Nef_2

How to use Nef_2 Demo

Main Functionality

- Reset application
- Creating a new window
- Print
- Close the current window
- Quit the application

Nef_2 visualisation using lists

- Select nef for visualisation
- Toggle ON/OFF nef visualisation

Building and erasing nefs

- Create a Nef polyhedron consisting of one point
- Create a Nef polyhedron consisting of a halfplane
- Create a Nef polyhedron from a simple polygon
- Erase an existing Nef polyhedron

Constructive Operations

- Intersection
- Union
- Difference
- Symmetric Difference
- Complement
- Interior
- Closure
- Boundary
- Regularization

Persistance

- Save the current Nef polyhedron
- Load an existing Nef polyhedron
- Load an existing simple polygon and construct the Nef polyhedron from this polygon

Reset application

Press Ctrl+N combination keys or go to File menu and choose "New". All nefs constructed will be erased, the window's visible area will be set to default. (-1, 1, -1, 1)

Create a new window

Press Ctrl+W combination keys or go to File menu and choose "New Window". A new window will appear, the window's visible area will be set to default. (-1, 1, -1, 1)

Print

Press Ctrl+P combination keys or go to File menu and choose "Print". The visible area on the screen will be outputed to the print device of your choice. There are printers that does not support the raster opertions. I have used XOR to achieve the transparency effect.

Close the current window

Press Ctrl+X combination keys or go to File menu and choose "Close". You may do it for any window other than the initial one, this operation will close only the one you have choosen. If you do this for the initial parent window, it will close the others too.

Quit the application

Press Ctrl+Q combination keys or go to File menu and choose "Quit". When you quit the application, all the windows you have created will be destroyed.

Select Nef for visualisation

You can visualise at most two nef polyhedrons at one time. There are two lists that correspond to each nef you can display. The left one corresponds to the blue nef, the right one correspons to the gray one. To select a nef polyhedron from the list just press the left mouse button over the item's text. You should see the result on the widget, if the polyhedron corresponds to the current visible area. The default one is (-1, 1, -1, 1). You should notice that you can see both nef polyhedrons even if there are overlapping parts. The gray one is always on top.

Toggle ON/OFF nef visualisation

Selecting and unselecting nef items from the nef_2 lists, you can toggle ON or OFF the visualisation of nefs already created. To unselect an item just press once again on it using the left mouse button.

Create a Nef polyhedron consisting of one point

Left click on the "Input point" layer. Be sure there is no layer activated in standard toolbar that eat events. To be sure, press the arrow button situated on the standard toolbar. Left Click anywhere on the application's drawing area (the black rectangle) to create the new nef_2. This one will be also added at the end of both nef_2 lists. You will see only the new created nef on the screen, and the lists will reflect the changes.

Create a Nef polyhedron consisting of a halfplane

Left click on the "Input line" layer. Be sure there is no layer activated in standard toolbar that eat events. To be sure, press the arrow button situated on the standard toolbar. Left Click anywhere on the application's drawing area (the black rectangle) to fix the first point that generates the line. Use the mouse to position the second point. Once you have determined the second point, press the left mouse button once again. This will create a Nef consisting of a halfplane determined by the oriented line, the line being also included.

Create a Nef polyhedron from a simple polygon

Left Click on the "Input Simple Polygon" layer. Be sure there is no layer activated in the standard toolbar that eat events. To be sure, press the arrow button situated on the standard toolbar. Left Click anywhere on the application's drawing area (the black rectangle) to insert points in the polygon. You may press "Esc" key if you want to erase the last point. Once you have completed the polygon press the right click to close the polygon. This will create a Nef polyhedron from the simple polygon, the boundary line being included.

Erase an existing Nef polyhedron

To erase an existing Nef polyhedron, you have to select one from the list, it does not matter which one, the left or the right, and to press delete key. This action will remove the nef selected from the lists of the current window and from all the other lists opened in different windows. This happens in case you are working with multiple windows. There is one problem that I could not get rid of. If you are working with multiple windows and remove one nef that is currently displayed in some other window, that window will continue to display the removed nef. I will try to remove this drawback in the near future. The workaround could be to reselect the desired nefs in that window before doing more operations.

Intersection

After selecting the blue Nef from the left list and the gray Nef from the right list, press the "INTERSECTION" button on the operations toolbar. This will compute the INTERSECTION between those two nefs. The exact operation is AND(BLUE, GRAY). You will see the new Nef added in both top lists.

Union

After selecting the blue Nef from the left list and the gray Nef from the right list, press the "UNION" button on the operations toolbar. This will compute the UNION between those two nefs. The exact operation is OR(BLUE ,GRAY). You will see the new Nef added in both top lists.

Difference

After selecting the blue Nef from the left list and the gray Nef from the right list, press the "DIFFERENCE" button on the operations toolbar. This will compute the DIFFERENCE between those two nefs. The exact operation is DIF(BLUE, GRAY). You will see the new Nef added in both top lists.

Symmetric Difference

After selecting the blue Nef from the left list and the gray Nef from the right list, press the "SYMMETRIC DIFFERENCE" button on the operations toolbar. This will compute the SYMMETRIC DIFFERENCE between those two nefs. The exact operation is SYM_DIF(BLUE, GRAY) = OR(DIF(BLUE, GRAY), DIF(GRAY, BLUE)). You will see the new Nef added in both top lists.

Complement

This unary operation returns the complement of the BLUE Nef polyhedron in the plane. Select the Nef polyhedron of your choice and press the COMPLEMENT toolbar button. You will see the new Nef added in both top lists.

Interior

This unary operation returns the interior of the BLUE Nef polyhedron selected. Select the Nef polyhedron of your choice and press the INTERIOR toolbar button. You will see the new Nef added in both top lists.

Closure

This unary operation returns the closure of the BLUE Nef polyhedron selected. Select the Nef polyhedron of your choice and press the CLOSURE toolbar button. You will see the new Nef added in both top lists.

Boundary

This unary operation returns the boundary of the BLUE Nef polyhedron selected. Select the Nef polyhedron of your choice and press the BOUNDARY toolbar button. You will see the new Nef added in both top lists.

Regularization

This unary operation returns the regularized polyhedron of the BLUE Nef polyhedron selected. It is in fact the closure of the interior. Select the Nef polyhedron of your choice and press the REGULARIZATION toolbar button. You will see the new Nef added in both top lists.

Save the current Nef polyhedron

Press Ctrl+S combination keys or go to File menu, then choose "Save Nef_2". A save file dialog will appear, the default name given is "nef_2.cgal". You may change the name then press "Save" or hit "Enter" key. To cancel the save process just press Esc key.
The Nef polyhedron saved does not contain the visible area.

Load an existing Nef polyhedron

Press Ctrl+L combination keys or go to File menu and choose "Load Nef_2". A load file dialog will appear, having a filter that displays only the files with "cgal" extension. Choose a file then press "Open" button or hit "Enter" key.
The Nef polyhedron saved does not contain the visible area.

Load an existing simple polygon and construct the Nef polyhedron from this polygon

Press Ctrl+O combination keys or go to File menu and choose "Load Polygon_2". A load file dialog will appear, having a filter that displays only the files with "cgal" extension. Choose a file then press "Open" button or hit "Enter" key.
The CGAL polygon saved does not contain the visible area.

Last modified: Tue Jun 3 10:59:20 MEST 2003