Spatial Sense 4-1 PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A

Transcription

1 Spatial Sense 4-1

2 Table of Contents Spatial Sense Constructing Shapes from Mat Plans Constructing 3-view Orthographic Projections from Mat Plans Constructing Mat Plans from 3-View Orthographic Projections Constructing Isometric Drawings from Mat Plans Matching Isometric Drawings with Mat Plans Combining Isometric Drawings Hidden-View Lines and 3-View Orthographic Projections Matching Isometric Drawings with 3-view Orthographic Projections Constructing Isometric Drawings from 3-View Orthographic Projections Constructing 3-view Orthographic Projections from Isometric Drawings Surface Identification (Orthographic Projections - Isometric Drawings) Dot Paper Isometric Paper Drawing Mat

3 Constructing Shapes from Mat Plans Being able to represent the shape of a three-dimensional object on a two-dimensional surface is very important as it allows others to interpret the object s shape. This information can then be used to construct the object. Although not used in industry, mat plans are one of the simplest methods to represent three-dimensional objects. They are ideal in developing a spatial awareness; however, they have limitations which you will discover as you proceed through the following exercises. 1. Construct the building illustrated in the mat plan below using cube-a-links. Orient your building correctly on the building mat provided. Turn the building mat so that you can look at the front, back, left, or right side of your building straight on. You should see a 2-D pattern of squares. Decide which side of the building (front, back, right, left, or top) matches each of the diagrams below. a) b) c) d) e) 4-3

4 Constructing 3-view Orthographic Projections from Mat Plans 1. Shown below is the right side view of a cube building. Draw the left side view. Confirm the accuracy of your drawing using cube-a-links. 2. Use the mat plan below to construct the building on a building mat. Draw the top, front, and right views (3-view orthographic). Note: To assist in drawing these views for the first time, it may be helpful to tape three pieces of transparency sheets together to form three sides (front, top, and right side view) of a cube. The construction can then be placed neatly against the inside corner of the transparency to allow the three views to be drawn and labelled. Once complete, remove the tape holding the transparency together to provide you with the three views on a flat, two-dimensional, surface. 3. Use the mat plans below to construct the buildings on a building mat. Draw the top, front, and right views (3-view orthographic) for each building. a) b) c) 4-4

5 4. Use the mat plans below to construct the buildings on a building mat. Match each building with the correct set of 3-view orthographic drawings shown below. a) b) c) 4-5

6 5. Use the mat plans below to construct the buildings on a building mat. Draw the top, front, and right views (3-view orthographic) for each building. a) b) c) Use the mat plan below to construct the building on a building mat. Draw the top, front, and right views (3-view orthographic) for the building. 4-6

7 6. On a building mat, use the mat plan below to construct a cube building. Match the building constructed from the mat plan above to one of the three sets of 3-view orthographic drawings below. 4-7

8 7. Use cube-a-links and the provided mat plans to build each of the 5 buildings. Place each building on a building mat and write the letter of the building in front of the building. When all buildings have been constructed, match each building with one of the sets of 3-view orthographic drawings on the following page. Justify each match in writing. Mat Plans 4-8

9 8. Match the buildings constructed (previous mat plans) with the 3-view orthographic drawings given below. 3-view orthographic Set 1 3-view orthographic Set 2 3-view orthographic Set 3 Top 3-view orthographic Set 4 Front Right 3-view orthographic Set 5 4-9

10 9. Below are the mat plans for four different buildings. Construct a model of each building on a building mat. 10. Match the buildings constructed above with the following 3-view orthographic projections. 4-10

11 10. (continued). 4-11

12 Constructing Mat Plans from 3-View Orthographic Projections Note: There may be more than one mat plan that will represent each 3-view orthographic projections in questions Use the 3-view orthographic projections given below to construct a model of each building on a building mat. Draw the corresponding mat plan for each building. 4-12

