polygon filling
play

Polygon Filling Werner Purgathofer Linked Lists flexible data - PowerPoint PPT Presentation

Apr 29, 2023 •392 likes •968 views

Einfhrung in Visual Computing 186.822 Polygon Filling Werner Purgathofer Linked Lists flexible data structure x 1 x 2 pointer data (link to next element) list^ list^.next^ list x 1 x 2 x 1 x 2 x 1 x 2 list^.next

  1. Einführung in Visual Computing 186.822 Polygon Filling Werner Purgathofer

  2. Linked Lists flexible data structure … x 1 x 2 pointer data (link to next element) list^ list^.next^ list … … … x 1 x 2 x 1 x 2 x 1 x 2 list^.next list^.next^.next Werner Purgathofer / Einf. in Visual Computing 2

  3. Linked Lists: Removal of First Element list 1 2 3 4 5 list = list^.next Werner Purgathofer / Einf. in Visual Computing 3

  4. Linked Lists: Inserting New First Element list 1 2 3 4 5 new 0 new^.next = list Werner Purgathofer / Einf. in Visual Computing 4

  5. Linked Lists: Inserting New First Element list 1 2 3 4 5 new 0 new^.next = list list = new Werner Purgathofer / Einf. in Visual Computing 5

  6. Linked Lists: Exchanging Elements 2 & 4 last1 help last2 list 1 2 3 4 5 help = last1^.next^.next Werner Purgathofer / Einf. in Visual Computing 6

  7. Linked Lists: Exchanging Elements 2 & 4 last1 help last2 list 1 2 3 4 5 help = last1^.next^.next last1^.next^.next = last2^.next^.next Werner Purgathofer / Einf. in Visual Computing 7

  8. Linked Lists: Exchanging Elements 2 & 4 last1 help last2 list 1 2 3 4 5 help = last1^.next^.next last1^.next^.next = last2^.next^.next last2^.next^.next = help Werner Purgathofer / Einf. in Visual Computing 8

  9. Linked Lists: Exchanging Elements 2 & 4 last1 help last2 list 1 2 3 4 5 help = last1^.next^.next last1^.next^.next = last2^.next^.next last2^.next^.next = help help = last1^.next Werner Purgathofer / Einf. in Visual Computing 9

  10. Linked Lists: Exchanging Elements 2 & 4 last1 help last2 list 2 3 4 5 1 help = last1^.next^.next last1^.next^.next = last2^.next^.next last2^.next^.next = help help = last1^.next last1^.next = last2^.next Werner Purgathofer / Einf. in Visual Computing 10

  11. Linked Lists: Exchanging Elements 2 & 4 last1 help last2 list 1 2 4 5 3 help = last1^.next^.next last1^.next^.next = last2^.next^.next last2^.next^.next = help help = last1^.next last1^.next = last2^.next last2^.next = help Werner Purgathofer / Einf. in Visual Computing 11

  12. Repetition: What is Inside a Polygon? odd-even rule nonzero-winding- number rule ??? Werner Purgathofer / Einf. in Visual Computing 12

  13. Inside-Outside Tests area-filling algorithms “interior”, “exterior” for self-intersecting polygons? odd-even rule nonzero-winding-number rule same result for simple polygons Werner Purgathofer / Einf. in Visual Computing 13

  14. What is Inside?: Odd-Even Rule inside/outside switches at every edge straight line to the outside: even # edge intersections = outside odd # edge intersections = inside 4 3 2 1 2 1 2 1 4 3 1 1 2 3 Werner Purgathofer / Einf. in Visual Computing 14

  15. What is Inside?: Nonzero Winding Number point is inside if polygon surrounds it straight line to the outside: same # edges up and down = outside different # edges up and down = inside Werner Purgathofer / Einf. in Visual Computing 15

  16. Fill-Area Primitives for polygon area (solid-color, patterned) scan-line polygon fill algorithm intersection points located and sorted consecutive pairs define interior span attention with vertex intersections exploit coherence (incremental calculations) flood fill algorithm Werner Purgathofer / Einf. in Visual Computing 16

  17. Scan-Line Fill: Sorted Edge Table E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A The sorted edge table contains all polygon edges sorted by lowest y-value y max x start 1/m Werner Purgathofer / Einf. in Visual Computing 17

  18. Scan-Line Fill: Sorted Edge Table sort all edges by smallest y-value edge entry: [max. y-value, x-intercept, inverse slope] y B x C 1/m CB y D x C 1/m CD active-edge list for each scan line contains all edges crossed by that scan line incremental update consecutive intersection pairs (spans) filled Werner Purgathofer / Einf. in Visual Computing 18

  19. Sorted Edge Table E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A The sorted edge table contains all polygon edges sorted by lowest y-value y max x start 1/m Werner Purgathofer / Einf. in Visual Computing 19

