Interactive Boolean operations for conceptual design of 3-D solids

Abstract

Interactive modeling of 3-D solids is an important and difficult problem in computer graphics. The Constructive Solid Geometry (CSG) modeling scheme is highly attractive for interactive design, due to its support for hierarchical modeling and Boolean operations. Unfortunately, current algorithms for interactive display of CSG models require expensive special-purpose hardware that is not easily available.In this paper we present a method for interactive display of CSG models using standard, widely available graphics hardware. The method enables the user to interactively modify the affine transformations associated with CSG sub-objects. The application we focus upon is that of conceptual design, a stage in the design process in which rapid, interactive visualization of the model and high-level design operations are of crucial importance, while the objects are relatively simple.The method converts the CSG graph to a novel Convex Differences Aggregate(CDA) representation. The CDA utilizes graph re-writing techniques, efficient geometric algorithms on convex objects and a built-in hierarchical acceleration scheme. The CDA rendering algorithm is very simple, takes advantage of standard graphics hardware, and makes efficient use of system resources by splitting the work between the graphics system and the CPU.

Breps as Displayable-Selectable Models in Interactive Design of Families of Geometric Objects

“…Algorithms for rapid visualization of CSG objects on standard platforms are beginning to appear. For example, [Rappoport96c] describes an algorithm which combines graph re-writing, hierarchical convex differences and efficient geometric algorithms (based on convex hulls of 3-D points) to visualize non-trivial CSG models interactively , using the standard graphics pipeline with a z-buffer and a stencil bit plane.…”

“…Usually, the numerical parameters are the ones which we want to be capable of modifying interactively. For example, we want to modify affine operations and visualize interactively the results of Boolean operations defined on the object [Rappoport96c], or we modify constraint parameters and want to see the geometric and physical behavior of the object. As a result, a slower, incremental on-demand computation of Picking is acceptable.…”

Generalized Partial Differential Equations for Interactive Design

“…They are boundary based methods such as polygon based design 18 , extrusions and surface of revolution 25 , polynomial patches 14 ; procedural modeling such as implicit surfaces 1 and fractals 34 ; and volumetric models such as constructive solid geometry 30 and subdivision 11 . Using these design techniques the common types of geometric operation often carried out include, adding detail to various regions of geometry, trimming and blending, Boolean operations and standard geometric transformations.…”

Method of trimming PDE surfaces

“…Such techniques include boundary based methods such as polygon based design [12], extrusions and surface of revolution [20], polynomial patches [8]; procedural modelling such as implicit surfaces [2]; and volumetric models such as constructive solid geometry [21] and subdivision [6]. Among these free-form surface design techniques the most widely used are polynomial patches and subdivision.…”