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Curves and Surfaces, CAGD


At the end of this module, the student will have understood and be able to explain (main concepts) :
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
Radial basis functions
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...