Geometric Primitives Based Deformation Techniques For Arbitrary Meshes

Surface modeling plays an important role in the fields of product design, computer animation, and games. Continuous surfaces, typically in NURBS form, have been widely used due to their accurate mathematical expressions. They are efficient in storage and offer benefits in shape manipulations. However, NURBS surfaces are incapable of representing objects with complex topologies. Recently laser scan technology has been improved significantly and becomes a viable option in capturing geometries of complicated objects. Meshes reconstructed from scanned data are capable of representing complex shapes for product design and biological shapes for computer animation and games. However, processing meshes is a rather difficult task since it is hard to find the intrinsic properties, such as topology, curvature, and sampling from the geometric data using traditional tools.For free form modeling, Sederberg and Parry introduced a method capable of performing very large surface deformations using a lattice around the model or using constraints to directly manipulate the vertices of the given mesh. It is a powerful technique to generate a desired shape from a given model. FFDs (Free-Form Deformations) techniques, unlike other modeling techniques, which create completely new models, deform the given meshes globally or locally and generate the deformed meshes. In general, there are two types of FFDs: deformation with a lattice and deformation with constraints.We present an approach to deform arbitrary meshes based on geometric primitives. The basic idea is to predefine a certain set of geometric primitives, such as points, curves, spheres, cubes and deform the specific areas of the objects aligning those of the given geometric primitives. In general, point and curve primitives are able to provide sharp corners and ridge features; sphere primitives are able to achieve smoothing effects and provide semi-sharp features; and cube primitives are able to handle sharp corners, sharp edges and flat faces with the corners, edges and faces of the cubesrespectively. We use Bezier-shaped displacement reference curves to determine the new position of the vertices on the deforming surfaces. The proposed approach is fast and robust, and can support real-time interactive mesh editing and handle arbitrary meshes thanks to re-sampling and subdivision operations.The proposed method has the following properties:Area control: Users can specify the deforming area of the given mesh with a closed path on the surface to define the influence region of the deformation. Only the geometries in deforming area may be deformed according to editing operations. Users are also given the option to determine if the transition near the path should be smooth.Arbitrary mesh handling: The proposed method can handle meshes with arbitrary topologies, such as meshes with arbitrary number of genus.Geometric primitives based editing: predefined geometric primitives are simple but efficient to provide variant of deforming operations in real-time.