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Geometric Modeling and CAD
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Assignment 3 (B-spline curve/surface)(Submission deadline: 17.11.2011)
Notes on 2D Transformation
Sample code for rotation and file input Sample input file PDF on input from file
Assignment 2 (Hermite/Bezier surface)(Submission deadline: 27.09.2011, 2pm for Hermite Surface, For the Bezier surface, 12.10.2011)
Assignment 1 (Hermite curve)(Submission deadline: 29.08.2011, 2pm)
Notes on Affine and Convex combination
Notes on points and vectors
Class timings (for July-Nov 2011)
- Tuesdays 11.00 to 11.50 a.m.
- Wednesdays 10.00 to 10.50 a.m.
- Fridays 2.00 to 2.50 p.m.
Course syllabus (subjected to minor changes)
- Intoduction to Geometric Modeling - Affine and convex combination
- Intoduction to Equations - Implicit, explicit, parametric
- Cubic Hermite curves - Algebraic and geometric form, Blending functions,
Subdivision, Reparameterization and Composite Hermite curves (C^n and G^n continuity).
- Bezier curves - Control polygons and Bernstein basis, DeCasteljau algorithm, First and second derivatives at the ends, Continuity aspects.
- B-Spline Curves - periodic, open and non-uniform knot vectors and
corresponding curves, Rational B-splines, NURBS, and Quadratic variety.
- Transformations in 2D and 3D, affine transformation.
- Hermite Surface - Algebraic and geometric form, Subdivision and Reparameterization, Continuity of surfaces
- Bezier surface - Control net representation, Direct and indirect DeCasteljau algorithm for Bezier surface, Continuity aspects.
- B-Spline Surfaces - periodic, open and non-uniform knot vectors and
corresponding surfaces, Rational B-splines, NURBS.
- Intoduction to Solid Modeling - Topology of surfaces, Euler and
modified form of equations.
- Representations - Quadtree, Octree, Halfspace, Boundary Representation
(B-Rep), Constructive Solid Geometry (CSG)
- Boolean operations in 2D - Set membership classification, Union, Difference and Intersection
Books
- Geometric Modeling, Michael E. Mortenson
- Mathematical Elements of Computer Graphics, David Rogers and Alan Adams
- Curves and Surfaces for CAGD, Geral E. Farin
- Introduction to Solid Modeling, Martii Mantyla
Requirements
First of all, the student should show willingness to learn. This course will require the students to
possess basic knowledge on "C" programming (which they would have gained through ED1200,
Introduction to computation and visualization). As the course is only in the third semester, students have sufficient
time (during their holidays) to brush up their C programming and learn the basics/update OpenGL knowledge. In particular, the students should start learning on dynamic memory allocation for single, double, triple pointers and random number generation.
The course is a combination of mathematical foundations and implementation of curves, surfaces
and solids. Students are expected to put in a lot of effort during this course, as is the case for
other courses.
Installation and downloadables
Grading Policy
- Six Assignments - 30 marks
- Two quizzes - 15 marks each
- End Semester - 40 marks
Attendance Policy
- Attendance will be taken at the start of each class, and NOT towards the end.
- Students will get atttendance for the class only if they enter before I finish my call for all student names.
- Absent for medical reason should be supported by medical certificate from appropriate authority.
- Mid-semester attendance report will be sent to all the students (or only the class leader). Students, short of attendance, are supposed to take corrective action.
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