Solid Primitives Research Articles

フィレットのＣＳＧ表現法に関する研究 平面間稜線と頂点まわりの場合

This paper presents how to make a solid model of the fillet volume for rounding corners such as vertices or edges. In order to be able to handle the fillet volume in CSG representation for geometric modeling, Sweep Operation is applied to generate the fillet volume. The outline is described below : 2-D Fillet Pattern, Spine, Sweep Axis and the object which is constructed by cubic primitive solids, are given. Then the fillet pattern, defined on a sectional plane which is normal to the spine, is swept along the sweep axis. Swept Volume consists of a set of space points which are inside or on the fillet patterns from start to end of sweep. Fillet Volume is generated as a result of swept volume, and can be added to the object for modeling of final shape with corner rounding. The algorithm of this work has been implemented in the CAD/CAM system TIPS-1. According to experimental results, it is clear that the work is effective for geometric modeling of an object being constructed by cubic primitive solids and fillet volume.

Screen-Area Coherence for Interactive Scanline Display Algorithms

This article proposes and demonstrates a technique enabling polygon-based scanline hidden-surface algorithms to be used in applications that require a moderate degree of user interaction. Interactive speeds have been achieved through the use of screen-area coherence,a derivative of frame-to-frame coherence and object coherence. This coherence takes advantage of the face that most of the area of the screen does not change from one frame to the next in applications that have constant viewing positions for a number of frames and in which a majority of the image remains the same. One such application, the user interface of constructive solid geometry (CSG) based modelers, allows a user to modify a model by adding, deleting, repositioning, and performing volumetric Boolean operations on solid geometric primitives. Other possible applications include robot simulation, NC verification, facility layout, surface modeling, and some types of animation. In this article, screen-area coherence is used as the rationale for recalculating only those portions of an image that correspond to a geometric change. More specifically, this article describes a scanline hidden-surface removal procedure that uses screen-area coherence to achieve interactive speeds. A display algorithm using screen-area coherence within a CSG-based scanline hidden-surface algorithm was implemented and tested. Screen-area coherence reduced the average frame update time to about one quarter of the original time for three test sequences of CSG modeling operations.

フィレットのＣＳＧ表現法に関する研究 二次曲面間相貫線まわりの場合

This paper presents how to make a solid model of the fillet volume which surrounds the intersection line between two quadratic surfaces. In order to be able to handle the fillet volume in CSG representation method for geometric modeling, Sweep Operation is applied to generate fillet volume. The outline is described below : Two primitive solids with quadratic surfaces, such as cylinder, cone or sphere, are given in a condition of being connected to each other, then their intersection lines are led analytically. 2-D fillet pattern, defined on a sectional plane which crosses the intersection line, is swept along the intersection line. Swept Volume consists of a set of space points which are inside or on the fillet patterns from start to end of sweep. Fillet Volume is generated as a result of swept volume, and can be handled the same as the primitive solids. The algorithm of this work has been implemented in the CAD/CAM system TIPS-1. According to experimental results, it became clear that the work was effective for geometric modeling of an object constructed by quadratic surfaces and fillet volume.

An apporach to automatic three‐dimensional finite element mesh generation

AbstractRecently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well‐proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi‐automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three‐dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so‐called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.

Solid modeling for architectural design using octpaths

A modeling system for Architectural Design which is based on a very general data structure is presented. Octpaths break the modeling space into solid and not solid material thus describing an entire volume of 3-D objects. Boolean operators are used to combine solid primitives. Very efficient algorithms allow the design of complex objects in a limited raster-oriented computing environment.

A null-object detection algorithm for constructive solid geometry

Constructive solid geometry ( CSG ) is the primary scheme used for representing solid objects in many contemporary solid modeling systems. A CSG representation is a binary tree whose nonterminal nodes represent Boolean operations and whose terminal nodes represent primitive solids. This paper deals with algorithms that operate directly on CSG representations to solve two computationally difficult geometric problems—null-object detection ( NOD ) and same-object detection ( SOD ). The paper also shows that CSG trees representing null objects may be reduced to null trees through the use of a new concept called primitive redundancy, and that, on average, tree reduction can be done efficiently by a new technique called spatial localization. Primitive redundancy and spatial localization enable a single complex instance of NOD to be converted into a number of simpler subproblems and lead to more efficient algorithms than those previously known.

A new class of transitional blended finite elements for the analysis of solid structures

AbstractRecently developed computer aided design systems for the design and modification of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, etc.) and macro solids (combinations of primitives). To provide an effective finite element analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled finite element mesh. In this paper we describe a new class of transitional blended finite elements which make substantially simpler the task of finite element mesh generation and local mesh refinement. Computational experience indicates that numerical accuracy is not compromised by use of these flexible elements.

Global and local deformations of solid primitives

New hierarchical solid modeling operations are developed, which simulate twisting, bending, tapering, or similar transformations of geometric objects. The chief result is that the normal vector of an arbitrarily deformed smooth surface can be calculated directly from the surface normal vector of the undeformed surface and a transformation matrix. Deformations are easily combined in a hierarchical structure, creating complex objects from simpler ones. The position vectors and normal vectors in the simpler objects are used to calculate the position and normal vectors in the more complex forms; each level in the deformation hierarchy requires an additional matrix multiply for the normal vector calculation. Deformations are important and highly intuitive operations which ease the control and rendering of large families of three-dimensional geometric shapes.

Ray casting for modeling solids

This paper presents ray casting as the methodological basis for a CAD/CAM solid modeling system. Solid objects are modeled by combining primitive solids, such as blocks and cylinders, using the set operators union, intersection, and difference. To visualize and analyze the composite solids modeled, virtual light rays are cast as probes. By virtue of its simplicity, ray casting is reliable and extensible. The most difficult mathematical problem is finding line-surface intersection points. So surfaces such as planes, quadrics, tori, and probably even parametric surface patches may bound the primitive solids. The adequacy and efficiency of ray casting are issues addressed here. A fast picture generation capability for interactive modeling is the biggest challenge. New methods are presented, accompanied by sample pictures and CPU times, to meet the challenge.

The synthesis of solids bounded by many faces

A technique is presented which allows a class of solid objects to be synthesized and stored using a computer. Synthesis begins with primitive solids like a cube, wedge, or cylinder. Any solid can be moved, scaled, or rotated. Solids may also be added together or subtracted. Two algorithms to perform addition are described. For practical designers, the technique has the advantage that operations are concise, readily composed, and are given in terms of easily imagined solids. Quite short sequences of operations suffice to build up complex solids bounded by many faces.