Glossary   

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Contents

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3-space

Cartesian coordinate system where a point is represented by an ordered triple of coordinate variables (x, y, z).

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A

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Acorn

Acorn, or minimum body, is the simplest type of body, a body of zero dimension, having one vertex positioned by default at the origin. Topologically it comprises of a single shell, single face, and a single vertex.

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Amalgamation

When the supplied curves have different knot vectors, amalgamation of the curves will create the same knot vector for each curve by addition of corresponding knot points on the relevant curves.

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Analytic

The class of surfaces and curves which are tractable by analytic methods, e.g. circles, lines, planes, spheres. B-surfaces and B-curves are non-analytic.

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Angular Resolution

The largest angle allowed between two direction vectors that Parasolid regards as parallel.
When Parasolid compares two direction vectors they are considered to be parallel if the angle between them is less than 10e-11 radians. This is the smallest angle that Parasolid will resolve; if any two directions differ by more than this angular resolution they will be considered distinct.

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Archiving

Archiving is the process of saving the data in Parasolid's internal memory to external storage. An saved file can contain one or more parts or a partition.

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Assembly

An item of topology representing a collection of instances of parts held as a composite entity. The sub-parts may be either bodies or sub-assemblies.

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Attribute

A data structure that can be attached to any topological entity or group entity. Attributes contain fields of particular types which are specified in the attribute definition.
Attributes are modified following modeling operations. The type of modification depends upon the specific modeling operation and the class of the attribute.

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Attribute Definition

Specifies the format of fields of an attribute using this definition, along with the types of entity that the attribute may be attached to, and the effect of modeling operations on the attribute.

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Axis

A 3-space direction used to define rotations, or rotational symmetry.

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B

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B-curve

A parametrically defined curve whose shape is governed by control vertices.

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Bezier

A special case of NURB, in which the knot set takes a predefined form. In this case the B-spline basis functions are the Bernstein polynomials of the given order.

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Bezier Weight

Weights are associated with control vertices and affect how closely the curve or surface passes by its control vertices. This gives an additional level of shape control over the geometry.
With non-rational curves, all the control vertices are given the same unit weight.

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Blending

The rounding off of edges by replacing the edges with faces which smoothly join the faces adjacent to the original edge.

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Body

The basic "unit" of modeling. A body is composed of one or more components. If a body contains more than one component, it is a disjoint body.

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Boolean

Boolean operations take their name from the primitive logical combinations 'and', 'or', 'not' as investigated by BOOLE. They are operations that are used to combine bodies by uniting, subtracting and intersecting to create new bodies.

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Boundary Circuit

Sequence of edges around a face or collection of faces.

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Boundary Conditions

Used to prescribe the behavior of B-surfaces and B-curves at the boundaries of their definition. For example:

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Bounded Curve

A finite portion of a curve. Defined by the curve geometry and two points lying on the curve.

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B-rep

Boundary representation. Parasolid is a B-rep geometric modeler, in that it represents solids (and other types of body) by their boundaries.

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B-spline Curve

A generalization of the Bezier form in which a composite B-curve is represented by an array of B-spline vertices, and a knot vector.

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B-surface

A parametrically defined surface whose shape is governed by control vertices.

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Bulletin Board

Changes to model entities can be recorded on the bulletin board to give an application the facility to trace how a model has changed in the course of one or more modeling operations.

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C

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Capping

The covering of holes or wounds in a body, via the fitting of new surfaces.

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Chain

A row or column of control vertices in the control net of a B-surface.

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Chamfer

Related to a blend. Instead of modifying an edge by smoothing it over, the edge is shaved with a flat cutter, creating two new sharp (not smooth) edges and an extra face, the surface of which is either a plane, cone or B-surface.

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Chord

The vector between two points on a curve.

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Cliff Edge Blend

A special case of a blended edge in which the newly created blend face is tangent to only one of the faces adjacent to the original edge. The other adjacent face is deleted. A typical example is when either the upper or lower edge of the step is blended with a radius greater than the depth of the step.

