Syllabus

Introduction to Computer Graphics:
Overview of Computer Graphics, Computer Graphics Application and Software (Description of some graphics devices, Input Devices for Operator Interaction, Display Technologies)

Geometric Modeling:
Basics of Geometric and Solid Modeling, Conventions, Mathematical Representation of Geometric Elements.

Transformations:
2D and 3D Transformations, Translations, Rotation, Reflection, Scaling, Homogeneous Coordinates and Matrix Representation, Combined Transformation, Solid Body Transformations, Rotation About an Arbitrary Point, Reflection through an Arbitrary Line, Rotation about an Arbitrary Axis in Space, Reflection through an Arbitrary Plane, Affine and Perspective Geometry, Perspective Transformations, Vanishing Points, Orthographic Projections, Axonometric Projections, Oblique Projections.

•Curves:
Parametric Curves, Conic Curves, Representation of Space Curves, Parametric Cubic Curves, Cubic Splines, Hermite, Bezier, B-spline and Rational B-spline Curves, Composite Curves, Reparameterization.

Surfaces:
Parametric Surfaces, Tangent & Twist Vectors, Reparameterization, Plane Surface, 16 point form, 4 curve form surface, Ruled Surface, Surface of Revolution, Tabulated Cylinder, Lofted Surface, BicubicSurface, Bezier, B-spline Surfaces, Coons Patch, Offset Surface, Rational Surface.

Solid Modeling:
Solid Models and Representation Schemes, Fundamentals of Solid Modeling, Pure Primitive Instancing, Half spaces, Spatial Occupancy Enumeration, Cell Decomposition, OctreeEncoding, Constructive Solid Geometry (CSG), Boundary Representation (B-Rep), Sweep Representation, Analytical Solid Modeling.

Students will understand computer graphics principles applications in design and Solid representations in computer graphics.

Students will apply 2D/3D transformations including translation, rotation, reflection, and scaling using homogeneous coordinates and matrix representations.

Students will implement various projection systems including perspective transformations with vanishing points, orthographic projections, axonometric projections, and oblique projections.

Students will design parametric curves including cubic splines, Hermite, Bézier, B-spline, and rational B-spline curves for geometric modeling applications.

Students will create parametric surfaces, ruled surfaces, surfaces of revolution, and implement Bézier and B-spline surfaces for 3D modeling.

Students will understand computer graphics principles, applications in design, and solid representations in computer graphics.

Students will apply 2D/3D transformations, including translation, rotation, reflection, and scaling, using homogeneous coordinates and matrix representations.

Students will implement various projection systems, including perspective transformations with vanishing points, orthographic projections, axonometric projections, and oblique projections.

Students will design parametric curves, including cubic splines, Hermite, Bézier, B-spline, and rational B-spline curves for geometric modeling applications.

Students will create parametric surfaces, ruled surfaces, surfaces of revolution, and implement Bézier and B-spline surfaces for 3D modeling.

Donald Hearn, M. Pauline Baker, Warren Carithers, omputer Graphics with OpenGL, Pearson Education , This book is a comprehensive resource for computer graphics, covering fundamental principles, 2D/3D transformations, projection systems (perspective, orthographic, etc.), and geometric modeling. It includes practical implementations using OpenGL, making it suitable for understanding solid representations and transformations. The book also introduces curves and surfaces.

James D. Foley, Andries van Dam, Steven K. Feiner, John F. Hughes, Computer Graphics: Principles and Practice, Addison-Wesley , This is a foundational text in computer graphics, often referred to as the "bible" of the field. It covers transformations, projections, and advanced topics like parametric curves (Bézier, B-splines) and surfaces. It provides both theoretical insights and practical applications for geometric modeling.

David F. Rogers, J. Alan Adams, Mathematical Elements for Computer Graphics, McGraw-Hill Education , This book focuses on the mathematical foundations of computer graphics, including transformations (translation, rotation, scaling), projections, and parametric curves/surfaces (Bézier, B-splines). It is particularly useful for students seeking a deeper understanding of the mathematical aspects of Geometric and Solid Modelling.

Gerald Farin, Curves and Surfaces for Computer-Aided Geometric Design –A Practical Guide, Morgan Kaufmann , This book specializes in computer-aided geometric design (CAGD), covering parametric curves (cubic splines, Hermite, Bézier, B-splines) and surfaces in detail. It is an excellent resource for providing practical guidance for implementing geometric modeling techniques in design applications.

Journals
ACM Transactions on Graphics (TOG)
Computer-Aided Design (CAD)
IEEE Computer Graphics and Applications

Conferences
SIGGRAPH (Special Interest Group on Computer Graphics and Interactive Techniques)
Symposium on Geometry Processing (SGP)