1. Engineering Geometry
Engineering geometry is the basic geometric elements and forms used in engineering design.
Engineering and technical graphics are concerned with the descriptions of shape, size, and operation of engineered products.
The shape description of an object relates to the positions of its component geometric elements in space. To be able to describe the shape of an object, you must understand all of the geometric forms, as well as how they are graphically produced.

2. Coordinate Space 2-D Space: Cartesian coordinate system:
A 2-D coordinate system establishes an origin at the intersection of two mutually perpendicular axes, labeled X (horizontal) and Y (vertical).
The origin is assigned the coordinate values of 0,0.
X: positive to the right of the origin, and negative to the left.
Y: positive above the origin, and negative below
Polar coordinate system:
Distance from the origin (0,0), and angle measured from the positive X-axis.
Distance is always positive.
Counterclockwise angle is positive; clockwise is negative.

3. 2-D Cartesian coordinate system

4. 3-D Coordinate Space Cartesian coordinate system
Three mutually perpendicular axes (X, Y, and Z) intersect at the origin (0,0,0)
The right-hand rule is used to determine the positive direction of the axes.
A rectangular prism is created using the 3-D coordinate system by establishing coordinate values for each corner.
Cylindrical coordinates
locate a point on the surface of a cylinder by specifying a distance and an angle in the X-Y plane, and the distance in the Z direction.
Spherical coordinates
locate a point on the surface of a sphere by specifying an angle in one plane, an angle in another plane, and one height.
Absolute coordinates vs. Relative coordinates
World coordinate system vs. Local coordinate system

5. 3-D Cartesian coordinate system

6. Locating points

7. Right-hand rule for axes directions

8. Cylindrical coordinates

9. Spherical coordinates

10. Geometric Elements Point, Line, Circle, Arc
Parallel lines, perpendicular lines, intersecting lines
Tangent line
Curved lines: single curved vs. double curved
Circle: points equidistant from one point (the center)
circumference, radius, chord, diameter, secant, semicircle, arc, sector, quadrant, segment, tangent, concentric circles

11. Circle definitions

12. Geometric Elements
Conic sections: formed by intersection of a plane with a right circular cone
Parabola: set of points equidistant from a fixed point (focus), and a fixed line (directrix)
Hyperbola: set of points whose distances from two fixed points (foci) have a common difference
Ellipse: set of points whose distances from two fixed points (foci) have a constant sum
Polygons and Polyhedrons; prisms and pyramids

13. Ellipse

14. HYPERBOLA

15. PARABOLA

16. ELLIPSE

17. CIRCLE

18. Quadrilaterals

19. Polygons

20. Regular polyhedra

21. Prisms

22. Pyramids

23. Design Visualization
A dynamic process between the mind, the eyes, and some physical stimulus such as a drawing or an object.

24. Hand/eye/mind connection

25. Solid Object Features
Edges – lines that represent the boundary between two faces of an object.
Faces – areas of uniform or gradually changing lightness and are always bounded by edges.
Limiting element – a line that represents the farthest outside feature of a curved surface.
Vertex – point where more than two edges meet.

26. Solid object features

27. Visualization Techniques
Solid Object Combinations and Negative Solids
Cutting Planes
Normal
Rotated about single axis – inclined face
Rotated about two axes – oblique face
Planes of Symmetry
Developments – flattened “skin” of object

28. Combining solid objects

29. Removing solid objects

30. Removing solid objects

31. Subtracting progressively larger wedges

32. Subtracting progressively larger pyramids

33. Additive and subtractive techniques can be used to make a solid geometric form

34. Normal cutting plane

35. Cutting plane rotated about single axis

36. Cutting plane rotated about two axes

37. Cutting plane rotation

38. Planes of symmetry

39. Surface cutting planes

40. Development

41. Image plane

42. Object-image plane orientation

43. Normal faces

44. Camera metaphor

45. Normal face projection

46. Edge views of normal face

47. Inclined face projection

48. Inclined and normal faces

49. Oblique face projection