# Curves and Surfaces, CAGD

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts) :
CAGD:
Control points (instead of data to be interpolated or approximated)
Bézier curves and de Casteljau algorithm. NURBS
Bernstein basis on a triangle (or a simplex), Bézier surfaces
From continuity conditions to geometric conditions on control points
Surfaces :
Generalised interpolation; solving ODE or PDE by generalised interpolation or generalised mean squares.
Tensor product of functions
Finite elements in the Bernstein basis
Polyharmonic splines
The student will be able to :
CAGD: use a CAGD software to build a form with specified features (e.g. a hand)
Curves :
Draw a Bézier curve by using de Casteljau algorithm
Determine a B-spline curve (a NURBS curve) and the associated de Casteljau algorithm.
Surfaces :
Choose a type of multivariate function in order to solve a concrete problem (tensor product function, finite elements, radial basis functions, polyharmonc splines...), and handle these functions.

## Needed prerequisite

Cubic splines
Multivariate functions
Basis of functional analysis (functional optimisation, distributions, Hilbert spaces)
Stability and condition number
Use of matlab

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...