Special Characters |
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| 2D-Curve | A 2D-Curve is defined in the u-v-Parameterspace of the surface. A 2D-Curve yields information of the surface, for example the curvature of the surface. | |
| 3D compass | The 3D compass is a three-axis system used to define the plane into which any action is performed. It is displayed whenever you are creating an element or applying modifications to this element. | |
| 3D-Curve | Normally a curve is a 3D-Curve. A 3D-Curve placed on a surface does not yield any information about the surface. | |
| 3D-Tool | A UI-Tool is sometimes called 3D-Tool. | |
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| absolute grid | See Grid | |
| align object | Some commands need as input curves or surfaces. If only one object is needed as input we call it the reference object. If
the command needs two objects and we want do distinguish between objects we call it for example align object and reference object. Look at the matching command. The first selected object is called the align object and the second selected object is called the reference object. If the Option Both is off only the align object is modified. |
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| approximation | A surface or a curve is converted into a NURBS surface or a NURBS curve. | |
| attenuation | Factor to attenuate the speed with of the mouse displacement. | |
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| basic surface | If a surface is trimmed at an arbitrary curve, it is sometimes wanted that the trimmed surface yields the information about
the input surface. This input surface is called Basic Surface (if it is not trimmed). A trimmed surface is called a face and the underlying untrimmed surface is called the Basic surface. If a surface is not trimmed, it makes no sense to distinguish between this surface and the Basic surface. If you break it, the result is not a face and in general the resulting surface does not meet the starting surface exact, there is an Approximation. |
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| Bézier curve | A Bézier Curve is a polynomial Curve in the 3D-Space (x, y, z - Space), which was transformed with a change of its Basis. The new Basis is the set of Bernstein Polynomials. The change of the basis creates in a canonical way a set of points. These points are called the Control Points of the Bézier Curve. | |
| blend curve | A curve created to connect two pre-existing curves. | |
| blend surface | A surface created to connect two pre-existing surfaces. | |
| B-Spline | A B-Spline is a Curve in the 3D-Space (x, y, z - Space), which contains more than one segment. Each segment can be considered as a Bézier Curve. These Bézier Curves are merged very well to avoid Control Points and knots at the segment boundaries. The parameter values at the segment boundaries are called knots. These knots can be distributed equal spaces. Uniform B-Spline (UBS) or arbitrary distributed, Non Uniform B-Spline (NUBS). | |
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| chain of curves | A chain of curves contains at least one curve. If there are more than one curve, the endpoint of the first curve has to meet the start point of the second curve and so on. Gaps and overlapping are not allowed. | |
| chordal distance | The chordal distance between two points on a curve is the length of the curve between these two points. We have a curve and on this curve two different points. The shortest distance between these two points is measured along a line. This line needs not to be on the curve. The chordal distance between these two points is measured on the curve. It is the length of the curve between these two points. We have a surface and on this surface two different points. The shortest distance between these two points is measured along a line. This line needs not to be on the surface. The chordal distance between these two points is measured on the surface. It is the length of the shortest curve on the surface between these two points. |
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| chordal parameterization | The chordal parameterization of a curve connects the length of the curve with a parameter value. The parameter 0.2 is where the curve has 20% of its length. The parameter 0.5 is in the middle of the curve. B-Splines can not be parameterized absolute exact chordal but the chordal parameterization can be approximated. For a surface the Chordal Parameterization works accordingly. | |
| cloud of points | A set of points in space. A cloud of points may consist of a single point or several million points. | |
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| discrete | See Grid | |
| domain | Set of topologically arranged cells | |
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| face | A face is a trimmed surface. A face has an underlying Basic Surface. | |
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| G0 | If the endpoint of curve K1 meets the endpoint of curve K2 then we say: At this point both curves are connected with order
of continuity G0. If one edge of surface S1 meets an edge of the surface S2 then we say along this edge both surfaces are connected with the order of continuity G0. If the G0-continuity is missed then we have a so called G0-error. This error is an absolute error, a distance, and it is measured in mm or inches. |
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| G1 | The curve K1 and the curve K2 are connected with the order of continuity G0 in the point P. If both curves in the point P
run into the same direction, this means the angle between the tangents of both curves is 0, then we say the order of continuity
is G1. The surface S1 and the surface S2 are connected with the order of continuity G0 along the curve C. We take the normal of S1 in a point near the curve C and run with this normal over the border to S2. If the normal does not change its angle from one point of the border of S1 to the nearest point of S2 then we say the order of continuity is G1. If the G1-continuity is missed then we have a so called G1-error. This error is an absolute error, an angle, and it is measured in deg of rad. |
