/// <summary>
/// Correction #2 - The Next Object
/// Estimate how next object placement affects the difficulty of hitting current object.
/// </summary>
private static double calculateNextObjectPlacementCorrection(MovementExtractionParameters p)
{
if (p.NextObject == null || p.LastToCurrent.RelativeLength == 0)
{
return(0);
}
Debug.Assert(p.CurrentToNext != null);
double movementLengthRatio = p.LastToCurrent.TimeDelta / p.CurrentToNext.Value.TimeDelta;
double movementAngleCosine = cosineOfAngleBetweenPairs(p.LastToCurrent, p.CurrentToNext.Value);
if (movementLengthRatio > movement_length_ratio_threshold)
{
if (p.CurrentToNext.Value.RelativeLength == 0)
{
return(0);
}
double correctionNextMoving = correction_moving_spline.Interpolate(movementAngleCosine);
double movingness = SpecialFunctions.Logistic(p.CurrentToNext.Value.RelativeLength * 6 - 5) - SpecialFunctions.Logistic(-5);
return(movingness * correctionNextMoving * 0.5);
}
if (movementLengthRatio < 1 / movement_length_ratio_threshold)
{
if (p.CurrentToNext.Value.RelativeLength == 0)
{
return(0);
}
return((1 - movementAngleCosine) * SpecialFunctions.Logistic((p.CurrentToNext.Value.RelativeLength * movementLengthRatio - 1.5) * 4) * 0.15);
}
p.CurrentObjectTemporallyCenteredBetweenNeighbours = true;
// rescale CurrentToNext so that it's comparable timescale-wise to LastToCurrent
var timeNormalizedNext = p.CurrentToNext.Value.RelativeVector / p.CurrentToNext.Value.TimeDelta * p.LastToCurrent.TimeDelta;
// transform nextObject to coordinates anchored in lastObject
double nextTransformedX = timeNormalizedNext.DotProduct(p.LastToCurrent.RelativeVector) / p.LastToCurrent.RelativeLength;
double nextTransformedY = (timeNormalizedNext - nextTransformedX * p.LastToCurrent.RelativeVector / p.LastToCurrent.RelativeLength).L2Norm();
double correctionNextFlow = AngleCorrection.FLOW_NEXT.Evaluate(p.LastToCurrent.RelativeLength, nextTransformedX, nextTransformedY);
double correctionNextSnap = AngleCorrection.SNAP_NEXT.Evaluate(p.LastToCurrent.RelativeLength, nextTransformedX, nextTransformedY);
p.LastToNextFlowiness = SpecialFunctions.Logistic((correctionNextSnap - correctionNextFlow - 0.05) * 20);
return(Math.Max(PowerMean.Of(correctionNextFlow, correctionNextSnap, -10) - 0.1, 0) * 0.5);
}
/// <summary>
/// Correction #1 - The Previous Object
/// Estimate how second-last object placement affects the difficulty of hitting current object.
/// </summary>
private static double calculatePreviousObjectPlacementCorrection(MovementExtractionParameters p)
{
if (p.SecondLastObject == null || p.LastToCurrent.RelativeLength == 0)
{
return(0);
}
Debug.Assert(p.SecondLastToLast != null);
double movementLengthRatio = p.LastToCurrent.TimeDelta / p.SecondLastToLast.Value.TimeDelta;
double movementAngleCosine = cosineOfAngleBetweenPairs(p.SecondLastToLast.Value, p.LastToCurrent);
if (movementLengthRatio > movement_length_ratio_threshold)
{
if (p.SecondLastToLast.Value.RelativeLength == 0)
{
return(0);
}
double angleCorrection = correction_moving_spline.Interpolate(movementAngleCosine);
double movingness = SpecialFunctions.Logistic(p.SecondLastToLast.Value.RelativeLength * 6 - 5) - SpecialFunctions.Logistic(-5);
return(movingness * angleCorrection * 1.5);
}
if (movementLengthRatio < 1 / movement_length_ratio_threshold)
{
if (p.SecondLastToLast.Value.RelativeLength == 0)
{
return(0);
}
