polygon filling
play

Polygon Filling Werner Purgathofer Linked Lists flexible data - PDF document

Sep 25, 2023 •242 likes •507 views

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

  1. Einführung 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 x 2 x 1 x 2 x 1 x 2 list^.next list^.next^.next 1 Werner Purgathofer / Einf. in Visual Computing 1

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

  3. Linked Lists: Inserting New 1 st Element list 1 1 2 2 3 3 4 4 5 5 new 0 new^.next = list list = new list = new 4 Werner Purgathofer / Einf. in Visual Computing Linked Lists: Exchanging Elements 2 & 4 help last2 last1 list 1 1 2 2 3 3 4 4 5 5 help = last1^.next^.next 5 Werner Purgathofer / Einf. in Visual Computing 3

  4. Linked Lists: Exchanging Elements 2 & 4 help last2 last1 list 1 1 2 2 3 3 4 4 5 5 help = last1^.next^.next last1^.next^.next = last2^.next^.next 6 Werner Purgathofer / Einf. in Visual Computing Linked Lists: Exchanging Elements 2 & 4 help last2 last1 list 1 1 2 2 3 3 4 4 5 5 help = last1^.next^.next last1^.next^.next = last2^.next^.next last2^.next^.next = help 7 Werner Purgathofer / Einf. in Visual Computing 4

  5. Linked Lists: Exchanging Elements 2 & 4 help last2 last1 list 1 1 2 2 3 3 4 4 5 5 help = last1^.next^.next last1^.next^.next = last2^.next^.next last2^.next^.next = help help = last1^.next 8 Werner Purgathofer / Einf. in Visual Computing Linked Lists: Exchanging Elements 2 & 4 help last2 last1 list 1 1 2 2 3 3 4 4 5 5 help = last1^.next^.next last1^.next^.next = last2^.next^.next last2^.next^.next = help help = last1^.next last1^.next = last2^.next 9 Werner Purgathofer / Einf. in Visual Computing 5

  6. Linked Lists: Exchanging Elements 2 & 4 help last2 last1 list 1 1 2 2 3 3 4 4 5 5 help = last1^.next^.next last1^.next^.next = last2^.next^.next last2^.next^.next = help help = last1^.next last1^.next = last2^.next last2^.next = help 10 Werner Purgathofer / Einf. in Visual Computing Fill-Area Primitives for polygon area (solid-color, patterned) scan-line polygon fill algorithm intersection points located and sorted intersection points located and sorted consecutive pairs define interior span attention with vertex intersections exploit coherence (incremental calculations) flood fill algorithm 11 Werner Purgathofer / Einf. in Visual Computing 6

  7. 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 A The sorted edge table contains all polygon edges sorted by lowest y-value y max x start 1/m 12 Werner Purgathofer / Einf. in Visual Computing Scan-Line Fill: Sorted Edge Table sort all edges by smallest y-value edge entry: [max y value x intercept inverse slope] [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 13 Werner Purgathofer / Einf. in Visual Computing 7

  8. 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 A The sorted edge table contains all polygon edges sorted by lowest y-value y max x start 1/m 14 Werner Purgathofer / Einf. in Visual Computing 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 A Active Edge List When processing from bottom to top, keep a list of all active edges 15 Werner Purgathofer / Einf. in Visual Computing 8

  9. 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 A Active Edge List incremental update! y F x A 1/m AF y B x A 1/m AB 16 Werner Purgathofer / Einf. in Visual Computing 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 A Active Edge List y F x A 1/m AF y B x A 1/m AB 17 Werner Purgathofer / Einf. in Visual Computing 9

  10. 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 A Active Edge List y E x F 1/m FE y B x A 1/m AB 18 Werner Purgathofer / Einf. in Visual Computing 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 A Active Edge List y E x F 1/m FE y B x A 1/m AB 19 Werner Purgathofer / Einf. in Visual Computing 10

  11. 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 A Active Edge List y E x F 1/m FE y B x A 1/m AB 20 Werner Purgathofer / Einf. in Visual Computing 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 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 21 Werner Purgathofer / Einf. in Visual Computing 11

  12. 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 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 22 Werner Purgathofer / Einf. in Visual Computing 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 A Active Edge List y E x F 1/m FE y D x C 1/m CD 23 Werner Purgathofer / Einf. in Visual Computing 12

  13. 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 A Active Edge List y E x F 1/m FE y D x C 1/m CD 24 Werner Purgathofer / Einf. in Visual Computing 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 A Active Edge List y E x F 1/m FE y E x D 1/m DE 25 Werner Purgathofer / Einf. in Visual Computing 13

  14. 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 A Active Edge List y E x F 1/m FE y E x D 1/m DE 26 Werner Purgathofer / Einf. in Visual Computing 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 A Active Edge List 27 Werner Purgathofer / Einf. in Visual Computing 14

  15. 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 28 Werner Purgathofer / Einf. in Visual Computing Scan-Line Fill: Intersecting Vertices 2 intersection 1 points along scan lines that li th t 1 1 2 intersect polygon 2 vertices. → either special handling (1 or 2 intersections?) p g ( ) → or move vertices up or down by ε 29 Werner Purgathofer / Einf. in Visual Computing 15

  16. 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 recursive calls 30 Werner Purgathofer / Einf. in Visual Computing Flood-Fill: Boundary and Seed Point area must be distinguishable from boundaries boundaries seed point example: area defined within multiple color boundaries 31 Werner Purgathofer / Einf. in Visual Computing 16

