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Course name
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Code/No
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Credits
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Registered credits
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Prerequisite
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Lecture
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Lab
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Training
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Geometric Modeling
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COCS 483
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3
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0
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0
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3
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COCS324
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Course Objectives:
The goal of this course is to introduce the theory of geometric modelling. Terminology and overview of its applications.
Basic geometry representations of curves and surfaces. Curvatures, curvature estimation; parametric, and splines representations.
Differential geometry and subdivision for curves and surfaces. Basic CAD operations.
Interpolation, knot insertion, c1- and c2-continuous spline curves as well as continuous surfaces.
Course Learning Outcomes
Upon finishing this course, the students should be able to:
- Distinguish the capabilities of different solutions used for curve representation.
- Discuss complexity, strengths, and weakness of multiple geometric techniques/algorithms.
- Compare and contrast the use of many polynomial interpolations’ schemes.
- Explain how to maintain smoothness transition between curves’ endpoints; and the representation of different kinds of continuous curves/surfaces.
- Describe the application of de Casteljua’s algorithm, and the analytical form of Bezier curves in constructing 2D curves/surfaces models.
- Implementing control-points-based curves using several geometric algorithms.
- Understand how to construct complex wireframe geometric models from simple primitives, such as quadratic/cubic curves and surfaces.
Assessment Strategy:
Students will be assessed in this course based on a set of exams, assignments and/or projects, presentations.
Note: The instructor reserves the right to make changes to this syllabus as necessary.
Text Book:
1- Primary Book: G. Farin, Curves and Surfaces for CAGD, Academic Press, 5th Edition, 2002.
2- David Salomon, Curves and Surfaces for Computer Graphics, Springer, 5th Edition, 2006.
3- Fletcher Dunn and Ian Parberry, 3D Math Primer for Graphics and Game Development, 2nd Edition, 2011.
4- Eric Lengy, Mathematics for 3D Game Programming and Computer Graphics, 3rd Edition, 2012.
5- Michael E., Mathematics for Computer Graphics Application, 2nd Edition, Industrial Press Inc., Mortenson, 1999.
6- Michael E. Mortenson, Geometric Modeling, 3rd Edition, Wiley Computer Publishing, 2006.
Other Reference:
Extra Resources: Books, Papers, Internet…etc.
Time table for distributing theoretical course contents
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Number
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Description
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Duration in weeks
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1
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Introduction to Geometric Modeling
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1
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2
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de Casteljau Algorithm and Bezier Curves
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1
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3
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Derivatives and Subdivision of Bezier Curves
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1
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4
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Complexity Improve and Degree Elevation of Bezier Curves
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1
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5
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Polynomial Interpolation: Aitken, Lagrange, Vandermonde and Hermite Schemes
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1
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6
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c1- and c2-Continuous Spline Curves
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1
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7
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The de Boor Algorithm and B-spline Curves
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1
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8
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Knot Insertion for B-spline Curves and Subdivision
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1
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9
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Rational Bezier and B-spline Curves
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1
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10
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Bezier Surfaces; de Casteljau Algorithm and Surfaces
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1
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11
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Bezier Surfaces Partial Derivatives and Continuity
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1
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12
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Modelling with Rational Bezier and B-splines (NURBS)
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1
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13
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Final Exam
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|
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