A small convenience header-only library for linear algebra.
Dependencies: None
Installation: Download the header file geometry.h, include it, and you're ready to go.
Usage: In namespace geom::, the library offers a struct for storing n-dimensional vectors in R^n or Z^n (i.e. with floating point- or integer coordinates) with several constructors, and overloads their operators.
Furthermore, it offers a namespace geom2d:: with some convenient functions for two-dimensional algebra like cross product, perpendicular and normal, angle calculation, and higher level stuff like segment intersection, polygon area and convex hull calcuation.
You can find the example code in this repository in test/examples/.
Ex1: Vector initialisation, operators, norm & dist
#include "geometry/geometry.hpp"
#include <cassert>
typedef geom::Vec<double,3> Vec3d; //All our vectors have three double coordinates
int ex1() {
Vec3d v1( 1.0, -1.0, -2.2 );
Vec3d v2( 3.0, 1.0, -0.2 );
Vec3d sub_v1v2 = v1 - v2;
std::cout << "sub_v1v2: " << sub_v1v2.print() << std::endl; //sub_v1v2 == (-2.0, -2.0, -2.0 )
Vec3d normalised = geom::normalize( sub_v1v2 );
std::cout << "sub_v1v2 normalised: " << normalised.print() << std::endl; //normalised ==(-sqrt(1/3), -sqrt(1/3), -sqrt(1/3)
assert( geom::in_range( geom::norm( normalised ), 1.0 ) ); //Double calculation isn't exact! Therefor, check result up to double precision
std::cout << "Example1 successful executed!" << std::endl;
return 0;
}Ex2: polygons & their area
#include "geometry/geometry.hpp"
typedef geom::Vec<int,2> Vec2i; //All our vectors have two integer coordinates
int ex2(){
Vec2i v1( 0, 0 );
Vec2i v2( 2, 0 );
Vec2i v3( 1, 1 );
geom2d::polygon<int> p ( {v1,v2,v3} );
double polygon_area = geom2d::area(p);
std::cout << "Polygon area: " << polygon_area << std::endl; //polygon_area == 1
assert( geom::in_range(polygon_area, 1.0) );
return 0;
}Ex3: Point in polygon test & convex hull
#include "geometry/geometry.hpp"
int ex3(){
geom2d::polygon<double> p( { { 0.0,-0.1 },{ -0.1,0.0 },{ 0.0,0.1 },{ 0.1,0.0 } } );
std::cout << "Point in polygon test: " << geom2d::point_in_polygon( { -0.04,0.02 }, p ) << std::endl; //Check if a point is in polygon
assert( geom2d::point_in_polygon( { -0.04,0.02 }, p ) );
std::vector<geom2d::Vec2D<int>> c ( { { 1,1 },{ -1,-3 },{ 0,1 },{ 10,10 },{ 2,-1 },{ -1,5 },{ -3,-5 },{ 3,-1 },{ 5,6 },{ 8,8 },{ 2,4 },{ 0,5 } } );
auto conv_hull = geom2d::convex_hull( c ); //Compute the convex hull of a set of 2d-points, yielding a polygon conv_hull
std::cout << geom::print( conv_hull ) << std::endl;
assert( conv_hull.size() == 5 );
return 0;
}The functionality of this library initially grew due to my personal need for it. Several projects, which I did not want to depend on a library as overkill as Boost, rely on this simple collection of linear algebra functions. The API might still change in the future. If you have any suggestions, find errors, miss some functions or want to give general feedback/criticism, I'd love to hear from you. Of course, contributions are also very welcome.
Distributed under the MIT Software License (X11 license). (See accompanying file LICENSE.)