Quaternions at this precision can't represent very slow rotations sam…

…pled at very high frequency, so now there's "stochastic small rotations" -- very small rotations will pseudorandomly be rounded up to a small rotation that *can* be represented by a Quaternion, or down to 0. The probability of being rounded up or down is based on the size of the very small rotation compared to our minimum very small rotation. Over time, this means small / slow rotations get represented pretty well.

The user can comment out #define GMH_STOCHASTIC_SMALL_ROTATIONS_ENABLED in order to disable this.

GamepadMotion.hpp

@@ -8,6 +8,11 @@
 #include <math.h>
 #include <algorithm> // std::min, std::max and std::clamp
 
+#define GMH_STOCHASTIC_SMALL_ROTATIONS_ENABLED
+#ifdef GMH_STOCHASTIC_SMALL_ROTATIONS_ENABLED
+#include <cstdlib> // std::rand
+#endif
+
 // You don't need to look at these. These will just be used internally by the GamepadMotion class declared below.
 // You can ignore anything in namespace GamepadMotionHelpers.
 class GamepadMotionSettings;
@@ -565,7 +570,20 @@ namespace GamepadMotionHelpers
 		const Vec axis = Vec(inGyroX, inGyroY, inGyroZ);
 		const Vec accel = Vec(inAccelX, inAccelY, inAccelZ);
 		const float angleSpeed = axis.Length() * (float)M_PI / 180.0f;
-		const float angle = angleSpeed * deltaTime;
+		float angle = angleSpeed * deltaTime;
+
+#ifdef GMH_STOCHASTIC_SMALL_ROTATIONS_ENABLED
+		// because cos angle for small angles will hit 1 very quickly and do nothing for slow rotations, we go stochastic for small values
+		static const float stochasticThreshold = 0.0005f;
+		const float absAngle = std::abs(angle);
+		if (absAngle < stochasticThreshold && absAngle > 0.0f)
+		{
+			const float random01 = rand() / (RAND_MAX + 1.0f);
+			const float angleSign = angle > 0.0f ? 1.0f : -1.0f;
+			const float probability = absAngle / stochasticThreshold;
+			angle = angleSign * (random01 < probability ? stochasticThreshold : 0.0f);
+		}
+#endif
 
 		// rotate
 		Quat rotation = AngleAxis(angle, axis.x, axis.y, axis.z);
@@ -1244,3 +1262,5 @@ inline void GamepadMotion::GetCalibratedSensor(float& gyroOffsetX, float& gyroOf
 	gyroOffsetZ = GyroCalibration.Z * inverseSamples;
 	accelMagnitude = GyroCalibration.AccelMagnitude * inverseSamples;
 }
+
+#undef GMH_STOCHASTIC_SMALL_ROTATIONS_ENABLED