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IAT 106 Spatial Thinking and Communicating Spring 2015

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1 IAT 106 Spatial Thinking and Communicating Spring 2015

2 Course Team IAT 106 Spatial Thinking and Communicating Instructor:
—the best and most fun course you'll take— Instructor: Rob Woodbury Teaching Assistants: Naghmi Shireen, Mahsoo Salimi

3 The SPATIAL THINKING Team
Rob Woodbury Mahsoo Salimi Naghmi Shireen

4 Acknowledgment Many people have made this course.
Instructors Prof. John Dill, Prof. Halil Erhan, Prof. Mike Sjoerdsma, Prof. Ben Youssef, Prof. Rob Woodbury, SIAT# Learning Designer Barb Berry, Course Coordinator Prof. Janet McCracken, @ denotes initial team member # denotes continuing team member While the course has evolved and been tuned each offering since its initial design, the essence remains. We had great fun in putting it together and in growing it, and hope you will enjoy the result. And have fun doing so!

5 Course Objectives An introduction to: You will learn how to:
Spatial thinking Graphical representation Communicating Graphically You will learn how to: think and work in the world of 3D sketch real-world 3D objects build digital models using modern 3D modeling tools turn sketches and computer-aided design models into real physical objects [course projects].

6 Course Outline by Week – this may change
Part I: The Nature of Spatial Thinking Part II: Space, Objects, and Operations Week 2: Sketching and Dimensioning Week 3: Projections 1:intro to ortho proj; simple multi-view, pictorial (parallel) projections (intro to axonometric, isometric projections) Week 4: Missing view and missing line problems: using projections and isometric sketches; intro to SolidWorks Week 5: Isometric methods; perspective; model making. Modeling with SolidWorks Week 6 Auxiliary Views & Cross-sections, Assemblies in SolidWorks; degrees of freedom Week 7: Representing Ideas with Sketches Week 8: Midterm Exam Week 9: 3-D Solid Modelling - Creating Parts in SolidWorks Week 10: Solid works assemblies; constraints and mates. Week 11: Creating Physical models: materials and fabrication Week 12: Making an effective poster; industrial design examples; Week 13: Final Presentations and Course Wrap up F I N A L E X A M

7 Course Schedule Labs: Hands-on learning, quizzes, TA feedback
Lectures: Presentation and discussions Tuesdays: 10:30am– 12:20pm Labs: Hands-on learning, quizzes, TA feedback Mondays 12:30-3:20 Labs D105 (3130), D106 (3140) Mondays 3:30-6:20 Labs D107 (3130), D108 (3140) Office Hours: Rob Tuesday (Blenz) Naghmi 330 – 430 Tuesday (Blenz) Mahsoo 330 – 430 Tuesday (Blenz) Check Canvas & with your instructor and TA NB: if you miss a lecture, you will be less able to do the lab. NB: Course Week: Tuesday to following Monday

8 Assessment* Lab assignments and homework 23% Project 1 6% Project 2 6%
Midterm exam 20% SolidWorks quiz 5% Final project with poster 15% Final exam 25% TOTAL 100% * any changes will be minor & announced in advance

9 Assessment Individual work earns 78% of the marks.
Group work counts for 22%. These proportions may change slightly. NB: To pass, students must obtain at least 50% on combined Midterm & Final Exams. NB: Midterm Exam includes portion on use of 3D modeling system, SolidWorks.

10 Logistics (1/5) Website: Lecture and Lab Material
Login using your sfu id and password. Please verify this TODAY! General course info: Canvas Assignments: submit through Canvas (digital) or with TA (paper) General announcements , or in Canvas’ “Announcements” Check your often!

11 Logistics (2/5) To Access Canvas:
We use Canvas to manage course assignments. To Access Canvas: Look for “sign-in” drop-down menu on SFU home page You should be able to sign in using your assigned SFU user id and password. Please verify this TODAY! If you have a problem, see a TA or check with the SIAT office. Lecture slides & lab material are (or soon will be!) on the course website:

12 Logistics (3/5) Text: Bertoline, G. & Wiebe, E. (2010), 6th Ed., Fundamentals of Graphics Communication, McGraw Hill (special limited edition for this course) Paper copy: at bookstore E-copy of limited edition for $45.70 USD. https://create.mheducation.com/shop/#/catalog/details/?isbn= E-copy: available of full edition for about $90 US. Gives limited term access (e.g. 90 days).