  20. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List When processing from bottom to top, keep a list of all active edges Werner Purgathofer / Einf. in Visual Computing 20

  21. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List incremental update! y F x A 1/m AF y B x A 1/m AB Werner Purgathofer / Einf. in Visual Computing 21

  22. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y F x A 1/m AF y B x A 1/m AB Werner Purgathofer / Einf. in Visual Computing 22

  23. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y B x A 1/m AB Werner Purgathofer / Einf. in Visual Computing 23

  24. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y B x A 1/m AB Werner Purgathofer / Einf. in Visual Computing 24

  25. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y B x A 1/m AB Werner Purgathofer / Einf. in Visual Computing 25

  26. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y B x A 1/m AB y B x C 1/m CB y D x C 1/m CD Werner Purgathofer / Einf. in Visual Computing 26

  27. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y B x A 1/m AB y B x C 1/m CB y D x C 1/m CD Werner Purgathofer / Einf. in Visual Computing 27

  28. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y D x C 1/m CD Werner Purgathofer / Einf. in Visual Computing 28

  29. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y D x C 1/m CD Werner Purgathofer / Einf. in Visual Computing 29

  30. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y E x D 1/m DE Werner Purgathofer / Einf. in Visual Computing 30

  31. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List y E x F 1/m FE y E x D 1/m DE Werner Purgathofer / Einf. in Visual Computing 31

  32. Sorted Edge Table / Active Edge List E y E x D 1/m DE D B y B x C 1/m CB y D x C 1/m CD C F y E x F 1/m FE y F x A 1/m AF y B x A 1/m AB A Active Edge List Werner Purgathofer / Einf. in Visual Computing 32

  33. Scan-Line Fill: Incremental Update incremental update of intersection point slope of polygon boundary line: m 1 = + = + x x y y 1 m k+1 k k+1 k (for 2 successive scanlines) (x k+1 , y k+1 ) y k + 1 (x k , y k ) y k Werner Purgathofer / Einf. in Visual Computing 33

  34. Scan-Line Fill: Intersecting Vertices 2 intersection 1 points along scan lines that 1 2 intersect polygon 2 vertices → either special handling (1 or 2 intersections?) → or move vertices up or down by ε Werner Purgathofer / Einf. in Visual Computing 34

  35. Flood-Fill Algorithm pixel filling of area areas with no single color boundary start from interior point “flood” internal region 4-connected, 8-connected areas reduce stack size by eliminating several recursive calls Werner Purgathofer / Einf. in Visual Computing 35

  36. Flood-Fill: Boundary and Seed Point area must be distinguishable from boundaries seed point example: area defined within multiple color boundaries Werner Purgathofer / Einf. in Visual Computing 36

  37. Flood-Fill: Connectedness Definition: Definition: 4-connected means, that a 8-connected means, that a connection is only valid in connection is valid in these these 4 directions 8 directions Werner Purgathofer / Einf. in Visual Computing 37

  38. Examples for 4-connected and 8-connected a 4-connected area an 8-connected area has an 8-connected border has a 4-connected border Werner Purgathofer / Einf. in Visual Computing 38

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Polygon Filling (Rasterization) 1 Point-in-polygon test How do we tell if a point is inside

Polygon Filling (Rasterization) 1 Point-in-polygon test How do we tell if a point is inside

Computer Graphics Course 2005 Polygon Filling (Rasterization) 1 Point-in-polygon test How do we tell if a point is inside or outside a polygon? 2 Point-in-polygon test Odd-even rule: count the number of times a line from the point

336 views • 11 slides
Polygon Filling Goal intensify the pixels that belong to the polygon Issues which pixels belong

Polygon Filling Goal intensify the pixels that belong to the polygon Issues which pixels belong

Polygon Filling Goal intensify the pixels that belong to the polygon Issues which pixels belong to the polygon Approach use a (horizontal) scan line that traverses the polygon intensify the pixels along the spans (the segments of

895 views • 50 slides
Polygon Filling (Rasterization) 1 2 Point- -in in- -polygon test polygon test Point

Polygon Filling (Rasterization) 1 2 Point- -in in- -polygon test polygon test Point

Computer Graphics Course Point-in-polygon test 2005 How do we tell if a point is inside or outside a polygon? Polygon Filling (Rasterization) 1 2 Point- -in in- -polygon test polygon test Point Point-in-polygon test Non Non-

563 views • 4 slides
Computer Graphics CS 4731 Lecture 25 Polygon Filling & Antialiasing Prof Emmanuel Agu Computer

Computer Graphics CS 4731 Lecture 25 Polygon Filling & Antialiasing Prof Emmanuel Agu Computer

Computer Graphics CS 4731 Lecture 25 Polygon Filling & Antialiasing Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) Defining and Filling Regions of Pixels Methods of defining region Pixel defined:

