2. Section 3 Descriptive Geometry Chapter 14 Intersections

3. Permission granted to reproduce for educational use only. 3 © Goodheart-Willcox Co., Inc. Objectives List the basic types of geometric surfaces and intersections. Describe how intersections are formed and identify the common methods used in their construction. Construct intersections using manual and CAD procedures. List the applications of intersections in construction and manufacturing.

4. Permission granted to reproduce for educational use only. 4 © Goodheart-Willcox Co., Inc. Intersection Defined by objects passing through each other. Common in building designs, aerospace applications, and automotive parts. Classified by types of geometrical surfaces involved.

5. Permission granted to reproduce for educational use only. 5 © Goodheart-Willcox Co., Inc. Types of Geometrical Surfaces Ruled geometrical surfaces Plane surfaces Single-curve surfaces Warped surfaces Double-curve geometrical surfaces

6. Permission granted to reproduce for educational use only. 6 © Goodheart-Willcox Co., Inc. Ruled Geometrical Surfaces

7. Permission granted to reproduce for educational use only. 7 © Goodheart-Willcox Co., Inc. Double-Curve Geometrical Surfaces

8. Permission granted to reproduce for educational use only. 8 © Goodheart-Willcox Co., Inc. Gore Method May be used for approximate development of spherical surface.

9. Permission granted to reproduce for educational use only. 9 © Goodheart-Willcox Co., Inc. Spatial Relationships Point location on line. Intersecting lines and nonintersecting lines in space. Visibility of crossing lines in space. Visibility of line and plane in space. Location of piercing point.piercing point Location of line through point and perpendicular to oblique plane.

10. Permission granted to reproduce for educational use only. 10 © Goodheart-Willcox Co., Inc. Point Location on a Line Solved by orthographic projection.

11. Permission granted to reproduce for educational use only. 11 © Goodheart-Willcox Co., Inc. Intersecting and Nonintersecting Lines in Space Solved by orthographic projection. Common point must exist for lines to intersect.

12. Permission granted to reproduce for educational use only. 12 © Goodheart-Willcox Co., Inc. Visibility of Crossing Lines in Space Solved by projecting crossing point to adjacent view. Line “touched” first in adjacent view determines visibility.

13. Permission granted to reproduce for educational use only. 13 © Goodheart-Willcox Co., Inc. Visibility of a Line and Plane in Space Solved by projecting crossing points to adjacent view. Object “touched” first in adjacent view determines visibility.

14. Permission granted to reproduce for educational use only. 14 © Goodheart-Willcox Co., Inc. Location of the Piercing Point of a Line with a Plane Solved by orthographic projection method or auxiliary view method. Manual projection techniques used in manual drafting. Construction lines created in CAD.

15. Permission granted to reproduce for educational use only. 15 © Goodheart-Willcox Co., Inc. Location of the Piercing Point (Orthographic Projection Method)

16. Permission granted to reproduce for educational use only. 16 © Goodheart-Willcox Co., Inc. Location of the Piercing Point (Auxiliary View Method)

17. Permission granted to reproduce for educational use only. 17 © Goodheart-Willcox Co., Inc. Location of a Line Perpendicular to an Oblique Plane

18. Permission granted to reproduce for educational use only. 18 © Goodheart-Willcox Co., Inc. Intersection Procedures May be used for problems involving 2D objects, 3D objects, or combinations of both. Regular projection methods used in 2D manual and CAD drafting. Solid modeling more useful for 3D CAD applications.

19. Permission granted to reproduce for educational use only. 19 © Goodheart-Willcox Co., Inc. Methods Used for Solving Intersection Problems Orthographic projection method Auxiliary view method Cutting plane method

20. Permission granted to reproduce for educational use only. 20 © Goodheart-Willcox Co., Inc. Intersection of Two Planes Using Orthographic Projection

21. Permission granted to reproduce for educational use only. 21 © Goodheart-Willcox Co., Inc. Intersection of Two Planes Using Orthographic Projection

22. Permission granted to reproduce for educational use only. 22 © Goodheart-Willcox Co., Inc. Intersection of an Inclined Plane and a Prism