13 Logistics (4/5) Classroom etiquette described in the course syllabus:
…refrain from disruptive behavior such as holding side conversations and using laptops to surf the web or check . However, see next slide on SolidWorks. Use of cellular phones, iPods, and PDAs is not permitted during lecture and lab. Turn off your cell phone prior to start of each lecture and lab.

14 Logistics (5/5) Bring to every class and lab:
Pencils and an eraser A pen Both plain and sketching paper Tools to acquire (needed for project labs): X-acto knife or equivalent; Steel-backed ruler; compass; scissors; For sketching paper (we’ll show you where to get this): Grid paper: starting from Week 3 Isometric paper: starting from Week 4 Be prepared!

15 SolidWorks An important part of this course is learning a powerful 3D modeling tool: SolidWorks. Many assignments & projects require using SolidWorks. Other courses you may take in later years also use SolidWorks. Where do you find the software? SIAT-supplied software on all Lab Computers Buy your own 12-month license ($150 US) Limited # (~20) free licenses (to 31 Dec 2015) Your computer must meet SolidWorks’ system requirements: https://www.solidworks.com/sw/support/SystemRequirements.html If interested, me ASAP:

16 Projects in IAT106 - 1 We use projects, large and small, to
Provide examples of spatial thinking and to let you apply what you're learning in ways besides the usual homework exercises and To illustrate the power of using different kinds of “representations” to help us think spatially and to communicate our ideas As you’ll see, the projects will involve Drawings/sketches Digital representations Physical representations

17 Projects in IAT106 - 2 So … what are these “projects”?
LDD/Gimbal … to get started Here you use digital and physical “representations” or models A simple “polyhedron” Then a more complex version, 2 polyhedrons, articulated You’ll use sketches, SolidWorks (digital) and physical models A linkage mechanism Sketches, digital (SolidWorks and a simulation) and physical Final project, an “Automated Mechanical Toy (AMT)” Several sets/versions of sketches, a complete SolidWorks model and the actual physical model How do all these relate to one another … ??

18 Part I: Nature of Spatial Thinking

19 Objectives Describe spatial thinking and differentiate it from other modes of thinking Describe the importance of spatial thinking and communication in everyday life Appreciate the role of representations in spatial thinking Do a lot of spatial thinking. This is the fun part!

20 For What Jobs is Spatial Thinking Needed?
Jobs in Entertainment, eg Animation, Games, … Jobs in Design (Industrial, Engineering, Architecture) Jobs in Business Jobs in Science (Physics, Medicine, Biology, Engineering) Jobs in Medicine . . . Q: Doesn’t that seem like most all jobs? A: How very observant!

21 Tetris -- http://www.nintendo.com/
Entertainment Movies Video Games Toys Tetris Lego Tetris -- (00:18) (00:30)

22 Entertainment: Halo 3 (3:13)

23 Science Space DNA Human Body Challenger Case Sun-Earth-Moon DNA
Dna clip (1:07) Earth-sun-moon clip (00:07)

24 Science: Human Body Synovial joints (2:00)

25 Americas Cup –“Foiling” changes everything
Sport Americas Cup –“Foiling” changes everything (3:18)

26 The skier’s perspective changes everything
Sport The skier’s perspective changes everything (0:21)

27 Design: Antikythera Mechanism
Antikythera mechanism: Is probably the first computing device. The first image was recovered in a ship wreck some 100 years ago. See July 2011 article in IEEE Computer. Predicts the movement of the sun, the moon and other planets/stars <link to IEEE article> (100 – 150 BC)

28 Design: Antikythera Mechanism
(3:13)

29 Design: Aviation Museum, Roham Sheikholeslami
Design: Architecture Design: Aviation Museum, Roham Sheikholeslami

30 Design: Beijing Airport, Foster + Partners
Design: Architecture Design: Beijing Airport, Foster + Partners

31 Design: Beijing Airport, Foster + Partners
Design: Architecture Design: Beijing Airport, Foster + Partners

32 Design: Beijing Airport, Foster + Partners
Design: Architecture Design: Beijing Airport, Foster + Partners

33 Design: Deutz High Performance Engine
Design: Engineering Build it … Then run it … Build Engine Run Engine (1:21) (1:39) Design: Deutz High Performance Engine

34 Information: Geography and Spatial Information

35 Other Modes of Thinking Beside Spatial
Verbal, logical, mathematical, statistical… They can be distinguished in terms of their representational and reasoning system: Verbal -> using linguistic symbols Mathematical -> symbols or reasoning system (e.g., logic, algebra, calculus, set theory).

