Duality Demo

User Interface

Insert Mode

• To insert a POINT, select Insert Mode AND POINT. Then click the left mouse button on either plane. WHEN ENTERING A POINT, BE CAREFUL THAT YOU DO NOT GET CONFUSED WITH ENTERING A SEGMENT THAT HAS TWO COINCIDING ENDPOINTS. The BSP queries may not work as you expected when this happens.
• To insert a SEGMENT, select Insert Mode AND SEGMENT. Then click the left mouse button to mark the first POINT, drag out the desired SEGMENT length and orientation before releasing the button.

Query Mode

• To insert a LINE Query, select Query Mode AND SEGMENT(LINE). Enter the LINE object by a left CLICK. PLEASE EDIT THE ROTATION AND TRANSLATION OF THE QUERY IN "EDIT MODE", as if you were editing a LINE.
• To select a SEGMENT for a MULTIPLE-SEGMENT query, highlight a segment and LEFT CLICK.
• To insert a Triangle object, select Query Mode AND Triangle. The first click anchors the first vertex, second click anchors the second vertex, and third click completes the triangle.
• To insert a Circle object, select Query Mode AND Circle. Place the center of the circle by a left mouse click. The radius can be changed by selecting EDIT MODE and drag the circle while holding the CONTROL key. The Cicle may be moved in EDIT mode by dragging the cirlce without holding the CONTROL key.

Edit Mode

• POINT - Left CLICK and drag the POINT. Hold Alt to restrict rectilinear translations.
• SEGMENT - Left CLICK and drag on main SEGMENT to translate the object without rotation. Left CLICK and drag on either end POINT to translate an endpoint. Left CLICK, CONTROL, and drag on SEGMENT to rotate SEGMENT without translation. Hold down ALT key to restrict rectilinear mouse movements.
• Line - Same as line except no endpoint editing
• Triangle - Left CLICK on triangle edges to translate Triangle, on an endpoint to translate endpoint. ALT key for recctilinear restriction.
• Circle - Left CLICK and drag on cirlce to translate the object. Hold CONTROL key for changing the radius.
• Wedge - Translation is same as Line but rotation is restricted around the fulcrum. Left CLICK and drag fulcrum to translate wedge without rotation.
• Dual line families of Triangle and Circle - EDITING NOT SUPPORTED

Remarks

• I fail to recognize the dual relationship for the LINE query.
• I did not the implement the Point Query.
• The set of lines that stabs a set of segments correspond to the dual vertices that are contained in all of the corresponding dual wedges in the dual plane.
• An "interesting" dual relationship is demonstrated in the Cirlce object. Mouse over a Circle object and you'll see two yellow vertices in the primal plane. By default, these primal vertices are symmetric about the x axis. The corresponding dual lines are parallel within the dual "conic" formed by the Circle. Hold SHIFT and mouse over the Cirlce again, the primal vertices that are symmetric about the center of the Circle will be highlighted. The dual lines are symmetric about the the "inner axis" of the conic. Finally, hold the CONTROL key, the vertices that are symmetric about the y axis will be highlighted. The resulting dual lines are symmetric about the intersecting axis of the dual conic.

Sources