1. TA 101: Technical Arts 2015-16 II Dr. Prishati Raychowdhury
Department of Civil Engineering
IIT Kanpur
Office: FB 330; Phone: 6692

2. Lecture 16
Space Geometry

3. Recall: Glass box method for orthographic

4. A Point in Space d h P h d PT Horizontal Plane H.P. V.P.
Vertical Plane PF

5. A Line in Space
Consider Line AB aH HP bH C A
FVP aF aP B TL bP bF
PVP

6. A Line in Space
Consider Line AC aH TL cH HP C A cP
FVP aF aP B cF
PVP

7. A Line in Space
Consider Line BC cH bH HP C A cP
FVP TL cF B bP bF
PVP

8. Normal View or True Shape
The term ‘Normal’ means ‘perpendicular’ or at ‘right angles’
A Normal View is one in which the ‘direction of sight’ is perpendicular to a line/plane
The Normal View of a line shows the True Length of the line
The Normal View of a plane shows the True Shape of the plane
A Normal View may or may not be in one of the principal orthographic views/projections

9. Point View
A Line lying on two principal planes of projection will appear in NORMAL VIEW (i.e., in TRUE LENGTH) in two views, and as a POINT VIEW (PV) in the third view N PV N PV N N N N PV
Horizontal-Frontal
Horizontal - Profile
Frontal- Profile

10. Point View
A ‘Point View’ of a line is that view, which shows the line as a ‘single point’
The ‘direction of sight’ is parallel to the line in the Point View (PV)

11. Edge View
An ‘Edge View’ of a plane is that view, which shows the plane as a ‘line’.
The ‘direction of sight’ should be parallel to the plane in an Edge View (EV) EV
H.P.
P.P.
F.P.
True Shape EV

12. Space Geometry Terminology
In order to describe an object completely, one needs to be able to perform one or more of the following tasks
Find the ‘Point View’ (PV) of a line
Find the ‘Normal View’ of a line
Find the ‘True Length (TL)’ of a line
Find the ‘Edge View (EV)’ of a plane
Find the ‘Normal View’ of a plane
Find the True Size and Shape of a surface
Find angle between lines and planes
Find spacing between ‘elements’ of an object

13. Important Observations: Lines
TL?
TL? TL TL PV
H.P.
F.P.
P.P.
TL?
TL?
TL? TL TL PV TL TL PV

14. Finding True Length of a Line
Direct Formula
= 0 X Y
(x2, y2, z2) X Z
(x1, y1, z1) TL

15. Finding True Length of a Line
Direct Formula
= 0 X Y TL X Z

16. Finding True Length of a Line
Method of Rotation Y X Z TL X

17. Finding True Length of a Line
Method of Rotation Y TL X Z X

18. Finding True Length of a Line
Method of Auxiliary Plane Y X TL Z X

19. Auxiliary Plane: Conceptd2 H d1 AH BH TL AA A BA H d1 F AF d2 AA B
TRUE LENGTH(TL) F AA BA BF P A BA
LINE OF
SIGHT
Notice the distances from the hinge lines

20. Auxiliary Plane: ConceptPV bH H A1
bA2, aA2 d aH
Line of Sight
bA1 A2 A1 TL H
aA1 F d aF
Notice the direction of Projectors bF
Notice the distance Measurements along Projectors

21. Auxiliary Plane: Conceptd1 d1 PV bH H A1
bA2, aA2 d aH
Line of Sight
bA1 A2 A1 TL H d
aA1 F aF
Notice the direction of Projectors bF
Notice the distance Measurements along Projectors

22. Thank You