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Closed

Generally, closed means "returning to the beginning or without boundaries". Specific definitions are:

 

Note: Both closed surfaces and closed sheets enclose a volume of space.

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Component

A set of connected entities in a body. A body is composed of one or more components.

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Connectivity

The adjacency relationship between edges, faces and vertices.

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Construction Geometry

Items of geometry (surfaces, curves and points) which can be attached directly to a body or a partition as extra information.

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Continuity

The continuity between the patches of a B-surface or segments of a B-surface can be of various levels:
'C' Continuity for curves and surfaces:
'G' Continuity for curves:
'G' Continuity for surfaces:

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Control Net

The 3-space polyhedron formed from all the control vertices of a B-surface.

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Control Vertex

The 3-space point which controls the shape of a B-curve or B-surface. It may have a weight associated with it. Also called a control point.

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Convex Hull

The smallest convex polyhedron enclosing all the control vertices of a B-curve or B-surface. It also encloses the curve or surface. Although every control vertex is contained in it, they will not in general all be on the boundary.
For a NURB with more than one patch it is possible to define convex hulls for various subsets of the control point set, which enclose portions of the spline.

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CSG

Constructive Solids geometric modeler. A modeler that represents solids procedurally. Compare with "B-rep".

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Curve

Curves, which are geometric entities, are principally attached to edges or fins of the model, they can also be attached to bodies and KI assemblies as construction geometry or be free in the session world.

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Cusp

A discontinuity of tangent direction or surface normal.

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D

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Degeneracy

On a curve or surface, a place where the parametrization collapses so that a range of parameter values correspond to a single 3-space point.

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Delta

Byte-stream (usually, file) output through the Frustrum which records the changes required to move from one pmark to an adjacent one.

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Derivative

The first derivative of a curve is a vector valued function whose value at any parameter is a linear approximation to the curve at that parameter.
The first partial derivative with respect to one of the parameters of a surface is a function whose value is the linear approximation to the curve obtained by holding the other parameter constant.

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Dimension

The number of double precision numbers that are used to define a control vertex together with its weight:

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Disjoint

A body is disjoint if it contains more than one component.

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Downward interfaces

A generic term for the interfaces to Parasolid that lie "beneath" the modeler; that is, they are themselves called by Parasolid. Usually, there are two downward interfaces: the frustrum (q.v.) and the GO (q.v.).

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Drafting Lines

Lines that represent edges which are hidden by the interiors of faces.

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E

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Edge

A fundamental item of topology representing a bounded piece of a single curve. Edges reference their face, curve, fins and bounding vertices.

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Edge Orientation Flag

Indicates whether the direction of the edge is parallel (true) or anti-parallel (false) to the underlying curve tangent direction.

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End Conditions

When creating a spline curve or surface by interpolating a set of points, end conditions are used to tie down otherwise unused degrees of freedom at either end of the curve or any of the boundaries of the surface. They may be either:

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Entity

An entity is an item in the model which can be accessed by the application.

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Error code

An integer value returned from every PK function call that denotes whether an error occurred in the function call. If zero, then the function completed with no errors. If non-zero, then your application must take appropriate action, depending on the nature of the error.

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Evaluator

The functionality which provides parametrization and de-parametrization for a curve or surface.

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Exact (Geometry)

Identical mathematical representation of curve or surface, when changing from one type of geometrical representation to another.

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Exact (Topology)

Topological entity which does not have a tolerance stored with respect to its underlying geometrical entity.

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F

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Face

A fundamental item of topology representing a bounded piece of a single surface. Faces reference their shell, surface and bounding loops (including edges).

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Face Normals

In Parasolid all face normals point out of the material of the body. For faces bounding voids this means into the void. A face normal is determined by the normal of the surface attached to the face and sense of the face.

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Face Orientation Flag

Indicates whether the direction of the face normal is parallel (true) or anti-parallel (false) to the underlying surface normal.

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Faceted Model

A 3D model whose faces are approximated by flat facets. Faceting is also known as 'tessellation'. Flat facets are a combination of vertices and straight edges that form planar facets.

