Development and Surface Intersection
Development and Surface Intersection
This domain tests flattening 3D surfaces into true-shape developments and finding where surfaces meet. It is used for ducts, sheet-metal work and packaging.
Core rules
- Parallel-line development suits prisms and cylinders; radial-line development suits pyramids and cones.
- A development needs true lengths. Use an auxiliary view or rotation to find the true length of a slant edge.
- For a right cylinder, the stretch-out length is πD. Divide the circumference into equal parts and project corresponding heights.
- For a right pyramid, each triangular face is developed from true slant edges; for a cone, use the sector radius equal to the slant height.
- The intersection line is found where corresponding projections cross; project points between views before developing.
Worked example
A cylinder has diameter 40 mm and height 60 mm, cut obliquely so one side is 60 mm and the opposite side 40 mm. Development width = π x 40 = 125.7 mm. Divide the top view into 12 equal arcs; project each point to the front view to obtain its height; transfer the 12 spacings across the 125.7 mm stretch-out and plot the heights. Join with a smooth curve. Reasoning: the circumference unrolls as a straight length, while the varying cut appears as a curve.
Traps
- Using vertical height instead of slant height for a cone.
- Forgetting that πD is the full circumference.
- Developing from a foreshortened view.
- Omitting the seam line.
- Plotting too few points on an intersection curve.