Keyframe: Move Bezier code into extra function, parameterise

Bezier interpolation code is now in a dedicated function and can be
used to either find a Y from a known X or a X from a known Y, with a
given allowed error.

src/KeyFrame.cpp

@@ -39,6 +39,44 @@ namespace {
 	bool IsPointBeforeX(Point const & p, double const x) {
 		return p.co.X < x;
 	}
+
+	double InterpolateBezierCurve(Point const & left, Point const & right, bool const needY, double const target, double const allowed_error) {
+		double const X_diff = right.co.X - left.co.X;
+		double const Y_diff = right.co.Y - left.co.Y;
+		Coordinate const p0 = left.co;
+		Coordinate const p1 = Coordinate(p0.X + left.handle_right.X * X_diff, p0.Y + left.handle_right.Y * Y_diff);
+		Coordinate const p2 = Coordinate(p0.X + right.handle_left.X * X_diff, p0.Y + right.handle_left.Y * Y_diff);
+		Coordinate const p3 = right.co;
+
+		double t = 0.5;
+		double t_step = 0.25;
+		do {
+			// Bernstein polynoms
+			double B[4] = {1, 3, 3, 1};
+			double oneMinTExp = 1;
+			double tExp = 1;
+			for (int i = 0; i < 4; ++i, tExp *= t) {
+				B[i] *= tExp;
+			}
+			for (int i = 0; i < 4; ++i, oneMinTExp *= 1 - t) {
+				B[4 - i - 1] *= oneMinTExp;
+			}
+			double const x = p0.X * B[0] + p1.X * B[1] + p2.X * B[2] + p3.X * B[3];
+			double const y = p0.Y * B[0] + p1.Y * B[1] + p2.Y * B[2] + p3.Y * B[3];
+			bool const stop = abs(target - (needY ? x : y)) < allowed_error;
+			bool const move_left = (needY ? x : y) > target;
+			if (stop) {
+				return needY ? y : x;
+			}
+			if (move_left) {
+				t -= t_step;
+			}
+			else {
+				t += t_step;
+			}
+			t_step /= 2;
+		} while (true);
+	}
 }
 
 
@@ -231,39 +269,7 @@ double Keyframe::GetValue(int64_t index) const {
 	// BEZIER curve!
 	assert(candidate->interpolation == BEZIER);
 
-	double const X_diff = candidate->co.X - predecessor->co.X;
-	double const Y_diff = candidate->co.Y - predecessor->co.Y;
-	Coordinate const p0 = predecessor->co;
-	Coordinate const p1 = Coordinate(p0.X + predecessor->handle_right.X * X_diff, p0.Y + predecessor->handle_right.Y * Y_diff);
-	Coordinate const p2 = Coordinate(p0.X + candidate->handle_left.X * X_diff, p0.Y + candidate->handle_left.Y * Y_diff);
-	Coordinate const p3 = candidate->co;
-
-	double t = 0.5;
-	double t_step = 0.25;
-	do {
-		// Bernstein polynoms
-		double B[4] = {1, 3, 3, 1};
-		double oneMinTExp = 1;
-		double tExp = 1;
-		for (int i = 0; i < 4; ++i, tExp *= t) {
-			B[i] *= tExp;
-		}
-		for (int i = 0; i < 4; ++i, oneMinTExp *= 1 - t) {
-			B[4 - i - 1] *= oneMinTExp;
-		}
-		double const x = p0.X * B[0] + p1.X * B[1] + p2.X * B[2] + p3.X * B[3];
-		double const y = p0.Y * B[0] + p1.Y * B[1] + p2.Y * B[2] + p3.Y * B[3];
-		if (abs(index - x) < 0.01) {
-			return y;
-		}
-		if (x > index) {
-			t -= t_step;
-		}
-		else {
-			t += t_step;
-		}
-		t_step /= 2;
-	} while (true);
+	return InterpolateBezierCurve(*predecessor, *candidate, true, index, 0.01);
 }
 
 // Get the rounded INT value at a specific index