')')x8“@Y#‚€@–€€€€‚’:€0€ē¬Ó€†"€‰€‚’’’The WinScheme EditorK@ŽA8 >€'€€‚€ € €€ €€ ‚‚’A Powerful Programming Environment3DScheme incorporates the acclaimed WinScheme Editor. Programs are written and executed right out of the editor itself, giving you the best of all possible worlds. But this is no ordinary editor, as the following features show:| “@ZBo#®€*g+.€€€†"€$€ ‚’€ €’<€ €„=€Z€†"€/€ ‚’’’)ŽAƒB' €€„=€Z€ ’= ZBĄB1w’’’’’’’’’’’’ĄBśBNext page 12:ƒBśB5 :€ €€†"€ ‚†"€0’FĄB@C1’’’’’’’’’’’’@CEAutomatic indentationɚśB D/ ,€5€€‚‚€ €€ ‚’Automatic Indentation of ExpressionsYou can set up the WinScheme Editor so that it automatically typesets your programs, indenting them like this:0@C9D, (€ €€ †"€1‚’ɦ DE# €M€€ ’This control over the layout of your programs is independent of whether you are using a fixed-pitch font (such as Courier) or a variable-pitch font (such as Arial).E9DGE1 ’’’’’’’’’’’’GE GParenthesis matching–`EŻF6 :€Į€€‚‚€ €€ €€ ‚‚’Parenthesis MatchingWhenever you type a parenthesis or move the insertion point next to one, the WinScheme Editor checks to see whether the parenthesis opens or closes a valid Scheme expression. If it does, the editor draws a box around the expression, or highlights its opening and closing parentheses, or both, or neither¾it's your choice..GE G+ &€€€ †"€2’HŻFSG1’’’’’’’’’’’’SGIContext-sensitive jumpsU GćH; D€«€€‚‚€ €€ € € € € ‚’Context-sensitive JumpsWhat kind of argument does the primitive procedure magnitude take? Is it guaranteed to be present in every Scheme? Just type "magnitude" in a document and press Ctrl+F1, or simply click the right mouse button on the word, and you will be taken directly to the relevant topic in the 3DScheme knowledge base..SGI+ &€€€ †"€3’AćHRI1J’’’’’’’’ ’’’’RI[KColored programsŪ«I-K0 .€W€€‚‚€ €€ ‚‚’Coloring of Syntactic ElementsDisplaying a program in color is not a gimmick. It is an effective way to improve the program's readability and, with it, your productivity. Do you suspect that a definition has too many right parentheses? Are you concerned that your code might contain invalid forms? The WinScheme Editor's program-coloring capabilities can help you identify or avoid these typical programming problems..RI[K+ &€€€ †"€4’I-K¤K16’’’’’’’’!’’’’¤K‘MIndexing of Scheme filesæ[KcM/ ,€!€€‚‚€ €€ ‚’Indexing of Scheme FilesAt all times, the WinScheme Editor keeps all the definitions in your file of Scheme code at your fingertips. Click once on the filename button in the status bar and a menu pops up with an alphabetical listing of all the procedures you have defined. Choose the one you want, and the editor selects the whole of the corresponding definition and takes you directly there..¤K‘M+ &€€€ †"€5’= cMĪM1ŗ’’’’’’’’"’’’’ĪMKOMDI Features}(‘MKOU x€S€‚A€‚‚€‚€ €€ €‚†"€6‚€ €€ €€ €’Features of the Multiple Document InterfaceThe WinScheme Editor's MDI Features Speed bar Menu bar Status bar Document WorkspaceąÆĪM7€1^P =„#’’’’7€µ„Getting Started with 3DSchemeChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext960026906')');IfThen(IsMark(`Ack'KO7€KO),`DestroyButton(`Ack'):DeleteMark(`Ack')')sKOŖ€Y#‚€6–€€€€‚’:€&€ē¬Ó€†"€‰€‚’’’Getting Startedc&7€ ƒ= H€O€€‚ˆ"€7€ €€ € € ‚’Getting Started With 3DSchemeIf you're new to Scheme or to solid modeling, you can get some serious leverage by reading the new Getting Started text book by Edward C. Martin (pp. 250, paperbound). The book begins by leading you through the basics of solid modeling. What is a solid? A face? A lump? An edge? A view? How do you specify positions and vectors in three-space? How can solids be united, intersected, and subtracted? Each concept is illustrated with diagrams, together with code that you can actually run using 3DScheme.Ø{Ŗ€µ„- (€ł€€ ‚‡"€8’The book then takes you through the Scheme programming language and on to the techniques for manipulating and visualizing entities. Throughout, you are encouraged to tackle solid modeling projects ranging from short, simple tasks (such as the barbell above) to longer, more challenging tasks such as simulating the bending of wires (the paper clip on the left, for example).= ƒņ„1w’’’’’’’’$’’’’ņ„,…Next page 13:µ„,…5 :€ €€†"€ ‚†"€9’1ņ„]…1U’’’’’’’’%’’’’]……$,……" €€€ ’Ž­]…_†1cŠ‡v&’’’’_†ä‰The 3DScheme Knowledge BaseChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext958552399')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')&…Ž†Y#‚€N–€€€€ ‚’:€>€ē¬Ó€!†"€‰€ ‚’’’The 3DScheme Knowledge Base}_†[‰o ¬€€€‚€ € € € € €€ ‚‚ēe Šb€!ˆ"€:‰€ €€ €€ €€ €€ € € ‚’The 3DScheme Knowledge Base3DScheme comes loaded with a vast repository of knowledge concerning 3DScheme, Scheme in general, and the ACISŅ Solid Modeler.Over 1000 help topics, professionally laid out and written by experienced technical authors, incorporate more than 5000 hypertext hot links and 150 annotated figures to lead you to the information you need with a minimum of fuss. Topics cover all aspects of the programming environment, the R4RS Scheme Standard, and the ACIS Scheme extensions.‰_Ž†ä‰* $€¾€›ƒ€ € € ’Click on the plaque to access a sampling of the help topics in the 3DScheme knowledge base.= [‰!Š1w’’’’’’’’'’’’’!Š[ŠNext page 15:ä‰[Š5 :€"€€ †"€ ‚†"€;’Ėš!Š&‹1°Šó(’’’’&‹ ŽExamplesChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext958547896')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')&[Š„‹Y#‚€N“€€€€ ‚’:€>€ē¬Ó€!†"€‰€ ‚’’’The 3DScheme Knowledge Base4÷&‹ŁŒ= H€ń€€‚€ ˆ"€€ € € € ‚’ExamplesThe topics listed on this menu board are chosen from over a thousand that form the 3DScheme knowledge base. Each topic describes just one of the more than 450 primitive procedures that make up 3DScheme's solid modeling extension.0„‹ , (€ €€ †"€<‚’ŁŁŒ Ž) €³€€ € € ’In addition to covering the solid modeling extension in its entirety, whole sections of the knowledge base are dedicated to explaining and describing Scheme, as well as 3DScheme's powerful development environment.= HŽ1w’’’’’’’’)’’’’HŽ‚ŽNext page 14: Ž‚Ž5 :€"€€ †"€ ‚†"€=’> HŽĄŽ1,’’’’’’’’*’’’’ĄŽŗĮArgument: ...d‚Ž0ĄI `€7€€‚‚€"€ ‚‚€€€ €€ €€ €€ ‚’Argument Information... (an ellipsis)In the syntax template of an entry in the WinScheme Help System, an ellipsis following some number, n, of arguments of the same type signifies that n – 1 or more arguments of that type are acceĄŽ0Ą‚Žptable at that point. For example,Š'ĄŽŗĮc ”€O€Pų „ 0ĄųĮ1Ö’’’’’’’’+’’’’ųĮĀArgument: ent˜ZŗĮĀ> L€“€€‚‚€"€ €"€ €"€ ‚‚€€ ’Argument Informationent, ent1, ent2, ...Arguments of this form are entities.BųĮŅĀ1Ę’’’’’’’’,’’’’ŅĀVĆArgument: entlist„RĀVĆ2 4€¤€€‚‚€"‚‚€ €€ ’Argument InformationentlistArguments of this form are lists of entities.?