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Skew lines
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Skew LinesES 1 WFXY
Skew Lines
Lines that are not parallel, perpendicular or intersecting So what?
Skew Lines
Lines that are not parallel, perpendicular or intersecting So what?
These lines may represent roads, pipes or cables.
To connect these, resources must be used: longer distances are more costly:
Shortest distance
Shortest horizontal distance
Common Perpendicular Method
A
B
1 2
A
B1
2
To find the shortest distance using the common perpendicular method: Create a reference plane
with a line in PV
Common Perpendicular Method
A
B1
2
A
B1
2
A
B
1 2
A
B1
2
To find the shortest distance using the common perpendicular method: Create a reference plane
with a line in PV
Common Perpendicular Method
A
B1
2
A
B1
2
A
B
1 2
A
B1
2To find the shortest distance using the common perpendicular method: Project the points into
this new RP
A
B12
Common Perpendicular Method
A
B
1 2
A
B1
2To find the shortest distance using the common perpendicular method: Draw a perpendicular
line from the PV to the other line
A
B12
Common Perpendicular Method
A
B
1 2
A
B1
2
To find the shortest distance using the common perpendicular method: Complete the views by
projecting this SD (TL)
A
B12
Common Perpendicular Method
A
B1
2
A
B1
2
A
B
1 2
A
B1
2
A
B12
Common Perpendicular Method
What if the lines are shown in TL and appear to be intersecting?
Common Perpendicular Method
A
2
A
1
1
Since both lines are both TL, their intersection at that view is the SD
B
B
2
Common Perpendicular Method
A
2
A
1
1
Projecting this to the other side would give its TL
B
B
2
Parallel Plane Method
A
2
A
1
1
Create a plane based on a line. This plane should be parallel to the other line
B
B
2
Parallel Plane Method
A
2
A
1
1
Create a plane based on a line. This plane should be parallel to the other line
B
B
2
Parallel Plane Method
A2
A
1
1
To find the SHD, create a perpendicular RP to the RP where the two lines appear to be parallel
B
B
2
2A
1
B
Parallel Plane Method
A2
A
1
1
Note: The SHD is difficult to see at this example but should be horizontal at FRP
B
B
2
A
2A
1
1
B
B
2
Parallel Plane Method
A2
A
1
1
SD can be found by the intersection of the TL of the two lines. The intersection is the PV of the SD.
B
B
2
A
2A
1
1
B
B
2