A straight line can be defined as the shortest distance between two points. Projections of endpoints of the line are joined to get projections of the line.
The reference planes are used to describe the position of the line. For example, the line is parallel to VP, the line is inclined to HP, etc.
While drawing projections of lines we should know different positions of lines with respect to refernce planes. Following are different positions of a line with respect to reference planes and projections of lines.
1. Line parallel to HP and VP
Top View ab: In the above figure line, AB is parallel to HP and parallel to VP. ‘ab’ is the projection of line AB in HP. This is the top view of line AB. Line AB is parallel to HP so we get the true length of AB in HP.
As the line is parallel to VP, the distances of projections of endpoints A and B in HP (i.e. a and b) from the XY line are the same. So we get the top view which is parallel to the XY line.
Front View a’b’: In the same way, we get a’b’. The projection of line AB in VP is the front view which is true length (because the line is parallel to VP). This view is parallel to the XY line because the line is parallel to HP, distances of projections of endpoints a’ and b’ from the XY line are the same. Projections of lines are as shown in the figure.
2. Line parallel to HP and inclined to VP
Top View ab: In the above figure line, AB is parallel to HP and inclined to VP. ‘ab’ is the projection of line AB in HP. This is the top view of line AB. Line AB is parallel to HP so we get the true length of AB in HP.
As the line is inclined to VP, the distances of projections of endpoints A and B in HP (i.e. a and b) from the XY line are different. So we get the top view which is inclined to the XY line.
Front View a’b’: In the same way, we get a’b’. The projection of line AB in VP is the front view which is apparent length i.e. smaller than the actual length of AB (because the line is inclined to VP). This view is parallel to the XY line because the line is parallel to HP, distances of projections of endpoints a’ and b’ from the XY line are the same. Projections of lines are as shown in the figure.
3. Line perpendicular to HP and parallel to VP
Top View ab: In the above figure line AB is perpendicular to HP and parallel to VP. ‘ab’ is the projection of line AB in HP. This is the top view of line AB. Line AB is perpendicular to HP so we get the point in HP.
Front View a’b’: In the same way, we get a’b’. The projection of line AB in VP is the front view which is the true length of AB (because the line is parallel to VP). This view is perpendicular to the XY line. Projections of lines are as shown in the figure.
4. Line parallel to VP and inclined to HP
Top View ab: In the above figure line, AB is parallel to VP and inclined to HP. ‘ab’ is the projection of line AB in HP. This is the top view of line AB. Line AB is inclined to HP so we get the apparent length of AB i.e. smaller than the actual length of AB.
As the line is parallel to VP, the distances of projections of endpoints A and B in HP (i.e. a and b) from the XY line are the same. So we get the top view which is parallel to the XY line.
Front View a’b’: In the same way, we get a’b’. The projection of line AB in VP is the front view which is the true length of AB (because the line is parallel to VP). This view is inclined to the XY line because the line is inclined to HP, distances of projections of endpoints a’ and b’ from the XY line are different. Projections of lines are as shown in the figure.
5. Line perpendicular to VP and parallel to HP
Front View a’b’: In the above figure line AB is perpendicular to VP and parallel to HP. a’b’ is the projection of line AB in VP. This is the front view of line AB. Line AB is perpendicular to VP so we get the point in VP.
TOP View ab: In the same way, we get ab. The projection of line AB in HP is the top view which is the true length of AB (because the line is parallel to HP). This view is perpendicular to the XY line. Projections of lines are as shown in the figure.
6. Line inclined to HP and VP
Front View a’b’: In the above figure line AB is inclined to VP. a’b’ is the projection of line AB in VP. This is the front view of line AB. This view is apparent in length i.e. smaller than the actual length of AB. Front view a’b’ is inclined to XY line because the line is inclined to HP also.
TOP View ab: In the same way, we get ab. The projection of line AB in HP is the top view which is the apparent length of AB i.e. smaller than the actual length of AB. Top view ab is inclined to XY line because the line is inclined to VP also. Projections of lines are as shown in the figure.
7. Line inclined to HP and VP and parallel to profile Plane
Profile Plane is a reference plane that is perpendicular to HP and VP.
Front view a’b’ and top view ab both are the apparent length of line AB because the line is inclined to HP and VP.
Front view a’b’ and top view ab both are perpendicular to the XY line because the line is parallel to the profile plane. Projections of lines are as shown in the figure.
Important points to remember in Projections of lines
- When the line is parallel to any reference plane, projection in the same plane will appear as true length.
- When the line is parallel to any reference plane, the projection in the other plane will be a horizontal line.
- When the line is perpendicular to any reference plane, projection in the same plane will appear as a point.
- When a line is perpendicular to any reference plane, projection in the other plane will be a vertical line.
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