# Working with 2Geom FAQ

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## Introduction

Questions that arise during coding with 2geom are put here. To see other 2geom related questions go to the general lib2geom FAQ. Bugs can be reported at SF: 2geom bug tracker.

## Questions

### How do I use the 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).

### How to create a straight line (for types: Path, pwd2, d2pw)?

```   Path p;
p.appendNew<LineSegment>(a, b);

Piecewise<D2<SBasis> > pwd2 = Piecewise<D2<SBasis> >(D2<SBasis>(Linear(a[X], b[X]), Linear(a[Y], b[Y])));
```

### How to convert from Path (or PathVector) to pwd2 to d2pw to path and back?

```   D2<Piecewise<SBasis> > y;
Piecewise<D2<SBasis> > x;
Path p;
PathVector pvec;
//Assume the above vars are initialized
x = p.toPwSb();
y = make_cuts_independant(x);          // pwd2 -> d2pw
x = sectionize(y);                     // d2pw -> pwd2
p = path_from_piecewise(x, tolerance); // pw2d -> path
x = paths_to_pw(pvec);                 // pathvector -> pwd2
```

How do i convert from d2pw to path?

### How do I calculate the bounding box of a path?

```   Rect r = path.boundsFast();
```

or

```   Rect r = path.boundsExact();
```

### How do I convert 2geom to svgd and back?

```   #include "live_effects/n-art-bpath-2geom.h"
...
std::vector<Geom::Path> path_2geom;
gchar * svgd = SVGD_from_2GeomPath( path_2geom );
std::vector<Geom::Path> newpath_2geom = SVGD_to_2GeomPath(svgd);
g_free(svgd);
```

Above appears out-dated, try:

```   #include <svg/svg.h>
...
std::vector<Geom::Path> path_2geom;
gchar * svgd = sp_svg_write_path( path_2geom );
g_free(svgd);
```

### What does "compose" do?

Compose is the mathematical operation f(?) o g(?) = f(g(?)). Any transformation, be it translation or mesh distort, can be considered a composition of the original path P(t)->(u,v) and a function T(u,v)->(x,y) which takes each point in the plane to a new point. We write this transformation as compose(T, P). For examples of such composition at work look at the toys

• '2dsb2d', which composes the path with a polynomial mesh function called a coons patch
• 'plane3d', which composes the path with a 3d projection onto a plane surface
• 'center-warp', which shows how repeated composition produces the tweak tool effect
• 'path-along-path' which shows how composition allows mapping a shape along a path

### A dot product ?

the dot() function is here for you.

```   point1 = Geom::Point(10,2);
point2 = Geom::Point(0,1);
dot(point1,point2);         // = 2
```

2Geom provides various compose operations for functions representable using piecewise sbasis functions, as well the ability to compose arbitrary functions defined directly in code. Almost all the mathematics is performed in sbasis space.
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