  17. Flood-Fill: Connectedness Definition: Definition: 4-connected means, 8-connected means, that a connection is that a connection is only valid in these 4 valid in these 8 directions directions 32 Werner Purgathofer / Einf. in Visual Computing Examples for 4- and 8-connected a 4 connected area a 4-connected area an 8 connected area an 8-connected area has an 8-connected has a 4-connected border border 33 Werner Purgathofer / Einf. in Visual Computing 17

  18. Simple Flood-Fill Algorithm void floodFill4 (int x, int y, int new, int old) { int color; /* set current color to new */ getPixel (x, y, color); if (color = old) { setPixel (x, y); floodFill4 (x–1, y, new, old); /* left */ floodFill4 (x, y+1, new, old); / up / floodFill4 (x y+1 new old); /* up */ floodFill4 (x+1, y, new, old); /* right */ floodFill4 (x, y–1, new, old) /* down */ }} 34 Werner Purgathofer / Einf. in Visual Computing Bad Behavior of Simple Flood-Fill 2 1 3 4 recursion sequence 35 Werner Purgathofer / Einf. in Visual Computing 18

  19. Span Flood-Fill Algorithm floodFill4 produces too high stacks (recursion!) ( ) solution: incremental horizontal fill (left to right) recursive vertical fill (first up then down) 36 Werner Purgathofer / Einf. in Visual Computing Good Behavior of Span Flood-Fill 1 2 recursion sequence 37 Werner Purgathofer / Einf. in Visual Computing 19

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 pointer

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

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

968 views • 57 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
Adaptive Operator Selection with Rank-based Multi-Armed Bandits Alvaro Fialho, Marc Schoenauer

Adaptive Operator Selection with Rank-based Multi-Armed Bandits Alvaro Fialho, Marc Schoenauer

Adaptive Operator Selection with Rank-based Multi-Armed Bandits Alvaro Fialho, Marc Schoenauer & Mich` ele Sebag 26th COW, April 22., 2013 Context Operator Selection Credit Assignment Empirical Validation Conclusion Outline 1 Context

642 views • 45 slides
Gravity and the planar spin-2 Schr odinger equation Eric Bergshoeff Groningen University work

Gravity and the planar spin-2 Schr odinger equation Eric Bergshoeff Groningen University work

Newton-Cartan Geometry Newton-Cartan Gravity Non-Relativistic Matter Comments Gravity and the planar spin-2 Schr odinger equation Eric Bergshoeff Groningen University work done in collaboration with Jan Rosseel and Paul Townsend workshop

701 views • 39 slides
Catmandu What is it? a Perl library a command line tool to import , transform and

Catmandu What is it? a Perl library a command line tool to import , transform and

Catmandu What is it? a Perl library a command line tool to import , transform and export (library) data in a pragmatic way can handle large streams of data Where do i find it? http://librecat.org/

1.02k views • 84 slides
14 Allocation Dirichlet Latent Lecture : Taheri Sara Scribes : Chu 4am Exam Man Tue

14 Allocation Dirichlet Latent Lecture : Taheri Sara Scribes : Chu 4am Exam Man Tue

14 Allocation Dirichlet Latent Lecture : Taheri Sara Scribes : Chu 4am Exam Man Tue 12 : Midterm Exam focus Open Format book understanding on : , IEM ) Everything 8 Lecture Content to up ' . ( VBEM 9810 lectures

440 views • 21 slides
Adaptive Quiz Generation Using Thompson Sampling Fuhua (Oscar) Lin, PhD Athabasca University,

Adaptive Quiz Generation Using Thompson Sampling Fuhua (Oscar) Lin, PhD Athabasca University,

Adaptive Quiz Generation Using Thompson Sampling Fuhua (Oscar) Lin, PhD Athabasca University, Canada Third Workshop eliciting Adaptive Sequences for Learning ( WASL 2020 ) Cyberspace, 6 July, 2020 Co-located with the AIED 2020 Outline

352 views • 21 slides
Multi-agent learning Multi-a rmed bandit algo rithms Gerard Vreeswijk , Intelligent Software

Multi-agent learning Multi-a rmed bandit algo rithms Gerard Vreeswijk , Intelligent Software

Multi-agent learning Multi-a rmed bandit algo rithms Gerard Vreeswijk , Intelligent Software Systems, Computer Science Department, Faculty of Sciences, Utrecht University, The Netherlands. Thursday 30 th April, 2020 Contents Author: Gerard

2k views • 173 slides
Mac OS X : System Integrity Protection Nicolas RUFF - nruff(at)google(dot)com Proprietary

Mac OS X : System Integrity Protection Nicolas RUFF - nruff(at)google(dot)com Proprietary

Mac OS X : System Integrity Protection Nicolas RUFF - nruff(at)google(dot)com Proprietary Proprietary Introduction Proprietary Proprietary What is SIP? SIP: "System Integrity Protection", a.k.a. "rootless". SIP restricts

370 views • 15 slides
EM-MAC: A Dynamic Multichannel Energy-Efficient MAC Protocol for Wireless Sensor Networks Lei

EM-MAC: A Dynamic Multichannel Energy-Efficient MAC Protocol for Wireless Sensor Networks Lei

EM-MAC: A Dynamic Multichannel Energy-Efficient MAC Protocol for Wireless Sensor Networks Lei Tang, Yanjun Sun, Omer Gurewitz, and David B. Johnson Presentation at ACM MobiHoc 2011, May 2011 The Objectives of EM-MAC Spread traffic to

614 views • 24 slides

More recommend