Add Intersection of line and convex

codebook/8_Geometry/Intersection_of_line_and_convex.cpp

@@ -0,0 +1,32 @@
+int TangentDir(vector<pll> &C, pll dir) {
+  return cyc_tsearch(SZ(C), [&](int a, int b) {
+    return cross(dir, C[a]) > cross(dir, C[b]); 
+  });
+}
+#define cmpL(i) sign(cross(C[i] - a, b - a))
+pii lineHull(pll a, pll b, vector<pll> &C) {
+  int A = TangentDir(C, a - b);
+  int B = TangentDir(C, b - a);
+  int n = SZ(C);
+  if (cmpL(A) < 0 || cmpL(B) > 0) 
+    return pii(-1, -1); // no collision
+  auto gao = [&](int l, int r) {
+    for (int t = l; (l + 1) % n != r; ) {
+      int m = ((l + r + (l < r ? 0 : n)) / 2) % n;
+      (cmpL(m) == cmpL(t) ? l : r) = m;
+    }
+    return (l + !cmpL(r)) % n;
+  };
+  pii res = pii(gao(B, A), gao(A, B)); // (i, j)
+  if (res.X == res.Y) // touching the corner i
+    return pii(res.X, -1);
+  if (!cmpL(res.X) && !cmpL(res.Y)) // along side i, i+1 
+    switch ((res.X - res.Y + n + 1) % n) {
+      case 0: return pii(res.X, res.X);
+      case 2: return pii(res.Y, res.Y);
+    }
+  /* crossing sides (i, i+1) and (j, j+1)
+  crossing corner i is treated as side (i, i+1)
+  returned in the same order as the line hits the convex */
+  return res;
+} // convex cut: (r, l]

codebook/content.tex

@@ -199,6 +199,8 @@ \subsection{PointInConvex*} % test by CF 104114 B, CF 101242 J (World Finals' pr
 \lstinputlisting{8_Geometry/PointInConvex.cpp}
 \subsection{TangentPointToHull*} % test by CF 104114 B, CF 101242 J (World Finals' problem)
 \lstinputlisting{8_Geometry/TangentPointToHull.cpp}
+\subsection{Intersection of line and convex} % test by aizu CGL_4_C, probably not enough
+\lstinputlisting{8_Geometry/Intersection_of_line_and_convex.cpp}
 \subsection{minMaxEnclosingRectangle*} % test by UVA 819
 \lstinputlisting{8_Geometry/minMaxEnclosingRectangle.cpp}
 \subsection{VectorInPoly*} % test by qoj 5479