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 aFbF or aHbH

10. Auxiliary Planes Auxiliary plane parallel to line aHbHTL
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 D3 D3 aobo
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 Azimuth
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: Find point view 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.