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| G2 | The curve K1 and the curve K2 are connected with the order of continuity G1 in the point P. We look at the curvature vector
of K1 in point P and the curvature vector of K2 in point P. If both vectors have the same direction and the same absolute value,
then we say the order of continuity is G2. The surface S1 and the surface S2 are connected with the order of continuity G1 along the curve K. If each curve on S1 which runs over the border to S2 can be continued with another curve on S2 and their order of continuity is G2 then we say both surfaces are connected with the order of continuity G2. If the G2-continuity is missed then we have a so called G2-error. This error is a relative error and it is calculated with the following formula. K1 may have the radius R and K2 may have the radius r at the common point, with r<R, then yields:
This formula is not valid for extremely small values of r and extremely large values of R. The maximum of this error is 1. Sometimes this error is measured in percent % then its maximum is 100%. In CATIA the percentage is taken, but the percentage sign is omitted. The values are between 0 and 100. |
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| G3 | The curve K1 and the curve K2 are connected with the order of continuity G2 in the point P. For the definition of the G3-continuity
we look at the curvature hedgehog, as it can be created with the command
Porcupine Curvature Analysis. We look at the envelope of
the curvature hedgehog. If this envelope has at the desired point G1-continuity then we say the order of continuity between both
curves is G3. If the G3-continuity between both curves is missed, the G1-continuity of the envelope is missed, then we have a so called G3-error between both curves. This error is an absolute error, an angle, and it is measured in deg of rad and it is the G1-error of the envelope. G3-continuity between surfaces is defined on the curves between both surfaces on the same way. |
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| gaussian curvature | The Gaussian curvature is calculated from the Max Principal and the Min Principal curvature with the following formula: Gauss = sig(MaxPrincCurvature)*sig(MinPrincCurvature)*sqrt(abs(MaxPrincCurvature*MinPrincCurvature)) Sig is the sign (of MaxPrincCurvature and MinPrincCurvature) and can only have the value +1 or -1. |
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| global deformation | A deformation that is applied globally to a set of elements, as opposed to a deformation successively applied to different elements. | |
| grid | There are Commands, which have in their Properties panel the option Translate Grid. If Grid is ON and the Grid value is not
0, then it is impossible to snap to points, which are not on the Grid. Example: If the Grid value is 25 then it is only possible to snap to points with the distance of 25 mm in each coordinate. We have an Absolute Grid, short Grid. The Absolute Grid has a Grid point at the origin of the Model Coordinate System. It can be switched on with Translation, Grid. The other Grid is the Relative Grid. The Relative Grid has a Grid Point at its starting point of modification. The Relative Grid can be switched on with Translate Discrete. |
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| hedgehog | The Hedgehog is always perpendicular to its curve. The length of the spikes is proportional to the radius or curvature (depends on the selected option) of the curve. In most cases the value of the length is scaled. | |
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| inflection line | Curve, lying on a surface, which curvature value is 0 at each point. | |
| inflection point | An inflection point of a curve is a point on the curve where the curve changes its curvature. In this point, the curvature is 0. | |
| iso-Curve | An Iso-Curve is a curve on a surface. One parameter, u or v, runs from 0 to 1 and the other parameter is constant. Iso is the prefix for constant. For example isobar. | |
| isophote | An Isophote is a curve on a surface. All points of this curve of the isophote have the same illumination from a given light source. The illumination of all points of this curve is constant. Iso is the prefix for constant. For example isobar. | |
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| match curve | A curve deformed so as to connect another curve, while taking the continuity type into account. | |
| match surface | A surface deformed so as to connect another surface, while taking the continuity type into account. | |
| Max Principal curvature | To measure the Max Principal curvature in a point of a surface we use the following method: Intersect the surface with all planes containing the normal of the surface in this point. Each plane creates a planar curve, which has a curvature value in this point. This value can be positive or negative. The maximum of all this curvature values is the Max Principal curvature of the surface in this point. |
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| mesh line | A line on a surface used to deform this surface according to various laws, and types of deformation. | |
| min Principal curvature | To measure the Min Principal curvature in a point of a surface we use the following method: Intersect the surface with all planes containing the normal of the surface in this point. Each plane creates a planar curve, which has a curvature value in this point. This value can be positive or negative. The minimum of all this curvature values is the Min Principal curvature of the surface in this point. |
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| model coordinate system | The model coordinate system is the system which is fix and can not be changed by the user. The orientation is displayed on the bottom right side in the graphic window. The default orientation of the compass equals the model coordinate system. Its orientation can be changed by the user. | |
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| NUBS | See B-Spline | |
| NUPBS | A NUBS, Non Uniform B-Spline is also called NUPBS, to make it more clear that it is a polynomial curve and not a rational curve. See NURBS | |
