PADL(ID:5286/pad003)

Rochester parts assembler language 

for Part and Assembly Description Language

CSG (Constructive Solid Geometry) language for CAD/CAM

Voelker & Requicha University of Rochester

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Related languages
PADL => PADL-1   Implementation
References:
  • An Introduction to PADL, Production Automation Technical Memorandum 22 University of Rochester, December 1975 view details
  • Requicha, A.A.G. "Mathematical models of rigid solid objects", University of Rochester, College of Engineering and Applied Science, Technical Memorandum 28. 1977 view details
  • Requicha, Aristides A. G. "Representations for rigid solids: theory, methods, and systems" Comput. Surv. 12, 4 (Dec. 1980), pp437-464. view details
  • Jones, R. A. review of Requicha CSurv (PADL) in ACM Computing Reviews October 1981 view details Abstract: In this article, Requicha covers the three major areas listed in his title. The theory and methods for rigid solid representation are covered in depth, but the survey of extant modeling systems is too brief and dated.

    First, he surveys the theoretical and conceptual issues in order to build a background for discussing representational schemes for rigid solids, approaching the topic with both intuitive and rigorous methods. He discusses the formal properties of representational schemes in general, i.e., what is meant mathematically by a "solid." He defines a modeling space and develops the ideas of a representation scheme, completeness, and uniqueness. Informally, he discusses conciseness, ease of creation of solids by a user, and efficiency of use.

    With this foundation, he moves on to discuss at length seven different classes of representational schemes. Again he uses intuitive as well as formal presentations, and investigates the drawbacks as well as advantages of each scheme for use in a computer-based system. The seven are:
    1) Ambiguous and informal schemes, such as traditional engineering drawings.
    2) Pure primitive instancing schemes, which are families of objects represented by fixed length tuples. An individual object is called a "primitive instance." He points out the lack of a means to combine primitive instances to create more complex objects, and remarks: "Such schemes are akin to languages defined by grammars in which it is not possible to combine words to form sentences."
    3) Spatial occupancy enumeration schemes, where a solid is represented by a list of occupied cells ("voxels") in a spatial grid.
    4) Cell decomposition schemes, a generalization of decomposition by triangulation. He points out that decompositions are unambiguous but not unique, and are difficult to perform on curved solids.
    5) Constructive solid geometry schemes, where solids are binary trees where nonterminal nodes are operations and terminal nodes are either sets in E3 or rigid motion transformations. These schemes are investigated in some detail, probably because of the author's prior involvement in the PADL project, which used a CSG scheme. He points out that while it is easy for humans to create some classes of objects with a CSG scheme, it is not efficient in a computer-based system for producing line drawings of objects. However, other advantages, plus the potential implementation on VLSI hardware, make the future look promising.
    6) Sweep representations, where a two- or three-dimensional shape is translated or rotated, leaving a "sweep path." He points out the importance of these schemes in manufacturing applications to answer questions of material removal by tool paths and dynamic interference by moving parts.
    7) Boundary representation schemes, where a solid is represented by subdividing the boundary into "faces" and representing each face by its edges and vertices. Triangulation is the most common method of creating faces. Because of their use in computer graphics and finite element analysis, boundary representations are covered in considerable detail.

    This section is closed with a discussion of hybrid schemes, combining two of the seven, such as CSG and sweep scheme, and the known conversions from one scheme to another.

    In the third section Requicha briefly surveys current computer- based geometric modeling systems. Here the major weakness of the article arises, for "current" means 1978, when the text was submitted. It is unfortunate that there was a two-year delay before the article was revised and accepted. This survey consists primarily of a table listing systems and the representation schemes used.

    The author concludes with an outline proposal for a modeling system that meets the requirements seen to be necessary in the survey of schemes, but overcomes the limitations identified with any one of them. He proposes using CSG representation internally, but allowing sweep-based or boundary-based input, taking advantage of the conversions surveyed in the second section.

    In addition to the CSG representation, boundary representations and spatial enumeration representations can be developed by translation algorithms from the CSG. These would allow the complementary advantages of each to be developed to overcome the limitations of having only a single representation scheme.

  • Requicha, A. A. G. and H. B. Voelcker, "Solid Modeling: A Historical Summary and Contemporary Assessment" view details
          in IEEE Computer Graphics and Applications, 2(2) March 1982 view details