260 views • 22 slides
Computer Graphics CS 543 Lecture 12c Polygon Filling & Antialiasing Prof Emmanuel Agu

Computer Graphics CS 543 Lecture 12c Polygon Filling & Antialiasing Prof Emmanuel Agu

Computer Graphics CS 543 Lecture 12c Polygon Filling & Antialiasing Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) Announcement Course Evaluations Now online Will be available from Friday, Dec 6

431 views • 25 slides
CS488 Polygon Filling, Point and Line Clipping Luc R ENAMBOT 1 Last time How line segments

CS488 Polygon Filling, Point and Line Clipping Luc R ENAMBOT 1 Last time How line segments

CS488 Polygon Filling, Point and Line Clipping Luc R ENAMBOT 1 Last time How line segments are drawn into the frame buffer Began to talk about how polygons are filled in the frame buffer. Today: more about filling polygons and

1.04k views • 31 slides
Polygon Filling Werner Purgathofer Linked Lists flexible data structure x 1 x 2 x 1 x 2

Polygon Filling Werner Purgathofer Linked Lists flexible data structure x 1 x 2 x 1 x 2

Einfhrung in Visual Computing 186.822 186.822 Polygon Filling Werner Purgathofer Linked Lists flexible data structure x 1 x 2 x 1 x 2 pointer data (link to next element) list^ list list .next list^ next^ list x 1

507 views • 26 slides
CS488 Polygon Clipping and Circles Luc R ENAMBOT 1 Previous Lectures Frame buffers

CS488 Polygon Clipping and Circles Luc R ENAMBOT 1 Previous Lectures Frame buffers

CS488 Polygon Clipping and Circles Luc R ENAMBOT 1 Previous Lectures Frame buffers Drawing a line (Midpoint Line Algorithm) Polygon Filling (Edge-table algorithm) Line Clipping (Cohen-Sutherland algorithm) Polygon Clipping

527 views • 31 slides
P l Polygon Filling Filli Werner Purgathofer Werner Purgathofer Linked Lists fl flexible data

P l Polygon Filling Filli Werner Purgathofer Werner Purgathofer Linked Lists fl flexible data

Einfhrung in Visual Computing g p g 186.822 P l Polygon Filling Filli Werner Purgathofer Werner Purgathofer Linked Lists fl flexible data structure ibl d x 1 x 2 pointer data (link to next element) (link to next element) list^

867 views • 57 slides
Safe filling for all Higher standards in low-capacity filling 1 Safe filling for all! The Kosan

Safe filling for all Higher standards in low-capacity filling 1 Safe filling for all! The Kosan

Safe filling for all Higher standards in low-capacity filling 1 Safe filling for all! The Kosan Crisplant Group World leading provider of solutions and services to the LP gas industry Equipment installed in more than 2600 sites in

330 views • 22 slides
Polygon Triangulation Computational Geometry The Art Gallery Problem Guarding and

Polygon Triangulation Computational Geometry The Art Gallery Problem Guarding and

Yazd Univ. Polygon Triangulation Computational Geometry The Art Gallery Problem Guarding and Triangulations Computing triangulation 1392-1 Partitioning a Polygon into Monotone Pieces Triangulating a Monotone Polygon 1 / 37

1.23k views • 90 slides
CS488 Geometric Transformations Luc R ENAMBOT 1 Previous Lectures Frame buffers Drawing

CS488 Geometric Transformations Luc R ENAMBOT 1 Previous Lectures Frame buffers Drawing

CS488 Geometric Transformations Luc R ENAMBOT 1 Previous Lectures Frame buffers Drawing a line (Midpoint Line Algorithm) Polygon Filling (Edge-table algorithm) Line Clipping (Cohen-Sutherland algorithm) Polygon Clipping

697 views • 50 slides
Tank Car Filling Limit & Filling Density Standards Overload a condition that

Tank Car Filling Limit & Filling Density Standards Overload a condition that

Dennis Campbell Hazmat Trainer FRA Office: (281) 259-4923 Cell: (281) 723-3862 Tank Car Filling Limit & Filling Density Standards Overload a condition that occurs when the load is greater than the system was designed to

1.11k views • 55 slides
Polygon Leak Detection Trace & Access Services Jamie Nash LD Director Polygon Trace &

Polygon Leak Detection Trace & Access Services Jamie Nash LD Director Polygon Trace &

Polygon Leak Detection Trace & Access Services Jamie Nash LD Director Polygon Trace & Access Agenda Introduction to LD How we find leaks Case study IOT Preventative Technology Questions Flaws in traditional

623 views • 18 slides
Ordering! CS294S Spring 2020 Riya Verma Project Motivation - Slot filling Form Filling -

Ordering! CS294S Spring 2020 Riya Verma Project Motivation - Slot filling Form Filling -

