Engi 1504 – Graphics

1. Engi 1504 – Graphics Lecture 6: Descriptive Geometry II • Properties of planes • Midterm issues • Class assignment # 7

2. Properties of Planes • Two limiting cases of a plane: • True shape • Edge view • Can be used to solve any problem involving planes

3. Properties of Planes • At least three lines are required to define a plane • Edge view must be found before a true shape can be found

4. Finding the Edge view of a Plane • A plane will be seen as an edge if any line in it is seen as a point. • It is often easier to add a line (where we want it) than to use an existing line • Recall: a line must show true length before it can be seen as a point

5. Finding the Edge view of a Plane • We can find the true length of any line (AB, BC, or CA) using an auxiliary plane parallel to it. • Then we can find the line as a point, which will show the plane as an edge. • This requires two auxiliary planes – there is an easier way! • We will create a True length line in the plane.

6. Finding the Edge view of a Plane • Note: none of the given lines are parallel to a folding line, and hence not true length. • So we construct a true length line in the plane and then show it as a point. • This requires only one auxiliary view

7. Finding the Edge view of a Plane True Length • Draw a line in the plane parallel to a folding line (say in the front view). • Project the endpoints into the top view. This line is true length • Now we have a true length line, so all we have to do is show it as a point. X2 x1

8. Edge View of a Plane cont. • To find the point view of AX, we construct a folding line perpendicular to AX and project onto auxiliary plane 3 3 a3x3 2 D Point view D

9. Edge View of a Plane cont. • Project B and C onto plane 3 and join the points to show plane ABC as an edge

10. True Shape of a Plane • If we place an auxiliary plane parallel to the edge view, then the plane can be seen as true shape. • Recall: An edge view must be found first • So we place an auxiliary plane parallel to the edge view and project the plane onto it

11. True Shape of a Plane • Draw the plane in edge view. • Place a folding line parallel to the edge view. • Project all points onto the auxiliary plane (plane 4 in this case) and join them. • Recall: the distance from the folding line is found from the view adjacent to the edge view (plane 2 here)

12. a4 Plane shows true shape b4 c4

13. The Slope of a Plane • The slope of a plane is the angle it make with the horizontal. • Slope is seen only in the front or profile view (the elevation views) • Recall: slope can only be determined from a true length line. • So, the TL line used to find the edge view of the plane must be in the top view so that the edge of the plane appears in the horizontal view

14. The Slope of a Plane • Create a TL line in the horizontal view • Find the edge view of the plane • Measure the angle it makes with the horizontal 54o slope

15. The Strike of a Plane N • The strike of a plane is the angle that a true length line in the plane makes with the North (top view) • So strike is the bearing of the horizontal line AX strike 54o slope

16. Summary Find edge view of a plane: • Draw a line parallel to a folding line and project the line into the adjacent view, where it will be true length • Find a point view of this line and project other points in the plane. The plane will appear as an edge Find true shape of a plane: • Find edge view of a plane and create an auxiliary view parallel to the edge view • Project the points defining the plane onto this auxiliary view. The plane will be true shape

17. Break Time • Take 5 minute break