The tables list each entity’s Parameter Data after its leading type number. The parameter delimiter and record delimiter rules are on the File structure page, and every record may end with the two optional pointer groups described there. Types and forms are in the entity register. Coordinates are in the entity’s definition space (XT, YT, ZT); the Directory Entry’s transformation matrix places it in model space. Entities not listed here are listed under “Not described” on the overview.
Circular Arc (100)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | ZT | Real | Displacement of the arc’s plane from the XT, YT plane |
| 2–3 | X1, Y1 | Real | Arc centre |
| 4–5 | X2, Y2 | Real | Start point |
| 6–7 | X3, Y3 | Real | Terminate point |
The arc runs counterclockwise from the start to the terminate point, which selects it from its complementary arc. A full circle has coincident start and terminate points.
Composite Curve (102)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | N | Integer | Number of constituent entities (N ≥ 1) |
| 2 … 1+N | DE(1) … DE(N) | Pointer | Directory Entries of the constituents, in order |
A composite curve cannot consist of a single Point or a single Connect Point. Points and connect points do not take part in the composite’s parameterisation, which is built from its constituent curves’ parameter ranges.
Conic Arc (104)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1–6 | A, B, C, D, E, F | Real | Coefficients of the conic A·x² + B·x·y + C·y² + D·x + E·y + F = 0 |
| 7 | ZT | Real | ZT coordinate of the plane of definition |
| 8–9 | X1, Y1 | Real | Start point |
| 10–11 | X2, Y2 | Real | Terminate point |
The parent conic is classified by Q1, the determinant of the 3×3 matrix with rows (A, B/2, D/2), (B/2, C, E/2) and (D/2, E/2, F); Q2, the determinant of the 2×2 matrix (A, B/2), (B/2, C); and Q3 = A + C. It is an ellipse if Q2 > 0 and Q2·Q3 < 0, a hyperbola if Q2 < 0 (with Q1 non-zero) and a parabola if Q2 = 0 (with Q1 non-zero); the specification’s exact conditions on Q1 were cut by the text extraction, so check them there. An elliptical arc runs counterclockwise from start to terminate point; for a parabola or hyperbola the parameters pick out one portion and no direction applies. A conic must be in standard position (axes parallel to XT and YT, centred about the ZT axis, vertex at the origin for a parabola) and a Transformation Matrix moves it into place. Degenerate conics (a point or a line) must use other entities. The form number is informational. The conic equation’s written parameterisation is in the specification and Appendix C.
Copious Data and its forms (106)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | IP | Integer | Interpretation flag: 1 x,y pairs with a common z; 2 x,y,z triples; 3 x,y,z and i,j,k sextuples |
| 2 | N | Integer | Number of n-tuples (N ≥ 2 for linear paths) |
| IP = 1 (forms 1, 11, 20, 21, 31–38 and 40; form 63 may use any IP) | |||
| 3 | ZT | Real | Common z displacement |
| 4 … | X(1), Y(1) … X(N), Y(N) | Real | Points; the last ordinate is index 3+2N |
| IP = 2 (forms 2 and 12) | |||
| 3 … | X(1), Y(1), Z(1) … Z(N) | Real | Points; the last is index 2+3N |
| IP = 3 (forms 3 and 13) | |||
| 3 … | X(1), Y(1), Z(1), I(1), J(1), K(1) … K(N) | Real | Points with vectors; the last is index 2+6N |
Forms 20 and 21 (centreline), 31 to 38 (section) and 40 (witness line) use IP = 1 only. For forms 20 and 21 and the section forms N is even and the display is segments from point 1 to 2, 3 to 4 and so on. For the witness line N is odd and at least 3. The section forms draw these line patterns: 31 parallel segments from edge to edge; 32 parallel segments in pairs; 33 alternating solid line and collinear dashes; 34 quadruples of parallel lines; 35 triples of two solid lines and dashes between them; 36 parallel dash sets; forms 37 and 38 follow in the specification.
