Chapter 3 Visualization
Objectives • Recognize that 3-D spatial skills are necessary for success in engineering • Describe how a person’s spatial skills develop as they age • Examine the types of questions used to assess a person’s spatial skill level
Objectives (cont’d.) • Show how you can improve your 3-D spatial skills through techniques that include • Drawing different corner views of an object • Rotating objects about one or more axes • Sketching object reflections and making use of symmetries
Objectives (cont’d.) • Show how you can improve your 3-D spatial skills through techniques that include (cont’d.) • Considering cross sections of objects • Combining two objects to form a third object through Boolean operations
Introduction • To understand drawings, need to be able to visualize in three dimensions • Linked to creativity in design • 3-D spatial skills can be developed through practice
Background • IQ testing developed in early 20th century • Howard Gardner: multiple intelligences • Linguistic • Logical-Mathematical • Spatial • Bodily-Kinesthetic • Musical
Background (cont’d.) • Howard Gardner: multiple intelligences (cont’d.) • Interpersonal • Intrapersonal • Naturalist
Development of Spatial Skills • Acquired through natural progression • 1st stage: 2-D spatial skills • 2nd stage: 3-D spatial skills • Advanced stage: 3-D combined with measurement • Spatial skills not emphasized in schools • Can be developed through practice and exercise
Types of Spatial Skills • Spatial perception • Spatial visualization • Mental rotations • Spatial relations • Spatial orientation
Assessing Spatial Skills FIGURE 3.03. A problem similar to that found on the Differential Aptitude Test: Space Relations. FIGURE 3.04. A problem similar to that found on the Purdue Spatial Visualization Test: Rotations.
Isometric Corner Views of Simple Objects FIGURE 3.09. The relationship between coded plans, a building, and an isometric sketch.
Isometric Corner Views of Simple Objects (cont’d.) FIGURE 3.10. A simple coded plan with corners labeled. FIGURE 3.11. Sketched isometric views from the corners of the coded plan in Figure 3.10.
Object Rotations about a Single Axis FIGURE 3.12. A shape rotated about a pivot point in 2-D space. FIGURE 3.18. A 3-D object rotated 90 degrees counterclockwise about the z-axis.
Object Rotations about a Single Axis (cont’d.) FIGURE 3.21. Positive and negative rotations about the y-axis.
Object Rotations about a Single Axis (cont’d.) • Notation FIGURE 3.22. Object rotations specified by notation.
Rotation of Objects by More Than 90 Degrees about a Single Axis FIGURE 3.23. An object rotated 180 degrees about an axis.
Equivalencies for Rotations about a Single Axis • A positive 180 degree rotation is equivalent to a negative 180 degree rotation • A negative 90 degree rotation is equivalent to a positive 270 degree rotation • A positive 90 degree rotation is equivalent to a negative 270 degree rotation
Rotation about Two or More Axes FIGURE 3.29. Object rotations about two axes—order not commutative.
Equivalencies for Object Rotations about Two or More Axes FIGURE 3.30. Equivalent rotations about two axes.
Reflections and Symmetry FIGURE 3.32. An object located at a distance from the plane and its reflection. FIGURE 3.31. An object and its 3-D reflection.
Symmetry FIGURE 3.33. Objects and their planes of symmetry. FIGURE 3.34. A comparison of object reflection and symmetry.
Symmetry (cont’d.) FIGURE 3.35. Object reflection through rotation.
Cross Sections of Solids • Visualizing cross-sections enables engineers to: • See how a building or device is put together • Think about how circuit boards stack up inside housing • Figure out how molecules combine • Cross-section: intersection between solid object and cutting plane
Cross Sections of Solids (cont’d.) FIGURE 3.39. Various cross sections of a cube. FIGURE 3.37. Cross sections of a cylinder.
Combining Solids FIGURE 3.40. Overlapping objects and volume of interference. FIGURE 3.41. Result of two objects joined.
Combining Solids (cont’d.) FIGURE 3.42. Result of two objects intersected. FIGURE 3.43. Result of two objects cutting.
Strategies for Developing 3-D Visualization Skills • The sketching of corner views • Easiest way to start large task is to make isometric views of small pieces • Look at the corner from which you are sketching to determine left and right sides • Sketch height of object • Draw other surfaces • Examine drawing to see where to add lines
Object Rotations about One Axis FIGURE 3.52. Rotation of surface B only. FIGURE 3.53. Rotation of surfaces C and D.
Object Rotations about Two or More Axes • Not as simple as one-axis procedure • Suggestions • Sketch object after first rotation and before second • Concentrate on a single key surface • Focus on a surface that was not visible originally
Reflections • Start with one surface that is fully visible in original view and reflection • Transfer it point by point • Each point and its reflection must be same distance from reflection plane
Object Symmetry FIGURE 3.67. An object with five planes of symmetry identified.
Cross-Sections FIGURE 3.69. Cross section of an object with an angled cutting plane.
Combining Solids FIGURE 3.74. An object created by an alternative series of combinations.
Summary • Learned about Gardner’s definitions of basic human intelligences • Discussed the way spatial intelligence is developed and assessed • Outlined several exercises that help develop spatial skills: • Constructing isometric sketches from different corner views
Summary (cont’d.) • Outlined several exercises that help develop spatial skills: (cont’d.) • Rotating 3-D objects about one or more axes • Reflecting objects across a plane and recognizing planes of symmetry • Defining cross sections obtained between cutting planes and objects • Combining two objects to form a third object by cutting, joining, or intersecting