13 1. (continued). 4-13

14 2. Construct a 3-D model using the following views. Draw the corresponding mat plan. 3. Construct a 3-D model using the following views. Draw the corresponding mat plan. 4. Construct a 3-D model using the following views. Draw the corresponding mat plan. 4-14

15 5. Construct a 3-D model using the following views. Draw the corresponding mat plan. 6. Construct a 3-D model using the following views. Draw the corresponding mat plan. 4-15

16 7. Construct a 3-D model using the following views. Draw the corresponding mat plan. 8. Construct a 3-D model using the following views. Draw the corresponding mat plan. 4-16

17 9. Construct a 3-D model using the following views. Draw the corresponding mat plan. 4-17

18 Constructing Isometric Drawings from Mat Plans Isometric drawing are an excellent way to represent three-dimensional objects because, unlike mat plans and orthographic projections, they give the illusion of three-dimensionality. 1. Using isometric paper, construct an isometric drawing for each of the following mat plans: 2. Use the isometric drawing tool at to draw an isometric drawing of each mat plan above. (Hint: Viewing Isometric Drawings on this website...when you are looking up and to the left you are seeing the front view; when you are looking up and to the right you are seeing the right side view.) Use the eye icon to check the mat plan and the top-front-right side orthographic views for agreement). 4-18

19 Matching Isometric Drawings with Mat Plans 1. Which of the following is not a corner view of the building represented by the mat plan? 4-19

20 2. On a building mat, build a cube model of each of the following three buildings. Identify which building is represented by each of the corner views (left front, front right, back left, and right back) illustrated in isometric drawings A- L. 4-20

21 3. Which corner of this building was the artist viewing to make the drawing at the right? 4-21

22 Combining Isometric Drawings 1. Which of these buildings can be made from the two basic shapes given? 4-22

23 2. Using cube models, show how the two basic shapes can be put together to make each of the buildings shown below? 4-23

24 Hidden-View Lines and 3-View Orthographic Projections Hidden-view lines are represented by broken line segments on an orthographic projection. Unlike solid object lines, hidden-view lines allow an orthographic projection to represent the edges of voids (hollow spaces) of an object that is not visible by the face being viewed. To assist in visualizing these objects it may be useful to use cube models to represent their shape Draw in the missing object lines or hidden-view lines on the orthographic projection. 4-24

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28 Enrichment The following problems involve slanting surfaces and are considered to be very challenging. To assist in visualizing these objects it may be useful to use malleable materials, as opposed to rigid cube models, to represent their shape 4-28

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30 Matching Isometric drawings with 3-View Orthographic Projections Match the letter of the set of orthographic views below to the number representing the correct isometric view on the following page letter answer letter answer letter answer letter answer letter answer letter answer letter answer letter answer letter answer letter answer

31 Matching isometric views with 3-view orthographic projections continued

32 Constructing Isometric Drawings from 3-View Orthographic Projections 1. Use the orthographic views of the set of stairs shown below to construct an isometric view and to build a cube-a-link model. 4-32

33 2. Use the orthographic views (top, front, right) of the machine component shown below to construct an isometric views and to a build cube-a-link model. 4-33

34 Constructing 3-View Orthographic Projections from Isometric Drawings 1. Draw three orthographic views (top, front, right) of the object below. Use the positions indicated by the short darkened line segments to position the views. 4-34

35 2. Draw three orthographic views (top, front, right) of the object below. Use the positions indicated by the short darkened line segments to position the views. 4-35

36 Surface Identification (Orthographic Projections - Isometric Drawings) 1. Find the numbers in the top, front, and right side views that correspond to the lettered surfaces in the isometric drawing. Create a table similar to the one below to record your answers. Top Front Right A B C D E F G H J K L M N 4-36

37 2. Find the numbers in the top, front, and right side views that correspond to the lettered surfaces in the isometric drawing. Create a table similar to the one below to record your answers. Top Front Right A B C D E F G H I J K L M 4-37

38 Dot Paper 4-38

39 Isometric Paper 4-39

40 Drawing Mat 4-40