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