The Arbitrary Rect To Circle Transition is the flat pattern (development) of a square-to-round transition piece: a duct or hopper section that joins a rectangular opening to a circular one. You enter the rectangle, the circle diameter, the height between them, how far the circle is offset from the centre of the rectangle and how it is tilted. The shape builds the transition in 3D from flat triangular facets and unrolls it into one flat profile that can be cut from plate and folded up. Bend lines can be marked on the pattern to guide the forming.
It appears in the shapes library under Thin Walled Developments. It is the general form of the transition: the top circle can be both offset and tilted. Rect To Circle Transition has neither offset nor tilt, and Shifted Rect To Circle Transition has the offsets but no tilt.
Arbitrary Rect To Circle Transition in PrimeShape: the property page (left) and the shape as a wireframe with its dimensions (right).
Insert point and how the shape is built
The insert point is the origin. In 3D the base rectangle (Base Width along X, Base Height along Y) lies at Z = 0 with its lower left corner on the origin, so it extends into +X and +Y. The top circle is above the base, in +Z. Its centre is Center H above the base, shifted from the centre of the rectangle by Top Offset X and Top Offset Y. The circle is then tilted by Top Angle Y, in the direction set by Top Angle Z.
The circle is divided into Dev. Segs straight segments, and each quarter of the circle is joined to one corner of the rectangle by a fan of triangles. Each side of the rectangle is joined to the circle by one larger triangle, except the side the seam is on, which is split into two triangles at the seam midpoint. The fan from each corner always takes a fixed quarter of the circle, starting from the point of the circle that is on the +X side of its centre when the circle is not tilted.
The flat pattern is a single closed profile:
•one long edge is the rectangle unrolled (four straight sides, with the side the seam is on split into two halves), and the other is the circle unrolled. The circle edge is made of straight segments, one per circle segment, not true arcs – more Dev. Segs gives a smoother edge
•the two straight ends are the seam, where the edges meet when the part is formed. The seam runs from the middle of the rectangle side at X = Base Width to the circle
The sizes are used exactly as entered – the shape has no plate thickness setting. Enter the sizes of the surface you want the development to match (for example the mean line of the wall when forming thick plate).
Properties
Property |
Description |
Default |
Top D |
Diameter of the top (circular) end (mm or inch). The property page does not accept less than 1. |
50 mm (2 in) |
Base Width |
Size of the base rectangle along X (mm or inch). The property page does not accept less than 1. |
100 mm (4 in) |
Base Height |
Size of the base rectangle along Y (mm or inch). The property page does not accept less than 1. |
150 mm (6 in) |
Center H |
Vertical height from the plane of the base rectangle to the centre of the top circle (mm or inch). This is not the slant length of the wall. No limit is set on the page. |
100 mm (4 in) |
Top Offset Y |
Distance along Y from the centre of the base rectangle to the centre of the top circle (mm or inch). Positive moves the circle towards the Base Height end of the rectangle, negative towards the Y = 0 side. 0 centres it in Y. The page allows the same size in both directions. |
-25 mm (-1 in) |
Top Offset X |
Distance along X from the centre of the base rectangle to the centre of the top circle (mm or inch). Positive moves the circle towards the Base Width end of the rectangle, negative towards the X = 0 side. 0 centres it in X. The page allows the same size in both directions. |
0 |
Top Angle Z |
Direction of the tilt of the top circle, as an angle round the vertical (Z) axis measured from X (degrees). At 0 the circle tilts in the X-Z plane. Has no effect when Top Angle Y is 0. |
0° |
Top Angle Y |
Tilt of the top circle from horizontal (degrees). 0 makes the top circle parallel to the base rectangle. No limit is set on the page. |
30° |
Dev. Segs |
Number of straight segments the top circle is divided into. The shape always uses a multiple of 4 (one equal share for each corner of the rectangle): the value is rounded down to a multiple of 4, and anything below 4 is treated as 4. The least the editor accepts is 3. |
24 |
Show Bends |
When on, a bend line is added at every fold between two adjacent facets. Every bend line is a straight line from a rectangle corner to a point on the circle. The rectangle sides and the circle edge are not bent, and the seam is not marked. Bend lines are marking geometry, not cuts. When off, no bend lines are added and only the profile is produced. |
On |
Bend Length (0 for Full) |
Length of the bend marks (mm or inch). With a value above 0, each bend line longer than 2.1 x this length is replaced by two short marks of this length, one at each end of the bend line; shorter bend lines are left full length. 0 marks every bend line full length. Cannot be negative. Only used when Show Bends is on. |
12.5 mm (0.5 in) |
The dimensions drawn on the shape are Center H, Base Width, Base Height, Top Angle Z, Top Angle Y, Top D, Top Offset X and Top Offset Y.
Notes and limits
•If the values give a transition that cannot be developed, the build stops before the profile is made and the property page shows Warning: Cannot build shape from these parameters.
•Each corner of the rectangle is always joined to the same quarter of the circle, whatever the offsets and tilt. With large offsets, a large tilt, or a circle bigger than the rectangle, the facets can become very thin or fold over. Check the 3D view before cutting.
•The circle edge is a straight-segment approximation. Check that Dev. Segs gives a smooth enough edge for the part size; a large transition may need more than the default 24.
•The development has no allowance for plate thickness, seam gap or weld preparation.
•The shape has no aliases (no former names).
The Arbitrary Rect To Circle Transition also has the Transform properties (Base X, Base Y, Rotation, Scale, Mirroring X), listed after the shape's own properties. Polar Array properties are only offered for 2D shapes, so this 3D shape has none.