| NURBS | A NURBS, Non Uniform Rational B-Spline, is a NUBS with a rational component. Rational means that the weight of the Control Points must not have the value 1. With a Rational Curve a Circle and a Hyperbola can be described exact. | |
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| order of continuity | There are four different orders of (geometric) continuity. They are abbreviated with GC-Continuity or G-Continuity. We will use G-Continuity and a number to mark the order of G-Continuity. We distinguish between G0-Continuity, G1-Continuity, G2-Continuity, G3-Continuity. These orders of continuity are of interest between curves and surfaces. For some types of curves and surfaces also for inner points of the curve or surface. | |
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| parameterization | Curves are parameterized with the parameter u. The parameter u runs from 0 to 1. Surfaces are parameterized with the parameters u and v. Both parameters run from 0 to 1. A special parameterization is the so called chordal parameterization. |
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| plane tool | The plane tool is an auxiliary coordinate system. Its x-y-plane is often used when the system needs a user-defined plane. Its z-axis is used if the system needs a vector. For example Symmetry. | |
| PNubs | A Pnupbs is a Nupbs, which lies on a surface and is connected with this curface. Connected means, that the Curve contains information, e.g. tangent and curvature of the surface. A PNubs is defined in the 2D-Papameterspace of the surface. | |
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| reference object | Some commands need as input curves or surfaces. If only one object is needed as input we call it the reference object. If
the command needs two objects and we want do distinguish between objects we call it for example align object and reference object. Look at the matching command. The first selected object is called the align object and the second selected object is called the reference object. If the Option Both is off only the align object is modified. |
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| reflection line | A curve visualized on a surface, that reflects the light emanating from a grid of neon located above the surface. | |
| relative grid | See Grid | |
| rolling ball | To imagine the creation of a fillet surface you can take the idea of the rolling ball which runs between the surfaces where the fillet has to be created. This rolling ball marks on each surface a curve. The fillet surface is created between these two curves. The radius of the rolling ball equals the radius of the wanted fillet. The radius can change while moving. | |
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| surface | In CATIA, surfaces are parameterized with the u- and v-Parameters running from 0 to 1. A surface has an order in u- and an order in v-Direction, 2<=order<=16. The simplest surface is a 4-Point-Patch of order 2 in u-Direction and order 2 in v-Direction. A surface can have only one patch or several patches. The command Goemetric Information shows you in the panel Geometric Analysis the available information. A surface can be trimmed for example by the command Break. It can be untrimmed by the command Untrim. A trimmed surface is called Face and contains all the information of the untrimmed surface. Because of this a command can work on the Face or on the (untrimmed) Basic Surface. |
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| topological | Concerned with relations between objects abstracted from exact quantitative measurements. | |
| topological operation | An operation retaining the topological properties of the element undergoing the specified transformation. | |
| trimmed surface | See Surface. | |
| trimming boundary | A trimming boundary limits a hidden part of a surface. Such a surface is called a Trimmed Surface or Face. We prefer the term
Face. The full information and mathematical description of the Basic Surface is preserved. The
Break command gives you the possibility to trim a surface
and to create a Face. Some commands can work on the Face or on the Basic Surface. The Option Panel of these commands has the switch Basic Surface. |
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| UBS | See B-Spline. | |
| u-Direction | Curves are defined as so called parametric curves. The parameter is u and it runs from 0 to 1. Surfaces are defined as so called parametric surfaces. The parameters are u and v and run from 0 to 1. |
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| UI-Tool | User Interface Tool. The output of a command is controlled with a UI-Tool. The UI-Tool can be a point or a vector or a circle. For example Isoparametric Curves (point), Fillet (vector) and Flange (circle). | |
| untrimmed surface | See Surface. | |
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| v-Direction | Surfaces are defined as so called parametric surfaces. The parameters are u and v and run from 0 to 1. | |
| Vector | Vector is a special word from the mathematical termonologie. A vector has a direction and a length. In the CAD-System a vector is used as a special UI-Tool. Length and angle (direction) describe the behavior of the object connected with this UI-Tool. For example Flange. The length can be changed by moving the mouse with the pressed left mouse button on the peak of the vector. The angle can be changed by rotating the circle, which occurs if the mouse is moved along the vector. Exact values for these two the vector describing parameters can be keyed in by clicking on the displayed digits of the values. If there are more than one describing vectors and you want to give the same value to all vectors press first the Crtl-Button and then click on the digits. |
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| View-Direction | The View Direction is the direction of sight of the CAD-User. The View Direction is perpendicular to the Screen Plane. | |
| View-Plane | The View Plane is a plane, which does not depend on the orientation of the Model Coordinate System or on the orientation of the View. The View Plane is a theoretical plane perpendicular to the direction of sight of the CAD-User. The View Plane is parallel to the Screen Plane. | |