36 Other Modes of Thinking Beside Spatial
Verbal, logical, mathematical, statistical…

37 Other Modes of Thinking Beside Spatial
Verbal language vs. A curve traced by a point that moves so that its distance from a given point is constant. Spatial language vs. X2 + y2 = r2. Mathematics language

38 Spatial thinking as a universal mode of thinking
Accessible to everyone to different degrees in different contexts As a means of problem solving Three important elements of spatial thinking: concepts of space tools of representation processes of reasoning

39 Spatial thinking entails knowing about
Space: relationships among units of measurement, different ways of calculating distance, the basis of coordinate systems, the nature of spaces structuring problems, exploring solution alternatives, finding answers, expressing solutions. Objects and Relationships Objects and … Assemblies: collections of objects and relationships Representation: relationships among views (plan vs elev), projections (mercator vs equal area) describe, explain, and communicate the structure, operation, and function of those objects and their relationships Reasoning Answer questions about the operations of assemblies. Spatial thinking entails knowing about Space: —for example, the relationships among units of measurement (e.g., kilometers versus miles), different ways of calculating distance (e.g., miles, travel time, travel cost), the basis of coordinate systems (e.g., Cartesian versus polar coordinates), the nature of spaces (e.g., number of dimensions [two- versus three-dimensional]); representation—for example, the relationships among views (e.g., plans versus elevations of buildings, or orthogonal versus perspective maps), the effect of projections (e.g., Mercator versus equal-area map projections), the principles of graphic design (e.g., the roles of legibility, visual contrast, andfigure-ground organization in the readability of graphs and maps); reasoning—for example, the different ways of thinking about shortest distances (e.g., as the crow flies versus route distance in a rectangular street grid), the ability to extrapolate and interpolate (e.g., projecting a functional relationship on a graph into the future or estimating the slope of a hillside from a map of contour lines), and making decisions (e.g., given traffic reports on a radio, selecting an alternative detour).

40 Functions of Spatial Thinking
Spatial thinking serves three purposes: Describing capturing, preserving, and conveying the properties of and relations among objects Analysing understanding the structure and behaviour of objects Inferring intent generating answers to questions about the design and function of objects Spatial thinking serves three purposes. It has (1) a descriptive function, capturing, preserving, and conveying the appearances of and relations among objects; (2) an analytic function, enabling an understanding of the structure of objects; and (3) an inferential function, generating answers to questions about the evolution and function of objects.

41 Part II: Objects, Space and Operations

42 Design a bridge N For pedestrians Across a canyon
Joining narrow paths on either side Paths are 10m above the river N 20m

43 How did you work? What words did you use? What drawings did you make?
What are the parts of your bridge? What measurements did you use? How many options did you make? How did your bridge change as you worked?

44 The elements of spatial thinking
: Objects structure the domain Space relates objects Operations change and move objects and space

45 1 — Objects Objects are things we work with.
For each domain there are different kinds of objects: Bridges: pier, span, truss, arch, stay,… Biology: gene, cell, protein, biota,… Sociology: neighborhood, stereotype, organization,… Astronomy: star, planet, gravity,… Business: invoice, statement, organization, staff,… Objects have names. Objects relate to other objects. The set of primitives is a way of capturing our encounters with a world full of objects (occurrences of phenomena): objects are the things that we are trying to understand (Golledge, 1995, 2002). For each domain of scientific knowledge, there are different sets of objects: in biology they might include genes, cells, proteins, biota, and so forth, and in sociology they might include neighborhoods, stereotypes, organizations, etc. In any domain, we can specify at least four fundamental properties of objects that allow us to reason and think about features of objects such as their (a) identity or name, (b) location in space, (c) magnitude, and (d) temporal specificity and duration. These properties allow for the identification of an object. In the case of geographic location, for example, identification requires a coordinate system that can be globally applied and understood, as in the latitude-longitude system, or can be locally contingent, as in terms of street names and numbers. Georeferencing ensures that each object has an unambiguous location specification, and thus the entire set of objects can be located in a space (e.g., the set of georeferenced place names in an atlas gazetteer, the set of nine-digit zip codes for addresses in the United States). 45

