CS709a: Algorithms and Complexity
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1 CS709a: Algorithms and Complexity Focus: Spatial Data Structures and Algorithms Instructor: Dan Coming Thursdays 4:00-6:45pm Office hours after class (or by appointment)
2 Today Presentation on UnitTest++ Calendar More details for Project Additional operations on spatial data structures Research paper selections?
3 Tentative Calendar / Paper selection due /9 Paper Presenter: Joe class day likely to be moved /6 Paper Presenter: Matt Present Project 3 in class (Project 3 Due 4/) Present Project in class (Project Due /5) 4/ Paper Presenter: Cody 4/9 Paper Presenter: James 3/5 Paper Presenter: Ray 4/6 Paper Presenter: Steve 3/ Paper Presenter: Mark 4/3 Paper Presenter: Roger 4/30 5/7-3 Finals Week Present Project in class (Project Due 3/), 3/4- Spring Break 3/6 Paper Presenter: Scott Final Projects and Presentations Due
4 Project More details Template - <int dimensions, class point_t, class T> point_t must have an operator[ ] to get dimension x_i Basic operations: constructor(const point_t& min, const point_t&max) copy constructor and operator=, destructor bool empty() const, void clear() max_depth() const ( if grid) build(std::inputiterator<point_t> first, std::inputiterator<point_t> last)
5 Project More details Data structure specific, consider how to specify grid spacing, splitting heuristic, etc.. Queries (set results, return the number found) Inclusive and non-inclusive versions int range_search_inclusive(const point_t& min, const point_t& max, std::vector<point_t>& results)const int radius_search_noninclusive(const point_t& center, const T & radius, std::vector<point_t>& results)const
6 Project Datasets on Course Website Computational Fluid Dynamics Wing Simulation Range Search Result
7 More Query Operations Single search, single result: Ray trace Single search, multiple result: Range search Multiple search, single result: Nearest of all pairs Multiple search, multiple result: All pairs within some distance of each other (collision detection)
8 Ray Trace on Point Data
9 Ray Trace on Point Data (0,00) (00,00) (6, 77) (35, 4) (7, 35) (5, 0) (8, 65) (85, 5) (00,0)
10 Ray Trace on Point Data (0,00) (00,00) (6, 77) (35, 4) (7, 35) (5, 0) (8, 65) (85, 5) (00,0)
11 Split On Points or Between Points? (0,00) (00,00) (00,0) (0,00) (00,00) (00,0) Empty space culling Ray Tracing
12 Ray-Plane Intersection Plane P: p. n = d Ray: o + t r Intersection: (o + t r). n = d o.n+tr.n=d t = (d - o. n) / (r. n) o P n r p
13 Brute Force Ray Trace function RayTrace(Point origin, Point direction real &r_time, hit_data & r_hit for each city in Cities for i = 0 to d real time; hit_data hit; if(raytrace(origin, direction, city, time, hit) if(time < rtime) rtime = time; r_hit = hit; fi fi end end end
14 Regular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3 (Could also use sparse matrix representations)
15 Regular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3 (Could also use sparse matrix representations)
16 Regular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3 (Could also use sparse matrix representations)
17 Regular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3 (Could also use sparse matrix representations)
18 Regular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3 (Could also use sparse matrix representations)
19 Regular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) Is there a repeating access pattern? Why? 3 (Could also use sparse matrix representations)
20 Irregular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) (Could also use sparse matrix representations)
21 Irregular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) (Could also use sparse matrix representations)
22 Irregular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) (Could also use sparse matrix representations)
23 Irregular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) (Could also use sparse matrix representations)
24 Irregular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) (Could also use sparse matrix representations)
25 Irregular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) (Could also use sparse matrix representations)
26 Irregular Grids (0,00) (00,00) (6, 77) Matrix as ND Array (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0) Is there a repeating access pattern? Why? (Could also use sparse matrix representations)
27 Multidimensional Range Trees (0,00) (00,00) (6, 77) Multidimensional Tree Data Structure (8, 65) 4 (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3
28 Multidimensional Range Trees (0,00) (00,00) (6, 77) Multidimensional Tree Data Structure (8, 65) 4 (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3
29 Multidimensional Range Trees (0,00) (00,00) (6, 77) Multidimensional Tree Data Structure (8, 65) 4 (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3
30 Multidimensional Range Trees (0,00) (00,00) (6, 77) Multidimensional Tree Data Structure (8, 65) 4 (35, 4) (7, 35) (5, 0) (85, 5) (00,0) 3
31 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
32 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
33 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
34 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
35 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
36 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
37 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
38 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
39 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
40 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) Worst case: Leaf > Root > Leaf (85, 5) (00,0)
41 Quadtrees (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
42 kd-trees (0,00) (00,00) (6, 77) (8, 65) (35, 4) (7, 35) (5, 0) Tree Data Structure (85, 5) (00,0)
43 kd-trees (0,00) (00,00) (6, 77) (8, 65) (35, 4) (7, 35) (5, 0) Tree Data Structure (85, 5) (00,0)
44 kd-trees (0,00) (00,00) (6, 77) (8, 65) (35, 4) (7, 35) (5, 0) Tree Data Structure (85, 5) (00,0)
45 kd-trees (0,00) (00,00) (6, 77) (8, 65) (35, 4) (7, 35) (5, 0) Tree Data Structure (85, 5) (00,0)
46 BSP Trees (0,00) (00,00) (6, 77) (8, 65) (35, 4) (7, 35) (5, 0) Tree Data Structure (85, 5) (00,0)
47 BSP Trees (0,00) (00,00) (6, 77) (8, 65) (35, 4) (7, 35) (5, 0) Tree Data Structure (85, 5) (00,0)
48 BSP Trees (0,00) (00,00) (6, 77) (8, 65) (35, 4) (7, 35) (5, 0) Tree Data Structure (85, 5) (00,0)
49 Bounding Volume Hierarchies (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) Some data not at leaves (00,0)
50 Intersection Against Bounding Volume Instead of Planes
51 Bounding Volume Hierarchies (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
52 Bounding Volume Hierarchies (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
53 Bounding Volume Hierarchies (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
54 Bounding Volume Hierarchies Test both enter and exit times from bounding volumes, why? (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
55 Bounding Volume Hierarchies (0,00) (00,00) (6, 77) Tree Data Structure (8, 65) (35, 4) (7, 35) (5, 0) (85, 5) (00,0)
56 Next Time Paper Selections Due More operations on spatial data structures Read: Chapter, Section 6 and 7 (pages 90-63)
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