**6.1 CAD surface modelling – Middle end**

The surface model uses mathematical tools that allow creation of complex shapes with greater interactivity. The geometry created in a model of surfaces have no thickness, geometry is a "shell" and therefore no mass and centre of gravity (although it can be estimated). These are the main features of a CAD surface model. In CAD, the modelled objects may be closed. Surfaces are created using interpolation between the lateral and longitudinal representing the outline of the geometry. Although current CAD systems can identify regions of the opposite surface, this does not necessarily represent regions of an internal or external object.

The surface modelling CAD systems are able to perform the modelling of any geometric shape, regardless of their complexity. They have sophisticated features for manipulation of the geometry modelled by allowing the geometry to be changed interactively to obtain the desired product. The manipulation of the surface is given by the movement of any point of the geometry in any direction.

Besides this possibility, four are associated tangent vectors at each point on the surface. Vectors can be edited as the direction and magnitude. These devices allow changing any part of the surface. The possibility and ease of editing of any point of geometry, ensuring continuity of tangency and curvature, is an important feature that distinguishes the CAD surface model.

Figure 19 illustrates examples of issues in the geometric model. In this case, using point geometry (Figure a) there were three editions: Figure b) point geometry has moved in the vertical direction, Y axis in this case. It is observed that the geometry accompanying the extent varied. Figure c) pushed up the value of the magnitude of a vector. Figure d) has changed the angle of one of the vectors. Importantly, the changes in vector magnitude and slope can occur before and/or after the selected point.

It should be noted also that the edited point corresponds to an intersection between a lateral and longitudinal. So when it wants to change a point on the surface where there is no such intersection, the user must create lateral and longitudinal in order to obtain an intersection point. The creation of these entities is trivial in geometric surface models. However, the interactivity to identify their position is characteristic of each specific software, facilitating or hindering the work for the user.

The continuity of a surface can be considered in a simplified form as its degree of smoothness. Surfaces are called Class A high-quality surfaces in terms of continuity of tangency and curvature. This term is often used in the automotive industry (Souza & Ulbrich, 2009).

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

The surface model uses mathematical tools that allow creation of complex shapes with greater interactivity. The geometry created in a model of surfaces have no thickness, geometry is a "shell" and therefore no mass and centre of gravity (although it can be estimated). These are the main features of a CAD surface model. In CAD, the modelled objects may be closed. Surfaces are created using interpolation between the lateral and longitudinal representing the outline of the geometry. Although current CAD systems can identify regions of the opposite surface, this does not necessarily represent regions of an

The surface modelling CAD systems are able to perform the modelling of any geometric shape, regardless of their complexity. They have sophisticated features for manipulation of the geometry modelled by allowing the geometry to be changed interactively to obtain the desired product. The manipulation of the surface is given by the movement of any point of

Besides this possibility, four are associated tangent vectors at each point on the surface. Vectors can be edited as the direction and magnitude. These devices allow changing any part of the surface. The possibility and ease of editing of any point of geometry, ensuring continuity of tangency and curvature, is an important feature that distinguishes the CAD

Figure 19 illustrates examples of issues in the geometric model. In this case, using point geometry (Figure a) there were three editions: Figure b) point geometry has moved in the vertical direction, Y axis in this case. It is observed that the geometry accompanying the extent varied. Figure c) pushed up the value of the magnitude of a vector. Figure d) has changed the angle of one of the vectors. Importantly, the changes in vector magnitude and

It should be noted also that the edited point corresponds to an intersection between a lateral and longitudinal. So when it wants to change a point on the surface where there is no such intersection, the user must create lateral and longitudinal in order to obtain an intersection point. The creation of these entities is trivial in geometric surface models. However, the interactivity to identify their position is characteristic of each specific software, facilitating or

The continuity of a surface can be considered in a simplified form as its degree of smoothness. Surfaces are called Class A high-quality surfaces in terms of continuity of tangency and curvature. This term is often used in the automotive industry (Souza &

shown below.

internal or external object.

the geometry in any direction.

hindering the work for the user.

slope can occur before and/or after the selected point.

surface model.

Ulbrich, 2009).

**6.1 CAD surface modelling – Middle end** 

Fig. 19. Geometric edition on the surface
