Ticket #3588: geometry1.patch

source/simulation2/helpers/Geometry.cpp

@@ -1 @@
-/* Copyright (C) 2015 Wildfire Games.
+/* Copyright (C) 2016 Wildfire Games.
  * This file is part of 0 A.D.
  *
  * 0 A.D. is free software: you can redistribute it and/or modify
@@ -196 +196 @@
     /*
      * We only consider collisions to be when the ray goes from outside to inside the shape (and possibly out again).
      * Various cases to consider:
-     *   'a' inside, 'b' inside -> no collision
-     *   'a' inside, 'b' outside -> no collision
-     *   'a' outside, 'b' inside -> collision
-     *   'a' outside, 'b' outside -> depends; use separating axis theorem:
+     *   'a' inside -> no collision
+     *   use separating axis theorem:
      *     if the ray's bounding box is outside the square -> no collision
      *     if the whole square is on the same side of the ray -> no collision
      *     otherwise -> collision
@@ -218 +216 @@
     fixed bu = b.Dot(u);
     fixed bv = b.Dot(v);
 
-    if (-hw <= bu && bu <= hw && -hh <= bv && bv <= hh) // TODO: isn't this subsumed by the next checks?
-        return true; // a is outside, b is inside
-
     if ((au < -hw && bu < -hw) || (au > hw && bu > hw) || (av < -hh && bv < -hh) || (av > hh && bv > hh))
         return false; // ab is entirely above/below/side the square
 
-    CFixedVector2D abp = (b - a).Perpendicular();
-    fixed s0 = abp.Dot((u.Multiply(hw) + v.Multiply(hh)) - a);
-    fixed s1 = abp.Dot((u.Multiply(hw) - v.Multiply(hh)) - a);
-    fixed s2 = abp.Dot((-u.Multiply(hw) - v.Multiply(hh)) - a);
-    fixed s3 = abp.Dot((-u.Multiply(hw) + v.Multiply(hh)) - a);
-    if (s0.IsZero() || s1.IsZero() || s2.IsZero() || s3.IsZero())
-        return true; // ray intersects the corner
-
-    bool sign = (s0 < fixed::Zero());
-    if ((s1 < fixed::Zero()) != sign || (s2 < fixed::Zero()) != sign || (s3 < fixed::Zero()) != sign)
-        return true; // ray cuts through the square
-
-    return false;
+    // Check if all points are on one side of a->b.
+    // This can be simplified by using the following equivalence:
+    // (x +- y +- z) are all > 0 or all < 0 <=> |x| > |y| + |z|
+    // and the linearity of scalar products.
+    // Furthermore, we already computed
+    // u.Dot((b-a).Perpendicular()) = (u.Perpendicular()).Dot(b-a) = av - bv, v.Dot(...) similarly
+    // Also, a.Dot(a.Perpendicular()) = 0.
+    fixed s0 = a.Dot(b.Perpendicular()).Absolute();
+    fixed s1 = (av - bv).Absolute().Multiply(hw) + (bu - au).Absolute().Multiply(hh);
+    return (s0 <= s1);
 }
 
 // Exactly like TestRaySquare with u=(1,0), v=(0,1)
@@ -248 +240 @@
     if (-hw <= a.X && a.X <= hw && -hh <= a.Y && a.Y <= hh)
         return false; // a is inside
 
-    if (-hw <= b.X && b.X <= hw && -hh <= b.Y && b.Y <= hh) // TODO: isn't this subsumed by the next checks?
-        return true; // a is outside, b is inside
-
     if ((a.X < -hw && b.X < -hw) || (a.X > hw && b.X > hw) || (a.Y < -hh && b.Y < -hh) || (a.Y > hh && b.Y > hh))
         return false; // ab is entirely above/below/side the square
 
     CFixedVector2D abp = (b - a).Perpendicular();
-    fixed s0 = abp.Dot(CFixedVector2D(hw, hh) - a);
-    fixed s1 = abp.Dot(CFixedVector2D(hw, -hh) - a);
-    fixed s2 = abp.Dot(CFixedVector2D(-hw, -hh) - a);
-    fixed s3 = abp.Dot(CFixedVector2D(-hw, hh) - a);
-    if (s0.IsZero() || s1.IsZero() || s2.IsZero() || s3.IsZero())
-        return true; // ray intersects the corner
-
-    bool sign = (s0 < fixed::Zero());
-    if ((s1 < fixed::Zero()) != sign || (s2 < fixed::Zero()) != sign || (s3 < fixed::Zero()) != sign)
-        return true; // ray cuts through the square
-
-    return false;
+    fixed s0 = a.Dot(abp).Absolute();
+    fixed s1 = abp.X.Absolute().Multiply(hw) + abp.Y.Absolute().Multiply(hh);
+    return (s0 <= s1);
 }
 
 /**
@@ -279 +259 @@
     fixed hh = halfSize.Y;
 
     CFixedVector2D p = axis.Perpendicular();
-    if (p.Dot((u.Multiply(hw) + v.Multiply(hh)) - a) <= fixed::Zero())
-        return true;
-    if (p.Dot((u.Multiply(hw) - v.Multiply(hh)) - a) <= fixed::Zero())
+    // We only check the "counterclockwisest" point.
+    // But first we check if the center is on the wrong side.
+    fixed s0 = p.Dot(a);
+    if (s0 >= fixed::Zero())
         return true;
-    if (p.Dot((-u.Multiply(hw) - v.Multiply(hh)) - a) <= fixed::Zero())
-        return true;
-    if (p.Dot((-u.Multiply(hw) + v.Multiply(hh)) - a) <= fixed::Zero())
-        return true;
-
-    return false;
+    s0 += u.Dot(p).Absolute().Multiply(hw) + v.Dot(p).Absolute().Multiply(hh);
+    return (s0 >= fixed::Zero());
 }
 
 bool Geometry::TestSquareSquare(