46 2 — Space Allows us to capture the fundamental spatial properties of objects One common concept of space is based on dimensionality and uses a dimensional system By limiting ourselves to objects in three-space for the moment, we can think about objects as instances of a point, a line, an planar "area", or a "volume" The languages of space allow us to capture the fundamental properties of objects. One language is based on dimensionality and uses a geometric (and graphic) dimensional series: by limiting ourselves to objects in three-space for the moment, we can think about objects as instances of a point, a line, an area, or a volume. As is clear from looking at a large- and a small-scale map of an area of Earth’s surface, a point on a large-scale map can become an area on a small-scale map. (To geographers, a large-scale map covers a small area of Earth’s surface and vice versa. This is an instance of the tuning of spatial thinking by means of a disciplinary convention that is perhaps counter-intuitive.) The language is a flexible way of describing spatial properties of objects. BUT--be careful in using this language across knowledge domains: a point in geometry is a dimensionless location, whereas a point on a map is an area, perhaps very small, on the surface of Earth. A second language is based on scale and uses scalar relations between objects to arrive at a sense of context (Montello, 1993). Context can be established by means of the terminal values that encompass the scale sequence, the lower bound of which often acts as a datum. The choice of terminal values can reflect extremes in our understanding of the phenomena studied. Thus, the stunning realization of the span of contemporary knowledge in Powers of Ten (Morrison et al., 1982) offers a visual model of the world that ranges from 1025 to 10-16, encompassing 42 powers of ten arranged around the datum of 1 meter, roughly the world at arm’s length (see Figure 2.3). Thus: The pages offer a reference frame, a marker for exploration of experience in the domain of astronomy, or of geography, or of biology, or of chemistry. Any physical object can be sought out in its proper place along the journey, and so given an appropriate context. (Morrison et al., 1982, p.190) The choice of bounds reflects a convention about the phenomenal range of the particular domain of knowledge (see also Packard, 1994). We can consider other properties related to scale: the limit of resolution, the units of measurement and the calibration of a scale, the conversion between different scales, and the standard benchmarks against which objects are compared. Other languages of space deal with frames of reference and directions. 46

47 2 — Space Derive a series of spatial concepts from the location properties of sets of objects. We can specify distance, angle, and direction (relative to a given frame of reference), sequence and order, connection and linkage. We can understand the structural properties of sets of objects in terms of boundaries, density, dispersion, shape, pattern, region, volume… The third step allows us to derive a series of spatial concepts from the (spatial or temporal) location properties of sets of objects. In two-space representations, we can specify distance, angle, and direction (relative to a given frame of reference), sequence and order, connection and linkage. We can understand the structural properties of sets of objects in terms of boundaries, density, dispersion, shape, pattern, and region. In three-space, we can also consider the properties of slope or gradient, peaks, and valleys. 47

48 3 — Operations Operations allow us to change and move objects in a space transform (e.g., translate, rotate, scale, shear) sets of objects within the space change the spatial scale at which we operate (by zooming in or out) change the units of dimensions (yd <-> m) change the dimensionality of the space (collapsing from three to two dimensions-i.e. projections) The fourth—and crucial—step captures the operations that allow us to manipulate and transform the space that we have created and to interpret the relations among objects in the set. We could, for example, translate or rotate sets of objects within the space or change the spatial scale at which we are operating (by zooming in or out) or change the distance metric (e.g., using a Manhattan or city-block metric versus a Euclidean or as-the-crow-flies metric) or change the dimensionality of the space (collapsing from three to two dimensions). Through processes of simplification, generalization, and classification, we can identify patterns in distributions of objects (see Chapter 3.8). We could describe patterns as random versus systematic, recognizing that these descriptions suggest something about the processes that may have given rise to the patterns, thus linking space and time. Systematic patterns can be clustered or uniform; uniform patterns in two-space can be built on either a rectangular or a triangular lattice. Shapes and patterns can display symmetry or be asymmetrical. We can look for outliers to patterns, breaks or discontinuities, and distortions in portions of the pattern. We could identify higher-order structures in the spatial structure such as systems, networks, or hierarchies based on concepts of sequence, linkage, dominance, and subordination. We can overlay sets of objects in the same space, looking for associations and correlations, or disaggregate complex spatial patterns into separate layers. We look for correlations (positive or negative) between layers. We can identify—and try to interpret—outliers or exceptions that do not conform to a pattern. We can interpolate between or extrapolate from objects. We can bring to bear interpretive axioms: for example, nearby objects are likely to be similar, but closer objects are likely to be more similar. From this we can consider nearest neighbors, distance decay effects, spatial autocorrelation, and so forth. (All of these operations can be performed on a GIS working with geospatial data; see Chapters 7 and 8.) At this point, the basis for the power of spatial thinking is clear: it lies in the range of operations that we can bring to bear on the description and explanation of spatial structures and the range of representations that we can use to capture those spatial structures. We can appreciate that power in another way, as well. This discussion of three sets of ideas—the language of space, spatial concepts, and operations—is based on only one member of the set of four primitives—spatial location. Each of the other three primitives—identity, magnitude, and temporal specificity and duration— can be approached spatially. Thus, identity gives rise to taxonomies and a range of spatial representations can be used to express the structure of classifications (trees, Venn diagrams, etc.). We can capture branching relations and ordination (super- and subordinates) and think about families, hierarchies, etc. The property of time gives rise to ideas such as growth, change, and development, all of which can be spatialized and represented. Magnitude can be considered an ordered series and therefore easily spatialized. 48

