**6. Application of CAD systems**

A CAD (Computer Aided Design/Drafting) has been developing to assist the design and part modelling through interaction with the computer which defines all geometric information necessary for manufacture. Currently there are a large number of systems available in the market, ranging in a first classification between 2D and 3D systems.

It should be aware that a CAD system may be more suitable for specific applications, and many of these systems should not be considered competitors. This is because there are CAD systems to meet product development activities and geometrical design which has powerful tools for modelling complex shapes, as well as CAD systems that supply more design functions properly. It is common to find companies working with 3D CAD systems inadequate to the tasks assigned.

Advanced Free Form Manufacturing by Computer Aided Systems – Cax 577

The quality of a curve is related to the mathematics used for this representation. Advanced CAD systems can offer different possibilities to generate a curve, in order to allow

Using parametric polynomial equations, Bezier-based methodology, the developers responsible for the development of each CAD software creates specific mathematical resources in order to allow greater control and ease of work to the user. This development of each software house is confidential and may represent the differential of the CAD software. Thus, only generic formulations of curves are discussed in the user guides for each software. Therefore, we will discuss below, some methodologies that differ from the creation of

Other mathematical formulations based on Bezier method have been developed for the representation of curves and surfaces in computer systems. The B-spline curve is also used for a parametric polynomial equation with modifications of the proposal Bezier, allowing among other things, to represent a curve using a polynomial of low degree, facilitating

The Spline NURBS (Non-Uniform Rational B-Spline) represents the state of the art for the representation of curves and surfaces in CAD system, providing better control of the curve, allowing local issues, and allows more efficient calculation. Basically, the methodology is

Fig. 19. Geometric edition on the surface

curves in different CAD systems.

**6.2 Mathematics for constructing curves** 

modelling of complex geometric forms, smooth and seamless.

computations, also allowing local changes of the curve.

based on NURBS B-Spline method, adding two main functions:

To assist in the correct definition of a specific CAD platform for a given application, CAD systems can be classified as: i) Low-end 2D CAD systems, ii) Middle-end 3D CAD systems modelling of solid objects or surfaces, iii) High-end CAD hybrid system allows the modelling of solid objects and surfaces, among other features. A CAD solid or surface model refers to its core used for the mathematical representation of three-dimensional objects as shown below.
