Locating Points & Lines in Space

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POINTS 2

Projection of a Point• Note that any two of the

glass box projections are sufficient to completely describe the three independent coordinates of a point in space.

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Projection of a Point• In descriptive geometry,

only the projections of the point are usually shown.

• The coordinate lines are shown here for illustration purposes

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Projection of a Point• Given the projection of a point in two of the planes, its

projection in the third plane can easily be determined

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Finding the missing projection of a point

• Given the top and the right side projections of a point, the front projection is found by erecting perpendiculars to the TF and FR folding lines.

• The frontal projection is at the intersection of the two perpendiculars.

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Finding the missing projection of a point

• Given the frontal and the top projections of a point, the right side projection is found by dropping a perpendicular to the FR folding line from the frontal projection, and measuring a distance from the FR folding line equal to the distance of the top projection from the TF folding line.

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Finding the missing projection of a point

• Given the frontal and the right side projections of a point, the top projection is found by dropping a perpendicular to the TF folding line from the frontal projection, and measuring a distance from the TF folding line equal to the distance of the right side projection from the FR folding line.

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Rule 2: Skip-a-view• The distance between the

projection of a point and the folding line is equal in any two views in three consecutive views with one view skipped

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LINES 10

Line projection• A line is the straight path

between two points

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Line projection• The projection of a line into

the front, top and right side planes is defined by the projection of its endpoints onto these planes.

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Projecting a line into other views

• Given the front and right side projections for a line a-b, the projection of line a-b in the top view is found by using the alignment rule and the skip-a-view rule on its endpoints.

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Projecting a line into other views

• Extend projection lines into the top view from the end points in the front view

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Projecting a line into other views

• Find the distances x and y from the line end points in the right side view to the fold line F/R, and transfer them into the top view.

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Point’s visibility (front and back)

• The front view by itself does not tell which point is in the front. This must be deduced from the top and right side projections.

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Point’s visibility (front and back)

• The point in the front appears closer to the TF folding line in the top projections, and closer to the FR folding line in the right side projection. In the example shown, point b is in front of point a

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Point’s visibility (up and down)

• The top view by itself does not tell which point is in the top. This must be deduced from the front and right side projections

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Point’s visibility (up and down)

• The point in the top appears closer to the TF folding line in the front projections, and closer to the TR folding line in the right side projection. In the example shown, point b is on top of point a.

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Point’s visibility (right and left)

• The right side view by itself does not tell which point is to the right. This must be deduced from the front and top projections.

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Point’s visibility (right and left)

• The point to the right appears closer to the FR folding line in the front projections, and closer to the TR folding line in the top projection. In the example shown, point b is to the right of point a..

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Rule 3: Visibility• The closer a point’s

projection is to the folding line in certain view, the more “priority in visibility” it has in the adjacent view.

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SAMPLE PROBLEMS 23

Sample Problem #1• Given point 1 (40, 25, 50),

locate the front and top views of point 2, which is 80mm to the right of point 1, 35mm below point 1, and 50mm behind point 1. Give the coordinates of point 2.

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Sample Problem #1 (Answer)• Given point 1 (40, 25, 50),

locate the front and top views of point 2, which is 80mm to the right of point 1, 35mm below point 1, and 50mm behind point 1. Give the coordinates of point 2.

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Sample Problem #2• Find the view of points 3, 4,

and 5 on line 1(20,85,25) – 2(140,15,25) that fit the following descriptions: point 3, 30mm above point 1; point 4, 105mm to the left of point 2; and point 5, 40mm in front of point 1. Give the coordinates of points 3, 4, and 5.

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Sample Problem #2• Find the view of points 3, 4,

and 5 on line 1(20,85,25) – 2(140,15,25) that fit the following descriptions: point 3, 30mm above point 1; point 4, 105mm to the left of point 2; and point 5, 40mm in front of point 1. Give the coordinates of points 3, 4, and 5.

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SEATWORK PROBLEMS 28

Seatwork Instructions:• Use a short bond paper.• Place margin all around at

10mm from edge of paper.• Draw a horizontal line

20mm below top margin to create a panel where you will write the word problem.

• Divide the rest of the space in equal parts depending on the requirement of the problem

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Seatwork Problem #2-1• Given point 1(20, 60, 25),

complete the views of line 1-2 such that point 2 is 50mm to the right of point 1, 60mm above point 1, and 40mm in front of point 1. Give the coordinates of point 2.

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Seatwork Problem #2-2• Triangle 1(30,45,20) –

2(80,85,20) – 3(140,20,20) is the base of a pyramid. The vertex V is 10mm behind point 1, 10mm to the left of point 2, and 70mm above point 3. Complete the top and front views of the pyramid. Give the coordinates of vertex V.

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