ŅĀ•Ć1µ’’’’’’’’-’’’’•Ć ÅArgument: gvecvVĆ Åc ”€'€€‚‚€"€ €"€ €"€ ‚‚€€ ā½P€‰€ āX÷L€‰€ €&€'€&€ ’Argument Informationgvec, gvec1, gvec2, ...Arguments of this form are three-dimensional gvectors. They are always represented externally in rectangular Cartesian form relative to the active coordinate system by a symbol of the form #[gvector x y z].> •ĆIÅ1¼’’’’’’’’.’’’’IÅĒĘArgument: pos~ ÅĒĘc ”€7€€‚‚€"€ €"€ €"€ ‚‚€€ ā½P€‰€ āX÷L€‰€ €&€'€&€ ’Argument Informationpos, pos1, pos2, ...Arguments of this form are positions in three-dimensional space. They are always represented externally in rectangular Cartesian form relative to the active coordinate system by a symbol of the form #[position x y z].< IÅĒ1O’’’’’’’’/’’’’ĒČArgument: x›ĒĘČx ¾€7€€‚‚€"€ €"€ €"€ ‚€"€ €"€ €"€ ‚€"€ €"€ €"€ ‚€"€ €"€ €"€ ‚‚€€ ’Argument Informationa, a1, a2, ...r, r1, r2, ...x, x1, x2, ...y, y1, y2, ...Arguments of this form are real numbers.IĒ_Č1;’’’’’’’’0’’’’_ČQÉActive coordinate systemņ¬ČQÉF Z€Y€€‚‚€ €€ āĖ‘‰€‰€ āŹ«#€‰€ ’Active coordinate systemThe active coordinate system is either the active working coordinate system, if there is one, or the model coordinate system, if not.< _ȍÉ1ą’’’’’’’’1’’’’É1ĢActive part¤DQÉ1Ģ` Ž€‰€€‚‚€ €€ ā!ä«€‰€ €€ €(€ €(€ ‚‚€&€'€&€ €'€ ’Active partA part is a grouping of top-level entities. The active part is the part to which newly-created entities are added by default, and it is the part that is accessed when an optional part argument is omitted in a procedure call. To discover which part is the active part, use the procedure part:active, and to make some specified part the active part, use the procedure part:set-active.Parts are always represented externally in the form #[part n], where n is a system-generated non-negative integer that serves as the part's identification number.< ÉmĢ1½’’’’’’’’2’’’’mĢīĶActive viewA1ĢīĶ@ N€ƒ€€‚‚€ €€ €€ €(€ €(€ ’Active viewThe active view is the view object in the context of which all the view:... procedures operate when no view argument is specified. Its identity may be discovered by using the procedure env:active-view, and a given view object may be made the active view by using the procedure env:set-active-view.= mĢ+Ī1“’’’’’’’’3’’’’+Ī¢ĻAuto-displayw=īĶ¢Ļ: B€{€€‚‚€ €€ €(€ €(€ ’Auto-displayBy default, a representation of each new entity is displayed in all views as the entity is created. Thus, by default, the auto-display feature is on. To determine the current state of this feature, use the procedure env:auto-display. To change its state, use the procedure env:set-auto-display.F+Ī 1d’’’’’’’’4’’’’ Cartesian coordinates¢Ļ ¢ĻŃa¢ĻŻp ®€Å€€ ˆ"€>€€€ €€ €€ €€ €€ €€ €€ €€ €€ €€ ‚’Cartesian coordinatesCartesian coordinates describe positions in relation to an origin and three axes (the x-axis, the y-axis, and the z-axis) that pass through the origin. The position with Cartesian coordinate (a,b,c), where a, b, and c are real numbers, is situated a units in the direction of the positive x-axis, b units in the direction of the positive y-axis, and c units in the direction of the positive z-axis away from the origin. (A negative number of units in a positive direction is equivalent to the corresponding positive number of units in the opposite direction.)%é < F€Ó€€ ‚€€ ā%#?€‰€ €€ ’If the axes are mutually perpendicular, then the coordinate system is said to be rectangular. If the positive directions of the x-, y-, and z-axes obey the right-hand rule, then the coordinate system is said to be regular.EŻG1x’’’’’’’’5’’’’GzDependency hierarchy3ūz8 >€ł€€ ˆ"€?€€ ’Dependency hierarchyGeometrical entities that share a common owner fit into one of the branches of the dependency hierarchy shown on the right.For example, a solid block is a top-level body that owns a number of dependent entities. In order of precedence, these are: one lump, one shell, six faces, six loops (one for each face), twelve edges (four for each loop, with each edge being a dependent of two loops), and eight vertices (two for each edge, with each vertex being a dependent of three edges).Bodies and points can never be anything but top-level entities. Faces, edges, and vertices can be top-level entities, but often are not. Lumps, wires, shells, and loops (whose names are printed in blue in the diagram) can never be top-level entities.@Gŗ1ö’’’’’’’’6’’’’ŗp Entity, definedLz : B€%€€‚‚€ €€ € €€ ‚‚‚’EntityAn entity is an abstract data structure that incorporates all the essential defining information relating to some permanent object within the ACISŅ Solid Modeler.It is not the object itself, nor does it represent the object in any way. However, a geometrical entity (such as an edge) includes everything the system needs to know in order to represent the associated object visually in a view window or in coded form in a file-associated view, situating it correctly in relation to any other represented objects.Šŗ I `€”€€ ‚€€ €(€ €€ €€ āŚŒT€‰€ ‚’Each entity has an owner, which may be identified by using the procedure entity:owner. Owners are entities too, and they have the additional property that they own themselves. This property makes them top-level entities. If an entity is distinct from its owner, then it is said to be a dependent entity of that owner. In addition, whenever geometrical entities share a single owner, they may be organized within a more refined dependency hierarchy.Q  p H ^€€€ ‚€&€'€&€ €'€ €'€ ā!µ€‰€ ’Entities are always represented externally in the form #[entity m n], where the positive integer m is a system-generated entity identification number and the non-negative integer n is the identification number of the part to which the entity belongs.H ø 1’’’’’’’’7’’’’ø  @Model coordinate systemHīp  @Z ‚€Ż€€‚‚€ € € ārÕ³€‰€ āĖ‘‰€‰€ ‚‚€ € āX÷L€‰€ ’Model coordinate systemThe coordinate system to which all positional referencing involved in 3DScheme's geometrical activities may ultimately be traced back. The positioning of any view coordinate system or working coordinate system is at all times describable in terms of the model coordinate system. Initially, when 3DScheme is first started, and whenever there is no active working coordinate system, the model coordinate system serves as the active coordinate system.