23. Permission granted to reproduce for educational use only. 23 © Goodheart-Willcox Co., Inc. Intersection of an Inclined Plane and a Prism

24. Permission granted to reproduce for educational use only. 24 © Goodheart-Willcox Co., Inc. Intersection of an Inclined Plane and a Prism

25. Permission granted to reproduce for educational use only. 25 © Goodheart-Willcox Co., Inc. Intersection of an Oblique Plane and a Prism

26. Permission granted to reproduce for educational use only. 26 © Goodheart-Willcox Co., Inc. Intersection of an Oblique Plane and a Prism

27. Permission granted to reproduce for educational use only. 27 © Goodheart-Willcox Co., Inc. Intersection of an Oblique Plane and an Oblique Prism

28. Permission granted to reproduce for educational use only. 28 © Goodheart-Willcox Co., Inc. Intersection of an Oblique Plane and an Oblique Prism

29. Permission granted to reproduce for educational use only. 29 © Goodheart-Willcox Co., Inc. Intersection of Two Prisms 1.Draw cutting plane in top view. 2.Project Points 1 and 2 to front view. 3.Project lines to Edge CC to locate Points 3 and 4. 4.Project remaining piercing points and draw intersection.

30. Permission granted to reproduce for educational use only. 30 © Goodheart-Willcox Co., Inc. Intersection of Two Prisms 1.Draw construction lines to locate Points 1, 2, 1, and 2. 2.Draw construction lines to locate Points 3 and 4. 3.Locate remaining piercing points and create intersection.

31. Permission granted to reproduce for educational use only. 31 © Goodheart-Willcox Co., Inc. Intersection of Two Prisms Using the Intersect Command

32. Permission granted to reproduce for educational use only. 32 © Goodheart-Willcox Co., Inc. Intersection of a Plane and a Cylinder 1.Draw parallel lines in top view and project intersections to front and side views. 2.Project points from edge view to front view. 3.Connect points to form intersection.

33. Permission granted to reproduce for educational use only. 33 © Goodheart-Willcox Co., Inc. Intersection of a Plane and a Cylinder 1.Draw horizontal construction lines in top view and project points to front and side views. 2.Draw construction lines to locate intersections in front view. 3.Create elliptical arcs to complete intersection.

34. Permission granted to reproduce for educational use only. 34 © Goodheart-Willcox Co., Inc. Intersection of an Oblique Plane and a Cylinder 1.Draw cutting planes in top view. 2.Project intersections to front view. 3.Connect piercing points to form intersection. 4.Complete with irregular curve.

35. Permission granted to reproduce for educational use only. 35 © Goodheart-Willcox Co., Inc. Intersection of an Oblique Plane and a Cylinder 1.Draw construction lines to create cutting planes in top view. 2.Draw construction lines to front view. 3.Create spline to connect piercing points and complete intersection.

36. Permission granted to reproduce for educational use only. 36 © Goodheart-Willcox Co., Inc. Intersection of an Oblique Plane and an Oblique Cylinder 1.Construct primary auxiliary view. 2.Pass cutting planes to edge view. 3.Project intersections to profile view to form line of intersection. 4.Transfer points to front view.

37. Permission granted to reproduce for educational use only. 37 © Goodheart-Willcox Co., Inc. Intersection of an Oblique Plane and an Oblique Cylinder 1.Draw construction lines to create primary auxiliary. Use Spline command to create cylinder ends. 2.Draw construction lines to create cutting planes. 3.Project intersections to profile view. Use Spline command to create line of intersection. 4.Transfer points to front view in similar manner.

38. Permission granted to reproduce for educational use only. 38 © Goodheart-Willcox Co., Inc. Intersection of a Cylinder and a Prism 1.Construct primary auxiliary view. 2.Pass cutting planes through top view. 3.Transfer planes to auxiliary. 4.Project intersections to front view. Draw lines of intersection.

39. Permission granted to reproduce for educational use only. 39 © Goodheart-Willcox Co., Inc. Intersection of a Cylinder and a Prism 1.Draw construction lines to create primary auxiliary view. 2.Create construction line cutting planes in top view. Offset planes in auxiliary view. 3.Project intersections to front view. Create lines of intersection using Spline command.

