Projection of Points Basics

Projection of Points – Point’s position will be given in data. We need to find out its projection on H.P. (Horizontal Plane) and on V.P. (Vertical Plane).

There are maximum four quadrant wise positions possible of point. As we all know about quadrant, there are 4 quadrants exist. See figure below.

Title: quadrants - Description: quadrants

Here are four quadrant wise positions for any point.

1.      Above H.P. and In Front of V.P. which shows point is in First Quadrant

2.      Above H.P. and Behind V.P. which shows point is in Second Quadrant

3.      Below H.P. and Behind V.P. which shows point is in Third Quadrant

4.      Below H.P. and In Front of V.P. which shows point is in Fourth Quadrant

See figure below.

Title: quadrants-point-positions - Description: quadrants-point-positions

Let us check these quadrants in H.P. (Horizontal Plane) and on V.P. (Vertical Plane) view. See figure below.

Title: quadrants-3d - Description: quadrants-3d

To find solution of problems based on projections we need to rotate H.P. (Horizontal Plane) in clockwise direction to 90º.

After this rotation of H.P. it will become parallel to V.P. See fig below.

Title: quadrants-rotation - Description: quadrants-rotation

Solved Example:

Data: A Point “M” is 40 mm above H.P. and 40 mm in front of V.P. Draw its projections.

Solution: As point’s position is above H.P. and In Front of V.P. it is in First Quadrant. See figure below.

Title: quadrants-point-position - Description: quadrants-point-position

We will get m’ projected on V.P. for front view which shows Elevation and m on H.P. for top view which shows Plan.

So, plan will be 40 mm in front of V.P. and Elevation will be 40 mm above H.P.

As per we discussed before for solution we need to rotate H.P. in clockwise direction up to 90º. See figure below.

Title: point-solution - Description: point-solution

So the solution for the above data is:

Title: final-point-projection - Description: final-point-projection

Plan: Projection on H.P.         Elevation: Projection on V.P.

In same way we can find projections for any point at any condition. Just remember to rotate H.P. at 90º while drawing solution.

Here are few important notes:

1.      When point is in 1st quadrant, its plan will be below XY (reference line) and elevation will be above XY.

2.      When point is in 2nd quadrant, its plan and elevation both will be above XY.

3.      When point is in 3rd quadrant, its plan will be above XY and elevation will be below XY.

4.      When point is in 4th quadrant, its plan and elevation both will be below XY.