A typical mathematician would probably say, "does the line segment intersect the circle/sphere or its interior?"
I too took "circle" to mean the "boundary of the circle", the points (x,y) which satisfy (*:R)=(x-Cx)+&*:(y-Cy) ; to include the interior, the equation changes to (*:R)>:(x-Cx)+&*:(y-Cy) . (C=(Cx,Cy) is the center.) ----- Original Message ----- From: Henry Rich <[email protected]> Date: Thursday, October 7, 2010 4:58 Subject: Re: [Jprogramming] Puzzle: line-circle/sphere intersection To: Programming forum <[email protected]> > I intend that a segment wholly inside the circle/sphere to be > counted as > intersecting. In other words, the circle/sphere is solid > and we want to > know if the segment touches any of it. > > Henry Rich > > On 10/7/2010 7:52 AM, R.E. Boss wrote: > > That was bad reading from my side. > > The formulas should be: > > > > ((S-C)<R)*.((E-C)<R) -...@+. ((S-C)>R)*.((E-C)>R) > > > > D=: +&.*:/"1 (S,:E)-"1 C > > > > (D<R) -...@+.&(*./) D>R > > > > Apart from that, the mathematics is not correct either. I will > give it > > another thought. > > > > > > R.E. Boss > > > > > >> -----Oorspronkelijk bericht----- > >> Van: [email protected] [mailto:programming- > >> [email protected]] Namens Bo Jacoby > >> Verzonden: donderdag 7 oktober 2010 13:02 > >> Aan: Programming forum > >> Onderwerp: Re: [Jprogramming] Puzzle: line-circle/sphere > intersection>> > >> Hello Boss. > >> > >> I do not understand your notation. Henry wrote "startpoint S > and endpoint > >> E". You wrote "endpoints A and B", but you use E in your > pseudo code. > >> Please explain. > >> > >> It seems to me that you must compute the distances (s) from C > to S, (e) > >> from C to E and (p) from C to the closest point P, (the > perihelion), and > >> you must determine (b) if P is between S and E. Intersection > occurs if > >> (s<R and e>R) or (s>R and e<R) or (b and p<R and > (s>R or e>R)). > >> > >> --- Den tors 7/10/10 skrev R.E. Boss<[email protected]>: > >> > >> Fra: R.E. Boss<[email protected]> > >> Emne: Re: [Jprogramming] Puzzle: line-circle/sphere intersection > >> Til: "'Programming forum'"<[email protected]> > >> Dato: torsdag 7. oktober 2010 09.49 > >> > >> Since the word 'intersect' is used, I assume you mean the > boundary of the > >> circle/sphere (and not the area), so that a line segment > which is > >> completely > >> inside is not intersecting. One point at the boundary means > intersecting,>> I > >> assume. > >> So the segment is not intersecting if and only if it is > completely inside > >> or > >> completely outside the circle/sphere. > >> > >> > >> If the line segment is given by the endpoints A and B, the > pseudo code is > >> rather straightforward: > >> > >> ((A-E)<R)*.((B-E)<R) -...@+. ((A-E)>R)*.((B-E)>R) > >> > >> so ones gets > >> > >> D=: +&.*:/"1 (A,:B)-"1 E > >> > >> (D<R) -...@+.&(*./) D>R > >> > >> (untested) > >> > >> > >> R.E. Boss > >> > >> > >>> -----Oorspronkelijk bericht----- > >>> Van: [email protected] [mailto:programming- > >>> [email protected]] Namens Henry Rich > >>> Verzonden: woensdag 6 oktober 2010 22:54 > >>> Aan: Programming forum > >>> Onderwerp: [Jprogramming] Puzzle: line-circle/sphere intersection > >>> > >>> Given circle/sphere with center C and radius R, and a line- > segment with > >>> startpoint S and endpoint E, write the J code to tell > whether the > >>> line-segment intersects the circle/sphere. > >>> > >>> R is an atom, the rest are lists with 2 or 3 atoms. > >>> > >>> This problem arises in collision detection for games and > simulators, or > >>> if you are trying to see whether a path intersects a round > obstacle.>>> > >>> I found a solution whose brevity surprised me. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