Plane (108)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1–4 | A, B, C, D | Real | Coefficients of the plane A·x + B·y + C·z = D |
| 5 | PTR | Pointer | Closed curve bounding the plane, or zero when unbounded (form 0) |
| 6–8 | X, Y, Z | Real | Location of the display symbol |
| 9 | SIZE | Real | Size of the display symbol |
Line (110)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1–3 | X1, Y1, Z1 | Real | Start point P1 |
| 4–6 | X2, Y2, Z2 | Real | Terminate point P2 (form 0); an arbitrary point the line passes through (forms 1 and 2) |
Default parameterisation: C(t) = P1 + t(P2 − P1), with 0 ≤ t ≤ 1 for form 0, 0 ≤ t < ∞ for form 1 (semi-bounded, from P1 through P2 without end) and −∞ < t < ∞ for form 2 (unbounded in both directions). Forms 1 and 2 shall use entity use flag 06 (construction geometry), and P1 and P2 count for the Global maximum coordinate value.
Parametric Spline Curve (112)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | CTYPE | Integer | 1 linear, 2 quadratic, 3 cubic, 4 Wilson-Fowler, 5 modified Wilson-Fowler, 6 B-spline |
| 2 | H | Integer | Degree of continuity with respect to arc length |
| 3 | NDIM | Integer | 2 planar, 3 nonplanar |
| 4 | N | Integer | Number of segments |
| 5 … 5+N | T(1) … T(N+1) | Real | Break points, first to last |
| 6+N … | AX, BX, CX, DX, AY, BY, CY, DY, AZ, BZ, CZ, DZ | Real | The twelve polynomial coefficients of each segment in turn, 12 per segment starting at 6+N (AX(1) is index 6+N, BX(1) 7+N) |
| 6+13N … | TPX0, TPX1, … for X, Y and Z | Real | The values of the X, Y and Z polynomials of segment N and their derivatives at u = T(N+1), the terminate point, each divided by the matching factorial |
The number of terminate-point values per axis is not stated here: the specification’s index column was only partly legible in the extracted text.
Parametric Spline Surface (114)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | CTYPE | Integer | Spline boundary type: 1 linear, 2 quadratic, 3 cubic, 4 Wilson-Fowler, 5 modified Wilson-Fowler, 6 B-spline |
| 2 | PTYPE | Integer | Patch type: 1 Cartesian product, 0 unspecified |
| 3 | M | Integer | Number of u segments |
| 4 | N | Integer | Number of v segments |
| 5 … 5+M | TU(1) … TU(M+1) | Real | Breakpoints in u |
| 6+M … 6+M+N | TV(1) … TV(N+1) | Real | Breakpoints in v |
| then | AX(i,j) … SX(i,j), AY … SY, AZ … SZ | Real | For each patch (i, j) in turn: 16 X coefficients, 16 Y and 16 Z, 48 per patch, starting with AX(1,1) |
The specification’s index column steps by 16 for each of X, Y and Z and ends the array at 7+M+N+48·(N−1) for patch (1,N), so patches are written for u first, then v.
Point (116)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1–3 | X, Y, Z | Real | Coordinates |
| 4 | PTR | Pointer | Subfigure Definition giving the display symbol, or zero for none |
Ruled Surface (118)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | DE1 | Pointer | First curve entity |
| 2 | DE2 | Pointer | Second curve entity |
| 3 | DIRFLG | Integer | 0 join first to first and last to last; 1 join first to last and last to first |
| 4 | DEVFLG | Integer | 1 developable, 0 possibly not |
Form 0 joins points of equal relative arc length on the two rails, whose own parameterisations are not used; form 1 joins points of equal relative parameter value.
Surface of Revolution (120) and Tabulated Cylinder (122)
| Type | Index | Name | Type | Meaning |
|---|---|---|---|---|
| 120 | 1 | L | Pointer | Line entity that is the axis of revolution |
| 120 | 2 | C | Pointer | Generatrix entity |
| 120 | 3 | SA | Real | Start angle in radians |
| 120 | 4 | TA | Real | Terminate angle in radians |
| 122 | 1 | DE | Pointer | Directrix curve entity |
| 122 | 2–4 | LX, LY, LZ | Real | Terminate point of the generatrix |
Direction (123) and Transformation Matrix (124)
| Type | Index | Name | Type | Meaning |
|---|---|---|---|---|
| 123 | 1–3 | X, Y, Z | Real | Direction ratios with respect to the X, Y and Z axes |
| 124 | 1–4 | R11, R12, R13, T1 | Real | Top row of the matrix |
| 124 | 5–8 | R21, R22, R23, T2 | Real | Second row |
| 124 | 9–12 | R31, R32, R33, T3 | Real | Third row |
R is a 3×3 matrix and T a translation. Form 0 (the default) has R orthonormal with determinant +1, so its columns are a right-handed triple; form 1 has determinant −1 (left handed). A matrix referenced by a View entity may not use form 1. Forms 10, 11 and 12 are used with the Node entity: they relate a node’s (u1, u2, u3) displacement system to the local (x, y, z) system as parallel Cartesian axes (10), cylindrical coordinates (11) and spherical coordinates (12), with the origin offset given by the fixed point (r₀, θ₀, φ₀). A matrix of 2D parametric use has T3 = R13 = R31 = R32 = R23 = 0 and R33 = 1.
