% 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 &J J