Hausdorff distance between two polygons in 2D Jarek Rossignac ...

Hausdorff distance between two polygons in 2D
Jarek Rossignac
Proc Onto(s,a,b) {RETURN((ab•as>0)==(ba•bs>0))}; # s projects onto segment (a.b)
Proc n(j) {RETURN((j+1) mod t)} # next vertex: t = total number of vertices in polygon
Proc M2(s,P) {
# minimum square distance from s to polygon P
d:=(sP 0 ) 2 ;
# init d to square of distance to vertex 0 of P
FOR j:=1 to |P| DO {
# for all edges of P
IF Onto(s,P j ,P k )
# case where I am on edge
THEN dd:=(P j P n(j) ¥P j s) 2 /(P j P n(j) ) # point-line distance.
ELSE dd:=(P j s) 2 ;
# case where I am on vertex
IF ddd THEN d:=dd;}
RETURN(d)}
Proc H2(A,B) {
RETURN(max(D2(A,B), D2(A,B));
# Maximum deviation squared between points on A and B
# candidates positions on A for her
# init deviation to zero
# for each candidate where she could try to hide
# minimum distance square from s to B
# adjust d if found better hiding place for her
# Symmetric Hausdorff distance between A and B
Proc Candidates(A,B) {
# Candidates on A for best hiding places away from B
C:=vertex_set(A);
# start by including all vertices of A
FOR j:=1 to |A| DO {
# for each edge A j A j+1 where she may hide
FOR a:=0 TO |B|–1 DO
FOR b:=0 TO |B|–1 DO { # case where Joe and I are on vertices of B
s:=VV(A j ,A n(j) , B a ,B b ); # position for her on edge equidistant from B a and B b
IF onto(s, A j ,A n(j) ) # she is still on her edge
THEN C+={s}}; # add point s to candidates. Remember it goes with a, b.
FOR a:=0 TO |B|–1 DO
FOR b:=0 TO |B|–1 DO { # case where Joe is at vertex a and I on an edge (b,n(b))
s:=VE(A j ,A n(j) ,B a ,B b , B n(b) ); # position for her on edge equidistant from B a and B b
IF onto(s, A j ,A n(j) ) # she is still on her edge
AND onto (s, B b , B n(b) ) # I am still on my edge
THEN C+={s}}; # add point s to candidates. Remember it goes with a, b.
FOR a:=0 TO |B|–1 DO
FOR b:=a+1 TO |B|–1 DO { # case where Joe and I are on edges of B
s:=EE(A j ,A n(j) ,B a ,B n(b) ,B b ,B n(b) ); # position for her on edge equidistant from ours
IF onto(s, A j ,A n(j) ) AND onto (s, B a , B n(a) ) AND onto (s, B b , B n(b) ) # all 3 on our edges
THEN C+={s}}} # add point s to candidates. Remember it goes with a, b.
RETURN(C) }

Proc VV(u,v,a,b)
# returns intersection of line(u,v) with the bisector of a and b
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s
v
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Proc VE(u,v,a,b,c)
# returns intersection of line(u,v) with parabola between point a and line(b,c)
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b
Proc EE(u,v,a,b,c,d)
# returns intersection of line through u and v with bisector of the line(a,b) and line(c,d)
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