Food Ordering! CS294S Spring 2020 Riya Verma Project Motivation - Slot filling Form Filling - Some transactions require more than simple slot filling - Account for factors such as history, user preferences, financial concerns, offering

323 views • 13 slides
Integrable and chaotic mappings of the plane with polygon invariants. Tim Zolkin 1 Sergei

Integrable and chaotic mappings of the plane with polygon invariants. Tim Zolkin 1 Sergei

1. Definitions, historical remarks and tools we need 2. Periodic integer maps with polygon invariants 3. Maps with polygon invariants Integrable and chaotic mappings of the plane with polygon invariants. Tim Zolkin 1 Sergei Nagaitsev 1 , 2 1

691 views • 65 slides
CS 5 4 3 : Com puter Graphics Lecture 9 ( Part I I ) : Raster Graphics: Polygons &

CS 5 4 3 : Com puter Graphics Lecture 9 ( Part I I ) : Raster Graphics: Polygons &

CS 5 4 3 : Com puter Graphics Lecture 9 ( Part I I ) : Raster Graphics: Polygons & Antialiasing Emmanuel Agu So Far Raster graphics: Line drawing algorithms (simple, Bresenhams) Today: Defining and filling regions

723 views • 24 slides
Lecture 1 Wireless Channel I-Hsiang Wang ihwang@ntu.edu.tw 2/20, 2014 Wireless

Lecture 1 Wireless Channel I-Hsiang Wang ihwang@ntu.edu.tw 2/20, 2014 Wireless

Lecture 1 Wireless Channel I-Hsiang Wang ihwang@ntu.edu.tw 2/20, 2014 Wireless channels vary at two scales Channel quality Time Large-scale fading: path loss, shadowing, etc. Small-scale fading:

3.11k views • 35 slides
Lecture 6 Announcements A2 will be posted by Monday at 9AM 2 Scott B. Baden / CSE 160 / Wi

Lecture 6 Announcements A2 will be posted by Monday at 9AM 2 Scott B. Baden / CSE 160 / Wi

Lecture 6 Announcements A2 will be posted by Monday at 9AM 2 Scott B. Baden / CSE 160 / Wi '16 Todays lecture Cache Coherence and Consistency False sharing Parallel sorting 3 Scott B. Baden / CSE 160 / Wi '16 Recapping

380 views • 37 slides
Synthetic Aperture Radar Backscatter and Coherence in in Tropical Forest Elsa Carla De Grandi,

Synthetic Aperture Radar Backscatter and Coherence in in Tropical Forest Elsa Carla De Grandi,

Mult lti-Temporal Pix ixel Trajectories of f Synthetic Aperture Radar Backscatter and Coherence in in Tropical Forest Elsa Carla De Grandi, Edward Mitchard, Iain Woodhouse, Dirk Hoekman, Astrid Verhegghen and Francesco Holecz

350 views • 12 slides
Uniform dispersal of robots with minimum visibility range Attila Hideg 1 and Tams Lukovszki 2 1

Uniform dispersal of robots with minimum visibility range Attila Hideg 1 and Tams Lukovszki 2 1

Uniform dispersal of robots with minimum visibility range Attila Hideg 1 and Tams Lukovszki 2 1 Budapest University of T echnology and Economics, Hungary Attila.Hideg@aut.bme.hu 2 Etvs Lrnd University, Budapest, Hungary

817 views • 49 slides
Java 2D Review of Abstract Windows Toolkit ( awt ) Java 2D graphical objects Java 2D

Java 2D Review of Abstract Windows Toolkit ( awt ) Java 2D graphical objects Java 2D

Java 2D Review of Abstract Windows Toolkit ( awt ) Java 2D graphical objects Java 2D rendering Abstract Windows Toolkit ( awt ) Review of import files awt has always provided a Graphics class - almost obsolete It now also

542 views • 16 slides
Bell-paired states inducing volume law for Entanglement Entropy in fermionic lattices Simone

Bell-paired states inducing volume law for Entanglement Entropy in fermionic lattices Simone

Bell-paired states inducing volume law for Entanglement Entropy in fermionic lattices Simone Paganelli in collaboration with: Giacomo Gori (SISSA) Auditya Sharma (Tel Aviv University) Pasquale Sodano (IIP , Natal) Andrea Trombettoni (SISSA)

703 views • 18 slides
Critical Reasoning for Beginners: Four Marianne Talbot Department for Continuing Education

Critical Reasoning for Beginners: Four Marianne Talbot Department for Continuing Education

Critical Reasoning for Beginners: Four Marianne Talbot Department for Continuing Education University of Oxford Michaelmas 2009 Last week we learned how to analyse arguments and set them out logic-book style Six steps to analysing an

807 views • 32 slides

More recommend