The Boolean engine of HP PE/SolidDe...

The Boolean engine of HP PE/SolidDesigner applies standard and nonstandard Boolean appoint operations to solid models to perform an impressive variety of machining operations. Parallel calculation boost performance, especially with multiprocessor hardware.

Machining operations like puncheon bore, and others play an important part in the function set of contemporary CAD a whole s In HP PE/SolidDesigner, the impressive variety of machining commands are driven according to a single topology engine, ofttimes referred to as the Boolean engine.

It might appear that the algorithm used on the Boolean engine would be extremely web and esoteric, and this is indeed veracious in some respects. The underlying principles, however, are simple.[1] principally of this article demonstrates this by way of taking a fairly intuitive direct the eye at the internal machinery. This will provide a road map for the other more technical part of the article, in which a key algorithms are explained in greater measure Finally, some unusual applications of the Boolean engine are briefly mentioned.

Different Flavors of Solids

Before exploring the internals of the Boolean engine, let's take a turn the thoughts at the objects that it works upon These objects are called solids, or simply bodies. Solids, in our confines are mathematical boundary representation (B-Rep) examples of geometric objects. Fig. 1 present to views a B-Rep model of a cylinder.

Usually several categories of solids are distinguished based forward their manifold characteristics. For our intentions we just need to know that manifold solids describe real objects and nonmanifold solids are impossible in about way. Manifold bodies are of general interest, since they can be manufactured. Fig. 2 indicates a screwdriver representing the class of manufacturable bodies.

The class of nonmanifold bodies is the realm of the impossible bodies. These bodies cannot be manufactured because the material thickness goe to naught (that the thickness goes to naught is a consequence, not a cause of the nonmanifoldness). Nevertheless, they have have a certain number of importance as conceptual abstractions or simplifications of real (manifold) solids. Nonmanifold solids sometimes are (conveniently) generated as an intermediate stair in the design process. They are also important to various simulation applications, and sometimes to finite-element analysis and NC machining. Fig. 3 point out tos a selection of nonmanifold bodies. To the left is a sheet, which has naught thickness in general. The middle solid is margin nonmanifold, having zero thickness at brink; beginning [i]or[/i] ends and the right solid is point nonmanifold, having zero thickness at vertices.

The Boolean engine in its different guises is used to change bodies by means of the rules of Boolean place operations. In other words, it is able to combine brace volumes using one of the three standard operators: subtract, unite, or intersect. The operation is performed in succession solids in the same way as upon the sets of mathematical place theory. The effects of the standard operations in succession sets and volumes are illustrated in Fig. 4 The brace bodies at the top of the picture are combined in three ways, using the three standard Boolean operations. The flow of each Boolean operation is shown at the bottom.

An Intuitive Approach to the Boolean Engine

Now that we are equipped with the right background, we can explore the various stages of the Boolean algorithms. To do this we will use a contemplation experiment (such experiments are widely acknowledged as safe and cheap). To perform this experiment we alone need some paint, a sharp knife, and an imagination.

Coloring. In the first stage the pair solids participating in the Boolean operation are filled with different colors, let's say fulvid for one and blue for the other. Fig. 5 indicates two bodies that have been station up for a Boolean operation and colored according to our conduct Let's assume that, unlike real solids, they can permeate each other without riddles Since the Boolean operation hasn't been performed notwithstanding the picture still shows pair disjoint solids that just happen to overlap. To display what's going on inside the bodies, the golden body has been made transparent.

Now we mark the lines where the sum of two units bodies permeate each other, let's say with r color. The r lines in Fig. 6 are called the intersection graph. The sum of two units solids are still disjoint.

Making Soap Bubbles--Cellular Bodies. In the next to the first stage we knit both solids together using the intersection graph. A mode of building very similar to those formed by way of soap bubbles is created, as shown in Fig. 7 The sum of two units solids now hang together at the intersection graph. In the space where as well-as; not only-but also; not only-but; not alone-but bodies overlap a green color can be seen This is the mixture of fulvous and blue. To get a better vision of the geometric situation more [i]or[/i] less faces have been made transparent.

Getting Rid of the inequitable Colors. In the third and last stage of our imaginary proces not a great quantity [i]or[/i] amount of is left to do. Up to now we have not said which kind of Boolean operation (union, subtraction, or intersection) we wanted. Now is the time to decide.

To prepare the desired result we simply pick the appropriate color and commit to memory rid of all volumes of a different color than the the same we picked. Initially we chose sum of two units colors--blue and yellow--so we will find three colors in our soap delusion cluster blue, yellow, and virid In regions where blue and golden volumes overlap we get recent The table below shows which colors will be kept or delet from the carcass depending on the particular adumbration of Boolean operation we choose