Quadtree representation of two-dimensional objects is performed with a tree that describes the recursive subdivision of the more complex parts of a picture until the desired resolution is reached. At the end, all the leaves of the tree are square cells that lie completely inside or outside the object. There are two great disadvantages in the use of quadtrees as a representation scheme for objects in geometric modeling system: The amount of memory required for polygonal objects is too great, and it is difficult to recompute the boundary representation of the object after some Boolean operations have been performed. In the present paper a new class of quadtrees, in which nodes may contain zero or one edge, is introduced. By using these quadtrees, storage requirements are reduced and it is possible to obtain the exact backward conversion to boundary representation. Algorithms for the generation of the quadtree, Boolean operations, and recomputation of the boundary representation are presented, and their complexities in time and space are discussed. Three-dimensional algorithms working on octrees are also presented. Their use in the geometric modeling of three-dimensional polyhedral objects is discussed.

Dental impaction defines a tooth that, instead of erupting to occupy its functional position, is partially or totally retained and remains within the bone. Retained teeth can be placed in the normal arch position through a combination of orthodontics and conventional surgical techniques, or a combination of orthodontics and laser surgery, as in the case here presented of a 14-year-old boy with an impacted first mandibular premolar, covered by bone, and with complete root formation and an erupted second premolar. The impacted premolar was surgically exposed using an Er,Cr:YSGG laser and at the same time an orthodontic bracket was bonded to provide traction to move the first premolar into its arch position.

Similar to other machinery products, numerous analysis and tests would consume large amount of manpower and resources before paddy machinery putting into the mass markets. A method to establish the Virtual Proving Ground (VPG) for paddy machinery is proposed. Parameters stored with model nodes are obtained by collision detection between machine and scene. Motion equations of transplanting mechanism are derived with some simple transformations referring to a rice transplanter. Then working process simulation of the rice transplanter in virtual reality environment is realized by calling functions encapsulated in Vega Prime in a VC++ environment. Moreover some solutions for researching virtual testing are proposed.

In order to making the virtual experiment results close to or equivalent to the real environmental effects, in addition to model realistic scenes, also need more accurate dynamic model. In this paper, based on research of hydraulic steering paddy and wheat combine harvester, first, used three-dimensional geometric model transformation technology to convert Pro/E model to a identified geometric model in VP virtual reality systems, second, used classical dynamics equations to build the mathematical model of this vehicle dynamics, finally, used VC++ programs to connect this two models, constructed a behavioral model of complete physics properties. This behavior model is not only more realistic than the geometry model in motion, but also it follows the laws of physics movement. It can effectively strengthen the authenticity of virtual experiment, provide an important platform to start agricultural machinery virtual characteristics test, and this Modeling Method can provide a reference for other agricultural machinery virtual reality platform to build.