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Computing & Information SciencesKansas State UniversityCIS 536/636Introduction to Computer GraphicsLecture 2 of 41William H. HsuDepartment of Computing and Information Sciences, KSUKSOL course pages: http://bit.ly/hGvXlH / http://bit.ly/eVizrE Public mirror web site: http://www.kddresearch.org/Courses/CIS636Instructor home page: http://www.cis.ksu.edu/~bhsuReadings:Today: Sections 2.2.3 – 2.2.4, 2.8, Eberly 2e – see http://bit.ly/ieUq45Next class: Section 2.3 (esp. 2.3.4), FVFH slidesAppendices 1-4, Foley, J. D., VanDam, A., Feiner, S. K., & Hughes, J. F. (1991). Computer Graphics, Principles and Practice, Second Edition in C. Viewing 1 of 4:Overview, ProjectionsLecture 2 of 41Computing & Information SciencesKansas State University2CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Lecture OutlineReading for Last Class: Sections 2.1, 2.2.1 – 2.2.2, Eberly 2eReading for Today: Sections 2.2.3 – 2.2.4, 2.8 Eberly 2eReading for Next Class: Section 2.3 (esp. 2.3.4), Foley et al. SlidesLast Time: Math Foundations, Matrix TransformationsPrecalculus review: parametric equations of linesVector spaces and affine spacesLinear systems, linear independence, bases, orthonormalityCumulative Transformation Matrices (CTMs)TranslationRotationScalingToday: Basic Viewing PrinciplesProjections: definitions, historyPerspective: optical principles, terminologyNext Class: Viewing and Normalizing Transformations (VT/NT)Computing & Information SciencesKansas State University3CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Where We AreComputing & Information SciencesKansas State University4CIS 536/636Introduction to Computer GraphicsLecture 2 of 41AcknowledgementsJames D. FoleyGeorgia Techhttp://bit.ly/ajYf2Q Andries van DamBrown Universityhttp://www.cs.brown.edu/~avd/ Steven K. FeinerColumbia Universityhttp://www.cs.columbia.edu/~feiner/ John F. HughesBrown Universityhttp://www.cs.brown.edu/~jfh/Andy van DamT. J. Watson University Professor of Technology and Education & Professor of Computer ScienceBrown UniversitySteve FeinerProfessor of Computer Science & Director, Computer Graphics and User Interfaces LaboratoryColumbia UniversityJohn F. HughesAssociate Professor of Computer ScienceBrown UniversityJim FoleyProfessor, College of Computing & Stephen Fleming Chair in TelecommunicationsGeorgia Institute of TechnologyComputing & Information SciencesKansas State University5CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Background:Basic Linear Algebra for CGReference: Appendix A.1 – A.4, Foley et alA.1 Vector Spaces and Affine SpacesEquations of lines, planesVector subspaces and affine subspacesA.2 Standard Constructions in Vector SpacesLinear independence and spansCoordinate systems and basesA.3 Dot Products and DistancesDot product in RnNorms in RnA.4 MatricesBinary matrix operations: basic arithmeticUnary matrix operations: transpose and inverseApplication: Transformations and Change of Coordinate SystemsAffine transformations© 2005 Trevor McCauley(Senocular)Computing & Information SciencesKansas State University6CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Review:Basic T, R, S TransformationsT: Translation (see http://en.wikipedia.org/wiki/Translation_matrix )GivenPoint to be moved – e.g., vertex of polygon or polyhedronDisplacement vector (also represented as point)Return: new, displaced (translated) point of rigid bodyR: Rotation (see http://en.wikipedia.org/wiki/Rotation_matrix) GivenPoint to be rotated about axisAxis of rotationDegrees to be rotatedReturn: new, displaced (rotated) point of rigid bodyS: Scaling (see http://en.wikipedia.org/wiki/Scaling_matrix)GivenSet of points centered at originScaling factorReturn: new, displaced (scaled) pointGeneral: http://en.wikipedia.org/wiki/Transformation_matrixComputing & Information SciencesKansas State University7CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Review:Lab 0Warm-Up Lab Account set-upLinux environmentSimple OpenGL exerciseBasic Account Set-UpSee http://support.cis.ksu.edu to understand KSU Department of CIS setupMake sure your CIS department account is set upIf not, use SelfServ: https://selfserv.cis.ksu.edu/selfserv/requestAccountLinux EnvironmentMake sure your CIS department account is set upLearn how to navigate, set your shell (see KSOL, http://unixhelp.ed.ac.uk)Lab 1 and first homeworks will ask you to render to local XWindows serverSimple OpenGL exerciseWatch OpenGL Primer Part 1 as neededFollow intro tutorials on “NeHe” (http://nehe.gamedev.net) as instructedTurn in: source code, screenshot as instructed in Lab 0 handoutComputing & Information SciencesKansas State University8CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Projections From 3-D to 2-D:Orthographic & PerspectiveAdapted from slides © 1997 – 2010 van Dam et al., Brown Universityhttp://bit.ly/hiSt0f Reused with permission.Computing & Information SciencesKansas State University9CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Drawing as ProjectionAdapted from slides © 1997 – 2010 van Dam et al., Brown Universityhttp://bit.ly/hiSt0f Reused with permission.Computing & Information SciencesKansas State University10CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Early Examples of PerspectiveAdapted from slides © 1997 – 2010 van Dam et al., Brown Universityhttp://bit.ly/hiSt0f Reused with permission.Computing & Information SciencesKansas State University11CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Key Features of Linear PerspectiveAdapted from slides © 1997 – 2010 van Dam et al., Brown Universityhttp://bit.ly/hiSt0f Reused with permission.Computing & Information SciencesKansas State University12CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Early Perspective: Ad HocAdapted from slides © 1997 – 2010 van Dam et al., Brown Universityhttp://bit.ly/hiSt0f Reused with permission.Computing & Information SciencesKansas State University13CIS 536/636Introduction to Computer GraphicsLecture 2 of 41Historical Setting forInvention of PerspectiveAdapted from slides © 1997 – 2010 van Dam et al., Brown Universityhttp://bit.ly/hiSt0f Reused with permission.Computing & Information SciencesKansas State University14CIS 536/636Introduction to Computer GraphicsLecture 2


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