Engi 1504 – Graphics

1. Engi 1504 – Graphics Lecture 6: Descriptive Geometry • Properties of lines • Properties of planes • Auxiliary planes • Midterm hints • Class assignment 6

2. Points and Lines • The point is the basic building block for an object.

3. Points and Lines • Standard notation • AF is the view of point A on the frontal plane • The height, width, and depth are specified with reference to the reference (folding lines)

4. Points and Lines • Note: • The distance behind a plane (say the front plane) is seen in all other adjacent views. • If the distance to point A from the folding line is known in one adjacent view, point A can be located in another adjacent view

5. Lines • A line is made up of two points • 3 views of line AB are shown

6. Lines • Vertical line – shows as a point in top view, parallel to front and right side planes • Horizontal – infinite positions, but all points must have equal elevation

7. Lines • Inclined line – parallel to front or right plane. Always parallel to one plane and inclined to the others • Oblique line – inclined to all principal planes

8. Auxiliary Planes • The length of a line can only be measured if it is seen in true length • Recall: A line can be seen true length if projected onto a plane parallel to it • So to find the true length of a line we draw an auxiliary folding line parallel to it.

9. Auxiliary Planes • Consider the front and top view of oblique line ab • We can draw an auxiliary plane parallel to either line aFbFor aHbH

10. Auxiliary Planes H1 TL • Auxiliary plane parallel to line aHbH • The line is perpendicular to horizontal (top) view H2 H1 H2

11. Point View of a line • Recall: A line can be seen as a point if projected onto a plane perpendicular to it • So an auxiliary plane perpendicular to a line that shows true length will show as a point. • Note: to show line as a point, need a view that shows true length first.

12. Point View of a line • Recall: A line can be seen as a point if projected onto a plane perpendicular to it • So an auxiliary plane perpendicular to a line that shows true length will show as a point. • Note: to show line as a point, need a view that shows true length first. D3 D3 aobo A O

13. Slope of a line • The slope (or grade) of a line is the inclination of the line with the horizontal • Slope can be measured in a view that shows vertical height and the line in true length • So we draw a folding line in the horizontal (top) view.

14. Slope of a line • So we need an auxiliary view (folded from the top view), that shows the line as true length • Slope is the angle between the true length line and a line parallel to the folding line

15. Direction of a line Bearing • The direction of a line (given as a compass reading) is seen only in the top view. Think of holding a compass. • A bearing is measured from either north or south, with north usually at top of page • Azimuth is measured from north and specified as an angle from 0-360º Azimuth

16. Summary Find true length of a line: • Place an auxiliary view parallel to the line and project two points on the line onto the auxiliary view Find point view of a line: • Need a true length line first • Locate an auxiliary view perpendicular to the true length line and project endpoints Find slope of a line • Need a true length line and an edge view of the horizontal • Find an auxiliary view (folded off the top view) that will show true length

17. Summary Continued … Things to remember about lines: • If a line is parallel to a folding line, it will appear true length in the adjacent view • Bearing and azimuth are seen only in the plan (top) view • If two lines intersect, the intersection point will correspond in all views • The shortest distance between two lines is seen where one of the lines appears as a point • Perpendicular lines appear perpendicular in any view in which one or both of the lines appear in true length • A line will appear true length in any view folded off a point view of the line.

18. Break Time • Take 5 minute break

19. Midterm Hints and Topics • Midterm exam is November 2nd • Lectures 1-5 are covered (Chapters 1-4 in text) • Review your assignments • Review visualization exercises • Practice as many problems as you can • Contact me if you are stuck. My office hours are 1-2 pm on Tuesdays and 9-10am on Thursdays • Student Questions?

20. Class Assignment #6 Point A is 15 m behind the frontal plane and 30 m below the horizontal plane. Point B is 33 m behind the frontal plane and 12 m below the horizontal plane. The line AB bears N 65º E. Using an appropriate scale draw a point view of line AB.