return((1 - movementAngleCosine) * SpecialFunctions.Logistic((p.SecondLastToLast.Value.RelativeLength * movementLengthRatio - 1.5) * 4) * 0.3);
}
p.LastObjectTemporallyCenteredBetweenNeighbours = true;
// rescale SecondLastToLast so that it's comparable timescale-wise to LastToCurrent
var timeNormalisedSecondLastToLast = -p.SecondLastToLast.Value.RelativeVector / p.SecondLastToLast.Value.TimeDelta * p.LastToCurrent.TimeDelta;
// transform secondLastObject to coordinates anchored in lastObject
double secondLastTransformedX = timeNormalisedSecondLastToLast.DotProduct(p.LastToCurrent.RelativeVector) / p.LastToCurrent.RelativeLength;
double secondLastTransformedY = (timeNormalisedSecondLastToLast - secondLastTransformedX * p.LastToCurrent.RelativeVector / p.LastToCurrent.RelativeLength).L2Norm();
double correctionSecondLastFlow = AngleCorrection.FLOW_SECONDLAST.Evaluate(p.LastToCurrent.RelativeLength, secondLastTransformedX, secondLastTransformedY);
double correctionSecondLastSnap = AngleCorrection.SNAP_SECONDLAST.Evaluate(p.LastToCurrent.RelativeLength, secondLastTransformedX, secondLastTransformedY);
double correctionSecondLastStop = SpecialFunctions.Logistic(10 * Math.Sqrt(secondLastTransformedX * secondLastTransformedX + secondLastTransformedY * secondLastTransformedY + 1) - 12);
p.SecondLastToCurrentFlowiness = SpecialFunctions.Logistic((correctionSecondLastSnap - correctionSecondLastFlow - 0.05) * 20);
return(PowerMean.Of(new[] { correctionSecondLastFlow, correctionSecondLastSnap, correctionSecondLastStop }, -10) * 1.3);
}
/// <summary>
/// Correction #3 - 4-object pattern
/// Estimate how the whole pattern consisting of second-last to next objects affects the difficulty of hitting current object.
/// This only takes effect when the pattern is not so spaced (i.e. does not contain jumps)
/// </summary>
private static double calculateFourObjectPatternCorrection(MovementExtractionParameters p)
{
if (!p.LastObjectTemporallyCenteredBetweenNeighbours ||
!p.CurrentObjectTemporallyCenteredBetweenNeighbours)
{
return(0);
}
Debug.Assert(p.CurrentToNext != null);
Debug.Assert(p.SecondLastToLast != null);
double gap = (p.LastToCurrent.RelativeVector - p.CurrentToNext.Value.RelativeVector / 2 - p.SecondLastToLast.Value.RelativeVector / 2).L2Norm() / (p.LastToCurrent.RelativeLength + 0.1);
return((SpecialFunctions.Logistic((gap - 1) * 8) - SpecialFunctions.Logistic(-6)) *
SpecialFunctions.Logistic((p.SecondLastToLast.Value.RelativeLength - 0.7) * 10) * SpecialFunctions.Logistic((p.CurrentToNext.Value.RelativeLength - 0.7) * 10) *
PowerMean.Of(p.SecondLastToCurrentFlowiness, p.LastToNextFlowiness, 2) * 0.6);
}
/// <summary>
/// Calculates attributes related to tapping difficulty.
/// </summary>
public static TapAttributes CalculateTapAttributes(List <OsuHitObject> hitObjects, double clockRate)
{
var(strainHistory, tapDiff) = calculateTapStrain(hitObjects, 0, clockRate);
double burstStrain = strainHistory.Max(v => v[0]);
var streamnessMask = CalculateStreamnessMask(hitObjects, burstStrain, clockRate);
double streamNoteCount = streamnessMask.Sum();
var(_, mashTapDiff) = calculateTapStrain(hitObjects, 1, clockRate);
return(new TapAttributes
{
TapDifficulty = tapDiff,
StreamNoteCount = streamNoteCount,
MashedTapDifficulty = mashTapDiff,
StrainHistory = strainHistory.Select(x => PowerMean.Of(x, 2.0)).ToArray()
});
}
/// <summary>
/// Calculates the strain values at each note and the maximum strain values
/// </summary>
