u02: Extract slope function

u02/include/util.h

@@ -39,3 +39,7 @@ std::tuple<float, float, float> barycentric_coordinates(int x0, int y0, int x1,
 
 // Sorts the points of a triangle to be in ascending order (y0 < y1 < y2).
 void sort_triangle_points(int &x0, int &y0, int &x1, int &y1, int &x2, int &y2);
+
+// This calculates the slope of a line from (x0, y0) to (x1, y1).
+// It handles special cases to ensure the return value will be real.
+float slope(int x0, int y0, int x1, int y1);

u02/src/tests.cpp

@@ -452,3 +452,16 @@ TEST_CASE("Sort triangle points (prop: y0 < y1 < y2)") {
   REQUIRE(y0 <= y1);
   REQUIRE(y1 <= y2);
 }
+
+TEST_CASE("Slope") {
+  REQUIRE(slope(5, 10, 20, 10) == 0.0);
+  REQUIRE(slope(0, 0, 10, 10) == 1.0);
+  REQUIRE(slope(0, 0, 10, -10) == -1.0);
+  REQUIRE(slope(0, 0, 10, 5) == 0.5);
+  REQUIRE(slope(0, 0, 10, -5) == -0.5);
+  REQUIRE(slope(0, 10, 10, 40) == 3.0);
+  REQUIRE(slope(0, 10, 10, -40) == -5.0);
+
+  // Special case: Infinite slope, must be normalized
+  REQUIRE(slope(10, 10, 10, 40) == 0.0);
+}

u02/src/util.cpp

@@ -180,3 +180,19 @@ void sort_triangle_points(int &x0, int &y0, int &x1, int &y1, int &x2,
     std::swap(y1, y2);
   }
 }
+
+float slope(int x0, int y0, int x1, int y1) {
+  float m = ((float)(y1 - y0)) / ((float)(x1 - x0));
+  if (std::isinf(m) || std::isnan(m)) {
+    // This is a special case for two things:
+    //
+    // IEEE 754 specifies ∞ × 0 / 0 × ∞ to be an invalid operation,
+    // and therefore return NaN.
+    // That makes the computation of Δy fail when x0 == x1.
+    //
+    // In the case that additionally y0 == y1,
+    // the expression is 0/0, also defined in IEEE 754 as invalid.
+    m = 0;
+  }
+  return m;
+}