Flash (125)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1–2 | X, Y | Real | Reference point |
| 3 | DIM1 | Real | First sizing parameter |
| 4 | DIM2 | Real | Second sizing parameter |
| 5 | ROT | Real | Rotation about the reference point in radians |
| 6 | DE | Pointer | Referenced entity (form 0) or zero |
Form 1 circular: DIM1 is the diameter, DIM2 and ROT are null, the reference is the centre. Form 2 rectangle: DIM1 the X length and DIM2 the Y length before rotation, ROT counter- clockwise from X to dimension 1, reference at the centre. Form 3 donut: DIM1 outer diameter, DIM2 inner diameter, ROT null. Form 4 canoe: DIM1 overall length, DIM2 overall width, ROT as for the rectangle, reference at the centre.
Rational B-Spline Curve (126)
With N = 1 + K − M and A = N + 2M:
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | K | Integer | Upper index of the sum (control points are numbered 0 to K) |
| 2 | M | Integer | Degree of the basis functions |
| 3 | PROP1 | Integer | 0 nonplanar, 1 planar |
| 4 | PROP2 | Integer | 0 open, 1 closed |
| 5 | PROP3 | Integer | 0 rational, 1 polynomial |
| 6 | PROP4 | Integer | 0 nonperiodic, 1 periodic |
| 7 … 7+A | T(−M) … T(N+M) | Real | Knot sequence |
| 8+A … 8+A+K | W(0) … W(K) | Real | Weights |
| 9+A+K … 11+A+4K | X(0), Y(0), Z(0) … X(K), Y(K), Z(K) | Real | Control points, in definition space |
| 12+A+4K, 13+A+4K | V(0), V(1) | Real | Starting and ending parameter values |
| 14+A+4K … 16+A+4K | XNORM, YNORM, ZNORM | Real | Unit normal, if the curve is planar |
Appendix B of the specification defines the basis functions. A periodic curve is evaluated exactly as a nonperiodic one; the flag is information for the receiver.
Rational B-Spline Surface (128)
With N1 = 1 + K1 − M1, N2 = 1 + K2 − M2, A = N1 + 2·M1, B = N2 + 2·M2 and C = (1 + K1)(1 + K2):
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | K1 | Integer | Upper index of the first sum |
| 2 | K2 | Integer | Upper index of the second sum |
| 3 | M1 | Integer | Degree of the first basis functions |
| 4 | M2 | Integer | Degree of the second basis functions |
| 5 | PROP1 | Integer | 1 closed in the first parametric direction, 0 not |
| 6 | PROP2 | Integer | 1 closed in the second direction, 0 not |
| 7 | PROP3 | Integer | 0 rational, 1 polynomial |
| 8 | PROP4 | Integer | 0 nonperiodic, 1 periodic in the first direction |
| 9 | PROP5 | Integer | 0 nonperiodic, 1 periodic in the second direction |
| 10 … 10+A | S(−M1) … S(N1+M1) | Real | First knot sequence |
| 11+A … 11+A+B | T(−M2) … T(N2+M2) | Real | Second knot sequence |
| 12+A+B … 11+A+B+C | W(0,0), W(1,0) … W(K1,K2) | Real | Weights, first index varying fastest |
| 12+A+B+C … | X(0,0), Y(0,0), Z(0,0), X(1,0) … Z(K1,K2) | Real | Control points, first index varying fastest |
| last four | U(0), U(1), V(0), V(1) | Real | Parameter ranges |
Offset Curve (130)
| Index | Name | Type | Meaning |
|---|---|---|---|
| 1 | DE1 | Pointer | Curve to offset |
| 2 | FLAG | Integer | 1 single uniform distance, 2 linearly varying, 3 as a function |
| 3 | DE2 | Pointer | Curve one coordinate of which gives the offset as a function of its parameter; 0 unless FLAG = 3 |
| 4 | NDIM | Integer | Coordinate of DE2 that describes the offset (FLAG = 3 only) |
| 5 | PTYPE | Integer | Tapered offset type: 1 function of arc length, 2 function of parameter (FLAG 2 or 3) |
| 6 | D1 | Real | First offset distance (FLAG 1 or 2) |
| 7 | TD1 | Real | Arc length or parameter of the first distance (FLAG 2) |
| 8 | D2 | Real | Second offset distance |
| 9 | TD2 | Real | Arc length or parameter of the second distance (FLAG 2) |
| 10–12 | VX, VY, VZ | Real | Unit vector normal to the plane of the curve |