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Fillet

Is an operation that rounds a corner of a profile or an edge of a solid to a specified radius. A fillet is a type of blend.

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Fin

Represents one side of an edge and may have a curve attached. Fins belong to loops which in turn bound faces. The direction of a fin is derived from the direction of its owning loop. By convention, the direction of a loop is anticlockwise when looking into a surface along its normal.

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Fin Orientation Flag

Indicates whether the direction of the fin is parallel (true) or anti-parallel (false) to the underlying curve tangent direction.

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Foreign Geometry

Foreign Geometry curves and surfaces are defined externally to the modeler by evaluators supplied by the application. By providing a Foreign Geometry downward interface (q.v.), specialist curves and surfaces not supported within Parasolid may be used in Parasolid modeling operations.

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Free Form

A general term that encompasses B-curves/surfaces and Foreign geometry.

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Frustrum

A suite of functions that the application developer must provide for use by the kernel. They are registered with Parasolid and are used for data input/output, graphical output and memory management. These functions separate Parasolid from machine specific operations.

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G

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General Body

Collection of entities (faces, edges and vertices) and 3-dimensional connected regions into which space is divided by the entities. Each region is either 'solid' or 'void', indicating whether or not it represents material.

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General helix

A helix, a tapered helix, or a spiral.

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Geometry

The geometrical elements of a solid are the points, curves and surfaces which specify shape and position.

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Gluing

Another term for knitting.

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GO

Set of functions which need to be written by the system builder in order to provide graphical output from the Parasolid rendering functions on the appropriate display hardware.

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Graphical output

The process of passing graphical data to the application for display. See also "Rendering".

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Group

Collections of geometrical and/or topological entities, attached to a part. They provide a way of collecting together related items within a part, and are updated by modeling operations.

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Growing

The healing of a wound created by a local operation by extending the faces and edges surrounding the wound.

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H

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Heavyweight function

Any Parasolid function that makes changes to the model, such as PK_BODY_boolean_2. See also "Lightweight function".

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Help geometry

User-supplied geometry that is used by Parasolid to choose a particular solution when a modeling operation yields several possible outcomes. If supplied, Parasolid chooses the body that contains geometry that is closest to the supplied help geometry.

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Hidden Line

Hidden line pictures distinguish lines which are visible from a given viewpoint from those lines which are hidden.

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I

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Image Space

Image space is the space in which the application remembers the model. Typically the X and Y axis will correspond to horizontal and vertical directions on the users screen. Parasolid rendering functions return data in model space. The application must transform the data to image space before drawing.

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Imported Model

A model created by knitting or BREP import, which is characterized by user-supplied tolerances attached to some or all of its faces, edges and vertices.

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Incremental Graphics

When a part changes, incremental graphics can be used to re-draw just the entities that have changed.

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Instance

A reference to a part by a assembly. The instance records the transformation to apply on the part to place it in the required position within the assembly.

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Interference Detection

The ability of the modeling system to detect if an object invades the internal space of another.

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Interrupt handler

An error handler that can be registered to handle user interrupts from your application.

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Intersection Curve

Curve generated by the intersection of two surfaces. Each such curve potentially represents only one branch of a surface/surface intersection. For example, when two equal sized cylinders intersect, four intersection curves will be defined.

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J

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Journal File

Record of PK function and KI routine calls made by the application, and the values returned by those calls. The journal file must be named at the start of the modeling session but the journalling may be switched ON or OFF as required.

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K

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Kernel

An alternative name for the Parasolid library.

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Kernel Interface

An interface to the Parasolid library (being replaced by the PK Interface).

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Key String

The name supplied by the application to refer to a saved file.

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Knitting

The joining together of bodies along edges. The edges must correspond geometrically to the specified edge tolerances for a valid model to result.

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Knot Vector

Also know as knot set. The non-decreasing set of parameter values that define the start and end of each patch or segment of a B-surface or B-curve. Together with the order, the knot vector uniquely defines a set of B-spline basis functions.