ø  @p Bø N@1Į’’’’’’’’8’’’’N@ĶCPolar coordinatesž @ĶC Š€’€€ ˆ"€@€€€ €€ €€ €€ €€ €€ €€ €€ €€ €€ ā%#?€‰€ €€ ’Polar coordinates; Cylindrical coordinatesPolar coordinates (also known as cylindrical coordinates) describe positions in relation to an origin, a polar axis (which is a ray with the origin as its endpoint), and a z-axis (which passes through the origin and is perpendicular to the polar axis). The position with polar coordinate (r,a,c), where r, a, and c are real numbers, is situated at a perpendicular distance of r units from the z-axis, in a plane that contains the z-axis and is rotated about the z-axis through an angle of a degrees from the XZ plane in the sense determined by the right-hand rule in relation to the positive z-axis, and at a distance of c units away from the origin in the direction of the positive z-axis.< N@ D1’’’’’’’’9’’’’ DŽHSide effectĮĶC%G[ „€ƒ€€‚‚€ āyœD€‰€ €€ €€ €€ ‚‚€€ €€ €€ ‚’Side effectSome Scheme expressions are evaluated with a view to causing some outcome to occur rather than for the purpose of obtaining a value. In fact, it is considered poor style¾and a generally unwise practice¾to make any use at all of the value returned by an expression of this type.The outcomes in question are known as side effects, and broadly speaking they fall into two categories: mutation (in which a Scheme object is modified, for example by having its value or some other aspect of its current state altered) and input/output (including video display, processing keyboard and mouse activity, file handling, and communication with peripheral devices such as printers).¹ƒ DŽH6 :€€€ ‚€€ €€ €(€ ’The order in which side-effect-producing expressions are evaluated can be crucial. To sequence the evaluation of such expressions, include them in begin-expressions. In addition to explicit begin-expressions, there are a small number of contexts¾for example, the bodies of let-expressions and lambda-expressions and the consequents of cond-clauses¾that include an implied begin.F%G$I1w’’’’’’’’:’’’’$IULSpherical coordinates1¶ŽHUL{ Āo€€ ˆ"€A€€€ €€ €€ €€ €€ €€ €€ €€ €€ ā%#?€‰€ €€ ’Spherical coordinatesSpherical coordinates describe positions in relation to an origin, a polar axis (which is a ray with the origin as its endpoint), and a z-axis (which passes through the origin and is perpendicular to the polar axis). The position with spherical coordinate (r,a,b), where r, a, and b are real numbers, is situated at a distance of r units from the origin, in a plane that contains the z-axis and is rotated about the z-axis through an angle of b degrees from the XZ plane in the sense determined by the right-hand rule in relation to the positive z-axis, and on a ray from the origin that makes an angle of a degrees with the positive z-axis.D$I™L1 ’’’’’’’’;’’’’™L`OThe right-hand ruleĒ‘UL`O6 :€#€€‚‚€ €€ ‚‚€€ ’The right-hand ruleA coordinate system is said to obey the right-hand rule if, when you hold your right hand in such a way that the thumb and the first two fingers are mutually perpendicular, and you align your thumb with the positive x-axis and your index finger with the positive y-axis, then your middle finger is aligned with the positive z-axis.The rotational sense determined according to the right-hand rule in relation to a gvector that specifies an axis of rotation is the direction in which the fingers of your right hand are pointing when you curl them in toward your palm while sticking your thumb out in the direction of the gvector.6™L–O1N’’’’’’’’<’’’’–OValuee)`O< F€S€€‚‚€ €€ ‚‚ā_ųłD€‰€ ’ValueEvery Scheme expression returns some –O`OScheme object as its value.Despite this, there are certain expressions whose intent is more imperative in nature. Such expressions are evaluated not so much for the value returned as for the side effect produced during the evaluation process.G–ON1ž’’’’’’’’=’’’’N„ƒView coordinate systemW „ƒN j€€€‚‚€ ‚‚€(€ €(€ €(€ €(€ āX÷L€‰€ ’View coordinate systemEach view has a permanent and unchangeable coordinate system, whose z-axis comes perpendicularly out of the associated view window toward the user, whose x-axis goes horizontally across the view window, and whose y-axis goes vertically up the view window.Until a view's characteristics are modified by using procedures such as view:set, view:set-eye, view:set-target, and view:set-up, its coordinate system coincides with the coordinate system that was active when it was created.JNļƒ1ń’’’’’’’’>’’’’ļƒ–ˆWorking coordinate system“G„ƒ£†m ؀€€‚‚€ €€ €€ ā½P€‰€ āŌEX}€‰€ ā)l;ƒ€‰€ ‚‚€(€ €(€ €(€ ‚’Working coordinate system; WCSA working coordinate system (or WCS) is an entity, consisting of an origin, an x-axis, a y-axis, and a z-axis, that together form a regular, rectangular Cartesian coordinate system. Positions and gvectors may be specified relative to a working coordinate system using Cartesian, polar (also known as cylindrical), or spherical coordinatizing methods.Working coordinate systems may be created using the procedures wcs and wcs:from-transform, and they may be distinguished from other Scheme objects using the predicate wcs?.ó£ļƒ–ˆP n€G€€ ‚€(€ €(€ €(€ €(€ ‚‚€€ €(€ €(€ ’The constituent parts of a working coordinate system may be extracted using the procedures wcs:origin, wcs:x-axis, wcs:y-axis, and wcs:z-axis.A working coordinate system is active if it is the system relative to which positions and gvectors are specified. To determine which WCS (if any) is active, use the procedure wcs:active. To designate a WCS as the active WCS, use the procedure wcs:set-active.Ī£†d‰1R v‡?’’’’d‰MĆsolid:areaChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875397396')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ŲF–ˆ<Š’#ō€„ń€€€€ †"€B‚€)āglvU€"‰€)āglvU€"‰€)āšrRQ€"‰€)€ ‚’€l€’0€n€†"€C‚€*€ ‚’’’(solid:area ent)(solid:area ent x)Procedure&d‰bŠ# €€€ ‚’h(<ŠŹ‹@ N€S€P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚’A pair, whose car component reports the total surface area of the input entity and whose cdr component estimates the maximum relative error achieved in the area calculation (that is, the maximum difference between the calculated value and the true value as a fraction of the true value).fbŠ0Žf š€€Pķ€„°ģ€ †"€Eƒ€ƒ€ ‚ƒ€ƒ€ €&€ €&€ €&€ ‚ƒ€ƒ€ €&€ ‚’·The entity argument must be a solid body.