Computer Aided Geometric Design

LearnCAx introduces a six week course that enables you to master the geometrical and mathematical techniques used in CAD software by programming them yourself. The course consists of a number of conventional lectures which includes fundamental, core and advanced topics. Computer Aided Geometric Design (CAGD) underlies applications from computer animation and special eff ects, to advanced modelling software for industrial design and architecture, to rapid prototyping machines that print 3-D objects in plastic, and many others. Geometric models represent the shapes and spatial relationships of the environment that is being studied, permitting a much deeper analysis than would be possible otherwise.
CAGD is the basis for modern design in most branches of industry, from naval, aeronautics to textile industry. The course aims to lay foundations of geometric and mathematical concepts which are needed to understand 3D modelling used in design software like AutoCAD, SolidWorks etc. The course focuses on algorithms & programming those algorithms step by step. The programming language used is C++ but they can be replicated in any language.

Ideal for:

  • Engineering Graduates and Post-Graduates (B.E / B.Tech / M.E. / M. Tech in Aerospace, Automobile, Mechanical, Computer Science, Industrial Production, Chemical, Petro-chemical, Bio-chemical and Bio-medical).
  • Third Year or Final Year Engineering Students.
  • Final Year B.E Students who are aspiring for higher education abroad
  • Working Professionals in Design, Manufacturing and Service Industry

Course Pre-requisites
Course has no prerequisites but participants having knowledge of C++ would get extra advantage.

Course Content
This course will introduce you to fundamentals of CAGD and will progress towards detailed algorithms using programming. The course provides knowledge of geometry and mathematical fundamentals and how to use various algorithms while solving CAD related problems.

Matrix and Vector Algebra 

  • Matrix
  • Operation on Matrices
  • Systems of Linear equations
  • Vectors
  • Operation on Vectors


  • 2D Transformations
  • 3D Transformation
  • Projections

Differential Geometry

  • Implicit and explicit representation
  • Arc Length
  • Tangent Vector and Tangent Line
  • Normal Vector and Curvature
  • Binormal vector and Torsion

Parametric Polynomial Curve 

  • Ferguson Curves
  • Hermite Coons

Bezier Curves 

  • Goals of mathematical curve de nition
  • Introduction to Bezier
  • Construction and Properties
  • Moving Control Points
  • De Casteljau’s Algorithm
  • Derivatives of a Bezier Curve
  • Subdividing a Bezier Curve
  • Degree Elevation of a Bezier Curve
  • Continuity Conditions
  • Parametric Continuity
  • Geometric Continuity

B-Spline Curves 

  • Introduction
  • Basis Function
  • Knot Vectors
  • Control Points
  • Construction and Properties
  • Open And Close Curves
  • Moving Control Points
  • Modifying Knots
  • Algorithms: De Boor Algorithm
  • Knot Insertion
  • Subdividing a B-Spline Curve


  • Basic Concepts of Surfaces
  • Bezier Surfaces
  • NURBS Surfaces


  • Intersection in 2D-Linear Components and Linear Components
  • Linear Components and Quadratic curves
  • Linear Components and Polynomial curves
  • Intersection in 3D-Linear Components and Planar Components
  • Linear Components and Quadric surfaces
  • Linear Components and Polynomial Surfaces


  • Projection of a point on Line
  • Projection of a point on Plane
  • Projection of a point on Curve
  • Projection of a curve on surface
  • Projection of a surface on surface

Demo Videos:

Determinant of a Matrix

Visualizing Linear Equations

Transpose of a Matrix

Course benefits:

The course aims to help participants get conversant with complex techniques of geometric designs and the applications. The conceptual foundation is the key to solve unassuming challenges faced in industrial application. This courses bridges the gap between theory and practice, as all the concepts and algorithms that you learn from video would be implemented in an application using C++ programming language. The development environment would be Visual Studio 2010 on windows, but the programs would run on other platforms too. Participants of this course would be provided a Visualization tool called “Vis3D” to see results of their algorithms in 2D and 3D.
In addition to all the benefits of an online course, the Learning Management System (LMS) tries to simulate as close as possible to class environment. Participants not only take courses, give tests and submit assignments but also discuss their problem with experience faculty at their convenience.

Course Format
The course consists of lecture videos, which are broken into small chunks, usually between eight and twelve minutes each. Total duration of the course would be six weeks. There will be approximately two to three hours of video content per week. There would be a problem set and programming assignment each week and there would also be a final exam at the end of the course before certificate.

Learning Support 


LearnCAx faculties mentor the particpants and are available to answer the queries raised. All possible efforts are made to every query and in special cases we also do conduct skype sessions to resolve the queries in time and facilitate learning process. LearnCAx faculty team comes from with a background of research and training and have vast industrial experience in computational domain.

Other Courses
Geometric Algorithms

CFD Courses:

  • CFD Modeling Using ANSYS ICEM CFD & ANSYS Fluent
    CFD Modeling Using STAR-CCM+ & STAR-CD
    Multiphase Flow Modeling Using ANSYS Fluent

Contact Us
LearnCAx (Initiative by Centre for Computational Technologies Pvt. Ltd)
1 Akshay Residency, 50 Anand Park, Aundh, Pune: 411007. India
Ph: +91 20 40098382, M: +91-8380097760


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