**6.3 Curvature continuity**

The continuity of geometry is one way to assess the quality of a geometric entity generated by CAD software. The level of continuity of geometry is related to the degree of smoothness along its length. Geometry can represent discontinuous aesthetic and functional implications in a product. The continuity of surfaces is a concept used to extrapolate the curves. Thus, it is used the concepts of continuity of curves to present and discuss this topic. A discontinuous curve may generate a discontinuous surface. The continuity of a geometry, curve or surface, can happen in two cases:


There are three size classes for the continuity of curves and surfaces.


Figure 24 illustrates the case for continuity in the connection between two different curves, connected by a user or other mechanism of software construction, as in the construction of borders to make cuts at the intersection of surfaces. These boundaries are spline curves calculated by the software and have degree of continuity. The quality of this curve can influence the surface generated by it.

As mentioned, the continuity can occur along a single curve, depending on the model used for its representation.

These are resources that help advanced modelling of complex geometries containing forms.

The continuity of geometry is one way to assess the quality of a geometric entity generated by CAD software. The level of continuity of geometry is related to the degree of smoothness along its length. Geometry can represent discontinuous aesthetic and functional implications in a product. The continuity of surfaces is a concept used to extrapolate the curves. Thus, it is used the concepts of continuity of curves to present and discuss this topic. A discontinuous curve may generate a discontinuous surface. The continuity of a geometry,

1. **Continuity of position:** occurs when two segments of the same entity or two separate entities, have in common only the point of contact (Figure 24b). This is the case of less

2. **Continuity of position and tangent:** occurs when a point between the segments analyzed, or two separate entities, have in common other than the contact tangent

3. **Continuity of position, tangency and curvature:** occurs when a point between the segments analyzed, or two different geometries have in common, the contact point, tangent vector and the same degree of curvature (Figure 24d). This is the case for better

Figure 24 illustrates the case for continuity in the connection between two different curves, connected by a user or other mechanism of software construction, as in the construction of borders to make cuts at the intersection of surfaces. These boundaries are spline curves calculated by the software and have degree of continuity. The quality of this curve can

As mentioned, the continuity can occur along a single curve, depending on the model used

Fig. 23. Changed the influence of the point P2 on the curve

b. Continuity in the connection between two distinct entities.

There are three size classes for the continuity of curves and surfaces.

**6.3 Curvature continuity** 

curve or surface, can happen in two cases:

a. Going over a single entity.

smoothness.

continuity.

for its representation.

vectors (Figure 24c).

influence the surface generated by it.

This can partition the curve internally into segments known as patches, and it often is not noticed by the user.

Fig. 24. Degree of continuity of continuity of a curve
