27. 27
Compound vs. Simple
Compound Mark
Technique
Simple Mark
Technique
Breadth vs. Depth
Compass4:max. depth 4
Compass8:max. depth 2 Possibly more depth
Ambiguity Yes NO
Space usage Grows quadratically Theoretical constant
Physical Motion Single zig-zag stroke Multiple simple
strokes
28. 28
Compound vs. Simple
Compound Mark
Technique
Simple Mark
Technique
Breadth vs. Depth
Compass4:max. depth 4
Compass8:max. depth 2 Possibly more depth
Ambiguity Yes NO
Space usage Grows quadratically Theoretical constant
Physical Motion Single zig-zag stroke Multiple simple
strokes
29. 29
Compound vs. Simple
Compound Mark
Technique
Simple Mark
Technique
Breadth vs. Depth
Compass4:max. depth 4
Compass8:max. depth 2 Possibly more depth
Ambiguity Yes NO
Space usage Grows quadratically Theoretical constant
Physical Motion Single zig-zag stroke Multiple simple
strokes
30. 30
Compound vs. Simple
Compound Mark
Technique
Simple Mark
Technique
Breadth vs. Depth
Compass4:max. depth 4
Compass8:max. depth 2 Possibly more depth
Ambiguity Yes NO
Space usage Grows quadratically Theoretical constant
Physical Motion Single zig-zag stroke Multiple simple
strokes
31. 31
Research Issues
Speed and accuracy
Hierarchy depth
Input footprint
Spatial overlap
Timeout threshold
Mark directions
on-axis off-axis
45. 45
Results Summary
Faster, more accurate
Increased hierarchy depth
Mark direction no effect on accuracy
Unaffected by input footprint
Space efficient
Timeout threshold: 2s upper bound
51. 51
Formula for Calculating Ambiguity
Let B be the branching factor of the menu (e.g., 4, 8)
Let D be the depth of the menu (i.e., number of levels)
Then, the total number of leaf nodes = B^D
Number of leaf nodes with unambiguous marks =
(number of marks with maximal number D-1 inflections) +
(number of marks with no inflections at all) =
B*(B-1)^(D-1) + B
Example calculations:
compass8-2 layout = 8*(7^1) + 8 = 64 (i.e., all leaves)
compass4-4 layout = 4*(3^3) + 4 = 112 (43% of all
leaves)
compass8-3 layout = 8*(7^2) + 8 = 400 (78% of all
leaves)
52. 52
0
0.5
1
1.5
2
2.5
3
3.5
4
4,2 4,3 8,2 8,3 4,2 4,3 8,2 8,3 4,2 4,3 8,2 8,3
Menu Layout (Number of items, depth)
Time(insecond)
compound
simple
Large Medium Small
0
0.5
1
1.5
2
2.5
3
3.5
4
4,2 4,3 8,2 8,3 4,2 4,3 8,2 8,3 4,2 4,3 8,2 8,3
Menu Layout (Number of items, depth)Time(insecond)
compound
simple
Large Medium Small
Drawing TimeReaction Time