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L

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Laminar Edge

An edge with only one fin (e.g. at the boundary of an open sheet body).

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Lightweight function

Any Parasolid function that performs a read only call to the kernel, such as PK_BSURF_ask. See also "Heavyweight function".

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Linear Resolution

A Parasolid model is very exact; typically points are not considered coincident unless they are less than 10e-8 apart (linear resolution).

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Load

See "Receive".

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Local Checking

Parasolid's local operations allow regions of a model to be modeled efficiently. Through local checking the integrity of these operations can be verified automatically. Local checking is optional and may be disabled in favor of improved performance.

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Local Coordinate System

Defines an entity in a convenient coordinate system and shows its position and orientation within the world coordinate system.

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Lofting

The creation of a B-surface by interpolating a set of pre-defined B-curves.

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Loop

A fundamental item of topology representing one boundary of a face as a closed connected set of edges.

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M

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Manifold Body

A body that exists in real terms. A manifold solid body must not have isolated points and lines of zero thickness. A sheet body does not (normally) have points of zero thickness.

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Matched region

A region of overlap between two topological entities that are geometrically coincident to a specified tolerance.

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Mark

Records the state of the modeling session at a given point, by creating a pmark in each partition.

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Modeling Resolutions

The fixed accuracies to which Parasolid performs all its calculations. Angular and linear resolutions are not independent but are related through the size box.

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Minimum Body

The simplest type of body, a body of zero dimension - it is just a point in space. Topologically it comprises of a single shell, single face, and a single vertex. Also known as an acorn body.

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Model

A fully defined model is the representation of a solid object stored in the modeler database. A model maybe incomplete.

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Model Space

Models are defined in object space. Some Parasolid operations, such as rendering, allow the model to be considered as transformed before the operation. A model so transformed is said to be in model space.

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N

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Negative body

A body that is inside out, so that the face normals point into the solid. The only operation that can be performed on a negative body is to negate it.

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Node Identifiers (Node IDs)

Integer values which are attached to all entities within a body (except for fins), and are unique within the body. Node identifiers, unlike entity tags, are saved with the body.

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Normal

A normal to a surface at a point on that surface is a vector which is locally perpendicular to the surface. The normal is usually described by a unit vector.
Surface normals to implicit surfaces are computed using the derivative of the surface function.
Surface normals to B-surfaces are computed by taking the cross products of the partial derivatives of the parametric function with respect to the u and v direction.

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Normal Edge

In a sheet body, an edge which has 2 fins of opposite senses.

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NULTAG

A tag to which no entity corresponds. Its principal use is by various KI routines which return it when there is no appropriate entity.
The equivalent PK value is 'PK_ENTITY_null'.

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NURB

A Non Uniform Rational B-spline (NURB) is a spline defined with respect to B-spline basis functions. The coefficients assigned to these basis functions are termed control vertices. In Parasolid the NURB may be:
Non-uniform means that the values in the knot vector are not necessarily uniformly spaced and may even be coincident.

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O

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Object Space

Object space is the Parasolid coordinate system in which a model is created.

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Obscured Line

A segment which is invisible in a given view due to being coincident (from that view) with another line (including silhouettes and drafting lines) to the front of it.

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Offset Surface

The surface from any point on which the minimum distance to the underlying surface is exactly equal to the required offset distance. In Parasolid the offset surface must be G1 continuous.

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Open

Generally, open means "not returning to its start, and possibly with a boundary". Specific definitions are:

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Order

The order of a B-curve or B-surface is the order of the polynomial or rational functions that make up the spline.
The order is equal to one more than the degree.

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Orphan

Entities in the session not attached to any part, although they may subsequently be so should they need to be preserved.

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Orthogonal Solution

A solution is regarded to be orthogonal relative to an entity, if either:

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P

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Parameter Space

The 1 (curve) or 2 (surface) dimensional space for parametrization to be defined in.

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Part

Either a single body or an assembly.

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Partition

Self-contained collection of bodies and other data items, which can be modeled with and rolled back independently of others in the session (which are in other partitions).

