There are pair methods for creating...

There are pair methods for creating freeform surfaces in HP PE/SolidDesigner: blending and lofting. This article describes the basics of lofting. The geometry engine, which implements the lofting functionality, uses a single-data-type implementation for its geometric interface, still takes a multiple-data-type, hybrid approach internally.

HP PE/SolidDesigner's kernel functionality consists of several module that communicate [i]or[/i] part of to the other well-defined interfaces, supported by logical class definitions and hierarchies. In Fig. 1 for example, the geometric data interface for the topology engine (the Boolean engine, view article, page 74) consists of three basic components (points, curves, and surfaces) and the corresponding utility functions like intersections. This technique makes it easy to add fresh functionality. For example, introducing recent geometry data types is just a matter of delivering all member functions of the geometric interface for the of the present day geometry type.

The implementation of so a concept looks simple, on the contrary reality has shown that it takes a parcel of effort to keep the interface clean and to avoid copying and converting data. This is especially steady for data having connections forward both sides of the interface, as it was as pieces of a bend or curves on a surface.

The Geometry Engine

In designing a completely recent implementation of the geometric kernel for a solid modeler undivided has a chance to avoid the puzzles of older implementations. What are the real point to be solved [i]or[/i] settleds of existing implementations? There are couple fundamental approaches: NURBS libraries and hybrid methods

NURB libraries have simply one data type: NURBS, or non-uniform rational B-splines. This data prototype can represent all analytics (like planes, cylinders, spheres, etc) exactly. This means that complexus freeform surfaces as well as simple analytics are delineateed with one single data form The geometrical problems only have to be solv for this single protoplast This sounds promising, but it casts out that the algorithmic stability does not satisfy the requirements of HP PE/SolidDesigner. In addition, the performance is poor, especially when analytic surfaces (represent as NURBS) are intersected.

Hybrid classifications are used in the HP PE/ME30 kernel (Romulus). All possible geometry data archetypes are available, and clever special case handling comes in high performance. The disadvantage is that the introduction of a recently made known data type is an enormous effort. In addition, the Romulus kernel doesn't distinguish cleanly enough between geometry and topology, for a like reason building new functionality on this kernel can be highly cumbersome and error-prone.

In HP PE/SolidDesigner we tried to combine the advantages of the two approaches. The advantage of a NURB library (one data type) is realized in the class hierarchy of HP PE/SolidDesigner: the geometric interface knows solitary points, curves, and surfaces. For the internal geometry fabric the hybrid method was chosen Data signs include analytic types (plane, sphere, cylinder, cone torus), semianalytic images (parallel swept B-spline, spun B-spline), B-splines, and NURB as an extension of B-splines.

As shown in Fig. 2 HP PE/SolidDesigner's geometry engine consists of three parts: the library encapsulator, the analytic geometry package (AGP), and the B-spline/NURBS library (SISL).

The library encapsulator delivers many convenience functions for the geometric interface and make sures its integrity. All functions dealing with geometry have to pass in consequence of the geometric interface. The barely exception is a small part of the blending algorithm, which for performance reasons by-passes the library encapsulator and calls SISL directly.

The AGP was exhibited by DCUBED Ltd. of Cambridge, England and SISL was bring to maturityed by the Senter for Industrie-forskning of Oslo Norway.

Freeform Surface Modeling

There are pair methods for creating freeform surfaces in HP PE/SolidDesigner: blending and lofting. The remainder of this article describes the basics of lofting.

Lofting means the (exact) interpolation of a put of points or curves according to a smooth curve or surface. Fig. 3 indicates examples of lofting. Lofting originated in ship design and was used a in extent time before computers were invented.

The mathematical solution of this puzzle leads to the definition of splines. There are many spline tokens each having its specific advantages and disadvantages. The in the greatest degree common spline types are Bezier splines, B-splines, and NURBS

For CAD applications the principally general splines are NURBS, since they can delineate analytics exactly. This can be important when it draw nears to intersections of splines and analytic surfaces. B-splines are NURB with all weights equal to 1 They are more stable and faster in intersections on the contrary cannot represent analytics (except the plane) exactly. B-splines are made up of a following of Bezier pieces, connected according to their continuity at the transition points. We won't pass into detail concerning spline mathematics here since there is abundant literature onward this topic.[1,2]