49 Summarizing The Process of Spatial Thinking
Define your basic objects (primitives) Define space: measures, concepts,… Develop operations based on spatial concepts to change and move space and objects Let’s apply the process to a Gimbal example

50 Gimbal Example Objects: Pivot, Ring, Base, Support
Pivot: a support that enables an object attached to rotate about an axis Ring: A circular structure that is supported by one or two pivots to either another ring or to the base. Space: Inner rings are smaller than the outer ring supporting them. Rotations occur about axes in space. The base sits on the XY plane. Each object has a local coordinate system. Operations change and move space and objects If the outer ring rotates about X-axis, the inner ring rotates with it; and if the inner ring rotates about its Y-axis, the object on the inner ring can be rotated about X and Y axes simultaneously. Two-Gimbal Mechanism

51 Another Example GUITAR MAKING

52 Creating a virtual guitar in SecondLife:
Modeling making a guitar using solid modeling methods Suzanne Vega’s Guitar by Robbie Dingo (3:05)

53 Building a real Yamaha guitar
(3:02)

54 Discussion How does the video clip of the virtual guitar express the objects and their relationships in virtual environment? How does Yamaha’s guitar (real) compare to Susan Vega’s guitar (virtual): differences and similarities in concepts, process, techniques, operations? How is the ‘space’ defined in both examples?

55 Visualization of a Guitar and its Parts
Objects, Language, Concepts, Operations? Spatial Context: Life, Physical, Intellectual?

56 Space? Space: both abstract structure and tool for relating objects
Space as an abstract term (see ) Space relates objects

57 Space? Space relates objects

58 Space in different contexts
Mathematics: An abstract conceptual framework within which we compare and quantify the distance between objects, their sizes, their shapes, and their speeds. Physics: a set of dimensions in which objects are separated and located, have size and shape, and through which they can move. the standard space interval is called a meter: the distance traveled by light in a vacuum in about 1/ second. Architecture: A volume defined by objects; when associated with a function, becomes a "place".

59 Properties of Space …compare and quantify the distance between objects, their sizes, their shapes, and their speeds number of dimensions for a space can be zero (a point), one (a line), two (a plane), more than three, finite or infinite… In our course, we study: 2D and 3D spaces, and sometimes with temporal (time) dimensions Space and objects as reference frames: contains, borders, divides

60 Representation of Space
Cartesian coordinate system: Defined by X, Y, and Z axes, the position of any point in three-dimensional space is given by means of three coordinates: x, y, z If any two axes are taken, they form 2D space, or a plane

61 Representation of Space
Cylindrical coordinate system: Defined by polar and longitudinal axes, the position of any point in three-dimensional space is given by means of three coordinates: r or ρ – radial distance Φ or φ – angular coordinate z – height Used in engineering analysis and in local navigation.

62 Representation of Space
Spherical coordinate system: Defined by zenith and reference directions, the position of any point in three-dimensional space is given by means of three coordinates: r or ρ – radial distance θ – polar angle Φ or φ – azimuth angle Used in celestial navigation, mathematics and physics.

