Multiscale Feature Model for Terrain Data Based on Adaptive Spatial Neighborhood

Algorithm 2

The algorithm of generating multi-resolution model of Hilbert space-filling curve.

Input: Cluster 𝜉.

Output: Space-filling curve (code arrangement of data block) CodeString.

Description: This algorithm generates the space-filling curve

   which contains all data blocks in cluster 𝜉, by judging

    the type and position of data blocks in cluster 𝜉.

(1) Initialization:

      (1.1) Define the top layer 𝑙 and bottom layer 𝑙^′ in cluster 𝜉.

      (1.2) Extract the first and the last data block from cluster 𝜉.

         According to this, decide the type 𝑇 of data block B^𝑙 in layer 𝑙.

      (1.3) Clear CodeString.

(2) Recall the function DeepTraverse_Cluster (B^𝑙, 𝑇, 𝑙).

(3) Modify the index file of cluster, and save the new index code

of data blocks in cluster.

(4) The end

DeepTraverse_Cluster (currentBlock, Type, 𝑙)

Function description: As Hilbert space filling curve,

        generate code of data block in cluster.

Parameter description: currentBlock is the current data block,

        Type is the type of current data block, 𝑙 is

        the layer of current data block.

(1) Get the four data blocks  B₁,B₂,B₃, and B₄ of currentBlock.

(2) Sort  B₁,B₂,B₃, and  B₄, as the type of Type

    (shown in Figures 4(a)–4(d)).

(3) Judge the data block is whether in cluster 𝜉:

      (3.1) If B_𝑖 is a data block in cluster 𝜉, then encode B_𝑖

         by the order after sorting, and add it into

         CodeString, where 𝑖=0,1,2, and 3.

      (3.2) If B_𝑖 is not a data block in cluster 𝜉, then ascertain

         the type of B_𝑖 by using rules, and make the recursion

         furthermore, where 𝑖=0,1,2, and 3.

    (3.2.1) If Type is I, then the types of B₁, B₂, B₃,

          and B₄ are Type III, Type I, Type I, and Type IV.

    (3.2.2) If Type is II, then the types of  B₁,B₂,B₃,

          and B₄ are Type IV, Type II, Type II, and Type III.

    (3.2.3) If Type is III, then the types of B₁,B₂,B₃, and

          B₄ are Type I, Type III, Type III, and Type II.

    (3.2.4) If Type is IV, then the types of B₁,B₂,B₃, and

          B₄ are Type II, Type IV, Type IV, and Type I.

    (3.2.5) According to the new order, judge data

           blocks on next layer

           For 𝑖=1 to 4:

         If 𝑙+1≤𝑙^′, then recall

         DeepTraverse_Cluster (B_𝑖, Type B_𝑖, 𝑙+ 1),

         where Type B_𝑖 denotes the new type of data block B_𝑖.

(4) The end of function.