40. Permission granted to reproduce for educational use only. 40 © Goodheart-Willcox Co., Inc. Intersection of Two Cylinders 1.Construct primary auxiliary view. 2.Pass cutting planes through top view. 3.Transfer planes to auxiliary. 4.Project intersections to front view. Draw lines of intersection.

41. Permission granted to reproduce for educational use only. 41 © Goodheart-Willcox Co., Inc. Intersection of Two Cylinders 1.Draw construction lines to create primary auxiliary view. 2.Create construction line cutting planes in top view. Offset planes in auxiliary view. 3.Project intersections to front view. Create lines of intersection using Spline command.

42. Permission granted to reproduce for educational use only. 42 © Goodheart-Willcox Co., Inc. Intersection of an Inclined Plane and a Cone 1.Draw diametric lines through top view. 2.Project intersections to base in front view. Draw lines to apex. 3.Project piercing points to top view. 4.Complete line of intersection.

43. Permission granted to reproduce for educational use only. 43 © Goodheart-Willcox Co., Inc. Intersection of an Inclined Plane and a Cone 1.Draw construction lines to locate diametric lines in top view. 2.Draw construction lines to base in front view. Draw construction lines to apex. 3.Project piercing points to top view. 4.Complete line of intersection using Spline command.

44. Permission granted to reproduce for educational use only. 44 © Goodheart-Willcox Co., Inc. Intersection of a Cylinder and a Cone 1.Draw diametric lines through top view. 2.Project intersections to front and profile views. 3.Project piercing points from profile view. 4.Complete lines of intersection.

45. Permission granted to reproduce for educational use only. 45 © Goodheart-Willcox Co., Inc. Intersection of a Cylinder and a Cone 1.Draw construction lines to locate diametric lines in top view. 2.Draw construction lines to front and profile views. 3.Project piercing points from profile view. 4.Complete lines of intersection using Spline command.

46. Permission granted to reproduce for educational use only. 46 © Goodheart-Willcox Co., Inc. Review Questions 1.A square prism is made up of _____. A. single-curve surfaces B. plane surfaces C. warped surfaces D. double-curve surfaces B. plane surfaces

47. Permission granted to reproduce for educational use only. 47 © Goodheart-Willcox Co., Inc. Review Questions 2.The point of intersection between a plane and a line inclined to the plane is called the _____ point. piercing

48. Permission granted to reproduce for educational use only. 48 © Goodheart-Willcox Co., Inc. Review Questions 3.The _____ method is sufficient for determining whether lines cross in space. A. auxiliary view B. cutting plane C. orthographic projection D. revolution C. orthographic projection

49. Permission granted to reproduce for educational use only. 49 © Goodheart-Willcox Co., Inc. Review Questions 4.In the _____ method, an edge view is normally constructed to serve as reference for completing the line of intersection. A. auxiliary view B. cutting plane C. orthographic projection D. revolution A. auxiliary view

50. Permission granted to reproduce for educational use only. 50 © Goodheart-Willcox Co., Inc. Review Questions 5.The _____ command is used to create section views of 3D models. A. Zoom B. Rotate C. Mirror D. Section Plane

51. Permission granted to reproduce for educational use only. 51 © Goodheart-Willcox Co., Inc. Review Questions 6.The _____ command can be used to create the line of intersection between a cylinder and a prism. A. Circle B. Rectangle C. Spline D. Array C. Spline

52. Permission granted to reproduce for educational use only. 52 © Goodheart-Willcox Co., Inc. Review Questions 7.Visibility of intersecting lines and planes in space is determined by _____. A. projecting points from adjacent views B. revolving lines C. secondary auxiliary projection D. successive revolution A. projecting points from adjacent views

53. Permission granted to reproduce for educational use only. 53 © Goodheart-Willcox Co., Inc. Glossary Double-curve geometrical surfaces Surfaces generated by a curved line revolving around a straight line in the plane of the curve. Intersection The line formed at the junction of surfaces where two objects join or pass through each other.

54. Permission granted to reproduce for educational use only. 54 © Goodheart-Willcox Co., Inc. Glossary Piercing point The point of intersection between a plane and a line inclined to that plane. Ruled geometrical surfaces Surfaces generated by moving a straight line.