·The optional second argument must be a real number between 0 and 1 that specifies the desired tolerance of the calculation as a maximum relative error. If this argument is omitted, a tolerance of 0.01 (that is, 1%) is used.·A reported maximum relative error of 0 indicates that the area has been determined analytically to within the limits of accuracy of the computer. Among the faces whose areas are evaluated analytically are the following:ækŹ‹ūĄT v€×€P)Ū~†°ģ)€ ƒƒ€ƒ€ ‚ƒƒ€ƒ€ ‚ƒƒ€ƒ€ ‚ƒƒ€ƒ€ ‚’ąa planar face bounded by linear and/or elliptical edges;ąa conical face that is a connected part of the curved surface of a circular cross-section cone and that is bounded by linear and/or circular edges;ąa cylindrical face that is a connected part of the curved surface of a circular cross-section cylinder and that is bounded by linear and/or elliptical edges0ŽūĄ–ˆ;ąa spherical face that is either the full surface of a sphere or a connected part of such a surface that is bounded by circular edges that all lie in longitudinal or latitudinal planes relative to the same diameter of the sphere. &0Ž!Į# €€€ ‚’2ūĄSĮ- *€ €€ †"€F‚‚’śk!ĮMƏ ģ€Ł€P¼F€-€ć$Kä€(‰€ćčńxS€(‰€ćÕżē€(‰€,€€(€€(€ć Łē€(‰€,€ćX ć€(‰€,€†"€G€&’Example:(define S (solid:sphere (position 0 0 0) 40))(define T (solid:torus (position 0 0 0) 25 5))(solid:unite S (entity:transform T (transform:translation (gvector 30 0 0))))(solid:subtract S (solid:block (position 20 -40 -40) (position -40 40 40)))(solid:area S) (11131.8839366993 . 0.00531887246513953)= SĮŠĆ1w’’’’’’’’@’’’’ŠĆÄĆNext page 18:MĆÄĆ5 :€$€€ †"€ ‚†"€H’Õ¤ŠĆ™Ä1<ó†A’’’’™ÄĖsolid:blend-edgesChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875399888')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ü^ÄĆ•Åž# Ą„ń˜€€€ †"€B‚€)āglvU€"‰€.āšrRQ€"‰€)āźiG€"‰€.āšrRQ€"‰€)€ ‚’€œ€’0€ž€†"€C‚€*€ ‚’’’(solid:blend-edges ent r)(solid:blend-edges entlist r)Procedure&™Ä»Å# €€€ ‚’Tō•ÅČ` Ž€ķ€P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚ę_ųłD€+†"€I‰€,ƒ€ €/€ ‚’A list of entities, namely, the owner(s) of the input edge(s).Replaces the input edge or each edge in the input list by a face that blends tangentially with the faces of the edge's owner that share the edge. Each replacement face is curved in such a way that its intersection with any plane perpendicular to the edge being replaced is a circular arc of radius r. In the case of a linear-edge, the replacement face is cylindrical, and in the case of a circular-edge, it is toroidal.j4»ÅyÉ6 :€k€P±€S‚°€ ‚†"€Eƒ‚’Makes all necessary adjustments to the display list and the data structure(s) associated with the owner(s) of the input edge(s), updating information about faces, edges, and vertices. Refreshes the display in all views.The input entity or each entity in the input list must be an edge of a solid body.&ČŸÉ# €€€ ‚’2yÉŃÉ- *€ €€ †"€F‚‚’/՟ÉĖZ ‚€Æ€P¼F€-ˆ"€J€ćX ć€(‰€,€€(€ˆ"€K‚’Example:(define B (solid:block (position -20 -20 -20) (position 20 20 20)))(define E (entity:edges B))(define E1 (car E))(define E2 (list-ref E 9))(solid:blend-edges (list E1 E2) 10)= ŃÉ=Ė1w’’’’’’’’B’’’’=ĖwĖNext page 19:ĖwĖ5 :€$€€ †"€ ‚†"€L’Ļž=ĖFĢ1ź‡ C’’’’FĢksolid:blockChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875403616')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')»6wĖĶ…#Ś€p„ńf€€€ †"€B‚€)āD¶x€"‰€.āD¶x€"‰€)€ ‚’€L€’0€N€†"€C‚€*€ ‚’’’(solid:block pos1 pos2)Procedure&FĢ'Ķ# €€€ ‚’fŻĶĻ‰ ą€Į€P±€S‚°ęyœD€+†"€D‰€,ƒ€ āX÷L€‰€ ‚ę_ųłD€+†"€I‰€,ƒ€ ā!µ€‰€ āqä怉€ ‚†"€Eƒ‚’A new entity, namely, the rectangular block that has diagonally opposite corners at the input positions and edges parallel to the axes of the active coordinate system.Adds the newly-created entity to the active part and, if the auto-display feature is on, adds the new entity to the display list and represents it in all views.The two input positions must not agree in any component of their coordinates relative to the active coordinate system.&'Ķ³Ļ# €€€ ‚’2Ļ - *€ €€ †"€F‚‚’³Ļ wĖ_÷³Ļkh ž€÷€P¼F€-ˆ"€M€†"€G€&€†"€G€&€†"€G€&’Example:(solid:block (position 0 0 0) (position 20 20 20)) #[entity 1 0](solid:block (position 10 10 0) (position 20 20 40)) #[entity 2 0](solid:block (position 0 0 0) (position -30 -20 -5)) #[entity 3 0]= Ø1w’’’’’’’’D’’’’ØāNext page 20:kā5 :€$€€ †"€ ‚†"€N’ĪØ°1[†žƒE’’’’°Esolid:coneChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875405974')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Ö²ā†$#‚i„ń¢€€ †"€B‚€)āD¶x€"‰€.āD¶x€"‰€.āšrRQ€"‰€.āšrRQ€"‰€)āD¶x€"‰€.āD¶x€"‰€.āšrRQ€"‰€.āšrRQ€"‰€)āšrRQ€"‰€)āD¶x€"‰€.āD¶x€"‰€.āšrRQ€"‰€.āšrRQ€"‰€)āšrRQ€"‰€)āD¶x€"‰€)€ ‚’€D’0€F†"€C‚€*€ ‚’’’(solid:cone pos1 pos2 r1 r2)(solid:cone pos1 pos2 r1 r2 x)(solid:cone pos1 pos2 r1 r2 x pos3)Procedure&°¬# €€€ ‚’Ē †s§ G€P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚ę_ųłD€+†"€I‰€,ƒ€ ā!µ€‰€ āqä怉€ ‚†"€Eƒ€/€ €/€ €€ €/€ €/€ €/€ €/€ ‚’A new entity, namely, the cone or cone frustum whose characteristics are determined by the arguments in the manner described below.Adds the newly-created entity to the active part and, if the auto-display feature is on, adds the new entity to the display list and represents it in all views.The first two numerical arguments, r1 and r2, must be non-negative and they cannot both be zero. The third numerical argument, x, must be positive. The three positions pos1, pos2, and pos3 must not be collinear.&¬™# €€€ ‚’2sĖ- *€ €€ †"€F‚‚’°™å j ¢€a€€ €/€ €/€ ‚‚€/€ €/€ €/€ €/€ ‚‚€/€ €&€ €/€ €/€ €/€ ‚’The cone or cone frustum that is created has as its central axis the line segment with endpoints at positions pos1 and pos2. The following comments deal with pos1 and the corresponding real number argument r1. Similar remarks are in order for the other pair of corresponding arguments, pos2 and r2.If r1 is 0, then the entity that is created is a cone that comes to a point at position pos1. If r1 is positive, then the entity that is created is a cone or cone frustum that has a planar face with pos1 at its center and perpendicular to the central axis (described above). The nature of this planar face depends on whether any optional arguments are provided.™oĖ~ * $€Ž€€ ‚€/€ ‚’If no optional arguments are provided, then the planar face is bounded by a circular edge with radius r1.‡Må  : D€œ€P¼F€ ‚€-ˆ"€O€‚’Example:(solid:cone (position 0 0 -25) (position 0 0 25) 15 0)?