NOTE: Attempt any FIVE questions selecting at least TWO questions from each section.

Section-I (4/9)

Euclidean Geometry

•    Basic concepts of Euclidean geometry

•    Scalar and vector functions

•    Barycentric coordinates

•    Convex hull

•    Affine maps: Translation, Rotation, Scaling, Reflection and shear

Approximation using Polynomials

•    Curve Fitting: Least squares line fitting, Least squares power fit, Data linearization method for exponential functions, Nonlinear least-squares method for exponential functions, Transformations for data linearization, Linear least squares, Polynomial fitting

•    Chebyshev polynomials, Padé approximations



Section-II (5/9)

 Parametric Curves (Scalar and Vector Case)

•    Cubic algebraic form

•    Cubic Hermite form

•    Cubic control point form

•    Bernstein Bezier cubic form

•    Bernstein Bezier general form

•    Uniform B-Spline cubic form

•    Matrix forms of parametric curves

•    Rational quadratic form

•    Rational cubic form

•    Tensor product surface, Bernstein Bezier cubic patch, Quadratic by cubic Bernstein Bezier patch, Bernstein Bezier quartic patch

•    Properties of Bernstein Bezier form: Convex hull property, Affine invariance property, Variation diminishing property

•    Algorithms to compute Bernstein Bezier form

•    Derivation of Uniform B-Spline form

Spline Functions

•    Introduction to splines

•    Cubic Hermite splines

•    End conditions of cubic splines: Clamped conditions, Natural conditions, 2nd Derivative conditions, Periodic conditions, Not a knot conditions

•    General Splines: Natural splines, Periodic splines

•    Truncated power function, Representation of spline in terms of truncated power functions, examples