Inleiding Topologie. Lecture Notes. Marius Crainic c⃝ Mathematisch Instituut. Universiteit Utrecht. Aangepast, November This is the web-site for the course “Inleiding Topologie” for the year ( blok 2, Fall ). Here you will find all the practical informations about the. Studying WISB Inleiding Topologie at Universiteit Utrecht? On StuDocu you find all the study guides, past exams and lecture notes for this course.

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This action manages the connections between curves in a wireframe, which is a vital step in the conversion to a solid. Wireframe points represent the vertices in the boundary representation B-rep toopologie the solid. The main purpose of this action is to determine which curves intersect and where they should be connected with a shared wireframe point. The most important criterion in this assessment is the value in the [Tolerance] field.

The process of searching for curve intersections is as follows. It should be clear that there is no one-size-fits-all tolerance.

Therefore it may be necessary to experiment a bit, and use [Undo] if results are not as intended. It may well be that most connections can be made automatically, but that a few cases remain inleuding require manual attention. If existing wireframe points are present and the [Change] button on the [Manual] tab is depressed, wireframe connections to these points can be inspected, made and broken.

Initially, moving the mouse pointer over wireframe points will highlight the curves that are connected to it. This way it is easy to scan for missing or incorrect connections, see the figure. After clicking on a specific wireframe point, connected curves are topoloie. By clicking on a selected curve it will be disconnected from the wireframe point, and selecting an unselected curve will connect inleifing if it runs by the wireframe point within the tolerance.

So if a curve cannot be connected, try again after increasing lnleiding value in the [Tolerance] field. A single new connection between two curves can be added by hand when the [Add] button on the [Manual] tab is depressed.

A new wireframe point will be added to which the selected curves are connected. If more than two curves should intersect at the same point, the inleidihg curves can be added afterwards as explained in Change existing connections.

Switching to the [Automatic] tab will initiate a search in which every curve in the wireframe is compared against every topolpgie curve. It is most practical to adjust the tolerance before switching the tab as changing the tolerance will restart the search. New wireframe points will be added for every inleidinh intersection that is found for the given tolerance.

Before pressing [Apply]the generated connections may be inspected by changing back to the [Manual] tab, pressing the [Change] button and hovering over the generated wireframe points as described in Change existing connections. If [Apply] is pressed while the [Automatic] tab is active, the action will immediately start a new search.

This is harmless and the action can be closed at any time. After connections have been generated, a validity check of the wireframe Checking the validity of wireframes can report a high number of duplicate points. Duplicate points can of course be resolved by deleting individual points from curves using [ Delete ] from the [ Toppologie the shape of a curve ] action, but the problem can likely be avoided by connecting with a more appropriate tolerance, or by reducing the mean fairing deviation of all curves using [ Bulk Change of All Curves ].

The reason why too low a tolerance can produce double points, even though otpologie in the input file run through identical coordinates, is the following. If polylines have been converted to curves by the import procedure see Intermezzo polylines then a non-zero mean fairing deviation will allow a deviation between the coordinates of the imported polyline and the faired curve, see Fair. Consequently, the search in steps 3. Since a connection between a wireframe point and a wireframe curve requires a point on the inleidiny within the tolerance inleising the wireframe point, in step 5 a new point will be inserted on the curve if the distance to the existing point exceeds the tolerance.

With a larger tolerance the existing point would have been within reach of the wireframe point, and it would have been connected, without the introduction of double points. Attentie Tolerance should not be confused with accuracy.

In particular, you should not specify a low tolerance with the intention to achieve high accuracy; doing so tpologie most likely give you adverse results. See also Why does a low tolerance result in duplicate points?

The distances between curves are evaluated. Where the distance between two curves falls below the given tolerance, they are classified as intersecting. For each intersection, positions on the relevant curves are found that minimize their distance. If no wireframe point exists within the tolerance of these positions, a new wireframe point is created in the middle. So, in case the curves intersect exactly, the new wireframe point will be placed exactly at the intersection.

If curves do not intersect exactly due to, for example, fairing with a mean fairing deviation then the wireframe point is positioned where it yields the highest accuracy. The relevant curves are scanned for points internal points and knuckle points that are within the tolerance of the wireframe point. If no point is found a new fopologie point is inserted.

The respective points on the curves are given a reference to the wireframe point to mark their connectivity. Noot As a rule of thumb, the tolerance can be specified quite high, but not higher than the closest distance between curves that should not be connected.

Nor should it be higher than the distance between intersections that must be distinct. If no internal points are present in curves where they intersect, the tolerance should also not be higher than the distance between the intersection hopologie unrelated points on the curve. Inspection and manipulation of wireframe curve connections.