Intersections
Drawing the Plan of
Valley and Hip Lines
Hip Roofs
When the slopes are equal and the heights of the eaves for two
intersecting roof surfaces are the same, in plan the line between these
two surfaces bisects the angle formed by their eave lines.
This applies to both the hip and the valley lines between two adjoining
roof surfaces, regardless of the slope or the pitch, as long as they are the
same for both surfaces.
When these conditions exist, and the eave line of the building is shown in
plan, the hip, valley, and ridge lines may all be drawn in the plan without
knowing anything about the pitch or slope, the height of the eaves, or the
height of the ridge of the building.
Hip Roofs
Figure (A) and Figure (B) show two houses whose roof plans are
Identical in spite of the difference in their roof slopes as shown in
The elevations.
Hip Roofs
Given a simple rectangular outline of a plan view of a hip roof in Figure (C)
The angles at the corners of the eaves are bisected (Figure (D)) forming
The hip lines.
Near each end of the building the two hip lines meet in a point at the highest
Level of the roof forming the beginning of the ridge line.
Hip Roofs
Given the plan view of the eave line of a building with a wing added
Figure (E).
The large rectangle is completed and the roof plan for that part of the
Building is drawn as show in Figure (F).
Another rectangle is blocked in with its width equal to the width of the
Wing as shown in Figure (G).
Figure (H) shows all of the lines on the combined roof including the
Valley line formed where the two roofs intersect.
Hip Roofs
Drawing the plan view of a hip roof on any building
Intersections
Finding the Intersection of a line and plane using
A horizontal cutting plane
Intersections
Finding the Intersection of a line and plane using
A vertical cutting plane