private static (List <Vector <double> >, double) calculateTapStrain(List <OsuHitObject> hitObjects,
double mashLevel,
double clockRate)
{
var strainHistory = new List <Vector <double> >
{
Vector <double> .Build.Dense(timescale_count),
Vector <double> .Build.Dense(timescale_count)
};
var currStrain = Vector <double> .Build.Dense(timescale_count);
// compute strain at each object and store the results into strainHistory
if (hitObjects.Count >= 2)
{
double prevPrevTime = hitObjects[0].StartTime / 1000.0;
double prevTime = hitObjects[1].StartTime / 1000.0;
for (int i = 2; i < hitObjects.Count; i++)
{
double currTime = hitObjects[i].StartTime / 1000.0;
// compute current strain after decay
currStrain = currStrain.PointwiseMultiply((-decay_coeffs * (currTime - prevTime) / clockRate).PointwiseExp());
strainHistory.Add(currStrain.PointwisePower(1.1 / 3) * 1.5);
double distance = (hitObjects[i].StackedPosition - hitObjects[i - 1].StackedPosition).Length / (2 * hitObjects[i].Radius);
double spacedBuff = calculateSpacedness(distance) * spaced_buff_factor;
double deltaTime = Math.Max((currTime - prevPrevTime) / clockRate, 0.01);
// for 1/4 notes above 200 bpm the exponent is -2.7, otherwise it's -2
double strainAddition = Math.Max(Math.Pow(deltaTime, -2.7) * 0.265, Math.Pow(deltaTime, -2));
currStrain += decay_coeffs * strainAddition *
Math.Pow(calculateMashNerfFactor(distance, mashLevel), 3) *
Math.Pow(1 + spacedBuff, 3);
prevPrevTime = prevTime;
prevTime = currTime;
}
}
// compute difficulty by aggregating strainHistory
var strainResult = Vector <double> .Build.Dense(timescale_count);
for (int j = 0; j < decay_coeffs.Count; j++)
{
double[] singleStrainHistory = new double[hitObjects.Count];
for (int i = 0; i < hitObjects.Count; i++)
{
singleStrainHistory[i] = strainHistory[i][j];
}
Array.Sort(singleStrainHistory);
Array.Reverse(singleStrainHistory);
double singleStrainResult = 0;
double k = 1 - 0.04 * Math.Sqrt(decay_coeffs[j]);
for (int i = 0; i < hitObjects.Count; i++)
{
singleStrainResult += singleStrainHistory[i] * Math.Pow(k, i);
}
strainResult[j] = singleStrainResult * (1 - k) * timescale_factors[j];
}
double diff = PowerMean.Of(strainResult, 2);
return(strainHistory, diff);
}
public override double Calculate(Dictionary <string, double> categoryRatings = null)
{
mods = Score.Mods;
accuracy = Score.Accuracy;
scoreMaxCombo = Score.MaxCombo;
countGreat = Score.Statistics.GetOrDefault(HitResult.Great);
countOk = Score.Statistics.GetOrDefault(HitResult.Ok);
countMeh = Score.Statistics.GetOrDefault(HitResult.Meh);
countMiss = Score.Statistics.GetOrDefault(HitResult.Miss);
greatWindow = 79.5 - 6 * Attributes.OverallDifficulty;
double multiplier = 2.14; // This is being adjusted to keep the final pp value scaled around what it used to be when changing things
// guess the number of misses + slider breaks from combo
double comboBasedMissCount;
if (Attributes.SliderCount == 0)
{
if (scoreMaxCombo < Attributes.MaxCombo)
{
comboBasedMissCount = (double)Attributes.MaxCombo / scoreMaxCombo;
}
else
{
comboBasedMissCount = 0;
}
}
else
{
double fullComboThreshold = Attributes.MaxCombo - 0.1 * Attributes.SliderCount;
if (scoreMaxCombo < fullComboThreshold)
{
comboBasedMissCount = fullComboThreshold / scoreMaxCombo;
}
else
{
comboBasedMissCount = Math.Pow((Attributes.MaxCombo - scoreMaxCombo) / (0.1 * Attributes.SliderCount), 3);
}
}
effectiveMissCount = Math.Max(countMiss, comboBasedMissCount);
// Custom multipliers for NoFail and SpunOut.