ļ~ D P n€ß€€‚€ €/€ €/€ €€ €/€ €/€ €/€€ ‚‚’If two optional arguments, x and pos3, are supplied¾and supposing, as noted above, that pos3 is not collinear with pos1 and pos2¾then the planar face is bounded by an elliptical edge whose axes are determined as follows:ßp #o ¬€į€Pų „=€x€ ƒ€ƒ€ €/€ ‚ƒ€ƒ€ €/€ €/€ €/€ ‚ƒ€ƒ€ €/€ €/€ €/€ ‚’·Draw the perpendicular to the cone's central axis that passes through the position pos3.·One axis of the ellipse has an endpoint at pos1, is parallel to the line just drawn through pos3, and has length r1.·The other axis of the ellipse also has an endpoint at pos1, is perpendicular to the first axis, and has length x multiplied by r1.&D I# €€€ ‚’£k# @8 @€Ų€P¼F€-ˆ"€P€‚‚’Example:(solid:cone (position -10 -10 -10) (position -10 -10 30) 15 5 3 (position 30 0 15))I @ā»IĒ@+ $€!€€ €/€ ‚‚’If only one optional argument, x, is provided, then the planar face is bounded by an elliptical edge whose axes are determined as follows:—+ @^Cl ¦€W€Pų „=€x€ ƒ€ƒ€ āX÷L€‰€ €/€ ‚ƒ€ƒ€ €/€ ‚ƒ€ƒ€ €/€ ‚ƒ€ƒ€ ‚’·If the cone's central axis is not parallel to the x-axis of the active coordinate system, then draw the line parallel to the x-axis that passes through pos1.·If the cone's central axis is parallel to the x-axis of the active coordinate system, then draw the line parallel to the z-axis that passes through pos1.·Choose any position (except pos1) on the line just drawn.·Using the chosen position as the second optional argument, find the axes of the ellipse by the method described above in the two-optional-argument case.&Ē@„C# €€€ ‚’},^CEQ p€]€P¼F€-ˆ"€Q€€ ‚ˆ"€R€€ ’Examples:(solid:cone (position 0 20 -30) (position -20 -20 30) 40 20 0.25)(In this example, the cone's central axis is not parallel to the x-axis.)(solid:cone (position -20 0 0) (position 20 0 0) 15 5 4)(In this example, the cone's central axis is parallel to the x-axis.)= „C>E1w’’’’’’’’F’’’’>ExENext page 21:ExE5 :€$€€ †"€ ‚†"€S’Ņ”>EJF1ž |G’’’’JF†solid:cylinderChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875408048')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ܦxE&H6#:‚Q„ń€–š¬W­[±]+µa € †"€B‚€)āD¶x€"‰€.āD¶x€"‰€)āšrRQ€"‰€)āD¶x€"‰€.āD¶x€"‰€.āšrRQ€"‰€)āšrRQ€"‰€)āD¶x€"‰€.āD¶x€"‰€.āšrRQ€"‰€)āšrRQ€"‰€.āD¶x€"‰€)€ ‚’D€,–š¬W­[±]+µa ’0€.†"€C‚€*€ ‚’’’(solid:cylinder pos1 pos2 r)(solid:cylinder pos1 pos2 r x)(solid:cylinder pos1 pos2 r x pos3)Procedure&JFLH# €€€ ‚’Pµ&HœJ› q€P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚ę_ųłD€+†"€I‰€,ƒ€ ā!µ€‰€ āqä怉€ ‚†"€Eƒ€/€ €/€ €/€ €/€ €/€ ‚’A new entity, namely, the cylinder whose characteristics are determined by the arguments in the manner described below.Adds the newly-created entity to the active part and, if the auto-display feature is on, adds the new entity to the display list and represents it in all views.Both numerical arguments, r and x, must be positive, and the three positions pos1, pos2, and pos3 must not be collinear.,LHČJ) "€€P±€S‚°€ ‚’2œJśJ- *€ €€ †"€F‚‚’ÅŒČJæL9 @€€€ €/€ €/€ ‚‚€/€ ‚‚’The cylinder that is created has as its central axis the line segment with endpoints at positions pos1 and pos2. Centered at each end of this axis and perpendicular to it, there are congruent planar faces the nature of which depends on whether any optional arguments are supplied.If no optional arguments are provided, then the planar face is bounded by a circular edge with radius r.…NśJDM7 >€ž€P¼F€-ˆ"€T€‚‚’Example:(solid:cylinder (position 0 0 -25) (position 0 0 25) 15)9ķæL}NL f€Ū€€ €/€ €/€ €€ €/€ €/€ €/€€ ‚‚’If two optional arguments, x and pos3, are supplied¾and supposing, as noted above, that pos3 is not collinear with pos1 and pos2¾then the planar face is bounded by an elliptical edge whose axes are determined as follows:åuDMn€p ®€ė€Pų „=€x€ ƒ€ƒ€ €/€ ‚ƒ€ƒ€ €/€ €/€ €/€ ‚ƒ€ƒ€ €/€ €/€ €/€ ‚‚’·Draw the perpendicular to the cylinder's central axis that passes through the position pos3.·One axis of the ellipse has an endpoint at pos1, is parallel to the line just drawn through pos3, and has length r1.·The other axis of the ellipse also has an}Nn€xE endpoint at pos1, is perpendicular to the first axis, and has length x multiplied by r1.”i}N8 @€Ō€P¼F€-ˆ"€U€‚‚’Example:(solid:cylinder (position 0 -10 -10) (position 0 -10 30) 15 3 (position 40 0 15))»n€Ź+ $€!€€ €/€ ‚‚’If only one optional argument, x, is provided, then the planar face is bounded by an elliptical edge whose axes are determined as follows:Ÿ3i„l ¦€g€Pų „=€x€ ƒ€ƒ€ āX÷L€‰€ €/€ ‚ƒ€ƒ€ €/€ ‚ƒ€ƒ€ €/€ ‚ƒ€ƒ€ ‚’·If the cylinder's central axis is not parallel to the x-axis of the active coordinate system, then draw the line parallel to the x-axis that passes through pos1.·If the cylinder's central axis is parallel to the x-axis of the active coordinate system, then draw the line parallel to the z-axis that passes through pos1.·Choose any position (except pos1) on the line just drawn.·Using the chosen position as the second optional argument, find the axes of the ellipse by the method described above in the two-optional-argument case.-Ź–„* $€€Pų „=€x€ ‚’‰8i„†Q p€u€P¼F€-ˆ"€V€€ ‚ˆ"€W€€ ’Examples:(solid:cylinder (position 10 20 -30) (position -10 -20 30) 40 0.25)(In this example, the cylinder's central axis is not parallel to the x-axis.)(solid:cylinder (position -20 0 0) (position 20 0 0) 15 4)(In this example, the cylinder's central axis is parallel to the x-axis.)= –„\†1w’’’’’’’’H’’’’\†–†Next page 22:†–†5 :€$€€ †"€ ‚†"€X’Ó¢\†i‡1©žƒJ I’’’’i‡?Žsolid:intersectChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875410363')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ÓB–†<ˆ‘#ņ€ˆ„ń~€€€ †"€B‚€)āglvU€"‰€.āglvU€"‰€.ā9ńI+€"‰€)€ ‚’€d€’0€f€†"€C‚€*€ ‚’’’(solid:intersect ent1 ent2 ...)Procedure&i‡bˆ# €€€ ‚’!»<ˆƒŠf š€{€P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚ę_ųłD€+†"€I‰€,ƒ€ €€ €€ ‚’An entity, namely, the first argument, modified as explained below.Modifies the first input entity so that only those parts of space that it shares with all the other inputs are retained. Updates the first entity's data structure, deletes all the other entities by removing them from the part(s) to which they belong and¾if they are displayed¾from the display list, and refreshes the relevant representations in all views.Ņ†bˆUŒL f€€Pķ€„°ģ€ †"€Eƒ€ƒ€ ‚ƒ€ƒ€ €€ ‚‚’·All the input entities must be solid bodies.·The boolean intersection operation is regularized in that, once the first input entity has been trimmed so as to include no points other than those that it shares with the second and subsequent input entities, any dangling faces, edges, and/or vertices are removed from what remains prior to the resulting entity being returned.2ƒŠ‡Œ- *€ €€ †"€F‚‚’ø'UŒ?