geometry.hpp File Reference

The basic geometric object types. More...

#include <stdexcept>
#include <utility>
#include <Eigen/Dense>

Classes
struct	ellipsoid_tree::Box
	Axis-aligned box {x : lo <= x <= hi componentwise}. More...
struct	ellipsoid_tree::Ball
	Ball {x : ||x - center|| <= radius}. More...
struct	ellipsoid_tree::Ellipsoid
	Ellipsoid E(tau) = {x : (x - mu)^T Sigma^{-1} (x - mu) <= tau^2}. More...
struct	ellipsoid_tree::Simplex
	Simplex conv(V.col(0), ..., V.col(K-1)): K vertices in R^dim, K <= dim+1. More...
struct	ellipsoid_tree::Segment
	Line segment from a to b (query object only; not a tree element type). More...
struct	ellipsoid_tree::Halfspace
	Halfspace {x : normal . x <= offset} (query object only; not a tree element type). More...

Namespaces
namespace	ellipsoid_tree

Functions
Box	ellipsoid_tree::bounding_box (const Eigen::Ref< const Eigen::VectorXd > &point)
	Degenerate bounding box of a single point (lo == hi == point).
Box	ellipsoid_tree::bounding_box (const Box &B)
	Bounding box of a box (the box itself).
Box	ellipsoid_tree::bounding_box (const Ball &B)
	Axis-aligned bounding box of a ball.
Box	ellipsoid_tree::bounding_box (const Ellipsoid &E, double tau)
	Tight axis-aligned bounding box of an ellipsoid at scale tau: half-width tau * sqrt(Sigma_kk) along axis k.
Box	ellipsoid_tree::bounding_box (const Simplex &S)
	Axis-aligned bounding box of a simplex (componentwise min/max of its vertices).
Box	ellipsoid_tree::bounding_box (const Segment &S)
	Axis-aligned bounding box of a segment.
std::pair< Eigen::MatrixXd, Eigen::VectorXd >	ellipsoid_tree::simplex_transform (const Eigen::Ref< const Eigen::MatrixXd > &V)
	Affine (barycentric) coordinate operator of a simplex.

Detailed Description

The basic geometric object types.

All objects are solid (filled) and closed: boundary points count as belonging to the object, and tangency counts as intersecting.