Theory SIMPLE-GEOMETRY

• Last modified: Tuesday, 5 July 1994
• Source code: simple-geometry.lisp
• List of other known theories

Theory documentation:

This theory attempts to capture basic geometric concepts used in mechanical systems modelling. These concepts include points, frames, position, and orientation but exclude notions of extent (i.e. the modelling of surfaces or solid geometry).

Notes:

• (c) 1993, 1994 Gregory R. Olsen and Thomas R. Gruber
  

Cross Reference Report:

Theories included by Simple-Geometry:

  3d-Tensor-Quantities
  Quantity-Spaces
  Standard-Dimensions

Theories that include Simple-Geometry:

  Mechanical-Components

3 classes defined:

    3d-Direction-Cosine
    3d-Frame
    3d-Point

No relations defined.

4 functions defined:

  Distance
  Orientation
  Position
  Simple-Rotation

1 instance defined:

  3d-Length-Space

The following constants were used from included theories:

• * defined as a function in theory Kif-Numbers
• * defined as a function in theory Basic-Matrix-Algebra
• * defined as a function in theory Physical-Quantities
• * defined as a function in theory Scalar-Quantities
• * defined as a function in theory Tensor-Quantities
• + defined as a function in theory Kif-Numbers
• + defined as a function in theory Basic-Matrix-Algebra
• + defined as a function in theory Physical-Quantities
• + defined as a function in theory Scalar-Quantities
• + defined as a function in theory Tensor-Quantities
• - defined as a function in theory Kif-Numbers
• - defined as a function in theory Basic-Matrix-Algebra
• - defined as a function in theory Physical-Quantities
• - defined as a function in theory Tensor-Quantities
• 3d-Dyad defined as a class in theory 3d-Tensor-Quantities
• 3d-Vector-Quantity defined as a class in theory 3d-Tensor-Quantities
• Arity defined as a function in theory Frame-Ontology
• Basis.Dimension defined as a function in theory Tensor-Quantities
• Class defined as a class in theory Frame-Ontology
• Cos defined as a function in theory Kif-Numbers
• Documentation defined as a relation in theory Frame-Ontology
• Dot defined as a function in theory Tensor-Quantities
• Function defined as a class in theory Kif-Relations
• Identity-Dimension defined as a object in theory Physical-Quantities
• Inverse defined as a function in theory Kif-Relations
• Length-Dimension defined as a object in theory Standard-Dimensions
• Matrix-Of-Columns defined as a function in theory Basic-Matrix-Algebra
• Matrix-Of-Rows defined as a function in theory Basic-Matrix-Algebra
• Member defined as a relation in theory Kif-Sets
• Nth-Domain defined as a relation in theory Frame-Ontology
• Orthogonal-Matrix defined as a class in theory Basic-Matrix-Algebra
• Orthonormal-Basis defined as a class in theory Tensor-Quantities
• Point-In defined as a relation in theory Quantity-Spaces
• Quantity-Space defined as a class in theory Quantity-Spaces
• Quantity.Dimension defined as a function in theory Physical-Quantities
• Row-Dimension defined as a function in theory Basic-Matrix-Algebra
• Scalar-Quantity defined as a class in theory Scalar-Quantities
• Sin defined as a function in theory Kif-Numbers
• Sqrt defined as a function in theory Kif-Numbers
• Subclass-Of defined as a relation in theory Frame-Ontology
• Tensor-To-Matrix defined as a function in theory Tensor-Quantities
• Zero-Element defined as a class in theory Basic-Matrix-Algebra

All constants that were mentioned were defined.