Forschungs- & Entwicklungsinformationsdienst der Gemeinschaft - CORDIS

Algebraic and numeric methods

This toolkit is intended to experiment on new algorithms in CAGD by using simultaneously algebraic, geometrical and numerical techniques.

It will be presented as a new Maple toolbox and its use will be web provided under request.

The main capabilities of this toolbox are:
Generation of polynomial and rational b-spline curves and surfaces:
- Reading IGES/VDA format
- Plotting IGES/VDA format

Polynomial and rational b-spline curve/surface manipulation Numerical generation of polynomial and rational B-spline curves and surfaces.

Computation of the B-spline curve/surfaces derivatives, using:
- Basis function method
- Control point method.
- Knot vector refinement.
- Bezier decomposition.
- Approximate implicitation.
- Offset computations.
- Approximation of rational B-spline curves/surfaces with polynomial ones, degree raising.

A small cagd system with exact/mixed arithmetic Experimentations with precision by using symbolic and numerical techniques.

Exact and generic implicititation.
- A-splines manipulation.
- Topologically reliable computation of f(x,y)=0 and g(x,y,z)=0.
- Symbolic/Numerical Polynomial System Solving (connection to external software in some cases).

Curve and surface intersections:
- Implicit-implicit
- Parametric-implicit
- Parametric-parametric
- Tangential intersections curve tracing through ode numerical solving Code generation (C, Visual Basic, ...) when possible.

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