The geometric continuity

Geometric Continuity with Interpolating

The Bezier formulation for parametric curves has many quali ties, among them the intuitive relationship between the shape of the control polygon and the shape of the curve , and the case of computation and subdivision. Other formulations , however, have become more popular because they offer local control, or because they are interpolating, or even more recently because they provide the added f...

Continuity and geometric logic

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieck’s view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers an...

On Geometric Continuity of Isophotes

It is a well known fact that we can deduce G continuous isophotes from a G continuous surface This paper gives answer to the reverse problem we deduce a G continuous surface from G continu ous isophotes on the surface We show how many families of isophotes we have to consider and what constraints apply Furthermore we apply the geodesic curvature and the thickness of isophotes as a surface inter...

Geometric continuity and convex combination patches

Geometric Continuity CG of Blending Curves

This paper deals with the study of the linear interpolation between C1G2 piecewise continuous curves. We establish some criteria to maintain C1G2 continuity for the linear interpolation constructed curves. For practice, we give an approach to maintain theC1G2 continuity of Bézier curves shape-blending process by adjusting the control points. We finish by proving and justifying the efficiency of...