The Truncated Cone produces the flat pattern (development) of a thin-walled cone with its top cut off by a plane. The cut plane can be level or tilted, and the apex of the cone can be offset from the centre of the base, so the same shape covers straight reducers, hoppers, oblique cones and cones with a sloping top. The pattern is cut flat from sheet and rolled or folded along the bend lines, and its two straight ends meet at the seam.
It appears in the shapes library under Thin Walled Developments. The shape window shows the 3D cone as well as the flat pattern; only the flat pattern is cut.
Truncated Cone in PrimeShape: the property page (left) and the shape as a wireframe with its dimensions (right).
How the shape is built
The cone is modelled in 3D with its base circle at height 0 and its apex at height Cone H, shifted sideways by Top Offset X and Top Offset Y. The base is divided into Dev. Segs equal steps, set round by Start Angle, and each step forms a flat triangular facet running up to the apex. Each facet is cut off at the truncation plane, and the facets are then laid out flat side by side to make the pattern.
The truncation plane passes through the point at Truncation H directly above the centre of the base (not under the apex). Trunc Angle Y tilts it from horizontal and Trunc Angle Z sets which way it tilts.
Insert point
The flat pattern starts from one seam edge. That edge lies along the X axis with its top (truncated) end on the insert point and its bottom (base) end further along X, at the slant length of that edge. The facets are laid out from there one after another, and the pattern closes with the second seam edge. The outline is one closed path: seam edge, top edge, seam edge, bottom edge.
Properties
Property |
Description |
Default |
Bottom D |
Diameter of the base circle. The base sits at height 0, centred on the origin of the 3D model. The code does not range-check it; 0 leaves no base circle. Length units. |
100 mm (4 in) |
Cone H |
Height of the apex of the full (untruncated) cone above the base. The cone is cut off by the truncation plane below this point. Length units. |
200 mm (8 in) |
Top Offset Y |
Y offset of the apex from the centre of the base. Accepts negative values. Any offset other than 0 makes an oblique (leaning) cone. Length units. |
0 |
Top Offset X |
X offset of the apex from the centre of the base. Accepts negative values. Length units. |
0 |
Truncation H |
Height of the truncation (top cut) plane, measured straight up from the centre of the base. The finished part runs from the base up to this plane. For a level plane this should be less than Cone H; the code does not check it. Length units. |
100 mm (4 in) |
Trunc Angle Z |
Direction of the tilt of the truncation plane, as an angle round the vertical axis from the X axis. Has no effect while Trunc Angle Y is 0. Degrees. |
0° |
Trunc Angle Y |
Tilt of the truncation plane from horizontal. The plane pivots about the point at Truncation H above the centre of the base. 0 gives a flat top parallel to the base. Degrees. |
0° |
Start Angle |
Rotates the facets round the cone, which moves where the seam (the two straight ends of the flat pattern) falls. Degrees. |
0° |
Dev. Segs |
Number of flat facets the cone is divided into. The pattern is built from this many straight-sided strips, so its top and bottom edges are chains of straight lines, not arcs. More segments follow the true curve more closely. Minimum 3. |
24 |
Show Bends |
True draws a bend line between each pair of neighbouring facets (Dev. Segs – 1 lines) as marking. False draws the outline only. |
True |
Bend Length (0 for Full) |
Length of the bend marks. Each bend line longer than 2.1 x this value is replaced by two marks of this length, one at each end. 0 marks the full length of every bend line. Minimum 0. Length units. The default is 12.5 mm in metric and 0.5 in (12.7 mm) in imperial units. |
12.5 mm (metric); 0.5 in (imperial) |
The dimensions drawn on the shape are Cone H, Bottom D, Truncation H, Trunc Angle Z, Trunc Angle Y, Top Offset X and Top Offset Y.
Limits and errors
The property page enforces only these limits: Dev. Segs has a minimum of 3, Bend Length has a minimum of 0, and Top Offset X and Top Offset Y accept negative values (their minimum is the negative of their maximum). The other values are not range-checked, so a value the geometry cannot use may be accepted.
If the shape cannot be built, the property page shows the red bar Warning: Cannot build shape from these parameters, the 3D model is cleared and the dimensions are not redrawn. The code does not list which values fail, so use the warning and the 3D view to find them.
The code does not check that the truncation plane cuts every facet between the base and the apex. With a steep Trunc Angle Y, or a Truncation H that does not fall inside the cone, the plane can miss some facet edges and the pattern can come out with no warning. Check the 3D view: the whole top edge should lie on the cut plane, between the base and the apex.
The top and bottom edges are straight chords across each facet. Increase Dev. Segs for a smoother curve on large cones.
The shape has no aliases (no former names).
This shape also has the Transform properties (Base X, Base Y, Rotation, Scale, Mirroring X), listed after the shape's own properties and the bend properties. The Polar Array group does not apply: it is for 2D shapes only, and this 3D development shape has none.