Ž‘ š€W€P¼F€-ˆ"€Y€ćX ć€(‰€,€ćT`ä€(‰€,€ć$Kä€(‰€,€†"€G€&ˆ"€Z€†"€G€&’Example:(define B (solid:block (position 0 0 0) (position 20 20 20)))(define C (solid:cylinder (position 0 0 -10) (position 0 0 30) 10))(define S (solid:sphere (position 0 0 10) 20))B #[entity 1 0](solid:intersect B C S) #[entity 1 0]= ‡Œ|Ž1w’’’’’’’’J’’’’|Ž¶ŽNext page 23:?Ž¶Ž5 :€$€€ †"€ ‚†"€[’Ö„|ŽŒ1¬ |‡K’’’’ŒZÉsolid:revolve-wireChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875412382')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ēJ¶ŽĄ# ˜„ń–€€€ †"€B‚€)āglvU€"‰€)āD¶x€"‰€)āĆV-€"‰€)āšrRQ€"‰€)€ ‚’ŒĄ¶Ž€t€’0€v€†"€C‚€*€ ‚’’’(solid:revolve-wire ent pos gvec a)Procedure&Œ„Ą# €€€ ‚’pĄÄl ¦€ €P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚ę_ųłD€+†"€I‰€,ƒ€ €/€ ā%#?€‰€ ‚’An entity, namely, the input entity, modified as explained below.Modifies the input entity so that it becomes the solid formed when the region enclosed by the input entity's wire revolves through an angle of a degrees about the axis specified by the position and gvector arguments, the sense of rotation being determined by the right-hand rule relative to the input gvector. (If the wire in question is open, then perpendiculars are dropped from its "loose ends" onto the axis of revolution, and the region that is revolved is the one that is bounded by the wire, the perpendiculars, and the axis.) Updates the display list as necessary and, if the input wire-body is displayed, refreshes the representation of the resulting solid body in all views.¶Y„ĄĖĘ] ˆ€µ€Pķ€„°ģ€ †"€Eƒ€ƒ€ €€ €€ ‚ƒ€ƒ€ €€ €€ ‚’·The input entity must be a wire-body containing only a single wire, which may be either open or closed but which must be planar. Furthermore, the wire (extended¾in the case of an open wire¾by any "closing" perpendiculars to the axis of revolution) must not intersect itself.·The input position and gvector must determine a line that is coplanar with the input wire-body's wire, but without actually intersecting the region enclosed by the wire (together¾in the case of an open wire¾with any "closing" perpendiculars and the axis itself) anywhere except at a vertex or on an edge.·mÄ‚ĒJ d€Ś€Pķ€„°ģ€ ƒ€ƒ€ €/€€ €€€ €0€ ‚’·The real number input, a¾known as the sweep angle¾must lie within the range from –360 to 360.&ĖĘØĒ# €€€ ‚’2‚ĒŚĒ- *€ €€ †"€F‚‚’€*ØĒZÉV z€Y€P¼F‚<€-ˆ"€\€€(€€(€‚ƒˆ"€]’Example:(define W (wire-body (list (circular-edge (position -20 -10 0) 10 -180 0) (circular-edge (position -30 0 0) 10 -90 90) (circular-edge (position -20 10 0) 10 0 180))))(solid:revolve-wire W (position 0 0 0) (gvector 0 1 0) 225)= ŚĒ—É1w’’’’’’’’L’’’’—ÉŃÉNext page 24:ZÉŃÉ5 :€$€€ †"€ ‚†"€^’ŠŸ—É”Ź1‰J ƈM’’’’”ŹZĶsolid:sphereChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875414434')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ø3ŃÉYĖ…#Ś€j„ńf€€€ †"€B‚€)āD¶x€"‰€.āšrRQ€"‰€)€ ‚’€F€’0€H€†"€C‚€*€ ‚’’’(solid:sphere pos r)Procedure&”ŹĖ# €€€ ‚’Ū_YĖZĶ| ʀÅ€P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚ę_ųłD€+†"€I‰€,ƒ€ ā!µ€‰€ āqä怉€ ‚†"€Eƒ’A new entity, namely, the sphere with its center located at the input position and its radius equal to the input real number.Adds the newly-created entity to the active part and, if the auto-display feature is on, adds the new entity to the display list and represents it in all views.The input real number must be positive.= Ė—Ķ1w’’’’’’’’N’’’’—ĶŃĶNext page 25:ZĶŃĶ5 :€$€€ †"€ ‚†"€_’Ņ”—Ķ£Ī1ō‡”O’’’’£ĪZsolid:subtractChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875416277')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ŅAŃĶuĻ‘#ņ€†„ń~€€€ †"€B‚€)āglvU€"‰€)āglvU€"‰€)ā9ńI+€1‰€)€ ‚’€b€’0€d€†"€C‚€*€ ‚’’’(solid:subtract ent1 ent2 ...)Procedure&£Ī›Ļ# €€€ ‚’ ŗuĻĒf š€y€P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚ę_ųłD€+†"€I‰€,ƒ€ €€ €€ ‚›ĻĒŃĶ’An entity, namely, the first argument, modified as explained below.Modifies the first input entity so that only those parts of space not included in any of the other inputs are retained. Updates the first entity's data structure, deletes all the other entities by removing them from the part(s) to which they belong and¾if they are displayed¾from the display list, and refreshes the relevant representations in all views.Ŗ^›ĻqL f€æ€Pķ€„°ģ€ †"€Eƒ€ƒ€ ‚ƒ€ƒ€ €€ ‚‚’·All the input entities must be solid bodies.·The boolean subtraction operation is regularized in that, once the space occupied by the second and subsequent input entities has been removed from the first input entity, any missing faces, edges, and/or vertices are attached to what remains prior to the resulting entity being returned.2Ē£- *€ €€ †"€F‚‚’·&qZ‘ š€U€P¼F€-ˆ"€Y€ćX ć€(‰€,€ćT`ä€(‰€,€ć$Kä€(‰€,€†"€G€&ˆ"€`€†"€G€&’Example:(define B (solid:block (position 0 0 0) (position 20 20 20)))(define C (solid:cylinder (position 0 0 -10) (position 0 0 30) 10))(define S (solid:sphere (position 0 0 10) 20))B #[entity 1 0](solid:subtract B C S) #[entity 1 0]= £—1w’’’’’’’’P’’’’—ŃNext page 26:ZŃ5 :€$€€ †"€ ‚†"€a’Ļž— 19 ƈ€Q’’’’ ©@solid:torusChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875420338')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Ė:Ńk‘#ņ€x„ń~€€€ †"€B‚€)āD¶x€"‰€)āšrRQ€"‰€)āšrRQ€"‰€)€ ‚’€T€’0€V€†"€C‚€*€ ‚’’’(solid:torus pos r1 r2)Procedure& ‘# €€€ ‚’ā,ks ¶ :_€P±€S‚°ęyœD€+†"€D‰€,ƒ€ €€/€ €€ €/€ ‚ę_ųłD€+†"€I‰€,ƒ€ ā!µ€‰€ āqä怉€ ‚†"€Eƒ€/€ €/€ €/€ €€ āX÷L€‰€ ‚’A new entity, namely, the torus centered at the input position, with major radius r1 and minor radius r2. (See the notes below for an explanation of these terms.)Adds the newly-created entity to the active part and, if the auto-display feature is on, adds the new entity to the display list and represents it in all views.The torus is formed by sweeping a circle (or circular arc) whose radius is the absolute value of r2 along a circular path whose radius is the absolute value of r1 and whose center is at position pos. The circular path is called the spine curve of the torus, and it lies in a plane that is parallel to the XY plane of the active coordinate system. During the sweep, the sweeping circle (or arc) is at all times perpendicular to the spine curve.