graphics programming, byung-gook lee, dongseo univ., e-mail:lbg@dongseo.ac.kr graphics programming...

Graphics Programming, Byung-Gook Lee, Dongseo Univ., E-mail:lbg@dongseo.ac.kr

Graphics Programming

Byung-Gook LeeDongseo Univ.

http://kowon.dongseo.ac.kr/~lbg/

Professor

• Room UIT208 NM801• lbg@dongseo.ac.kr• http://kowon.dongseo.ac.kr/~lbg• 320-1727, 010-9331-1453• Office hours Wed/Fri 13:00pm -16:00pm

Grading evaluation criteria

• Attendance, Participation and Creativity = 20%• 1 Projects = 30%

correctness (40%), efficiency (20%), elegance (20%), originality (20%).

• 2 Exams = 50%

Text & References

• Text : Focus on Curves and Surfaces,Kelly Dempski, GameDev.Net

• Ref. 1 : OpenGL SuperBible 2ed,Richard S. Wright. Jr. Michael Sweet,Waite Group Press.

• Ref. 2 : Interactive Computer Graphics a top-down approach with OpenGL 2ed,Edward Angel, Addison Wesley.

• Ref. 3 : Curves and Surfaces for Computer Aided Geometric Design, Gerald Farin, Aca-demic Press

References

• Ref. 4 : The NURBS book, Les Piegl and Wayne Tiller, Springer

• Ref. 5 : Spline Methods Drafts, Tom Lyche and Knut Morken

• Ref. 6 : Computer Graphics & Geometric Model-ing, Davis Salomon, Springer

• Software : Visual C++ with OpenGL• Prepare Files

http://kowon.dongseo.ac.kr/~lbg/cagd/http://kowon.dongseo.ac.kr/~lbg/cagd/

Computer Graphics

The generation of graphical output using a computer

• by developing software to accomplish the task• by using pre-existing application software like

Photoshop, 3D Studio Max, Maya, …

Computer Graphics

• Modeling• Animation• Rendering

Modeling

• The creation of mathematical models of 2D and 3D objects in the 3D environment of a com-puter.

Animation

• Topics include traditional principles of anima-tion, kinematic and dynamic modeling tech-niques, physical simulation, procedural meth-ods, and motion capture based animation.

Rendering

• These models, starting as a wire frame model, are digitally wrapped with textures and ren-dered with reflections, transparencies, and shadows to give a photo-realistic view of the object or building.

Web 3D

• VRML• Java3D• Cult3D• Shout3D• NeMoWeb• Lightwave

Computer Aided Geometric Design

interpolation spline bezier B-spline NURBS subdivision simplification parametrization

CAGD is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their efficients mathematical representation.

Affine combination

• Linear combinations

• Affine(Barycentric) combinations

• Convex combinations

• Barycentric coordinates

Affine combination

Euclidean coordinate system

Coordinate-free system

Polynomial interpolation

General polynomial Interpolation

• Lagrange polynomials

Examples of cubic interpolation

Bezier

• Paul de Faget de Casteljau, Citroen, 1959• Pierre Bezier, Renault, UNISUF system, 1962• A.R. Forrest, Cambridge, 1970

Bezier

Representation Bezier

Properties of Bezier

• Affine invariance• Convex hull property• Endpoint interpolation• Symmetry• Linear precision• Pseudo-local control

Bezier Degree Reduction

Spline curve

• J.Ferguson , Boeing Co., 1963• C.de Boor, W.Gordon, General Motors, 1963

• to interpolate given data • piecewise polynomial curves with certain dif-

ferentiability constraints • not to design free form curves

Piecewise cubic hermite interpolation

Cubic spline interpolation

Natural boundary condition

B-spline

• C. de Boor, 1972• W. Gordon, Richard F. Riesenfeld, 1974

• Larry L. Schumaker• Tom Lyche• Nira Dyn• Cohen

B-spline

Linear splines

Quadratic splines

Representation splines

Cubic splines

Spline problems

• Degree Elevation• Degree Reduction• Knot Insertion• Knot Deletion

Subdivision schemes

Subdivision Surfaces

Tony DerosePixar Animation Studios

Geri’s game

Quasi-interpolants

Polygonal Simplification

Multiresolution

Parametrization

3D meshparameterization

with fixed boundary

Texture Mapping

Image Compression

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spline methods drafts

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