A new parametric control method for freeform mesh models

Parametric modeling technology is difficult to apply to freeform mesh models since there is no efficient way to impose geometric constraints. In this paper, we propose a novel method to control freeform mesh models parametrically. Our approach is to construct a control mesh that surrounds an object model and then impose constraints on it. The control mesh is parametrically controlled and the shape of the object model is modified by using an existing freeform deformation method.This paper is mainly concerned with automated construction of a control mesh and treatment of geometric constraints. Procedures for creating a control mesh are as follows: 1) determine the optimal orientation of the model, 2) project the model along three axes and extract contours, 3) create 2D control polygons for the contours, and 4) construct the 3D control mesh from the 2D control polygons. Geometric constraints are imposed on the edges and faces of a control mesh. Types of constraints are given by either a relative relationship between elements or an absolute displacement. A new control mesh is calculated by solving these constraints and the original model is modified accordingly. We tested our algorithms for two freeform models.

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