| 13–14 | TT1, TT2 | Real | Starting and ending parameter values of the offset curve |
Connect Point (132), Node (134), Finite Element (136)
| Type | Index | Name | Type | Meaning |
|---|---|---|---|---|
| 132 | 1–3 | X, Y, Z | Real | Coordinates |
| 132 | 4 | PTR | Pointer | Display symbol geometry, or null |
| 132 | 5 | TF | Integer | Type flag |
| 132 | 6 | FF | Integer | Function flag: 0 not specified, 1 electrical signal, 2 fluid flow path |
| 132 | 7 | CID | String | Connect point function identifier (for example a pin number) |
| 132 | 8 | PTTCID | Pointer | Text Display Template for CID, or null |
| 132 | 9 | CFN | String | Connect point function name |
| 132 | 10 | PTTCFN | Pointer | Text Display Template for CFN, or null |
| 132 | 11 | CPID | Integer | Unique connect point identifier |
| 132 | 12 | FC | Integer | Connect point function code |
| 132 | 13 | SF | Integer | Swap flag: 0 may be swapped (default), 1 may not |
| 132 | 14 | PSFI | Pointer | Owning Network Subfigure Instance or Definition, or zero |
| 134 | 1–3 | X, Y, Z | Real | Nodal coordinates |
| 134 | 4 | PTR | Pointer | Transformation Matrix of form 10, 11 or 12 defining the nodal displacement coordinate system; zero is global Cartesian |
| 136 | 1 | ITOP | Integer | Topology type |
| 136 | 2 | N | Integer | Number of nodes |
| 136 | 3 … 2+N | DE(1) … DE(N) | Pointer | Node entities |
| 136 | 3+N | ETYP | String | Element type name |
The Finite Element topology type table (ITOP values) and the Connect Point type flag values were not read for this page; see the specification.
Offset Surface (140), Boundary (141), Curve on a Parametric Surface (142), Bounded Surface (143), Trimmed Surface (144)
| Type | Index | Name | Type | Meaning |
|---|---|---|---|---|
| 140 | 1–3 | NX, NY, NZ | Real | End of the offset indicator |
| 140 | 4 | D | Real | Offset distance on the indicator’s side if positive, the other side if negative |
| 140 | 5 | DE | Pointer | Surface to offset |
| 141 | 1 | TYPE | Integer | 0 only model space trimming curves; 1 model space curves plus parameter space curve collections (surface must be parametric) |
| 141 | 2 | PREF | Integer | Preferred representation: 0 unspecified, 1 model space, 2 parameter space, 3 equal |
| 141 | 3 | SPTR | Pointer | Untrimmed surface |
| 141 | 4 | N | Integer | Number of curves (N > 0) |
| 141 | 5, 6, 7, 8 … | CRVPT(1), SENSE(1), K(1), PSCPT(1,1) … PSCPT(1,K(1)), then the same for curves 2 to N | Pointer, Integer, Integer, Pointer | Model space curve; its sense (1 keep direction, 2 reverse); the number of associated parameter space curves (0 when TYPE = 0); those curves |
| 142 | 1 | CRTN | Integer | Creation: 0 unspecified, 1 projection of a curve, 2 intersection of two surfaces, 3 isoparametric curve |
| 142 | 2 | SPTR | Pointer | Surface the curve lies on |
| 142 | 3 | BPTR | Pointer | Curve B in the surface’s (u, v) space |
| 142 | 4 | CPTR | Pointer | The model space curve C |
| 142 | 5 | PREF | Integer | 0 unspecified, 1 S∘B preferred, 2 C preferred, 3 equal |
| 143 | 1 | TYPE | Integer | As for 141 |
| 143 | 2 | SPTR | Pointer | Untrimmed surface |
| 143 | 3 | N | Integer | Number of boundary entities |
| 143 | 4 … 3+N | BDPT(1) … BDPT(N) | Pointer | Boundary entities (type 141) |
| 144 | 1 | PTS | Pointer | Surface to trim |
| 144 | 2 | N1 | Integer | 0 if the outer boundary is the boundary of the surface’s domain D, 1 otherwise |
| 144 | 3 | N2 | Integer | Number of simple closed inner boundary curves |
| 144 | 4 | PTO | Pointer | Curve on a Parametric Surface forming the outer boundary, or zero |
| 144 | 5 … 4+N2 | PTI(1) … PTI(N2) | Pointer | Inner boundary curves (type 142) |
CSG primitives (150 to 168)
Vectors are unit vectors. Defaults apply when a field is empty.
