Fix FP exception in Wordrec::angle_change (issue tesseract-ocr#4242) (t…

…esseract-ocr#4243)

std::asin only allows arguments in [-1, 1], but rounding errors can
produce values which are slightly outside of this range and which
would cause a FP exception (or wrong calculation results).

Rename also the internally used function `TPOINT::length` to `TPOINT::length2`
because it calculates the square of the length.

Signed-off-by: Stefan Weil <sw@weilnetz.de>

src/ccstruct/blobs.h

@@ -81,8 +81,8 @@ struct TPOINT {
     return x * other.x + y * other.y;
   }
 
-  // Calculate length of vector.
-  int length() const {
+  // Calculate square of vector length.
+  int length2() const {
     return x * x + y * y;
   }
 

src/ccstruct/polyaprx.cpp

@@ -108,7 +108,7 @@ static void cutline(       // recursive refine
     edge = edge->next;
   } while (edge != last); // test all line
 
-  perp = vecsum.length();
+  perp = vecsum.length2();
   ASSERT_HOST(perp != 0);
 
   if (maxperp < 256 * INT16_MAX) {
@@ -389,17 +389,17 @@ static void fix2(  // polygonal approx
       break; // already too few
     }
     d12vec.diff(edgefix1->pos, edgefix2->pos);
-    d12 = d12vec.length();
+    d12 = d12vec.length2();
     // TODO(rays) investigate this change:
     // Only unfix a point if it is part of a low-curvature section
     // of outline and the total angle change of the outlines is
     // less than 90 degrees, ie the scalar product is positive.
     // if (d12 <= gapmin && edgefix0->vec.dot(edgefix2->vec) > 0) {
     if (d12 <= gapmin) {
       d01vec.diff(edgefix0->pos, edgefix1->pos);
-      d01 = d01vec.length();
+      d01 = d01vec.length2();
       d23vec.diff(edgefix2->pos, edgefix3->pos);
-      d23 = d23vec.length();
+      d23 = d23vec.length2();
       if (d01 > d23) {
         edgefix2->fixed = false;
         fixed_count--;

src/wordrec/chop.cpp

@@ -107,24 +107,31 @@ int Wordrec::angle_change(EDGEPT *point1, EDGEPT *point2, EDGEPT *point3) {
   vector2.x = point3->pos.x - point2->pos.x;
   vector2.y = point3->pos.y - point2->pos.y;
   /* Use cross product */
-  float length = std::sqrt(static_cast<float>(vector1.length()) * vector2.length());
+  float length = std::sqrt(static_cast<float>(vector1.length2()) * vector2.length2());
   if (static_cast<int>(length) == 0) {
     return (0);
   }
-  angle = static_cast<int>(floor(std::asin(vector1.cross(vector2) / length) / M_PI * 180.0 + 0.5));
-
-  /* Use dot product */
-  if (vector1.dot(vector2) < 0) {
-    angle = 180 - angle;
-  }
-  /* Adjust angle */
-  if (angle > 180) {
-    angle -= 360;
-  }
-  if (angle <= -180) {
-    angle += 360;
+  auto f = vector1.cross(vector2) / length;
+  // Avoid FP exception in std::asin caused by illegal values of f
+  // (caused by rounding errors).
+  if (f <= -1.0f) {
+    angle = -90;
+  } else if (f >= 1.0f) {
+    angle = 90;
+  } else {
+    angle = static_cast<int>(floor(std::asin(f) / M_PI * 180.0 + 0.5));
+    // Use dot product.
+    if (vector1.dot(vector2) < 0) {
+      angle = 180 - angle;
+    }
+    // Adjust angle.
+    if (angle > 180) {
+      angle -= 360;
+    } else if (angle <= -180) {
+      angle += 360;
+    }
   }
-  return (angle);
+  return angle;
 }
 
 /**