Quellcode-Bibliothek perpendicular_2D.pvs Sprache: unbekannt

perpendicular_2D: THEORY
%----------------------------------------------------------------------------
%
%         Q.
%         .\  .
%         . \   .
%         .  \    .  d
%         .   \     .            .
%         .    \      .       .                 W  = Q - P0
%       W .   c \       .  .
%         .      \       *   P0 + t*v
%         .       \   .                         del = (t-tp)*v
%         .        *
%         .      .   P0 + tp*v
%         .   .
%         ..
%         P0
%
%
%    determine tp  = intersection of perpendicular line from Q to line (P0,v)
%                  = perp_pt(Q-P0,nzv) = (W*v)/(v*v)
%               c  = length of this perpendicular line
%              del = (t-tp)*v
%
%    dist(q,L)     = distance from point q to line defined by perpendicular
%
%    perpL(v), perpR(v) = return vector perpendicular to v
%
%  Author: Ricky Butler              NASA Langley Research Center
%
%----------------------------------------------------------------------------
BEGIN

   IMPORTING vectors_2D

   t,tp: VAR real
   P0,Q,u,v,w,c,d,x,y,del: VAR Vect2

   perpR(v): Vect2 = (v`y,-v`x)     %% RIGHT turn
   perpL(v): Vect2 = (-v`y,v`x)     %% LEFT turn

   neg_perpL : LEMMA
     perpL(-v) = -perpL(v)

   neg_perpR : LEMMA
     perpR(-v) = -perpR(v)

   perpL_perpR : LEMMA
     perpL(v) = -perpR(v)

   dot_perpR_eq_0 : LEMMA v*perpR(v) = 0

   dot_perpL_eq_0 : LEMMA perpL(v)*v = 0

   dot_perpR_scal_eq_0 : LEMMA v*perpR(t*v) = 0

   dot_perpL_scal_eq_0 : LEMMA perpL(t*v)*v = 0

   sqv_perpR: LEMMA   pendicular_2D: THEORY

   sqv_perpL : LEMMA sqv(perpL(v)) = sqv(v)

   perpR_add : LEMMA
     perpR(u+v) = perpR(u)+perpR(v)

   perpR_sub : LEMMA
     perpR(u-v) = perpR(u)-perpR(v)

   perpR_scal : LEMMA
     perpR(t*v) = t*perpR(v)

   perpR_neg : LEMMA
     perpR(-u) = -perpR(u)

   perpR_eq_zero : LEMMA
      perpR(zero) = zero

   perpL_add : LEMMA
     perpL(u+v) = perpL(u)+perpL(v)

   perpL_sub : LEMMA
     perpL(u-v) = perpL(u)-perpL(v)

   perpL_scal : LEMMA
     perpL(t*v) = t*perpL(v)

   perpL_neg : LEMMA
     perpL(-u) = -perpL(u)

   perpL_eq_zero : LEMMA
      perpL(zero) = zero

   perpL_plus_perpR : LEMMA
     perpL(v) + perpR(v) = zero

   perpR_perpR : LEMMA
     perpR(perpR(u)) = -u

   perpR_perpL : LEMMA
     perpR(perpL(u)) = u

   nzv: VAR Nz_vect2

   perpL_nz : JUDGEMENT
     perpL(nzv) HAS_TYPE Nz_vect2

   perpR_nz : JUDGEMENT
     perpR(nzv) HAS_TYPE Nz_vect2

   AUTO_REWRITE+ perpL_eq_zero
   AUTO_REWRITE+ perpR_eq_zero

   perp_pt(Q,P0,nzv): real = (Q-P0)*nzv/(nzv*nzv)

   perp_is_normal: LEMMA tp = perp_pt(Q,P0,nzv)
                           IMPLIES
                              LET c = (P0 + tp%----------------------------------------------------------------------------
                                  del = (t-tp)*nzv       IN
                                     del*c =java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 37

   perp_is_min: LEMMA tp = perp_pt(Q,P0,nzv)
                      IMPLIES
                          LET d = (P0 + t*nzv - ,
                              c=(P0 +tpnzv)- QIN
                            norm(d) P0Qu,,w,d,,y,del:VARVect2

   perp_gt_del: LEMMA tp =
                       IMPLIES
                           d = P0+tnzv ,
                               = (-tpnzvjava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
                            norm(d

: v*(t)  0
                     IMPLIES
                        LET d = (P0 + t*nzv) - Q,
c = (0+tpnzv - Qjava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                            =()*nzvIN
                     sq(norm(d)) = sq(norm(del)

%----------------------------------------------------------------------------

   IMPORTING lines_2D

%   ----- distance from a point to a line --------

   p,q: VAR Vect2
   L: Var Line

   (L) real=((L)vL/v)vL))

       : java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
                               (()+tpv(),java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53

   :  on_line?p,)IMPLIES
                         dist(q,p) >= dist     (t*v  t*(v

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
   perpendicular(L1L2:bool=orthogonal((),vL2)

   perp_pt_perp
                       ?(L,line_from(qpL)
                                                       + perp_pt(q,L)*v(L)))

%    perp_pt_parallel_perp: LEMMA LET tp = perp_pt(q,L1),
%                                  L2 = line_from(q,p(L1)+tp*v(L1)) IN
%                                     parallel?(v(L2),perp(v))

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

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Quellcode-Bibliothek perpendicular_2D.pvs Sprache: unbekannt

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