, IEEE

Pages: pp. 350-351

In [ ^{1}], in Figs. 1, 2, 3, and 4, all occurrences of "-" between words and all occurrences of a space between words are gone; as a result, some words are also not aligned with the boxes and some occurrences of ")" also do not appear in the right places.

Corrections: Figs. 1, 2, 3, and 4 in [ ^{1}] should have appeared as follows (the correct version of [ ^{1}] is available from the author's Web site: http://cis.poly.edu/chiang/PTOT-vis09.pdf):

Figure Fig. 1. Persistent structure. (a) The node-copying technique, where each persistent node has three extra fields. (b) Persistent binary search tree (where we use the alphabetical order to compare the keys (letters)) after simulating a sequence of updates. Each node has one extra field. The number associated with a node/pointer denotes its version stamp. The numbers 1 to 7 on the top horizontal line denote the entry-point array $A$ . Version 5 is shown in red.

Figure Fig. 2. (a) The time-octree. (b) An example of the time tree for time interval $[0,5]$ . Each internal node labeled $[t_1,t_2]$ covers the time span $[t_1, t_2]$ , and each leaf labeled $[t]$ corresponds to time step $t$ .

Figure Fig. 3. Line-sweep process to insert/delete intervals $I_{c,t}$ to the time-octree. There are four time cells $(c_1,t_2), (c_2,t_3), (c_3,t_1), (c_4,t_3)$ whose $[\min, \max]$ intervals are respectively $[a, e], [b,g], [c,f], [d,h]$ . The vertical red line is the sweep line. The $[\min, \max]$ interval endpoints subdivide the scalar-value range $(-\infty, \infty)$ into ranges $R_0 = (-\infty, a)$ , $R_1 = [a,b)$ , $R_2 = [b,c)$ , $R_3 = [c, d)$ , $R_4 = [d,e]$ , $R_5 = (e,f]$ , $R_6 = (f, g]$ , $R_7 = (g,h]$ , $R_8 = (h,\infty)$ , where version $i$ of the time-octree corresponds to range $R_i$ . Isovalue $q$ lies in range $R_5$ , and version 5 of the time-octree contains exactly time cells $(c_2,t_3), (c_3, t_1), (c_4,t_3)$ , which are active for $q$ ; $(c_2,t_3)$ and $(c_4,t_3)$ belong to the octree of $t_3$ and $(c_3, t_1)$ belongs to the octree of $t_1$ .

Figure Fig. 4. (a) Standard representation. Inserting/deleting a leaf $C$ can create/remove many nodes (shown in red excluding $A$ ). (b) The compact representation. (c) With the compact representation, inserting/deleting a leaf $C$ (as the event in (a)) can create/remove at most one internal node, the *degree-2 fork* node $A$ .

- 1. C. Wang, and Y.-J. Chiang, "Isosurface Extraction and View-Dependent Filtering from Time-Varying Fields Using Persistent Time-Octree (PTOT),"
*IEEE Trans. Visualization and Computer Graphics,*vol. 15, no. 6, pp. 1367-1374, 2009.

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