if (mods.Any(m => m is OsuModNoFail))
{
multiplier *= Math.Max(0.90, 1.0 - 0.02 * effectiveMissCount);
}
if (mods.Any(m => m is OsuModSpunOut))
{
multiplier *= 1.0 - Math.Pow((double)Attributes.SpinnerCount / totalHits, 0.85);
}
double aimValue = computeAimValue();
double tapValue = computeTapValue();
double accuracyValue = computeAccuracyValue();
double totalValue = PowerMean.Of(new[] { aimValue, tapValue, accuracyValue }, total_value_exponent) * multiplier;
if (categoryRatings != null)
{
categoryRatings.Add("Aim", aimValue);
categoryRatings.Add("Tap", tapValue);
categoryRatings.Add("Accuracy", accuracyValue);
categoryRatings.Add("OD", Attributes.OverallDifficulty);
categoryRatings.Add("AR", Attributes.ApproachRate);
categoryRatings.Add("Max Combo", Attributes.MaxCombo);
}
return(totalValue);
}
private double computeAimValue()
{
if (Attributes.TotalObjectCount <= 1)
{
return(0);
}
// Get player's throughput according to combo
int comboTpCount = Attributes.ComboThroughputs.Length;
var comboPercentages = Generate.LinearSpaced(comboTpCount, 1.0 / comboTpCount, 1);
double scoreComboPercentage = ((double)scoreMaxCombo) / Attributes.MaxCombo;
double comboTp = LinearSpline.InterpolateSorted(comboPercentages, Attributes.ComboThroughputs)
.Interpolate(scoreComboPercentage);
// Get player's throughput according to miss count
double missTp = LinearSpline.InterpolateSorted(Attributes.MissCounts, Attributes.MissThroughputs)
.Interpolate(effectiveMissCount);
missTp = Math.Max(missTp, 0);
// Combine combo based throughput and miss count based throughput
double tp = PowerMean.Of(comboTp, missTp, 20);
// Hidden mod
if (mods.Any(h => h is OsuModHidden))
{
double hiddenFactor = Attributes.AimHiddenFactor;
// the buff starts decreasing at AR9.75 and reaches 0 at AR10.75
if (Attributes.ApproachRate > 10.75)
{
hiddenFactor = 1;
}
else if (Attributes.ApproachRate > 9.75)
{
hiddenFactor = 1 + (1 - Math.Pow(Math.Sin((Attributes.ApproachRate - 9.75) * Math.PI / 2), 2)) * (hiddenFactor - 1);
}
tp *= hiddenFactor;
}
// Account for cheesing
double modifiedAcc = getModifiedAcc();
double accOnCheeseNotes = 1 - (1 - modifiedAcc) * Math.Sqrt(totalHits / Attributes.CheeseNoteCount);
// accOnCheeseNotes can be negative. The formula below ensures a positive acc while
// preserving the value when accOnCheeseNotes is close to 1
double accOnCheeseNotesPositive = Math.Exp(accOnCheeseNotes - 1);
double urOnCheeseNotes = 10 * greatWindow / (Math.Sqrt(2) * SpecialFunctions.ErfInv(accOnCheeseNotesPositive));
double cheeseLevel = SpecialFunctions.Logistic(((urOnCheeseNotes * Attributes.AimDifficulty) - 3200) / 2000);
double cheeseFactor = LinearSpline.InterpolateSorted(Attributes.CheeseLevels, Attributes.CheeseFactors)
.Interpolate(cheeseLevel);
if (mods.Any(m => m is OsuModTouchDevice))
{
tp = Math.Min(tp, 1.47 * Math.Pow(tp, 0.8));
}
double aimValue = tpToPP(tp * cheeseFactor);
// penalize misses
aimValue *= Math.Pow(0.96, Math.Max(effectiveMissCount - miss_count_leniency, 0));
// Buff long maps
aimValue *= 1 + (SpecialFunctions.Logistic((totalHits - 2800) / 500.0) - SpecialFunctions.Logistic(-2800 / 500.0)) * 0.22;
// Buff very high AR and low AR
double approachRateFactor = 1.0;
if (Attributes.ApproachRate > 10)
{
approachRateFactor += (0.05 + 0.35 * Math.Pow(Math.Sin(Math.PI * Math.Min(totalHits, 1250) / 2500), 1.7)) *
Math.Pow(Attributes.ApproachRate - 10, 2);
}
else if (Attributes.ApproachRate < 8.0)
{
approachRateFactor += 0.01 * (8.0 - Attributes.ApproachRate);
}
aimValue *= approachRateFactor;
if (mods.Any(h => h is OsuModFlashlight))
{
// Apply object-based bonus for flashlight.
