P. Baudelaire and M. Gangnet. Planar maps: an interaction paradigm for graphic design. In Proc. of CHI'89, pages 313--318. Addison-Wesley, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of a segmented image by embedding it into the Euclidean plane and drawing a Jordan s curve between each pair of adjacent regions. The set of all these curves forms a connected planar graph called a topological map [Tut63] There are several examples of the use of planar maps in 2D graphics [BG88, BG89, Dom92, GHPV89] Let us briefly recall from Cori [Cor75] the following definition: Definition 1 A planar map is a decomposition of the Euclidean plane into a finite set V of points, a finite set E of disconnected open Jordan curves, each one having its extremities in V , and a finite set of ....

P. Baudelaire and M. Gangnet. Planar maps: an interaction paradigm for graphic design. In Proc. of CHI'89, pages 313--318. Addison-Wesley, 1989.

....a 4 decomp osition is called an elementary region. In the Euclidean plane, the topology of a set of connected contours is described by a topological map, or planar map [35, 14] which is the drawing of a planar graph on a orientable surface (planar maps are now widely used in 2D image synthesis [2, 21, 10, 15]) The Jordan theorem states that a closed curve C which is simple, that is which does not self intersect, separates the plane into two connected components P 1 , and P 2 . Any other curve with a point in P 1 and another in P 2 intersects C at least one time. It is well known that this property ....

P. Baudelaire and M. Gangnet. Planar maps: an interaction paradigm for graphic design. In Proc. of CHI'89, pages 313--318. Addison-Wesley, 1989.

....inclusion relation linking each infinite face with the finite face which contains them. The different steps performing the creation of the topological maps are summarized in figure 1. 3 Data structure encoding discrete maps Topological map can be efficiently encoded using combinatorial map(see. [17, 2, 4, 12]) A combinatorial map is a tuple (D; ff; oe) such that D is a set of elements called darts, ff and oe are two permutations defined on D, the permutation ff is a free fixed point involution. Each dart represents an half edge of the topological map and the orbits of ff encode the edges of the ....

P. Baudelaire and M. Gangnet. Planar maps: an interaction paradigm for graphic design. In Proc. of CHI'89, pages 313--318. Addison-Wesley, 1989.

....there is no way to mimic this method. If Fig. 3a is drawn by the user of a drawing application as four lines, it is impossible for him to color the rectangle (as in Fig. 3b) since no such rectangle exists. If the drawing were computed as a planar map, this dual interpretation would be possible. In [2], we have proposed two extensions to the 2D graphics drawing paradigm: a) objects are multicolor, multicontour shapes (i.e. planar maps) and b) they are constructed by iteration May 1989 Digital PRL Incremental Computation of Planar Maps 3 Figure 2: Graphic design by space division (B. Munari ....

....for constructing certain classes of drawings. An illustration is described as an ordered set of maps, painted in back to front order. As a map can have transparent faces, shapes with holes may be defined. User interface design issues in map based illustration software are further discussed in [2]. Figure 4: Map sketching. 3 B ezier Curve Interpolation and Intersection The geometry of a map is based on curves described in Bezier form. Other usual parametric curves can be converted to or approximated by curves defined in Bezier form. However, an application using planar maps (e.g. map ....

Baudelaire, P. and Gangnet, M. Planar Maps: an Interaction Paradigm for Graphic Design. In CHI'89 Proceedings, Addison-Wesley (1989).

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P Baudelaire and M Gangnet. Planar maps: an interaction paradigm for graphics design. In CHI'89. Addison-Wesley, 1989.

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