Fix some issues that may cause catastrophic floating point error#284
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simonlindholm merged 1 commit intokth-competitive-programming:mainfrom Jan 31, 2025
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These are fantastic catches. Thank you so much! |
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Made the following changes
p+d*ttoq+d*(t-1). The problem is if-a+sqrt(det) ≫ 1, then the termarg(v, q)is supposed to be identically zero, however ifq ≈ (0, 0)then it's possible thatp+d ≉ qandarg(v, q) ≉ 0, which results in a large error. Seea.cppin the attached file below.side != (s.cross(e, prev) < 0)is true, it is possible that the 4 points are almost collinear thatlineInterreturns the second value being(0, 0). With this change, whenever(a < 0) != (b < 0)then0 ≤ a / (a - b) ≤ 1, which means the point being pushed is always on the line betweenprevandcuri.e. no catastrophic error can happen. Seeb.cppin the attached file below.Attachment (demonstration of catastrophic failure): a.zip