Jorge Stolfi's Modula-3 libraries for geometry and linear algebra

These libraries include modules for geometric operations, linear algebra, and computer graphics.

• libm3geo: Linear algebra and projective geometry on spaces of small fixed dimensions.
  Requires libm3js, libm3geoN.

  These modules operate on vectors and matrices whose size is fixed at compile-time, and small enough for them to be passed through VAR parameters and results. The geometric modules use homogeneous coordinates, and pay attention to the signs as explained in the references listed at the end of the page.
  The main interfaces are LR2.i3, LR2x2.i3, LR3.i3, LR3x3.i3 (linear algebra), and HLR2.i3, HLR3.i3 (projective geometry).

  • Specific modules, for REAL vectors and matrices of 2 through 6 elements:
    | R2.i3 | R2.m3 | R2Rep.i3 | R2Extras.i3 |
    | R2x2.i3 | R2x2.m3 | R2x2Rep.i3 | R2x2Extras.i3 |
    | R3.i3 | R3.m3 | R3Rep.i3 | R3Extras.i3 |
    | R3x3.i3 | R3x3.m3 | R3x3Rep.i3 | R3x3Extras.i3 |
    | R4.i3 | R4.m3 | R4Rep.i3 | R4Extras.i3 |
    | R4x4.i3 | R4x4.m3 | R4x4Rep.i3 | R4x4Extras.i3 |
    | R5.i3 | R5.m3 | R5Rep.i3 |
    | R6Rep.i3 | R6.i3 | R6.m3 |
    | R6x6.i3 | R6x6.m3 | R6x6Rep.i3 |
  • Specific modules, for LONGREAL vectors and matrices of 2 through 6 elements:
    | LR2.i3 | LR2.m3 | LR2Rep.i3 | LR2Extras.i3 |
    | LR2x2.i3 | LR2x2.m3 | LR2x2Rep.i3 | LR2x2Extras.i3 |
    | LR3.i3 | LR3.m3 | LR3Rep.i3 | LR3Extras.i3 |
    | LR3x3.i3 | LR3x3.m3 | LR3x3Rep.i3 | LR3x3Extras.i3 |
    | LR4.i3 | LR4.m3 | LR4Rep.i3 | LR4Extras.i3 |
    | LR4x4.i3 | LR4x4.m3 | LR4x4Rep.i3 | LR4x4Extras.i3 |
    | LR5.i3 | LR5.m3 | LR5Rep.i3 |
    | LR6.i3 | LR6.m3 | LR6Rep.i3 |
    | LR6x6.i3 | LR6x6.m3 | LR6x6Rep.i3 |
  • Projective geometry opeations using REAL homogeneous coordinates in 2 and 3 dimensions:
    | HR2.i3 | HR2.m3 |
    | HR3.i3 | HR3.m3 |
  • Projective geometry opeations using LONGREAL homogeneous coordinates in 2 and 3 dimensions:
    | HLR2.i3 | HLR2.m3 |
    | HLR3.i3 | HLR3.m3 |
  • Generic modules, for vectors and matrices of arbitrary type and dimension:
    | Vector.ig | Vector.mg |
    | Matrix.ig | Matrix.mg |
  • Semi-generic interfaces, with operation on vectors and matrices that are type-independent but specific to particular dimensions:
    | Vector2Extras.ig | Matrix2x2Extras.ig |
    | Vector3Extras.ig | Matrix3x3Extras.ig |
    | Vector4Extras.ig | Matrix4x4Extras.ig |
  • Miscellaneous testing routines, generic and specific:
    | TestVector.mg | TestR3.m3 | TestR2.m3 | TestR4.m3 |
    | TestVecLoops2.m3 | TestVecLoops6.m3 |
    | TestHypot.m3 |

• libm3geoN: Linear algebra operations on "open" matrices and vectors.
  Requires libm3js.

  These modules operate on vectors and matrices whose size is determined at run-time, and may be different for each call. For that reason, the results are generally returned through VAR parameters.

  • Generic modules, for vectors and matrices of arbitrary type and representation:
    | VectorN.ig | VectorN.mg |
    | MatrixN.ig | MatrixN.mg |
    | GaussElim.ig | GaussElim.mg |
  • Specific modules, for open arrays of REAL:
    | RN.i3 | RN.m3 | RNRep.i3 |
    | RMxN.i3 | RMxN.m3 | RMxNRep.i3 |
    | GaussElimReal.i3 | GaussElimReal.m3 |

  • Specific modules, for open arrays of LONGREAL:
    | LRN.i3 | LRN.m3 | LRNRep.i3 |
    | LRMxN.i3 | LRMxN.m3 | LRMxNRep.i3 |
    | GaussElimLongReal.i3 | GaussElimLongReal.m3 |

References:

1. Oriented projective geometry.
   Academic Press, Boston, 1991 (237 pages).
   The geometry behind HR2.i3 and HR3.i3.
2. Fundamentos de Geometria Computacional.
   With Pedro J. de Rezende. . IX Escola de Computação, Recife, Brazil, 1994 (208 pages, in Portuguese).
   A shorter version of the above, with exercises.