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Part State

Describes whether or how a part has been saved. A part may be in one of the following states; new, stored, modified, unloaded, or anonymous.

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Patch

A single polynomial or rational piece of a Bezier surface.

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Periodic

A periodic curve or surface is closed and has a continuous parametrization. It is possible for a surface to be periodic and closed in the u direction but open and therefore non-periodic in the v direction.

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Piecewise

The piecewise standard form of a B-curve defines it as a collection of curve pieces. It is represented by an array of points of the curve and values for degree, dimension, rationality and representation method.

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Pierce faces

In hollowing operations, pierce faces are those faces in a body that are offset by zero, thereby opening up the body.

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PK Interface

An interface to the Parasolid library (replacing the KI - Kernel Interface).

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Pmark

Partition mark - point in a modeling session when a rollback mark is set in a partition, causing a delta to be output to the Frustrum.

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Pmark Graph

Conceptual map of the pmarks of a partition. Used by partitioned rollback

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Point

Points, geometric entities, are principally attached to vertices. They may also be attached to bodies as construction geometry.

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Protected code

The "modeling" part of any heavyweight function. See also "Unprotected code".

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R

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Rational

A spline is rational, if its segments or patches are rational functions. That is, they are the ratio of two polynomials.
A rational spline curve of degree greater than or equal to quadratic can exactly represent a conic section.
A rational spline surface of degree greater than or equal to quadratic can exactly represent a quadric surface (sphere, cone, cylinder, etc.).

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Receive

To read data which defines a part(s) or partition from a saved file. The data is restored into Parasolid's internal memory in the current session.

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Region

Of a body, an open connected subset of 3-dimensional space, whose boundary is a collection of vertices, edges, and oriented faces. Regions are either 'solid' or 'void', and they may be non-manifold. Bodies have one 'infinite' region which is void.

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Rendering

The process of producing graphical data for specified entities in order to produce a picture of them. See also "Graphical output".

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Reverse Flag

Every face has a reverse flag associated with it which indicates whether the face normal is in the same direction as the surface normal. When the reverse flag is true the face normal is anti-parallel to the surface normal and vice versa when the flag is false.

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Rollback

Enables a Parasolid session to be returned to a check pointed state, typically being used to undo the effects of an operation or series of operations that have not produced the expected result.

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Rolling Ball

A rolling ball blend surface is the envelope swept out by rolling a sphere along a given path.

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Rubber Face

Face with no surface geometry attached.

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Run-time error handler

An error handler that can be registered to handle some types of run-time error from your application.

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S

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Save

See "Transmit".

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Scribing

The addition of a new edge internal to a face, typically with a view to creating profiles.

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Segment

A single polynomial or rational piece of a spline curve.

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Sense Flags

Sense flags are items of data returned by enquiry and output functions which are used to determine the surface normal direction. They apply to two entities, one to indicate the sense of a face and the other to indicate the sense of a surface.
The sense of a face is said to be 'true' when the face normal is parallel to the surface normal and 'false' when they are anti-parallel.
The sense of a surface is said to be 'true' when the normal of the surface is the natural one of the surface.
Curves do not have sense flags in Parasolid.

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Self Intersecting

A solid body is said to be self intersecting when two points exist within the body that a path, which does not pass through faces of the body, cannot be found between.

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Session Transmit

An image of a session at a particular instant, which can be reloaded in a new session in order to recreate the former one. Also known as a 'snapshot'.

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Sewing

Process of uniting B-surface sheets until they enclose a volume to produce a sheet body that can then be converted into a solid body.

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Sheet Body

A laminar part with zero thickness.

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Shell

A fundamental item of topology representing a connected set of faces which bound a model.

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Silhouette Line

These are curves indicating where curved faces change from pointing towards the eye to pointing away from it, with respect to the given viewpoint.

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Singularity

Position on a surface where the normal is not defined. Typical singularities occur at the apex of a cone.

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Size Box

The volume within which Parasolid's modeling operations take place, defined as a cube of sides 1000 units. By convention most applications define one unit to correspond to one meter, therefore providing a modeling volume of one cubic kilometer.