øu‘+ C V€ź€P±€S‚°€ €/€ €/€ €/€ €/€ ‚‚’When r1 and r2 are both positive with r1 greater than r2, the torus produced looks like a ring doughnut:6s a 2 4€ €P ±€S‚°€ †"€b‚’×+ | D V€Æ€P±€S‚°€ €/€ €/€ €/€ €/€ ‚‚’When r1 and r2 are both positive with r2 greater than r1, the torus produced looks more like an apple. It has two isolated vertices which are located where the sweeping arc meets the axis of revolution.6a ² 2 4€ €P ±€S‚°€ †"€c‚’?ū| ńD V€÷€P±€S‚°€ €/€ €/€ €/€ €/€ ‚‚’When r1 is negative and r2 is positive with r2 greater than the absolute value of r1, the torus produced looks like a football or a lemon. It has two isolated vertices which are located where the sweeping arc meets the axis of revolution.6² '2 4€ €P ±€S‚°€ †"€d‚’&ńM# €€€ ‚’2'- *€ €€ †"€F‚‚’ķM©@1 0€Ū€P¼F€-€ €’Examples:The three tori illustrated above are generated (in unrendered form)©@Ń by evaluating the following expressions:(solid:torus (position 0 0 0) 30 10)(solid:torus (position 0 0 0) 20 30)(solid:torus (position 0 0 0) -20 30)= ę@1w’’’’’’’’R’’’’ę@ ANext page 27:©@ A5 :€$€€ †"€ ‚†"€e’Ļžę@ļA1”P S’’’’ļA Hsolid:uniteChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1875422354')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')Ļ> A¾B‘#ņ€€„ń~€€€ †"€B‚€)āglvU€"‰€.āglvU€"‰€)ā9ńI+€1‰€)€ ‚’€\€’0€^€†"€C‚€*€ ‚’’’(solid:unite ent1 ent2 ...)Procedure&ļAäB# €€€ ‚’±¾BūDf š€g€P±€S‚°ęyœD€+†"€D‰€,ƒ€ ‚ę_ųłD€+†"€I‰€,ƒ€ €€ €€ ‚’An entity, namely, the first argument, modified as explained below.Modifies the first input entity so that it acquires all the space occupied by one or more of the other inputs. Updates the first entity's data structure, deletes all the other entities by removing them from the part(s) to which they belong and¾if they are displayed¾from the display list, and refreshes the relevant representations in all views.?óäB:FL f€é€Pķ€„°ģ€ †"€Eƒ€ƒ€ ‚ƒ€ƒ€ €€ ‚‚’·All the input entities must be solid bodies.·The boolean union operation is regularized in that all internal faces, parts of faces, edges, parts of edges, or vertices are removed from the resulting solid before it is returned.2ūDlF- *€ €€ †"€F‚‚’“#:F H‘ š€O€P¼F€-ˆ"€Y€ćX ć€(‰€,€ćT`ä€(‰€,€ć$Kä€(‰€,€†"€G€&ˆ"€f€†"€G€&’Example:(define B (solid:block (position 0 0 0) (position 20 20 20)))(define C (solid:cylinder (position 0 0 -10) (position 0 0 30) 10))(define S (solid:sphere (position 0 0 10) 20))B #[entity 1 0](solid:unite B C S) #[entity 1 0]= lF]H1w’’’’’’’’T’’’’]H—HNext page 28: H—H5 :€$€€ †"€ ‚†"€g’1]HČH1U’’’’’’’’U’’’’ČHģH$—HģH" €€€2’Ē–ČH³I1ēȉ£„V’’’’³IÓJUsesChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext850561080')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')q?ģH$J2 4€€€€ ‚†"€‚€‚‚’Unlock the Door to the Next Dimension of Inspiring Uses‹³IÆJ}#Ź€*2*€€’<€€ēßōՀ!†"€h‰€‚’€€’0€€’€ †"€ i€‚’’’$$JÓJ" €€€2’= ÆJK1w’’’’’’’’W’’’’KJKNext page 29:ÓJJK5 :€€€ †"€ ‚†"€j’ŁØK#L1=„ƆX’’’’#LŚNMathematics EducationChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1157503309')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')rJK•LY#‚€4–€€€€ ‚’:€$€ē !€!†"€‰€ ‚’’’Using 3DSchemeEõ#LŚNP n€ļ€€‚‡"€k€ € € ‚ˆ"€l€€ € € ’A Slice Off the Old Block?If your students are interested in elementary geometry, then a five-minute 3DScheme program is all it takes to make a tool for visualizing conic sections.Or, if your focus is on radians and vectors, why not encourage your students to tackle the wire-bending project described in the Getting Started textbook that accompanies 3DScheme? With careful application of a little vector geometry, your students will be able to bend wires at the click of a mouse. = •LO1w’’’’’’’’Y’’’’OQONext page 16:ŚNQO5 :€€€ †"€ ‚†"€m’Ų§O5€1‡£„Ņ Z’’’’5€äƒEngineering EducationChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext850574839')');IfThen(IsMark(`Ack'),QO5€QO`DestroyButton(`Ack'):DeleteMark(`Ack')')rQO§€Y#‚€4–€€€€ ‚’:€$€ē !€!†"€‰€ ‚’’’Using 3DScheme85€߀# €*€€‚’The World's A Partą§€ö‚7 <€Ć€ Œ€ ‡"€n€ € ‚’Already well-received by engineers for its impressive number-manipulation abilities (including unlimited precision "bignum" integers, for example) and recognized as a powerful tool for the rapid development of working prototypes, Scheme becomes even more attractive when coupled with a solid modeling interface.The sound theoretical and educational foundation of 3DScheme means that students can learn to use solid modeling technologies with a minumum of fuss and bother.ī²ß€äƒ< F€g€ Œ€ ˆ"€€€ €€€ ’And, when the geometrical engine is none other than the industry standard ACISŅ Solid Modeler, your students get firsthand experience of today's most powerful technology.= ö‚!„1w’’’’’’’’[’’’’!„[„Next page 30:äƒ[„5 :€€€ †"€ ‚†"€o’Ż¬!„8…1*Ɔn \’’’’8……‰Computer Science EducationChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext850577944')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')r[„Ŗ…Y#‚€4–€€€€ ‚’:€$€ē !€!†"€‰€ ‚’’’Using 3DSchemeæ8…ƈF Z€€€‚€ €€ €€ ‚‚‡"€p€ € ‚’SchemeIf you are not currently using Scheme as part of your computer science courses, then consider the fact that many of the best schools and universities¾including MIT, Rice, Yale, and Berkeley¾are now doing so. In fact, over 200 of the most widely respected educational institutions around the world now use Scheme to teach paradigms of modern computer science, including functional and object-oriented programming.And if you're already using Scheme, then consider moving to 3DScheme. By providing an unlimited supply of fascinating projects, from the "build one of these" variety to challenging applications involving OOP design, it's a proven motivator for students of all abilities.Ö³Ŗ……‰# €g€€ ’And it's not only your students who will appreciate it. You can be sure your students will make a splash with your colleagues in the Mathematics and Engineering departments too!= ƈĀ‰1w’’’’’’’’]’’’’Ā‰ü‰Next page 31:…‰ü‰5 :€€€ †"€ ‚†"€q’ĖšĀ‰ĒŠ1×Ņ Ż ^’’’’ĒŠӍCAD UserChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext850581601')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')rü‰9‹Y#‚€4–€€€€ ‚’:€$€ē !€!†"€‰€ ‚’’’Using 3DSchemešEĒŠӍU x€€€‚€ € € ‚‚‡"€r€ € €€€ €€ €€ ’Working in the CAD Field?If you are faced with the prospect of making the switch from two-dimensional computer-assisted design to three-dimensional, 3DScheme provides a friendly, easy-to-use environment within which to familiarize yourself with all the new concepts.Or maybe you're looking for a way to continue work on your current project while you're away from the office workstation. 