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← Revision 8 as of 2003-09-24 23:23:42 ⇥
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| Deletions are marked like this. | Additions are marked like this. |
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| Given a line in one dimension from p1 to p2, we can find the line of length 1/2 (p2-p1) centered around the midpoint of the first line in MLPQ as follows: | This query demonstrates visually the nature and application of approximation. Assuming Scot didn't delete it he has the presentation to go with it: Approximation Theory and Motivation Presentation.ppt. |
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| begin%RECURSIVE% | begin%Boxes% |
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| /* First we must build the diff relation. It is interesting to note that this relation is what will limit the other relations */ diff(x,y,z) :- x-y>=0, -x+y>=0, z>=0, -z>=0. diff(x,y,z) :- diff(x1,y,z1), x-x1<=1, x-x1>=1, z-z1<=1, z-z1>=1. diff(x,y,z) :- diff(x,y1,z1), y-y1<=1, y-y1>=1, z1-z<=1, z1-z>=1. |
Choice(m,n) :- m=0, n=0. Choice(m,n) :- m=0, n=1. Choice(m,n) :- m=0, n=2. Choice(m,n) :- m=1, n=0. Choice(m,n) :- m=1, n=2. Choice(m,n) :- m=2, n=0. Choice(m,n) :- m=2, n=1. Choice(m,n) :- m=2, n=2. |
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| /* Our initial line */ line(0,6, 0). |
D(x,y,z) :- x-y=0, z=0. D(x,y,z) :- D(x1,y,z1), x-x1=1, z-z1=1. |
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| /* Recursive line definition */ line(x,y,d) :- line(p1,p2,d1), diff(p,p1,z1), diff(p2,p,z), diff(x,p1,z2), diff(p,x,z2), diff(p2,y,z3), diff(y,p,z3), d-d1 = 1. |
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| end%RECURSIVE% | M(x,y,z) :- x=0, y=0, z=0. M(x,y,z) :- M(x1,y,z1), D(z,z1,y), x-x1=1. M(x,y,z) :- M(x,y1,z1), D(z,z1,x), y-y1=1. /* Creates the first set of base lines length=1,3,9... */ BaseLine(x1,x2):- x1=0, x2=1. BaseLine(a1,d3):- BaseLine(a1,d1), l=3, M(l,d1,d3). Box(x,y,s) :- BaseLine(x,b), y-x=0, b-s=0. Box(x,y,s) :- Box(a,b,l), k=3, M(k,s,l), Choice(m,n), M(s,m,z1), D(x,a,z1), M(s,n,z2), D(y,b,z2). XBox(a1,c1,s) :- Box(a,c,l), k=3, M(k,s,l), D(a1,a,s), D(c1,c,s). fractal1(id,x,y) :- id=1, Box(a,b,l), x-a>=0, D(x1,l,a), x-x1<=0, y-b>=0, D(y1,l,b), y-y1<=0. fractal2(id,x,y) :- id=2, XBox(a,b,l), x-a>=0, D(x1,l,a), x-x1<=0, y-b>=0, D(y1,l,b), y-y1<=0. end%Boxes% |
This query demonstrates visually the nature and application of approximation. Assuming Scot didn't delete it he has the presentation to go with it: Approximation Theory and Motivation Presentation.ppt.
begin%Boxes%
Choice(m,n) :- m=0, n=0.
Choice(m,n) :- m=0, n=1.
Choice(m,n) :- m=0, n=2.
Choice(m,n) :- m=1, n=0.
Choice(m,n) :- m=1, n=2.
Choice(m,n) :- m=2, n=0.
Choice(m,n) :- m=2, n=1.
Choice(m,n) :- m=2, n=2.
D(x,y,z) :- x-y=0, z=0.
D(x,y,z) :- D(x1,y,z1), x-x1=1, z-z1=1.
M(x,y,z) :- x=0, y=0, z=0.
M(x,y,z) :- M(x1,y,z1), D(z,z1,y), x-x1=1.
M(x,y,z) :- M(x,y1,z1), D(z,z1,x), y-y1=1.
/* Creates the first set of base lines length=1,3,9... */
BaseLine(x1,x2):- x1=0, x2=1.
BaseLine(a1,d3):- BaseLine(a1,d1), l=3, M(l,d1,d3).
Box(x,y,s) :- BaseLine(x,b), y-x=0, b-s=0.
Box(x,y,s) :- Box(a,b,l), k=3, M(k,s,l), Choice(m,n),
M(s,m,z1), D(x,a,z1),
M(s,n,z2), D(y,b,z2).
XBox(a1,c1,s) :- Box(a,c,l), k=3, M(k,s,l), D(a1,a,s), D(c1,c,s).
fractal1(id,x,y) :- id=1, Box(a,b,l), x-a>=0, D(x1,l,a), x-x1<=0,
y-b>=0, D(y1,l,b), y-y1<=0.
fractal2(id,x,y) :- id=2, XBox(a,b,l), x-a>=0, D(x1,l,a), x-x1<=0,
y-b>=0, D(y1,l,b), y-y1<=0.
end%Boxes%