دانلود رایگان مقاله مدل سازی هندسی متغیر با محدودیت جعبه سیاه و DAGs

Abstract

CAD modelers enable designers to construct complex 3D shapes with high-level B-Rep operators. This avoids the burden of low level geometric manipulations. However a gap still exists between the shape that the designers have in mind and the way they have to decompose it into a sequence of modeling steps. To bridge this gap, Variational Modeling enables designers to specify constraints the shape must respect. The constraints are converted into an explicit system of mathematical equations (potentially with some inequalities) which the modeler numerically solves. However, most of available programs are 2D sketchers, basically because in higher dimension some constraints may have complex mathematical expressions. This paper introduces a new approach to sketch constrained 3D shapes. The main idea is to replace explicit systems of mathematical equations with (mainly) Computer Graphics routines considered as Black Box Constraints. The obvious difficulty is that the arguments of all routines must have known numerical values. The paper shows how to solve this issue, i.e., how to solve and optimize without equations. The feasibility and promises of this approach are illustrated with the developed DECO (Deformation by Constraints) prototype.

6. Conclusion

The DECO prototype described in this paper showed the feasibility and the promises of variational geometric modeling with black box DAGs, i.e., without equations. The proposed examples do not cover all the potential cases in geometric design but the reader can imagine that different or more complex examples can be treated with the same approach. The energy to minimize can be easily changed depending on the user’s goal. The user can also create simple constraints and use them to create his/her more elaborate ones. This work raises several issues, which are actually scientific locks. We mention some of them in the following.