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2D Rectangular Packing with LFF and LFF/T. Presented by Y. T. Wu. Overview. Introduction The Problem LFF Algorithm LFF/T Algorithm – An Improvement Experimental Results Conclusion Future Direction. Introduction.
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2D Rectangular Packing with LFF and LFF/T
Presented by Y. T. Wu
a corner < a side < a central void area
larger objects < smaller objects
Corner bounded
on bottom
and left
Corner bounded
on bottom
and right
Corner bounded
on top and left
Corner bounded
on top and right
K-D tree, with K = 4
struct kdtree{
kdkey_t kd_keys[4];
kdkey_t kd_lo_min_bound,
kd_hi_max_bound,
kd_other_bound;
struct kdtree *kd_father;
struct kdtree * kd_sons[2];
};
(x2, y2)
(x1, y1)
if K0(p)<K0(q), q is HISON
e (1, 10, 3, 13)
a (6, 1, 7, 3)
b (2, 6, 4, 9)
c (9, 7, 12, 8)
c (9, 7, 12, 8)
b (2, 6, 4, 9)
e (1, 10, 3, 13)
d (1, 4, 3, 7)
d (1, 4, 3, 7)
a (6, 1, 7, 3)
Fig. 1b) Placement of these 16 labelled rectangles in a 4-d binary tree
Fig. 1a) 16 labelled rectangles on a grid 0 x 13 in size
Starting with an empty work space (bounding rectangle)
Note: Before the pseudo-packing for the next candidate COPM is tried, one needs to remove the previous pseudo-packed COPM
For each candidate rectangle placement location, we look at the points that are immediate adjacent to each corner of the candidate rectangle (There are 8 points for measurement)
The 8 corner-adjacent ptsB has a larger tightness value (4) than A(3)
A
B
The LFF/T algorithm:
Starting with an empty work space (bounding rectangle)
If there is a location that the next rectangle in the sorted list can fit, then,
Else
Skip this rectangle
Calculate FFV of this candidate COPM as the occupied area.
Note: Before the pseudo-packing for the next candidate COPM is tried, one needs to remove the previous pseudo-packed COPM