Talk:Concyclic points: Difference between revisions
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this info should be merged somewhere --[[User:MarSch|MarSch]] 16:48, 7 November 2005 (UTC) |
this info should be merged somewhere --[[User:MarSch|MarSch]] 16:48, 7 November 2005 (UTC) |
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I think the page should mention that four points p1=(x1,y1), p2=(x2,y2), p3=(x3,y3), p4=(x4,y4) are concyclic (or collinear) if and only if the determinant of ((x1,y1,x1^2+y1^2,1), (x2,y2,x2^2+y2^2,1), (x3,y3,x3^2+y3^2,1), (x4,y4,x4^2+y4^2,1)) equals zero. (More generally, the sign of the determinant tells whether p4 is left or right of the "oriented" circle through p1, p2, p3.) This is known as the "InCircle" primitive of Guibas and Stolfi. See for example [http://graphics.stanford.edu/courses/cs268-16-fall/Notes/torino.pdf here] (the reference to the Guibas-Stolfi paper is given there).[[User:Gabn1|Gabn1]] ([[User talk:Gabn1|talk]]) 17:59, 17 February 2021 (UTC) |
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Latest revision as of 23:50, 1 April 2024
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Untitled
[edit]this info should be merged somewhere --MarSch 16:48, 7 November 2005 (UTC)
I think the page should mention that four points p1=(x1,y1), p2=(x2,y2), p3=(x3,y3), p4=(x4,y4) are concyclic (or collinear) if and only if the determinant of ((x1,y1,x1^2+y1^2,1), (x2,y2,x2^2+y2^2,1), (x3,y3,x3^2+y3^2,1), (x4,y4,x4^2+y4^2,1)) equals zero. (More generally, the sign of the determinant tells whether p4 is left or right of the "oriented" circle through p1, p2, p3.) This is known as the "InCircle" primitive of Guibas and Stolfi. See for example here (the reference to the Guibas-Stolfi paper is given there).Gabn1 (talk) 17:59, 17 February 2021 (UTC)