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Snapshot

An image of a session at a particular instant, which can be reloaded in a new session in order to recreate the former one. Also known as 'session transmit'.

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Solid Body

A three-dimensional body which occupies a continuous, finite volume.

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SP-curve

A 3-space curve defined by an equation in the parameter space of a surface. They are currently implemented as NURBs.

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Spline

A curve or surface made up of a number of polynomial or rational pieces, with levels of continuity defined between the pieces. The parameter values at which the spline changes from one piece to another are called knots, and the pieces are termed segments in the case of a curve and patches in the case of a surface.

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Splinewise

The splinewise standard form of a B-curve defines it as a continuous curve which meets specified constraints. It is represented by an array of position vectors and values representing its degree, end and tangency conditions and knot values.

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Splining

Creating a B-curve by interpolating a set of points and a B-surface by interpolating a mesh of points. The points will be at the ends of curve segments or at the corners of the surface patches.

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Surface

Surfaces, which are geometric entities, are principally attached to faces, but may also be attached as construction geometry.
Normally every face will have a surface attached to it, but it may be detached temporarily as the model is being built or modified.
A face with no surface attached is termed a rubber face.

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System Defined Attributes

Attribute types pre-defined by the system for common uses (e.g. face color and translucency, body density).

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T

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Tag

An application's handle on an entity, partition, mark or pmark.

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Target

A boolean 'operand', used in conjunction with the tool. The 'workpiece', it remains after the boolean.

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Tolerance

A resolution parameter, associated with an edge or vertex, representing the minimum distance that a point and an entity must be apart in order to be distinct.

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Tool

A boolean 'operand', used in conjunction with the target. The 'modifier', it will usually be destroyed by the boolean.

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Topological Entities

This class contains all the entities which describes the connectivity skeleton of the model.

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Topology

The topological elements of a solid are linked together in a network which represents their inter-connections or connectivity in terms of vertices, edges and faces.

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Tracking Data

High level data, accessed via the bulletin board. For example, this data may describe that a new face was created by sweeping a particular edge, where as the lower level data would describe what had happened to each topological entity.

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Transmit

To write data which defines a part(s) or partition into a saved file.

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Trimmed Curve

Trimmed curves contain curve and end-point data which is essential for algorithms which rely on extracting bounded curves of edges, in cases where the vertex points do not lie within the Parasolid linear resolution of edge curves.
Trimmed curves conveniently package the relevant data and therefore avoid expensive repeated computation of end-points.
The current implementation of trimmed curves can only be created in the KI interface (as it is not STEP-compliant).

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Trimmed Surface Sheet

A sheet body created by PK_SURF_make_sheet_trimmed, from a surface and loops of SP-curve geometry. Specifically for imported data.

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Tweaking

Performing a local operation on a particular face set of the model, with the result that their surfaces are replaced by the supplied ones, and the edge and vertex geometry is recalculated.

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U

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Unprotected code

The "non-modeling" part of any operation. This includes all lightweight functions, and the "non-modeling" part of any heavyweight function. See also "Protected code".

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User Fields

Used for saving an array of information with each entity, for example, a pointer into the system's data structure.

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V

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Vertex Matching

Ensures when faceting, that there are no gaps along the edges of the model, and that it is therefore suitable for Stereo Lithography Applications.

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W

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Weight

In the definition of the rational form of NURB, each control vertex has a weight associated with it. If all the weights of a NURB are equal, then the NURB is equivalent to the polynomial form. The weights are required to be positive (non-zero) numbers.

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Wire Body

A wire body is one step up from a minimum body - it is topologically one-dimensional, a set of connected edges.

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Wire Frame Picture

Pictures which depict models by drawing all their edges.

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World Coordinate System

Coordinate system in which the size box is defined. The origin is at the center of the size box and its axes are aligned with the size box.

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Wound

The undefined area left in a body by a local operation which has removed some faces from a body, or has partly defined a new body from faces of an existing body.
 

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