h********e
发帖数: 4 | 1 Can anybody tell me a fast and robust algorithm to determine whether a
vector point x is inside a cone formed by a set of vector points {x1, x2, ..
., xn}? x1, x2, ..., xn can be linear dependent. Cone is the linear
summation of {x1, x2, ..., xn} with non-negative coefficients.
A similar question is how to determine whether x is inside the convex hull
formed by {x1, x2, ..., xn}.
Thank you. | w***i
发帖数: 175 | 2 you may try the SWEEP operator,
J.H.Goodnight(1979), A Tutorial on the SWEEP Operator,
Americian Statistician, 33(3), 149-158. | w***i
发帖数: 175 | 3 i.e. run the regression of x on x_1, x_2, ..., x_n.
The ESS should be 0 and the coefficients should be non-negative and sum to 1 | D*******a
发帖数: 3688 | 4 formulate成LP
..
【在 h********e 的大作中提到】
: Can anybody tell me a fast and robust algorithm to determine whether a
: vector point x is inside a cone formed by a set of vector points {x1, x2, ..
: ., xn}? x1, x2, ..., xn can be linear dependent. Cone is the linear
: summation of {x1, x2, ..., xn} with non-negative coefficients.
: A similar question is how to determine whether x is inside the convex hull
: formed by {x1, x2, ..., xn}.
: Thank you.
| n******t
发帖数: 4406 | 5 找到hull之后，计算x和hull的相邻定点的连线的夹角，
如果都正的角或都是付的角那就是在里面,否则就在外面。
..
【在 h********e 的大作中提到】
: Can anybody tell me a fast and robust algorithm to determine whether a
: vector point x is inside a cone formed by a set of vector points {x1, x2, ..
: ., xn}? x1, x2, ..., xn can be linear dependent. Cone is the linear
: summation of {x1, x2, ..., xn} with non-negative coefficients.
: A similar question is how to determine whether x is inside the convex hull
: formed by {x1, x2, ..., xn}.
: Thank you.
| H****h
发帖数: 1037 | 6 平面上？
【在 n******t 的大作中提到】
: 找到hull之后，计算x和hull的相邻定点的连线的夹角，
: 如果都正的角或都是付的角那就是在里面,否则就在外面。
:
: ..
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