| Type | Parameters | Meaning |
|---|---|---|
| 150 Block | LX, LY, LZ, X1, Y1, Z1, I1, J1, K1, I2, J2, K2 | Edge lengths along local X, Y and Z; corner point (default 0,0,0); local X-axis (default 1,0,0); local Z-axis (default 0,0,1) |
| 152 Right Angular Wedge | LX, LY, LZ, LTX, X1, Y1, Z1, I1, J1, K1, I2, J2, K2 | LX is the length in local X at Y = 0, LY and LZ the lengths in Y and Z, LTX the X length at distance LY; corner, X-axis and Z-axis as for the block |
| 154 Right Circular Cylinder | H, R, X1, Y1, Z1, I1, J1, K1 | Height (H > 0), radius (R > 0), centre of the first face (default 0,0,0), axis direction (default 0,0,1) |
| 156 Right Circular Cone Frustum | H, R1, R2, X1, Y1, Z1, I1, J1, K1 | Height; larger face radius; smaller face radius (zero for a cone apex); centre of the larger face; axis direction |
| 158 Sphere | R, X1, Y1, Z1 | Radius; centre (default 0,0,0) |
| 160 Torus | R1, R2, X1, Y1, Z1, I1, J1, K1 | Distance from the torus centre to the centre of the revolved disc (perpendicular to the axis); disc radius; centre; axis direction (default 0,0,1) |
| 162 Solid of Revolution | PTR, F, X1, Y1, Z1, I1, J1, K1 | Curve to revolve (coplanar with the axis); fraction of a full rotation (default 1); a point on the axis (default 0,0,0); axis direction (default 0,0,1). Form 0: an open curve is projected from its ends to the axis; form 1: the curve is closed by a line joining its ends |
| 164 Solid of Linear Extrusion | PTR, L, I1, J1, K1 | Closed curve; extrusion length along the vector; unit vector (default 0,0,1) |
| 168 Ellipsoid | LX, LY, LZ, X1, Y1, Z1, I1, J1, K1, I2, J2, K2 | Semi-axis lengths in local X, Y and Z; centre; local X-axis (the major axis); local Z-axis (the minor axis) |
The parameter data of the primitives is real except for the curve pointer PTR.
Boolean Tree (180), Selected Component (182), Solid Assembly (184)
| Type | Index | Name | Type | Meaning |
|---|---|---|---|---|
| 180 | 1 | N | Integer | Length of the post-order list, operations and operands included (N > 2) |
| 180 | 2 … N+1 | PTR/IOP | Pointer or Integer | Post-order list: a negated pointer is an operand; a positive integer is an operation: 1 union, 2 intersection, 3 difference |
| 182 | 1 | BTREE | Pointer | Boolean Tree |
| 182 | 2–4 | SELX, SELY, SELZ | Real | A point in or on the desired component |
| 184 | 1 | N | Integer | Number of items |
| 184 | 2 … 1+N | PTR(1) … PTR(N) | Pointer | The items |
| 184 | 2+N … 1+2N | PTRM(1) … PTRM(N) | Pointer | The Transformation Matrix of each item |
The operations are regularised: lower-dimensional results disappear. Allowed operands are primitives, Boolean trees, Solid Instances and Manifold Solid B-Rep Objects. The matrix in field 7 of the Directory Entry positions the whole result. The specification’s figure 57 gives a worked tree of five operands and four operations.
Sources
- Initial Graphics Exchange Specification, IGES 5.3 – U.S. Product Data Association, 1996; sections 4.2 to 4.48