3DScheme can load and save parts¾groups of solid and wireframe entities¾in .sat format, so you can sketch out a new idea or polish an old one on your laptop or your home PC.= 9‹Ž1w’’’’’’’’_’’’’ŽJŽNext page 32:ӍJŽ5 :€€€ †"€ ‚†"€s’Ų§Ž"1<n € `’’’’"žĄComputer Graphic FunChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1500293151')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')„JŽ¦h# €<-€€€€ ‚’X€$€ē !€!†"€‰ē=PLń†"€‰€ ‚’’’Using 3DSchemeļ"ŠĄ/ ,€ß€€‚€ € € ‚‚’Computer Graphic FunIf you enjoy making ¦ŠĄJŽcomputer graphic designs, 3DScheme gives you the power you need. Your solid and wireframe inspirations can be visualized in ways that were never before possible for the casual computer user..¦žĄ+ &€€€ †"€t’= ŠĄ;Į1w’’’’’’’’a’’’’;ĮuĮNext page 33:žĄuĮ5 :€ €€ †"€ ‚†"€u’צ;ĮLĀ1ׯ ‹ b’’’’LĀLÄLEGO for the Brain?ChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1500295012')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')ruĮ¾ĀY#‚€4–€€€€ ‚’:€$€ē !€!†"€‰€ ‚’’’Using 3DSchemeŽLLĀLÄB R€›€€‚‡"€v€ € €€ €’LEGO for the Brain?3DScheme is so much fun that it may be just what you're looking for to divert your child's attention from computer games.It has the pizzazz of a video game and the allure of the ultimate construction puzzle. LEGOŌ for the brain.We think you'll remember what it feels like to be a kid in a toystore.= ¾Ā‰Ä1w’’’’’’’’c’’’’‰ÄĆÄNext page 34:LÄĆÄ5 :€ €€ †"€ ‚†"€w’ŠŸ‰Ä“Å1=€ ’’’’d’’’’“ÅÉHow to OrderChangeButtonBinding(`NavButton',`PopupId(`3dscheme.HLP',`HyperContext1690790852')');IfThen(IsMark(`Ack'),`DestroyButton(`Ack'):DeleteMark(`Ack')')4ĆÄĒÅ. ,€€€ ‚†"€‚‚’kѓÅ2Ēš#§L€€’4€€!€ƒ€ƒƒ€ ‚’€¾€!ł’l€Ą€†"€€3€4€5€6†"€ €7€3€5€8€ ‚’’’System Requirements:IBM PC 386 or greaterMS Windows 3.1 or later8 Mb or more of RAM3DScheme is a trademark of Schemers Inc. ACIS is a registered trademark of SPATIAL TECHNOLOGY INC.&ĒÅXĒ# €€€ ‚’Læ2Ē¤Č#耞Ņ€€’2€€P¼F€9€:€ € ‚’€Ī€P¼F’V€Š€„É€ꁃ€ ƒ€ ƒ€ ƒ€ ƒ€ ƒ€ € ‚’’’Call for more information:Schemers Inc2136 NE 68th Street, Suite 401Fort Lauderdale, FL 33308Phone:(305) 776-7376FAX:(305) 776-6174EMail:71020.1774@compuserve.com&XĒŹČ# €€€ ‚’6¤ČÉ1 2€ €ēßōՀ!†"€‰’= ŹČ=É1w’’’’’’’’e’’’’=ÉwÉNext page 17:ÉwÉ5 :€€€ †"€ ‚†"€x’1=ÉØÉ1U’’’’’’’’f’’’’ØÉĢÉ$wÉĢÉ" €€€2’1ØÉ’’’’1’’’’’’’’g’’’’’’’’’’’’&;”Helv’’’’’’’’’’’’’’’MS Sans Serif’’’’’’Times New Roman’’’’Arial’’Symbol’Courier NewCourier’€€’€€€€’’$€€€€€€’ ’€€€€€€ €’€’ }t§‚œ„H…Œ‡ĶˆZ£„xn \…Ż Ņ n £„„œ„2  €€C‡†€€ GŠ‡vŸˆŻ Ż ‹ Z ‡§‚ž„ŠvŸ‚£„Ÿˆ2 ‹ Ÿ‚H…H…€€\…‹Œ+ś‰ŁƒŠ‡Ņ ‹ ’‚§‚󇁆 žƒ|J ‡ƈ”€‰ˆ§‚C‡\…Œ=„‹ŒŒ‡ €£„ /&;)i24 \~hc13’’ZEZ’’’’ACISActive coordinate systemActive partActive view Auto-displayAutomatic indentationBending wiresBoolean operationsCAD Cartesian coordinates$Coloring of programs(Computer graphics,Computer Science0Computer-assisted design4Conic sections8Contents<Context-sensitive jumps@Coordinate system, activeDCoordinate system, modelHCoordinate system, viewLCoordinate system, workingPCoordinates, CartesianTCoordinates, cylindricalXCoordinates, polar\Coordinates, spherical`CurvesdCylindrical coordinateshEditorlEdward MartinpEngineeringtEntityxExample|Examples of Knowledge Base entries€Features of the editor's MDI„Getting StartedˆGraphicsŒHobbyistsHow to order”Indentation˜Indexing Scheme filesœIndustrial users Introduction¤Jumps to Knowledge BaseØKnowledge Base¬Martin, Edward“Matching parenthesesøMathematics¼MDI featuresĄModel coordinate systemÄOrdering informationČParenthesis matchingĢPartŠPart, activeŌPolar coordinatesŲProgramming EnvironmentÜprogramsąRenderingäReturn valuečReviewing 3DSchemeģRight-hand rulešSchemeōSchemers IncSide effectSolid Modelersolid:area solid:blend-edgessolid:blocksolid:conesolid:cylindersolid:intersect solid:revolve-wire$solid:sphere(solid:subtract,solid:torus0solid:unite4Solids8Spatial Technology<Spherical coordinates@syntax coloringDTextbookHTransformationsLUses of 3DSchemePValueTView coordinate systemXView, active\Views`WCSdWinScheme EditorhWire-bendinglWorking coordinate systemp€ˆ€ˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆw’ųˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆ/&;)Lz2ŸfؚAéGļ5’’h,h’’’’ContentssSunShine+Reviewing 3DSchemeReviewing NavigateFinding Your Way AroundžWhat Is 3DScheme?—‚Next page 1§‚The ACIS 3D Modeling Kernelj†Next page 2†Curve CreationrˆNext page 3‰ˆSolid CreationśNext page 4ViewsuNext page 5ŒTransformationsaNext page 6xBoolean OperationsjNext page 7Rendering€Next page 8€Graphical InteractionĀƒNext page 9ŁƒThe Scheme Programming Languagey‡Next page 10Š‡Scheme code example? Next page 11P The WinScheme EditorJNext page 12ZAutomatic indentationŸ‚Parenthesis matching„Context-sensitive jumps\…Colored programs ‡Indexing of Scheme filesŸˆMDI FeaturesȉGetting Started with 3DScheme¾Next page 13ĪŠThe 3DScheme Knowledge BaseeNext page 15vExamples~Next page 14Argument: ...'Argument: entArgument: entlistӁArgument: gvecę‚Argument: pos„Argument: xœ„Active coordinate systemH…Active partŒ‡Active viewĶˆAuto-display ŠCartesian coordinatesKDependency hierarchyGEntity, defined2 Model coordinate system€Polar coordinates’‚Side effectC‡Spherical coordinatesś‰The right-hand rule‹ŒValueView coordinate system Working coordinate systemósolid:areauNext page 18‡solid:blend-edgesõ…Next page 19†solid:blockūNext page 20 solid:coneģƒNext page 21žƒsolid:cylinderjNext page 22|solid:intersect8 Next page 23J solid:revolve-wire‡Next page 24‡solid:sphere±ˆNext page 25ƈsolid:subtractNext page 26”solid:torus€Next page 27€solid:unite)„Next page 28;„=„Uses”„Next page 29£„Mathematics Education“†Next page 16ƆEngineering EducationĆ Next page 30Ņ Computer Science Education_ Next page 31n CAD UserĪ Next page 32Ż Computer Graphic Fun€ Next page 33€ LEGO for the Brain?{ Next page 34‹ How to Order0ƒ Next page 17:ƒ <ƒ ąźh}ļlğźōŠąAéGļŽÄŸėōŠą1ß\ź°ÄŸģōŠą7ĶGļŅğ/&;)L4!ŸßŪźAAéGļ "’’V­’’)l;ƒC‡N={††O={†‰ˆP={†Q={†ŒR={†xS={†€W={†ē) Ż ęVzŅ :Ž Ž¢†¢‰ˆ¢Œ‘¢x’¢“¢€—¢:äc””„Z£›”Ć rNŸ”_ Ģ”Ī ųŁ˜óųŁ˜‡ųŁ˜†ųŁ˜ ųŁ˜žƒųŁ˜|ųŁ˜J ųŁ˜‡ųŁ˜Ćˆćcō˜xĖJšrˆv¾ēJ“Ų”ś2}I£uX_¤Z®ŗ¤ ‡¢V «a»ˆŸ«j0Ŗœ¬€9Ŗœ¬”źÜæ­0ƒ †#Ģ“€ŌӘ¶†ÕӘ¶ÖӘ¶Œ×Ә¶xŲӘ¶ŁÓ˜¶€ŻÓ˜¶ė>¹ė>¹+ė>¹=„ė>¹‹ ė>¹žė>¹§‚ ė>¹Łƒ ė>¹Š ė>¹€ÕéA»†ÖéA»‰ˆ×éA»ŲéA»ŒŁéA»xŚéA»ŽéA»g„Æ»h„Æ»+i„Æ»=„j„Æ»‹ k„Æ»žl„Æ»§‚m„Æ»Łƒn„Æ»Šo„Æ»€Ū2"¼ĀƒzI½{I½+|I½=„}I½‹ ~I½žI½Łƒ€I½ŠI½€‚I½"Ć½ Ęy‡ßäNĘ? õŹöŹ=„÷Ź‹ ųŹžłŹ§‚śŹŁƒūŹŠüŹ€żŹėCĖ‰ˆ€ėCĖėCĖŒƒėCĖ„ėCĖ€ˆėCĖ†|’ÅĪ}’ÅĪ+~’ÅĪ=„’ÅĪ‹ €’ÅĪž’ÅĪ§‚‚’ÅĪŁƒƒ’ÅĪŠ„’ÅĪ€XxpĻ†fŖĻŠgŖĻŠ+hŖĻŠ=„iŖĻŠ‹ jŖĻŠžkŖĻŠ§‚lŖĻŠŁƒmŖĻŠŠnŖĻŠ€ƒÖ#ŌvßōÕG¹?ŁZH¹?ŁŸ‚I¹?Ł„J¹?Ł\…K¹?Ł ‡L¹?ŁŸˆåōŠąęōŠą+ēōŠą=„čōŠą‹ 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