Lib2geom Goals

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This section outlines 2geom's domain - what it will do, and current state.

This is actually more of a class outline than features. A lot is implemented for the classes below, in current state, and certainly much more is possible (arguably infinite, but most would be out of the scope of the project).

Current State

Basic geometric primitives

Point and D2<T> provide the classical two dimensional point. A rectangle is a D2<Interval>, a 2d parametric polynomial is a D2<SBasis>. Most operations are lifted from T automatically, so for example, a matrix multiply applied to a Rect produces the smallest rect that would contain the result.

Matrix provides a 2D affine transformation(scale, rotate, translate). There is also a NR:Matrix which provides general linear algebra (using blas etc).

Polynomials (SBasis and Bezier) which can be cheaply transformed between basis. There are many operations on polynomials, ranging from traditional arithmetic (+, -, *, /), through higher functions (sin, sqrt) to geometric operators (unit_vector, curvature).

There are paths with various operations like intersection and bounding.

There are special geometric types like Circle, ConvexHull and Ray with optimised representations and operators (intersection, nearest point, roots).

To do list 2009

  • Clothoid support (clothoids where the curvature is a not-necessarily linear function, perhaps piecewise SBasis, add fitting)
  • Special geometric shapes (stuff like circles, oriented rectangles, spirals, triangles, regular polygons, inkscape-like polygons, etc)
  • Constraint system for advanced handle stuff
  • complete and tidy up intersection apis
  • complete offset implementation: at this stage only the hard part has been implemented
  • conic sections: we currently support line and ellipse from xAx form, add parabola and hyperbola; intersection
  • NURBS (2geom handles division approximation of polynomials, code just needs to be added to convert between standard forms (say x/w, y/w in bernstein and pw<d2<sb>>(t))
  • T-mesh form for 2D (and higher?) piecewise polynomials
  • enhance contour tracing algorithm (sb-2d-solver)
  • transform an svg stroke in an outline (extends offset curve code to handle SVG options)
  • variable width curve tracing (variant on path along path idea)
  • collinear tangent (find a line that smoothly connects two curves); extension of bezier clipping idea
  • tranform a path into a single curve (fitting) - improvements required
  • exploiting modern architecture features (cache coherence, multi-core, packet instruction set, gpgpu)
  • finish boolops (use faster and more robust sweep-window algorithm, add support for dB @ dB, dB @ B, B @ B where @ is any of the 16 boolean operators that make sense)
  • bucket fill (variant of bool ops for bucket filling)
  • path topology and numerical soundness graph

Design Decisions

  • Small, algebraic objects (Point/Matrix) will be mutable, whereas large objects like a pathset will be immutable. <justification here>
  • We are using an original development method we've dubbed "Toy Driven Development". Under this process graphical toys are implemented which allow playing with the features of the library.