Fast,Exact and Robust Set Operations on Polyhedrons Using Localized Constructive Solid Geometry Trees

Regularized Boolean operations have been widely used in 3D modeling systems. However, evaluating Boolean operations may be quite numerically unstable and time consuming, especially for iterated set operations. A novel and unified technique is proposed in this paper for computing single and iterated set operations efficiently, robustly and exactly. An adaptive octree is combined with a nested constructive solid geometry （CSG） tree by this technique. The intersection handling is restricted to the cells in the octree where intersection actually occurs. Within those cells, a CSG tree template is instanced by the surfaces and the tree is converted to planebased binary space partitioning （BSP） for set evaluation; Moreover, the surface classification is restricted to the ceils in the octree where the surfaces only come from a model and are within the bounding-boxes of other polyhedrons. These two ways bring about the efficiency and scalability of the operations, in terms of runtime and memory. As all surfaces in such a cell have the same classification relation, they are classified as a whole. Robustness and exactness are achieved by integrating plane-based geometry representation with adaptive geometry predicate technique in intersection handling, and by applying divide-and-conquer arithmetic on surface classification. Experimental results demonstrate that the proposed approach can guarantee the robustness of Boolean computations and runs faster than other existing approaches.

AN ALGORITHM OF DISTANCE CALCULATION BETWEEN A BOUNDING SPHERE AND A BOUNDING CSG PRIMITIVE

A simple method for calculating distance between a solid sphere and a constructive solid geometry (CSG) so lid primitive (including block, cone, cylinder, sphere, wedge and torus) is derived to support the collision detection algorithm. By decomposing the whole space into relative positions and geometric features of the sphere and the primitive considered, closed form distance formula are got. These calculations are very useful in the real time collision detection in which primitives are used as bounding volumes of complex objects.

HISTORICAL PROCEDURES AND G-DSG METHOD BASED MANUFACTURING PLANNING

Oriented to CAD/CAM seamless integration, this paper presents an idea for synthetically considering the qualitative history model, which represents the whole course of modeling, and the quantitative geometry model, which contains the extended Brep model, CSG and feature pedigree. History model building captures in background the dynamic interactive definition of engineering requirement and then explicitly conveys the original intention to successive application layers, which is conductive to the decision support of manufacturing planning in not only automatic geometry re constructing but also machining set up. G DSG theory as an earlier achievement is applied to generate the topology independent generalized mid model as an input to manufacturing planning, which is therefore simplified and its accuracy is simultaneously improved. Manufacturing planning lays emphasis on optimizing the mapping in both geometry and function from part itself to detail machining scheme. Comparatively, process planning pays more attention to the mapping to those items like tool, fixture, etc. Theoretically, such an idea is also beneficial to realizing the parametric NC machining trajectory generation and maintaining its dynamic consistency with the update of the design model.[WT5”HZ]

The Possibility of Angle Trisection （A Compass-Straightedge Construction） Kimuya M Alex

The objective of this paper is to provide a provable solution of the ancient Greek problem of trisecting an arbitrary angle employing only compass and straightedge （ruler）. （Pierre Laurent Wantzel, 1837） obscurely presented a proof based on ideas from Galois field showing that, the solution of angle trisection corresponds to solution of the cubic equation; x3 - 3x - 1 = 0, which is geometrically irreducible [1]. The focus of this work is to show the possibility to solve the trisection of an angle by correcting some flawed methods meant for general construction of angles, and exemplify why the stated trisection impossible proof is not geometrically valid. The revealed proof is based on a concept from the Archimedes proposition of straightedge construction [2, 3].

Design factors affecting the dynamic performance of soil suspension in an agitated, baffled tank

The effects of particle size, impeller clearance and impeller speed are assessed to show how condition variations influence power consumption in the water-solid slurry suspension in an agitated tank. The energy efficiency of slurry height variation, impeller type and diameter, and solid movement speed has been investigated with six soil series stirred in a soil-water slurry. Coarser sand particles are observed to significantly increase power consumption, while finer particles, for instance clay, decrease the stirring power requirement. The 3-blade HR100 SUPERMIX? impeller manufactured by SATAKE generally performs more efficiently than a conventional4-pitched blade turbine. The impeller's geometric design, including diameter and number of blades influences the impeller's energy efficiency, and HR100 impellers with greater diameters remarkably reduce power consumption. The tests demonstrated that the power required to provide off-bottom solid suspension and solid dispersion can be reduced dramatically by increasing the slurry height rather than by accelerating the impeller, if this option is possible.

A Sufficient Condition for a Wire-Frame Representing a Solid Modeling Uniquely

Generally speaking, it is impossible for a wire-frame to define a 3D object uniquely. But wire-frame as a graphics medium is still applied in some industrial areas. A sufficient condition is presented in this paper. If this condition is satisfied by a wire-frame, then the wire-frame can represent a 3D object uniquely The result is applied to manufacturing of progressive stripe.