% KineMacros.tex of April 18, 1984 5:56:14 am PST --- Stolfi

% Macros for two-sided plane and kinetic framework concepts

% DESIRABLE CHANGES

% KINETIC FRAMEWORK

\def\states{\hbox{\bi W\/}} % set of all states

% Short form state operators. Usage:
%  $\po s + \di s$ in normal math.

\def\po#1{\dot #1} % position of a state (or germ)
\def\ta#1{\bar #1} % tangent at a state
\def\cu#1{\breve #1} % curvature of a state
\def\ba#1{\vec #1} % base state of a germ
\def\di#1{\hat #1} % orientation vector of a line or state

\def\ne#1{{#1}^{\char n}} % negative of a state
\def\an#1{{#1}^{\char a}} % antipode of a state or point
\def\op#1{{#1}^{\char o}} % antipode of a state or line

% Long form state operators

\def\pos{\mathop{\rm pos}} % position of a state (or germ)
\def\tan{\mathop{\rm tan}} % tangent at a state
\def\curv{\mathop{\rm curv}} % curvature of a state
\def\base{\mathop{\rm base}} % base state of a germ
\def\neg{\mathop{\rm neg}} % negative of a state
\def\opp{\mathop{\rm opp}} % opposite of line or state
\def\ant{\mathop{\rm ant}} % antipode of line or point
\def\dir{\mathop{\rm dir}} % orientation of a line or state

% counting states

\def\sss{\scriptscriptstyle }
\def\xp{^{\sss +}}
\def\xm{^{\sss -}}
\def\xpm{^{\sss \pm}}
\def\xmp{^{\sss \mp}}
\def\del{\Delta}

% winding numbers and co.

\def\wi{\omega} % winding number
\def\sw{\sigma} % sweeping number
\def\dg{\delta} % degree
\def\kr{\kappa} % crossing number