63 Objects in Space Location: Absolute position in a coordinate system
Relative position with respect to another object existing in the same space Tentative position, near, on top, south-west, behind. Distance: To origin (of the base coordinate system) To other object: in terms of coordinate system units, e.g. 100 meter, three block, four flours up Size: Measured by coordinate system units Measured by comparing another object, e.g. 1.5x bigger Shape (geometry): primitive (square, circle, triangle…) or complex (curvilinear, composite, nurbs …) Direction and orientation

64 General Operations: move and rotate
move and rotate, attach, detach, carve, cut… Move  Rotate 

65 General Operations: attach and detach

66 General Operations: cut and carve

67 Discussion Did you see any other operations in:
the guitar making videos? The gimbal? Look for Objects, Space and Operations.

68 Understanding Complex Objects
Objects made up of other objects: Assemblies

69 Composing vs. Decomposing
Problem-solving strategy: Divide-and-conquer strategy Divide object into less complex sub-objects Study relationship between them Define the assembly rules Use representations!

70 Art and Engineering Spatial thinking crosses disciplines
Objects … spatial relationships … assemblies…motion… Theo Jansen--engineering blends into art: Let’s decompose it … look at a “simple” sub-assembly of a single (wooden) Theo Jansen Linkage: A more pure (Kinetic) art eg:

71 Exploded view of Honda F1 car
Assemblies Exploded view of Honda F1 car

72 Assemblies: Animation
Engine disassembly (in SolidEdge) YouTube online Link: LEGO disassembly YouTube online Link: (1:15) (1:04)

73 Real Life Assembly Real engine disassembly (with wrenches and grease)
YouTube online Link: (5:28)

74 Canvas: Course Management System
We use Canvas to manage course assignments. To Access Canvas: Click “LogIn” and look for your course (here, IAT106) We use a website for all course material To access lecture slides and lab material: Go to schedule and look for appropriate week Material will be published in time for each week

75 Preparatory Lab Assignment:
Work individually Download Lego Digital Designer (or use it in a lab—it is in 3130 and 3140 at least, and may be in other labs). Build a simple LDD model for one of the following objects: Windmill Watermill Pinwheels Save your file as follows: <StudentName1>.lxf E.g: JohnDill.lxf Submit the file to Canvas Lab Page under Lab 1 Preparatory

76 Optional Readings for the curious
“The Nature of Spatial Thinking” Source: Learning to Think Spatially, National Research Council, The National Academies Press, 2006, pp "Using Computation to Decode the First Known Computer" Source: Computer 44.7 (2011):32-39. Q: Where to find them? A: On the course website. Go to Week 2 inside “Course Schedule” link.

77 N.B. On Writing This applies to all writing in this course.
We expect you to write to the best of your ability. We expect you use correct grammar, spelling and punctuation. We expect you to be concise, that is, to use fewer words rather than more. Poor writing will result in your work being given a zero mark, irrespective of its content.

78 N.B. On Plagiarism This applies to all work in this course.
We expect you to understand what constitutes plagiarism. We expect that you will never plagiarize. There is a plagiarism tutorial in Canvas (click on Modules in the left menu). Plagiarism will result in application of SFU plagiarism rules. These are tough. DON'T PLAGIARIZE!

79 Lab 1: Example from a previous year

80 References (Part I) Flight Pattern: Celestial Mechanics: Lego Commercial: Tetris: Halo3: DNA Animation: America’s Cup: Aerial Skiing: Antikythera Mechanism: Internet BackBone: Internet traffic: Deutz Engine Build: Deutz Engine Running:

81 References (Part II) Suzanne’s Guitar: Yamaha guitar: Acoustic Guitar Part Names: Classical Guitar Picture and part names: Guitar Internal Parts: More Guitar Part Names: Guitar-exploded-view: Toiletseat: Finger Joint (for materials): Computer Exploded View: Jet Engine NASA: Engine Disassembly: LEGO Disassembly: Real Engine Disassembly:

82 End of Lecture

83 Details of modeling Vega’s Guitar 7 slides
Appendix Details of modeling Vega’s Guitar 7 slides

84 Vega’s Guitar: Details - I

85 Vega’s Guitar: Details - II

86 Vega’s Guitar: Details - III

87 Vega’s Guitar: Details - IV

88 Vega’s Guitar: Details - V

89 Vega’s Guitar: Details - VI

90 Vega’s Guitar: Details - VII


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