aimValue *= 1.0 + 0.35 * Math.Min(1.0, totalHits / 200.0) +
(totalHits > 200
? 0.3 * Math.Min(1.0, (totalHits - 200) / 300.0) +
(totalHits > 500 ? (totalHits - 500) / 2000.0 : 0.0)
: 0.0);
}
// Scale the aim value down with accuracy
double accLeniency = greatWindow * Attributes.AimDifficulty / 300;
double accPenalty = (0.09 / (accuracy - 1.3) + 0.3) * (accLeniency + 1.5);
aimValue *= 0.2 + SpecialFunctions.Logistic(-((accPenalty - 0.24953) / 0.18));
return(aimValue);
}
protected override DifficultyAttributes Calculate(IBeatmap beatmap, Mod[] mods, double clockRate)
{
var hitObjects = beatmap.HitObjects as List <OsuHitObject>;
double mapLength = 0;
if (beatmap.HitObjects.Count > 0)
{
mapLength = (beatmap.HitObjects.Last().StartTime - beatmap.HitObjects.First().StartTime) / 1000 / clockRate;
}
double preemptNoClockRate = BeatmapDifficulty.DifficultyRange(beatmap.BeatmapInfo.BaseDifficulty.ApproachRate, 1800, 1200, 450);
var noteDensities = NoteDensity.Calculate(hitObjects, preemptNoClockRate);
// Tap
var tapAttributes = Tap.CalculateTapAttributes(hitObjects, clockRate);
// Finger Control
double fingerControlDiff = FingerControl.CalculateFingerControlDiff(hitObjects, clockRate);
// Aim
var aimAttributes = Aim.CalculateAimAttributes(hitObjects, clockRate, tapAttributes.StrainHistory, noteDensities);
double tapStarRating = tap_multiplier * Math.Pow(tapAttributes.TapDifficulty, star_rating_exponent);
double aimStarRating = aim_multiplier * Math.Pow(aimAttributes.FcProbabilityThroughput, star_rating_exponent);
double fingerControlStarRating = finger_control_multiplier * Math.Pow(fingerControlDiff, star_rating_exponent);
double combinedStarRating = PowerMean.Of(new[] { tapStarRating, aimStarRating, fingerControlStarRating }, 7) * 1.131;
HitWindows hitWindows = new OsuHitWindows();
hitWindows.SetDifficulty(beatmap.BeatmapInfo.BaseDifficulty.OverallDifficulty);
// Todo: These int casts are temporary to achieve 1:1 results with osu!stable, and should be removed in the future
double hitWindowGreat = (int)(hitWindows.WindowFor(HitResult.Great)) / clockRate;
double preempt = (int)BeatmapDifficulty.DifficultyRange(beatmap.BeatmapInfo.BaseDifficulty.ApproachRate, 1800, 1200, 450) / clockRate;
int hitCirclesCount = beatmap.HitObjects.Count(h => h is HitCircle);
int sliderCount = beatmap.HitObjects.Count(h => h is Slider);
int spinnerCount = beatmap.HitObjects.Count(h => h is Spinner);
int beatmapMaxCombo = beatmap.HitObjects.Count;
// Add the ticks + tail of the slider. 1 is subtracted because the "headcircle" would be counted twice (once for the slider itself in the line above)
beatmapMaxCombo += beatmap.HitObjects.OfType <Slider>().Sum(s => s.NestedHitObjects.Count - 1);
return(new OsuDifficultyAttributes
{
StarRating = combinedStarRating,
Mods = mods,
Length = mapLength,
TapStarRating = tapStarRating,
TapDifficulty = tapAttributes.TapDifficulty,
StreamNoteCount = tapAttributes.StreamNoteCount,
MashTapDifficulty = tapAttributes.MashedTapDifficulty,
FingerControlStarRating = fingerControlStarRating,
FingerControlDifficulty = fingerControlDiff,
AimStarRating = aimStarRating,
AimDifficulty = aimAttributes.FcProbabilityThroughput,
AimHiddenFactor = aimAttributes.HiddenFactor,
ComboThroughputs = aimAttributes.ComboThroughputs,
MissThroughputs = aimAttributes.MissThroughputs,
MissCounts = aimAttributes.MissCounts,
CheeseNoteCount = aimAttributes.CheeseNoteCount,
CheeseLevels = aimAttributes.CheeseLevels,
CheeseFactors = aimAttributes.CheeseFactors,
ApproachRate = preempt > 1200 ? (1800 - preempt) / 120 : (1200 - preempt) / 150 + 5,
OverallDifficulty = (80 - hitWindowGreat) / 6,
MaxCombo = beatmapMaxCombo,
TotalObjectCount = beatmap.HitObjects.Count,
HitCircleCount = hitCirclesCount,
SliderCount = sliderCount,
SpinnerCount = spinnerCount
});
}
