Exact distributions for shapes of random triangles in convex sets
1985 ◽
Vol 17
(02)
◽
pp. 308-329
◽
Keyword(s):
The paper starts with a simple direct proof that . A new formula is given for the shape-density for a triangle whose vertices are i.i.d.-uniform in a compact convex set K, and an exact evaluation of that shape-density is obtained when K is a circular disk. An (x, y)-diagram for an auxiliary shape-density is then introduced. When K = circular disk, it is shown that is virtually constant over a substantial region adjacent to the relevant section of the collinearity locus, large enough to contain the work-space for most collinearity studies, and particularly appropriate when the ‘strip’ method is used to assess near-collinearity.
Keyword(s):
1996 ◽
Vol 28
(02)
◽
pp. 384-393
◽
Keyword(s):
1987 ◽
Vol 35
(2)
◽
pp. 267-274
◽
1991 ◽
Vol 109
(2)
◽
pp. 351-361
◽
1977 ◽
Vol 81
(2)
◽
pp. 225-232
◽
Keyword(s):
1999 ◽
Vol 59
(1)
◽
pp. 147-152
◽
Keyword(s):
1985 ◽
Vol 28
(1)
◽
pp. 60-66
◽
Keyword(s):
1976 ◽
Vol 19
(4)
◽
pp. 467-471
◽
1978 ◽
Vol 30
(03)
◽
pp. 449-454
◽
1978 ◽
Vol 83
(3)
◽
pp. 419-427
◽
Keyword(s):