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Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 William H. Hsu Department of Computing.

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Presentation on theme: "Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 William H. Hsu Department of Computing."— Presentation transcript:

1 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 William H. Hsu Department of Computing and Information Sciences, KSU KSOL course pages: http://bit.ly/hGvXlH / http://bit.ly/eVizrEhttp://bit.ly/hGvXlHhttp://bit.ly/eVizrE Public mirror web site: http://www.kddresearch.org/Courses/CIS636http://www.kddresearch.org/Courses/CIS636 Instructor home page: http://www.cis.ksu.edu/~bhsuhttp://www.cis.ksu.edu/~bhsu Readings: Today: Section 2.3 (esp. 2.3.7), 2.6, 2.7, Eberly 2 e – see http://bit.ly/ieUq45http://bit.ly/ieUq45 Next class: This week: FVFH slides on Viewing Viewing 3 of 4: Normalizing Transformation and Fixed-Function Graphics Pipeline Lecture 5 of 41

2 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Lecture Outline Reading for Last Class: Chapters 2, 16, Eberly 2 e ; Foley et al. Slides Reading for Today: Section 2.3 (esp. 2.3.7), 2.6, 2.7, Eberly 2 e Reading for Next Class: §2.5.1, 3.1 Eberly 2 e Last Time: Basic Viewing Principles  Projections: definitions, history  Perspective: optical principles, terminology Today: View Volume Specification and Viewing Transformation  View volumes: ideal vs. approximated  Frustum in computer graphics (CG)  Specifying view volume in CG: Look and Up vectors  Aspect ratio, view angle, front/back clipping planes  Focal length  Parallel (cuboid) view volume & perspective frustum  Normalizing transformation (NT) & viewing transformation (VT) Next Time: Fixed-Function Graphics Pipeline

3 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Where We Are

4 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Acknowledgements James D. Foley Georgia Tech http://bit.ly/ajYf2Q Andries van Dam Brown University http://www.cs.brown.edu/~avd/ Steven K. Feiner Columbia University http://www.cs.columbia.edu/~feiner/ John F. Hughes Brown University http://www.cs.brown.edu/~jfh/ Andy van Dam T. J. Watson University Professor of Technology and Education & Professor of Computer Science Brown University Steve Feiner Professor of Computer Science & Director, Computer Graphics and User Interfaces Laboratory Columbia University John F. Hughes Associate Professor of Computer Science Brown University Jim Foley Professor, College of Computing & Stephen Fleming Chair in Telecommunications Georgia Institute of Technology

5 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Review: Types of Projections Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission.

6 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Review: Synthetic Camera for 3-D Viewing Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission.

7 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Review: Look and Up Vectors Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission.

8 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Review: View Volume for Parallel Projection

9 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Review: View Volume for Perspective Projection

10 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Viewing in Three Dimensions: Mathematics of Projections

11 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Stage 1: Specifying View Volume

12 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Examples of View Volume [1]: Perspective (Frustum)

13 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Examples of View Volume [2]: Parallel (Cuboid)

14 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Viewing Transformation: World (x, y, z) to Camera (u, v, w)

15 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Arbitrary View Volume Too Complex

16 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Stage 2: Normalizing to Canonical View Volume

17 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Viewing Transformation  Normalizing Transformation

18 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Building Viewing Transformation From View Specification

19 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Rotation [1]

20 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Rotation [2]

21 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Rotation [3]

22 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Rotation [4]

23 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Construction of Orientation Matrix

24 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Finding (u, v, w) from Position, Look, and Up [1]

25 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Finding (u, v, w) from Position, Look, and Up [2]

26 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Finding (u, v, w) from Position, Look, and Up [3]

27 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Finding (u, v, w) from Position, Look, and Up [4]

28 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Finding (u, v, w) from Position, Look, and Up [5]

29 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Transforming to Canonical View

30 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Overview

31 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Step 1

32 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Step 2

33 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Step 3

34 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Step 4

35 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Step 5

36 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Step 6

37 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Step 7

38 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Step 8

39 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Normalizing View Volume: Results

40 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Perspective Transformation [1]

41 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Perspective Transformation [2]

42 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Perspective Transformation [3]

43 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Perspective Transformation [4]

44 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Perspective Transformation [5]

45 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Perspective Transformation: End Result

46 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Stage 3: Making 2-D Image

47 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Clipping

48 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Final Projection: Viewport Mapping

49 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Adapted from slides © 1997 – 2010 van Dam et al., Brown University http://bit.ly/hiSt0fhttp://bit.ly/hiSt0f Reused with permission. Fixed Function Graphics Pipeline: Composite Transformation Matrix

50 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Putting It All Together: Coordinate Spaces & Transformations

51 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Summary Last Time: View Volume Specification and Viewing Transformation  View volumes: ideal vs. approximated  Specifying view volume in CG: Look and Up vectors  Aspect ratio, view angle, front/back clipping planes, focal length Today  Viewing transformation (NT)  Rotation  Finding camera coordinates (u, v, w) from Look, Up  Normalizing transformation (NT)  Perspective transformation D  Overall CTM of fixed-function pipeline  Intro to clipping Coming Week  Lab: OpenGL basics  Drawing lines, polygons  Parametric clipping

52 Computing & Information Sciences Kansas State University CIS 536/636 Introduction to Computer Graphics Lecture 5 of 41 Terminology Today: View Volumes, Viewing Transformation  Parallel projection (cuboid) view volume vs. perspective projection frustum  Front/back (near/far) clipping planes  World coordinates (canonical): (x, y, z)  User coordinates (arbitary): (u, v, w), aka (u, v, n) or (R, U, D) in Eberly  Perspective transformation D: “morphs” frustum into cuboid  Normalizing transformation: inverse of viewing transformation (easier) Other Topics  Clipping  Given view volume  Problem of determining visible elements of scene  Cumulative Transformation Matrices (CTM)  Translation, Rotation, Scaling (TRS)  Used to map arbitrary view to canonical view  Then “ready to take picture”

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