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Polygon Triangulation

Polygon Triangulation

Polygon Triangulation. ??? ?? ?. Art Gallery Problem. Want to cover all areas Assume that the art gallery is a simple polygon Does not intersect itself How many cameras do we need? Where do we put it? Getting an exact solution is NP-hard We just want to get a lower bound. Triangulation.

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1.14k views • 67 slides
Label placement

Label placement

Label placement. Rules, techniques. Labels on a map. Text, name of map features No fixed geographical position Labels of point features (0-dim), line features (1-dim), areal features (2-dim). Labels of point features. Cities on a small-scale map Heights of peaks

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792 views • 65 slides
Spatial Queries

Spatial Queries

Spatial Queries. R-tree: variations. What about static datasets? (no ins/del) Hilbert What about other bounding shapes?. R-trees - variations. what about static datasets (no ins/del/upd)? Q: Best way to pack points?. R-trees - variations. what about static datasets (no ins/del/upd)?

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772 views • 62 slides
Computational Geometry

Computational Geometry

Computational Geometry. Piyush Kumar (Lecture 3: Convexity and Convex hulls). Welcome to CIS5930. p. q. p. convex. non-convex. q. Convexity. A set S is convex if for any pair of points p,q ? S we have pq ? S. Convex Hulls : Equivalent definitions.

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566 views • 53 slides
3D Reconstruction of Objects behind Dense Occlusions

3D Reconstruction of Objects behind Dense Occlusions

3D Reconstruction of Objects behind Dense Occlusions. Vaibhav Vaish. Joint work with Rick Szeliski, Larry Zitnick, Sing Bing Kang, Brian Curless. SAP: Seeing through occlusions. Images: 82 Aperture: 1m. SAP: Seeing through occlusions. Images: 45 Aperture: 2m. SAP: Crowd scene.

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431 views • 33 slides
CSIS 7101: Spatial Data (Part 2) Efficient Processing of Spatial Joins Using R-trees

CSIS 7101: Spatial Data (Part 2) Efficient Processing of Spatial Joins Using R-trees

CSIS 7101: Spatial Data (Part 2) Efficient Processing of Spatial Joins Using R-trees. Rollo Chan Chu Chung Man Mak Wai Yip Vivian Lee Eric Lo Sindy Shou Hugh Wang. Efficient Processing of Spatial Join Using R-trees. What is Spatial Data?

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495 views • 28 slides
CS 6463: AT Computational Geometry Fall 2006

CS 6463: AT Computational Geometry Fall 2006

CS 6463: AT Computational Geometry Fall 2006. Plane Sweep Algorithms and Segment Intersection Carola Wenk. Closest Pair. Problem: Given P ? R 2 , | P |= n , find the distance of the closest pair in P. Plane Sweep: An Algorithm Design Technique.

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328 views • 24 slides
Visibility Computations:

Visibility Computations:

Visibility Computations:. Finding the Shortest Route for Motion Planning. COMP 290-072 Presentation Eric D. Baker Tuesday 1 December 1998. Motivation. Visibility graph computation has same motivation as other robot motion planning:

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353 views • 23 slides
Computational Geometry

Computational Geometry

Computational Geometry. Piyush Kumar (Lecture 3: Convexity and Convex hulls). Welcome to CIS5930. p. q. p. convex. non-convex. q. Convexity. A set S is convex if for any pair of points p,q ? S we have pq ? S. Convex Hulls : Equivalent definitions.

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384 views • 23 slides
Computational Geometry

Computational Geometry

Computational Geometry. Piyush Kumar (Lecture 3: Convexity and Convex hulls). Welcome to CIS5930. p. q. p. convex. non-convex. q. Convexity. A set S is convex if for any pair of points p,q ? S we have pq ? S. Convex Hulls : Equivalent definitions.

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241 views • 23 slides
Collision Detection

Collision Detection

Collision Detection. Michael Fuller. Overlap testing. Most Common Technique Most Error Prone Test if two bodies overlap. Overlap Example. TIME STEP 1. TIME STEP 2. TIME STEP 3. TIME STEP 4. Overlap Limitations. Fails for Small or Fast Moving Objects. TIME STEP 1. TIME STEP 2.

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489 views • 22 slides
Last Time: Plane Sweep Algorithms, Segment Intersection, + (Element Uniqueness)

Last Time: Plane Sweep Algorithms, Segment Intersection, + (Element Uniqueness)

Last Time: Plane Sweep Algorithms, Segment Intersection, + (Element Uniqueness). This time: Planar Subdivisions. Eventually, get to problems such as intersection of planar subdivisions, and show that these algorithms are easier (more efficient) than general segment intersection.

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268 views • 20 slides
Computational Geometry

Computational Geometry

Computational Geometry. Hwangryol Ryu Dongchul Kim. Computational Geometry. Intersection of line segment Basic geometric objects Point : ( x, y ) Line : {( x 1 ,y 1 ) , ( x 2 ,y 2 ) } Line segment : size of line is given. ( x 2, y 2 ). ( x 2, y 2 ). ( x 1, y 1 ). ( x 1, y 1 ).

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500 views • 19 slides
Geometric Intersection

Geometric Intersection

Geometric Intersection. Determining if there are intersections between graphical objects Finding all intersecting pairs Brute Force Algorithm Plane Sweep Algorithm. Applications. Integrated circuit design:. Computer graphics (hidden line removal):. Range Searching.

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202 views • 15 slides
Computing Voronoi Diagram

Computing Voronoi Diagram

Computing Voronoi Diagram. For each site p i , compute the common inter-section of the half-planes h(p i , p j ) for i ? j , using linear programming: O ( n 2 log n ) The worst case time bound is O ( n log n )

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219 views • 11 slides

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