3D Shapes
ARC |
ARC r, alpha, beta |
Y |
beta |
alpha |
X |
An arc (in Wireframe mode) or sector (in other modes) in the x-y plane with its center at the origin from angle alpha to beta with a radius of r. alpha and beta are in degrees.
SHAPES GENERATED FROM POLYLINES
These elements let you create complex 3D shapes using a polyline and a built-in rule. You can rotate, project or translate the given polyline. The resulting bodies are a generalization of some previously described elements like PRISM_ and CYLIND.
Shapes generated from a single polyline:
EXTRUDE
PYRAMID
REVOLVE
Shapes generated from two polylines:
RULED
SWEEP
TUBE
TUBEA
The first polyline is always in the x-y plane. Points are determined by two coordinates; the third value is the status (see below). The second polyline (for RULED and SWEEP) is a space curve. Apices are determined by three coordinate values.
Shape generated from four polylines:
COONS
Shape generated from any number of polylines:
MASS
General restrictions for polylines
•Adjacent vertices must not be coincident (except RULED).
•The polyline must not intersect itself (this is not checked by the program, but hidden line removal and rendering will be incorrect).
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• The polylines may be either open or closed. In the latter case, the first node must be repeated after the last one of the contour.
Masking
Mask values are used to show or hide characteristic surfaces and/or edges of the 3D shape. The mask values are specific to each element and you can find a more detailed description in their corresponding sections/chapters.
mask = j1 + 2*j2 + 4*j3 + 8*j4 + 16*j5 + 32*j6 + 64*j7 where j1, j2, j3, j4, j5, j6, j7 can be 0 or 1.
j1, j2, j3, j4 represent whether the surfaces are present (1) or omitted (0).
j5, j6, j7 represent whether the edges are visible (1) or invisible (0).
j1: base surface. j2: top surface. j3: side surface.
j4: other side surface. j5: base edges.
j6: top edges.
j7: cross-section/surface edges are visible, surface is not smooth.
To enable all faces and edges, set mask value to 127.
Status
Status values are used to state whether a given point of the polyline will leave a sharp trace of its rotation path behind.
0:latitudinal arcs/lateral edges starting from the node are all visible.
1:latitudinal arcs/lateral edges starting from the node are used only for showing the contour.
-1: for EXTRUDE only: it marks the end of the enclosing polygon or a hole, and means that the next node will be the first node of another hole.
Additional status codes allow you to create segments and arcs in the polyline using special constraints.
See “Additional Status Codes” on page 141 for details.
To create a smooth 3D shape, set all status values to 1. Use status = 0 to create a ridge. Other values are reserved for future enhancements.
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EXTRUDE
EXTRUDE n, dx, dy, dz, mask, x1, y1, s1,
..., xn, yn, sn
General prism using a polyline base in the x-y plane. The displacement vector between bases is (dx, dy, dz).
This is a generalization of the PRISM and SLAB statements. The base polyline is not necessarily closed, as the lateral edges are not always perpendicular to the x-y plane. The base polyline may include holes, just like PRISM_. It is possible to control the visibility of the contour edges.
n: the number of polyline nodes.
mask: controls the existence of the bottom, top and (in the case of an open polyline) side polygon.
si: status of the lateral edges or marks the end of the polygon or of a hole. You can also define arcs and segments in the polyline using additional status code values.
Parameter restriction: n > 2
Masking:
mask = j1 + 2*j2 + 4*j3 + 16*j5 + 32*j6 where j1, j2, j3, j5, j6 can be 0 or 1.
j1 (1): base surface is present.
j2 (2): top surface is present.
j3 (4): side (closing) surface is present.
j5 (16): base edges are visible.
j6 (32): top edges are visible.
Status values:
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Z |
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|
j6 |
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j2 |
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j3 |
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Y |
X |
n |
1 |
j1 |
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|||
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j5 |
||
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|
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|
|
|
2 |
0:lateral edge starting from the node is visible.
1:lateral edges starting from the node are used for showing the contour.
-1: marks the end of the enclosing polygon or a hole, and means that the next node will be the first vertex of another hole.
Additional status codes allow you to create segments and arcs in the planar polyline using special constraints.
See “Additional Status Codes” on page 141 for details.
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Examples:
EXTRUDE 14, 1, 1, 4, 1+2+4+16+32, 0, 0, 0, 1, -3, 0, 2, -2, 1, 3, -4, 0, 4, -2, 1, 5, -3, 0, 6, 0, 0, 3, 4, 0, 0, 0, -1, 2, 0, 0, 3, 2, 0, 4, 0, 0, 3, -2, 0, 2, 0, -1
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A=5: B=5
R=2: S=1 C=R-S D=A-R E=B-R
EXTRUDE 28, -1, 0, 4, 1+2+4+16+32, 0, 0, 0,
D+R*SIN(0), R-R*COS(0), 1, D+R*SIN(15), R-R*COS(15), 1, D+R*SIN(30), R-R*COS(30), 1, D+R*SIN(45), R-R*COS(45), 1, D+R*SIN(60), R-R*COS(60), 1, D+R*SIN(75), R-R*COS(75), 1, D+R*SIN(90), R-R*COS(90), 1, A, B, 0,
0, B, 0, 0, 0, -1, C, C, 0,
D+S*SIN(0), R-S*COS(0), 1, D+S*SIN(15), R-S*COS(15), 1, D+S*SIN(30), R-S*COS(30), 1, D+S*SIN(45), R-S*COS(45), 1, D+S*SIN(60), R-S*COS(60), 1, D+S*SIN(75), R-S*COS(75), 1, D+S*SIN(90), R-S*COS(90), 1, A-C,B-C,0,
R-S*COS(90), E+S*SIN(90), 1, R-S*COS(75), E+S*SIN(75), 1, R-S*COS(60), E+S*SIN(60), 1, R-S*COS(45), E+S*SIN(45), 1, R-S*COS(30), E+S*SIN(30), 1, R-S*COS(15), E+S*SIN(15), 1, R-S*COS(0), E+S*SIN(0), 1, C, C, -1
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