4.2 Functionality

4.2 Functionality

At this point the conceptualized animated zooming scale model is introduced in detail. The discussion starts with a description of the full zooming process using a zoom slider, followed by a description of the special features of the ZoomOut process.
Suppose Z_n is the current zoom level of the main map, Z_max the maximum ZoomIn level, and Z_min = 0 as the minimum ZoomOutlevel, for which the following applies:
Z ∈ N and Z_min ≤ Z_n ≤ Z_max

The following steps describe the developed scaling model as well as the exact process involved in using the zoom slider. A state diagram (Figure 4.2) and an activity diagram (Figure 4.2) illustrate this model. The individual steps involved are referenced by the numbers contained in the processes of the activity diagram:

The user points the mouse on the zoom slider, presses and holds down the left mouse key. As soon as he/she releases the key, the process is stopped and completed with Step 8.
The current zoom level Z_n is determined.
All tiles k within zoom level Z_n, which are fully or partially located in the visible area, as well as all pre-loaded tiles which border on this area, are determined.
The user decides on a zoom direction (ZoomIn or ZoomOut).
At this point the compatibility of the decision made in (4) with the current zoom level Z_i (in the first round Z_i = Z_n) is verified, ie. if Z_i = Z_min, respectively Z_i = Z_max, then ZoomOut or ZoomIn is not possible. In this case, a new zoom direction must be selected (Step 4). Otherwise the process continues with step (6).
The corresponding zoom-scale process occurs in tandem with the zoom slider operation (in the direction chosen in (4)):
- a) New zoom slider position P_i is determined.
- b) New zoom level Z_i = Z(P_i) is calculated.
- c) New (scaled) tile size K(Z_i) of the current zoom level Z_i is calculated on the basis of Z_n. The following rules apply:
  
  K(Z_i) = 2^{Z_i - Z_n} * K(Z_n) f�r Z_n < Z_i
  K(Z_i) = K(Z_n) f�r Z_n = Z_i
  K(Z_i) = 1 / (2^{(Z_n - Z_i)} * K(Z_n)) f�r Z_n > Z_i
  
  Starting with zoom level Z_n the tile size K(Z_n) is doubled with every new zoom level (for Z_n<Z_i; see equation 4.1) or halved (for Z_n>Z_i; see equation 4.3) so as to obtain the new tile size K(Z_i) for the currently active zoom level Z_i. At equal zoom levels (Z_n=Z_i) the tile sizes are of equal size (see equation 4.2).
  
  Note: The individual zoom levels serve only as defined interim values. The actual scaling process occurs continuously.
- d) During the ZoomIn or ZoomOut process all currently loaded (visible and non-visible) tiles are scaled to the calculated tile size K(Z_i) (more accurately: expanded or shrunk).
- e) Only for ZoomOut: As soon as all tiles k (as defined in (3)) are sized to a level where all are part of the visible area, additional tiles must be loaded in the background to avoid the creation of a white border during ZoomOut. A more detailed discussion on tile preloading in ZoomOut processes is provided in the following paragraph »Special Features of ZoomOut«.
As long as the left mouse key is held down (see Step 1), the user can change the zoom direction at any time, which brings the process back to (4). Once the mouse key is released, the zoom process is completed with (8).
The visible area is redrawn in the new zoom level Z_i including all required tiles (using standard tile size K(Z_n)). In addition (according to the principles outlined in the tiling method; see Section 2.3.5), all adjacent non-visible tiles are preloaded at the same size. This completes the zoom process.

State Diagram of Zoom Process Using Slider

Activity Diagram of Zoom Process Using Slider

Special Considerations for ZoomOut

Two solutions regarding the preloading of tiles in Steps 6e of the zoom process are introduced. The objective is to ensure quick tile loading (ie. without delay) and thereby eliminate the creation of a white border around a now smaller map.

A) As soon as a previously non-visible tile of k becomes part of the visible area, all non-visible tiles are newly defined and preloaded in the background at zoom level Z_n. They are stored as new, non-visible tiles in the DOM tree. All loaded tiles are immediately adjusted to thr current scale, ie. they are simultaneously adjusted to the same scale as the remaining tiles (where the calculated tile size is K(Z_i)).
The disadvantage: the zooming process requires a continuous loading of a large number of tiles which also have to be scaled in accordance with the remaining tiles. Therefore it is likely that performance is negatively impacted by an increased number of tiles.
B) A special feature of the second solution is a newly defined »ZoomOut tile«. In addition to the tiles k described in Step 3, during initialization of the application one additional tile k_* is loaded for the purpose of executing the Zoom Out process. k_* shows the geographic dimension of the complete map on one tile. The pre-defined tile pixel size K_* of k_* is to be larger than the pr-edefined tile size K_k of all tiles k by a factor of x: K_* = x * K_k, whereby x ≥ 1 and x ∈ R. A suitable value for x is dependent on the size of the whole map as well as the number of possible zoom levels; it is determined in the implementation (see Section 5.2.3). The center of the whole map is the geographic center of k_*.
The objective of this approach is to reduce the time-consuming reloading of tiles during a on-the-fly zoom-out procedure (featured in Solution (A)). Instead, k_* is used as a kind of base tile, with which the majority of the scale processes can be executed. This way, it is no longer necessary to keep loading and scaling new tiles in order to »fill in« the white area that would otherwise appear, especially since the high level of detail on these tiles is not even required for ZoomOut scaling.

At a certain level of magnification, however, the extensive »pixelation« of k_* will be a disadvantage. Depending on the zoom level intervals this can lead to an inability to identify map sections during high-scale processes.

4.2 Functionality

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