diff --git a/doc/g2_splines.md b/doc/g2_splines.md index 6ae600fa860aef28979b99e53d659192a7792350..9190cb471e9ce8439511613d90fb1634aa702135 100644 --- a/doc/g2_splines.md +++ b/doc/g2_splines.md @@ -3,7 +3,7 @@ G2 Splines implementation ## Description -This library provides a C++ implementation of the G2 Splines (Quintic splines).These splines are 2D parametric cuves defined by independant x and y 5th order polynomials in therms of the parameter *u*, in the range [0,length]. The curve can be completelly defined by fixing the initial and final states as well as a set of internal parameters (n1,n2,n3,n4). The state of a G2 splines is defined as +This library provides a C++ implementation of the G2 Splines (Quintic splines).These splines are 2D parametric curves defined by independant _x_ and _y_ 5th order polynomials in therms of the parameter *u*, in the range [0,length]. The curve can be completelly defined by fixing the initial and final states as well as a set of internal parameters (n1,n2,n3,n4). The state of a G2 splines is defined as * 2D position (x,y) * Heading @@ -17,10 +17,10 @@ These type of splines have several interesting properties that make them suitabl The main features of this library are: * The start and ending states can be defined by the user (*set_start_point()* and *set_end_point()*) and modified at any time. When these states are set or modified, the spline has to be re-generated. -* To reduce the computational cost, the spline is only generated when necesary or when the *generate()* function is explicitly called. The resolution can be selected by the user. -* Provides functions to evaluate the spline (get the state information) at any a single point or at all points. -* It uses the [gradient library](docs/gradient.md) to compute the maximum curvature and maximum curvature derivative (*get_max_curvature()* and *get_max_curvature_der()*). -* It also uses the [gradient library](docs/gradient.md) to find the closest point on the curve to a given point. These functions always return the distance of the closest point from the start of the spline, and, optionally, the state of this point. +* To reduce the computational cost, the spline is only generated when necessary or when the *generate()* function is explicitly called. The resolution can be selected by the user. +* Provides functions to evaluate the spline (get the state information) at any single point or at all points. +* It uses the [gradient library](gradient.md) to compute the maximum curvature and maximum curvature derivative (*get_max_curvature()* and *get_max_curvature_der()*). +* It also uses the [gradient library](gradient.md) to find the closest point on the curve to a given point. These functions always return the distance of the closest point from the start of the spline, and, optionally, the state of this point. * Provides a function to get a new spline which is a part of the original one (*get_part()*). The functions that use the gradinet descent algorithm can set the maximum error (*max_error*) and maximum number of iterations (*max_iter*). If not set, the default values are used: