UnrealEngineUWP/Engine/Source/Developer/MeshUtilities/Private/LayoutUV.cpp

// Copyright 1998-2016 Epic Games, Inc. All Rights Reserved.

#include "MeshUtilitiesPrivate.h"
#include "LayoutUV.h"
#include "DisjointSet.h"

DEFINE_LOG_CATEGORY_STATIC(LogLayoutUV, Warning, All);

#define CHART_JOINING	1

FLayoutUV::FLayoutUV( FRawMesh* InMesh, uint32 InSrcChannel, uint32 InDstChannel, uint32 InTextureResolution )
	: RawMesh( InMesh )
	, SrcChannel( InSrcChannel )
	, DstChannel( InDstChannel )
	, TextureResolution( InTextureResolution )
	, TotalUVArea( 0.0f )
	, LayoutRaster( TextureResolution, TextureResolution )
	, ChartRaster( TextureResolution, TextureResolution )
	, ChartShader( &ChartRaster )
{}

void FLayoutUV::FindCharts( const TMultiMap<int32,int32>& OverlappingCorners )
{
	double Begin = FPlatformTime::Seconds();

	uint32 NumIndexes = RawMesh->WedgeIndices.Num();
	uint32 NumTris = NumIndexes / 3;

	TArray< int32 > TranslatedMatches;
	TranslatedMatches.SetNumUninitialized( NumIndexes );
	TexCoords.SetNumUninitialized( NumIndexes );
	for( uint32 i = 0; i < NumIndexes; i++ )
	{
		TranslatedMatches[i] = -1;
		TexCoords[i] = RawMesh->WedgeTexCoords[ SrcChannel ][i];
	}

	// Build disjoint set
	FDisjointSet DisjointSet( NumTris );
	for( uint32 i = 0; i < NumIndexes; i++ )
	{
		for( auto It = OverlappingCorners.CreateConstKeyIterator(i); It; ++It )
		{
			uint32 j = It.Value();

			if( j > i )
			{
				const uint32 TriI = i/3;
				const uint32 TriJ = j/3;

				bool bUnion = false;

#if CHART_JOINING
				bool bPositionMatch = PositionsMatch( i, j );
				if( bPositionMatch )
				{
					uint32 i1 = 3 * TriI + (i + 1) % 3;
					uint32 i2 = 3 * TriI + (i + 2) % 3;
					uint32 j1 = 3 * TriJ + (j + 1) % 3;
					uint32 j2 = 3 * TriJ + (j + 2) % 3;

					bool bEdgeMatch21 = PositionsMatch( i2, j1 );
					bool bEdgeMatch12 = PositionsMatch( i1, j2 );
					if( bEdgeMatch21 || bEdgeMatch12 )
					{
						uint32 ie = bEdgeMatch21 ? i2 : i1;
						uint32 je = bEdgeMatch21 ? j1 : j2;
							
						bool bUVMatch = UVsMatch( i, j ) && UVsMatch( ie, je );
						bool bUVWindingMatch = TriangleUVArea( TriI ) * TriangleUVArea( TriJ ) >= 0.0f;
						if( bUVMatch && bUVWindingMatch )
						{
							bUnion = true;
						}
						else if( NormalsMatch( i, j ) && NormalsMatch( ie, je ) )
						{
							// Chart edge
							FVector2D EdgeUVi = TexCoords[ie] - TexCoords[i];
							FVector2D EdgeUVj = TexCoords[je] - TexCoords[j];
							
							// Would these edges match if the charts were translated
							bool bTranslatedUVMatch = ( EdgeUVi - EdgeUVj ).IsNearlyZero( THRESH_UVS_ARE_SAME );
							if( bTranslatedUVMatch )
							{
								// Note: may be mirrored
								
								// TODO should these be restricted to axis aligned edges?
								uint32 EdgeI = bEdgeMatch21 ? i2 : i;
								uint32 EdgeJ = bEdgeMatch21 ? j : j2;

								// Only allow one match per edge
								if( TranslatedMatches[ EdgeI ] < 0 &&
									TranslatedMatches[ EdgeJ ] < 0 )
								{
									TranslatedMatches[ EdgeI ] = EdgeJ;
									TranslatedMatches[ EdgeJ ] = EdgeI;
								}
							}
						}
					}
				}
#else
				if( VertsMatch( i, j ) )
				{
					// Edge must match as well (same winding)
					if( VertsMatch( 3 * TriI + (i - 1) % 3, 3 * TriJ + (j + 1) % 3 ) ||
						VertsMatch( 3 * TriI + (i + 1) % 3, 3 * TriJ + (j - 1) % 3 ) )
					{
						// Check for UV winding match too
						if( TriangleUVArea( TriI ) * TriangleUVArea( TriJ ) >= 0.0f )
						{
							bUnion = true;
						}
					}
				}
#endif

				if( bUnion )
				{
					// TODO solve spiral case by checking sets for UV overlap
					DisjointSet.Union( TriI, TriJ );
				}
			}
		}
	}

	// Sort tris by chart
	SortedTris.SetNumUninitialized( NumTris );
	for( uint32 i = 0; i < NumTris; i++ )
	{
		// Flatten disjoint set path
		DisjointSet.Find(i);
		SortedTris[i] = i;
	}

	struct FCompareTris
	{
		FDisjointSet* DisjointSet;

		FCompareTris( FDisjointSet* InDisjointSet )
		: DisjointSet( InDisjointSet )
		{}

		FORCEINLINE bool operator()( uint32 A, uint32 B ) const
		{
			return (*DisjointSet)[A] < (*DisjointSet)[B];
		}
	};
	SortedTris.Sort( FCompareTris( &DisjointSet ) );

	TMap< uint32, int32 > DisjointSetToChartMap;

	// Build Charts
	for( uint32 Tri = 0; Tri < NumTris; )
	{
		int32 i = Charts.AddUninitialized();
		FMeshChart& Chart = Charts[i];
		
		Chart.MinUV = FVector2D( FLT_MAX, FLT_MAX );
		Chart.MaxUV = FVector2D( -FLT_MAX, -FLT_MAX );
		Chart.UVArea = 0.0f;
		Chart.WorldScale = FVector2D::ZeroVector;
		FMemory::Memset( Chart.Join, 0xff );

		Chart.FirstTri = Tri;

		uint32 ChartID = DisjointSet[ SortedTris[ Tri ] ];
		DisjointSetToChartMap.Add( ChartID, i );

		for( ; Tri < NumTris && DisjointSet[ SortedTris[ Tri ] ] == ChartID; Tri++ )
		{
			// Calculate chart bounds
			FVector		Positions[3];
			FVector2D	UVs[3];
			for( int k = 0; k < 3; k++ )
			{
				uint32 Index = 3 * SortedTris[ Tri ] + k;

				Positions[k] = RawMesh->GetWedgePosition( Index );
				UVs[k] = TexCoords[ Index ];

				Chart.MinUV.X = FMath::Min( Chart.MinUV.X, UVs[k].X );
				Chart.MinUV.Y = FMath::Min( Chart.MinUV.Y, UVs[k].Y );
				Chart.MaxUV.X = FMath::Max( Chart.MaxUV.X, UVs[k].X );
				Chart.MaxUV.Y = FMath::Max( Chart.MaxUV.Y, UVs[k].Y );
			}

			FVector Edge1 = Positions[1] - Positions[0];
			FVector Edge2 = Positions[2] - Positions[0];
			float Area = 0.5f * ( Edge1 ^ Edge2 ).Size();

			FVector2D EdgeUV1 = UVs[1] - UVs[0];
			FVector2D EdgeUV2 = UVs[2] - UVs[0];
			float UVArea = 0.5f * FMath::Abs( EdgeUV1.X * EdgeUV2.Y - EdgeUV1.Y * EdgeUV2.X );

			FVector2D UVLength;
			UVLength.X = ( EdgeUV2.Y * Edge1 - EdgeUV1.Y * Edge2 ).Size();
			UVLength.Y = (-EdgeUV2.X * Edge1 + EdgeUV1.X * Edge2 ).Size();
			
			Chart.WorldScale += UVLength;
			Chart.UVArea += UVArea;
		}
		
		Chart.LastTri = Tri;

#if !CHART_JOINING
		if( Chart.UVArea > 1e-4f )
		{
			Chart.WorldScale /= Chart.UVArea;
		}
		else
		{
			Chart.WorldScale = FVector2D::ZeroVector;
		}

		//Chart.WorldScale.Set(1,1);

		TotalUVArea += Chart.UVArea * Chart.WorldScale.X * Chart.WorldScale.Y;
#endif
	}

#if CHART_JOINING
	for( int32 i = 0; i < Charts.Num(); i++ )
	{
		FMeshChart& Chart = Charts[i];

		for( uint32 Tri = Chart.FirstTri; Tri < Chart.LastTri; Tri++ )
		{
			for( int k = 0; k < 3; k++ )
			{
				uint32 Index = 3 * SortedTris[ Tri ] + k;

				if( TranslatedMatches[ Index ] >= 0 )
				{
					checkSlow( TranslatedMatches[ TranslatedMatches[ Index ] ] == Index );

					uint32 V0i = Index;
					uint32 V0j = TranslatedMatches[ Index ];

					uint32 TriI = V0i / 3;
					uint32 TriJ = V0j / 3;
					
					if( TriJ <= TriI )
					{
						// Only need to consider one direction
						continue;
					}
					
					uint32 V1i = 3 * TriI + (V0i + 1) % 3;
					uint32 V1j = 3 * TriJ + (V0j + 1) % 3;

					int32 ChartI = i;
					int32 ChartJ = DisjointSetToChartMap[ DisjointSet[ TriJ ] ];

					FVector2D UV0i = TexCoords[ V0i ];
					FVector2D UV1i = TexCoords[ V1i ];
					FVector2D UV0j = TexCoords[ V0j ];
					FVector2D UV1j = TexCoords[ V1j ];

					FVector2D EdgeUVi = UV1i - UV0i;
					FVector2D EdgeUVj = UV1j - UV0j;

					bool bMirrored = TriangleUVArea( TriI ) * TriangleUVArea( TriJ ) < 0.0f;
					
					FVector2D EdgeOffset0 = UV0i - UV1j;
					FVector2D EdgeOffset1 = UV1i - UV0j;
					checkSlow( ( EdgeOffset0 - EdgeOffset1 ).IsNearlyZero( THRESH_UVS_ARE_SAME ) );

					FVector2D Translation = EdgeOffset0;

					FMeshChart& ChartA = Charts[ ChartI ];
					FMeshChart& ChartB = Charts[ ChartJ ];

					for( uint32 Side = 0; Side < 4; Side++ )
					{
						// Join[] = { left, right, bottom, top }

						// FIXME
						if( bMirrored )
							continue;

						if( ChartA.Join[ Side ^ 0 ] != -1 ||
							ChartB.Join[ Side ^ 1 ] != -1 )
						{
							// Already joined with something else
							continue;
						}

						uint32 Sign = Side & 1;
						uint32 Axis = Side >> 1;

						bool bAxisAligned = FMath::Abs( EdgeUVi[ Axis ] ) < THRESH_UVS_ARE_SAME;
						bool bBorderA = FMath::Abs( UV0i[ Axis ] - ( Sign ^ 0 ? Chart.MaxUV[ Axis ] : Chart.MinUV[ Axis ] ) ) < THRESH_UVS_ARE_SAME;
						bool bBorderB = FMath::Abs( UV0j[ Axis ] - ( Sign ^ 1 ? Chart.MaxUV[ Axis ] : Chart.MinUV[ Axis ] ) ) < THRESH_UVS_ARE_SAME;

						// FIXME mirrored
						if( !bAxisAligned || !bBorderA || !bBorderB )
						{
							// Edges weren't on matching rectangle borders
							continue;
						}

						FVector2D CenterA = 0.5f * ( ChartA.MinUV + ChartA.MaxUV );
						FVector2D CenterB = 0.5f * ( ChartB.MinUV + ChartB.MaxUV );

						FVector2D ExtentA = 0.5f * ( ChartA.MaxUV - ChartA.MinUV );
						FVector2D ExtentB = 0.5f * ( ChartB.MaxUV - ChartB.MinUV );

						// FIXME mirrored
						CenterB += Translation;

						FVector2D CenterDiff = CenterA - CenterB;
						FVector2D ExtentDiff = ExtentA - ExtentB;
						FVector2D Separation = ExtentA + ExtentB + CenterDiff * ( Sign ? 1.0f : -1.0f );

						bool bCenterMatch = FMath::Abs( CenterDiff[ Axis ^ 1 ] ) < THRESH_UVS_ARE_SAME;
						bool bExtentMatch = FMath::Abs( ExtentDiff[ Axis ^ 1 ] ) < THRESH_UVS_ARE_SAME;
						bool bSeparate    = FMath::Abs( Separation[ Axis ^ 0 ] ) < THRESH_UVS_ARE_SAME;
	
						if( !bCenterMatch || !bExtentMatch || !bSeparate )
						{
							// Rectangles don't match up after translation
							continue;
						}

						// Found a valid edge join
						ChartA.Join[ Side ^ 0 ] = ChartJ;
						ChartB.Join[ Side ^ 1 ] = ChartI;
						break;
					}
				}
			}
		}
	}

	TArray< uint32 > JoinedSortedTris;
	JoinedSortedTris.Reserve( NumTris );

	// Detect loops
	for( uint32 Axis = 0; Axis < 2; Axis++ )
	{
		uint32 Side = Axis << 1;

		for( int32 i = 0; i < Charts.Num(); i++ )
		{
			int32 j = Charts[i].Join[ Side ^ 1 ];
			while( j != -1 )
			{
				int32 Next = Charts[j].Join[ Side ^ 1 ];
				if( Next == i )
				{
					// Break loop
					Charts[i].Join[ Side ^ 0 ] = -1;
					Charts[j].Join[ Side ^ 1 ] = -1;
					break;
				}
				j = Next;
			}
		}
	}

	// Join rows first, then columns
	for( uint32 Axis = 0; Axis < 2; Axis++ )
	{
		for( int32 i = 0; i < Charts.Num(); i++ )
		{
			FMeshChart& ChartA = Charts[i];

			if( ChartA.FirstTri == ChartA.LastTri )
			{
				// Empty chart
				continue;
			}
			
			for( uint32 Side = 0; Side < 4; Side++ )
			{
				if( ChartA.Join[ Side ] != -1 )
				{
					FMeshChart& ChartB = Charts[ ChartA.Join[ Side ] ];

					check( ChartB.Join[ Side ^ 1 ] == i );
					check( ChartB.FirstTri != ChartB.LastTri );
				}
			}
		}

		NumTris = 0;

		for( int32 i = 0; i < Charts.Num(); i++ )
		{
			FMeshChart& Chart = Charts[i];
			NumTris += Chart.LastTri - Chart.FirstTri;
		}
		check( NumTris == SortedTris.Num() );

		NumTris = 0;
		for( int32 i = 0; i < Charts.Num(); i++ )
		{
			FMeshChart& ChartA = Charts[i];

			if( ChartA.FirstTri == ChartA.LastTri )
			{
				// Empty chart
				continue;
			}

			uint32 Side = Axis << 1;

			// Find start (left, bottom)
			if( ChartA.Join[ Side ^ 0 ] == -1 )
			{
				// Add original tris
				NumTris += ChartA.LastTri - ChartA.FirstTri;

				// Continue joining until no more to the (right, top)
				int32 Next = ChartA.Join[ Side ^ 1 ];
				while( Next != -1 )
				{
					FMeshChart& ChartB = Charts[ Next ];

					NumTris += ChartB.LastTri - ChartB.FirstTri;
					Next = ChartB.Join[ Side ^ 1 ];
				}
			}
		}
		check( NumTris == SortedTris.Num() );

#if 1
		NumTris = 0;
		for( int32 i = 0; i < Charts.Num(); i++ )
		{
			FMeshChart& ChartA = Charts[i];

			if( ChartA.FirstTri == ChartA.LastTri )
			{
				// Empty chart
				continue;
			}

			// Join[] = { left, right, bottom, top }

			uint32 Side = Axis << 1;

			// Find start (left, bottom)
			if( ChartA.Join[ Side ^ 0 ] == -1 )
			{
				uint32 FirstTri = JoinedSortedTris.Num();
			
				// Add original tris
				for( uint32 Tri = ChartA.FirstTri; Tri < ChartA.LastTri; Tri++ )
				{
					JoinedSortedTris.Add( SortedTris[ Tri ] );
				}
				NumTris += ChartA.LastTri - ChartA.FirstTri;

				// Continue joining until no more to the (right, top)
				while( ChartA.Join[ Side ^ 1 ] != -1 )
				{
					FMeshChart& ChartB = Charts[ ChartA.Join[ Side ^ 1 ] ];

					check( ChartB.FirstTri != ChartB.LastTri );

					FVector2D Translation = ChartA.MinUV - ChartB.MinUV;
					Translation[ Axis ] += ChartA.MaxUV[ Axis ] - ChartA.MinUV[ Axis ];

					for( uint32 Tri = ChartB.FirstTri; Tri < ChartB.LastTri; Tri++ )
					{
						JoinedSortedTris.Add( SortedTris[ Tri ] );
						for( int k = 0; k < 3; k++ )
						{
							TexCoords[ 3 * SortedTris[ Tri ] + k ] += Translation;
						}
					}
					NumTris += ChartB.LastTri - ChartB.FirstTri;

					ChartA.Join[ Side ^ 1 ] = ChartB.Join[ Side ^ 1 ];
					ChartA.MaxUV[ Axis ] += ChartB.MaxUV[ Axis ] - ChartB.MinUV[ Axis ];
					ChartA.WorldScale += ChartB.WorldScale;
					ChartA.UVArea += ChartB.UVArea;

					ChartB.FirstTri = 0;
					ChartB.LastTri = 0;
					ChartB.UVArea = 0.0f;

					DisconnectChart( ChartB, Side ^ 2 );
					DisconnectChart( ChartB, Side ^ 3 );
				}

				ChartA.FirstTri = FirstTri;
				ChartA.LastTri = JoinedSortedTris.Num();
			}
			else
			{
				// Make sure a starting chart could connect to this
				FMeshChart& ChartB = Charts[ ChartA.Join[ Side ^ 0 ] ];
				check( ChartB.Join[ Side ^ 1 ] == i );
				check( ChartB.FirstTri != ChartB.LastTri );
			}
		}
		check( NumTris == SortedTris.Num() );

		check( SortedTris.Num() == JoinedSortedTris.Num() );
		Exchange( SortedTris, JoinedSortedTris );
		JoinedSortedTris.Reset();
#endif
	}
	
	// Clean out empty charts
	for( int32 i = 0; i < Charts.Num(); i++ )
	{
		while( i < Charts.Num() && Charts[i].FirstTri == Charts[i].LastTri )
		{
			Charts.RemoveAtSwap(i);
		}
	}

	for( int32 i = 0; i < Charts.Num(); i++ )
	{
		FMeshChart& Chart = Charts[i];

		if( Chart.UVArea > 1e-4f )
		{
			Chart.WorldScale /= Chart.UVArea;
		}
		else
		{
			Chart.WorldScale = FVector2D::ZeroVector;
		}

		TotalUVArea += Chart.UVArea * Chart.WorldScale.X * Chart.WorldScale.Y;
	}
#endif

	double End = FPlatformTime::Seconds();

	UE_LOG(LogLayoutUV, Display, TEXT("FindCharts: %s"), *FPlatformTime::PrettyTime(End - Begin) );
}

bool FLayoutUV::FindBestPacking()
{
	if( (uint32)Charts.Num() > TextureResolution * TextureResolution )
	{
		// More charts than texels
		return false;
	}
	
	const float LinearSearchStart = 0.5f;
	const float LinearSearchStep = 0.5f;
	const int32 BinarySearchSteps = 6;
	
	float UVScaleFail = TextureResolution * FMath::Sqrt( 1.0f / TotalUVArea );
	float UVScalePass = TextureResolution * FMath::Sqrt( LinearSearchStart / TotalUVArea );

	// Linear search for first fit
	while(1)
	{
		ScaleCharts( UVScalePass );

		bool bFit = PackCharts();
		if( bFit )
		{
			break;
		}

		UVScaleFail = UVScalePass;
		UVScalePass *= LinearSearchStep;
	}

	// Binary search for best fit
	for( int32 i = 0; i < BinarySearchSteps; i++ )
	{
		float UVScale = 0.5f * ( UVScaleFail + UVScalePass );
		ScaleCharts( UVScale );

		bool bFit = PackCharts();
		if( bFit )
		{
			UVScalePass = UVScale;
		}
		else
		{
			UVScaleFail = UVScale;
		}
	}

	// TODO store packing scale/bias separate so this isn't necessary
	ScaleCharts( UVScalePass );
	PackCharts();

	return true;
}

void FLayoutUV::ScaleCharts( float UVScale )
{
	for( int32 i = 0; i < Charts.Num(); i++ )
	{
		FMeshChart& Chart = Charts[i];
		Chart.UVScale = Chart.WorldScale * UVScale;
	}
	
	// Scale charts such that they all fit and roughly total the same area as before
#if 1
	float UniformScale = 1.0f;
	for( int i = 0; i < 1000; i++ )
	{
		uint32 NumMaxedOut = 0;
		float ScaledUVArea = 0.0f;
		for( int32 ChartIndex = 0; ChartIndex < Charts.Num(); ChartIndex++ )
		{
			FMeshChart& Chart = Charts[ChartIndex];

			FVector2D ChartSize	= Chart.MaxUV - Chart.MinUV;
			FVector2D ChartSizeScaled = ChartSize * Chart.UVScale * UniformScale;

			const float MaxChartEdge = TextureResolution - 1.0f;
			const float LongestChartEdge = FMath::Max( ChartSizeScaled.X, ChartSizeScaled.Y );

			const float Epsilon = 0.01f;
			if( LongestChartEdge + Epsilon > MaxChartEdge )
			{
				// Rescale oversized charts to fit
				Chart.UVScale.X = MaxChartEdge / FMath::Max( ChartSize.X, ChartSize.Y );
				Chart.UVScale.Y = MaxChartEdge / FMath::Max( ChartSize.X, ChartSize.Y );
				NumMaxedOut++;
			}
			else
			{
				Chart.UVScale.X *= UniformScale;
				Chart.UVScale.Y *= UniformScale;
			}
			
			ScaledUVArea += Chart.UVArea * Chart.UVScale.X * Chart.UVScale.Y;
		}

		if( NumMaxedOut == 0 )
		{
			// No charts maxed out so no need to rebalance
			break;
		}

		if( NumMaxedOut == Charts.Num() )
		{
			// All charts are maxed out
			break;
		}

		// Scale up smaller charts to maintain expected total area
		// Want ScaledUVArea == TotalUVArea * UVScale^2
		float RebalanceScale = UVScale * FMath::Sqrt( TotalUVArea / ScaledUVArea );
		if( RebalanceScale < 1.01f )
		{
			// Stop if further rebalancing is minor
			break;
		}
		UniformScale = RebalanceScale;
	}
#endif

#if 1
	float NonuniformScale = 1.0f;
	for( int i = 0; i < 1000; i++ )
	{
		uint32 NumMaxedOut = 0;
		float ScaledUVArea = 0.0f;
		for( int32 ChartIndex = 0; ChartIndex < Charts.Num(); ChartIndex++ )
		{
			FMeshChart& Chart = Charts[ChartIndex];

			for( int k = 0; k < 2; k++ )
			{
				const float MaximumChartSize = TextureResolution - 1.0f;
				const float ChartSize = Chart.MaxUV[k] - Chart.MinUV[k];
				const float ChartSizeScaled = ChartSize * Chart.UVScale[k] * NonuniformScale;

				const float Epsilon = 0.01f;
				if( ChartSizeScaled + Epsilon > MaximumChartSize )
				{
					// Scale oversized charts to max size
					Chart.UVScale[k] = MaximumChartSize / ChartSize;
					NumMaxedOut++;
				}
				else
				{
					Chart.UVScale[k] *= NonuniformScale;
				}
			}

			ScaledUVArea += Chart.UVArea * Chart.UVScale.X * Chart.UVScale.Y;
		}

		if( NumMaxedOut == 0 )
		{
			// No charts maxed out so no need to rebalance
			break;
		}

		if( NumMaxedOut == Charts.Num() * 2 )
		{
			// All charts are maxed out in both dimensions
			break;
		}

		// Scale up smaller charts to maintain expected total area
		// Want ScaledUVArea == TotalUVArea * UVScale^2
		float RebalanceScale = UVScale * FMath::Sqrt( TotalUVArea / ScaledUVArea );
		if( RebalanceScale < 1.01f )
		{
			// Stop if further rebalancing is minor
			break;
		}
		NonuniformScale = RebalanceScale;
	}
#endif

	// Sort charts from largest to smallest
	struct FCompareCharts
	{
		FORCEINLINE bool operator()( const FMeshChart& A, const FMeshChart& B ) const
		{
			// Rect area
			FVector2D ChartRectA = ( A.MaxUV - A.MinUV ) * A.UVScale;
			FVector2D ChartRectB = ( B.MaxUV - B.MinUV ) * B.UVScale;
			return ChartRectA.X * ChartRectA.Y > ChartRectB.X * ChartRectB.Y;
		}
	};
	Charts.Sort( FCompareCharts() );
}

bool FLayoutUV::PackCharts()
{
	uint32 RasterizeCycles = 0;
	uint32 FindCycles = 0;
	
	double BeginPackCharts = FPlatformTime::Seconds();

	LayoutRaster.Clear();

	for( int32 i = 0; i < Charts.Num(); i++ )
	{
		FMeshChart& Chart = Charts[i];

		// Try different orientations and pick best
		int32				BestOrientation = -1;
		FAllocator2D::FRect	BestRect = { ~0u, ~0u, ~0u, ~0u };

		for( int32 Orientation = 0; Orientation < 8; Orientation++ )
		{
			// TODO If any dimension is less than 1 pixel shrink dimension to zero

			OrientChart( Chart, Orientation );
			
			FVector2D ChartSize = Chart.MaxUV - Chart.MinUV;
			ChartSize = ChartSize.X * Chart.PackingScaleU + ChartSize.Y * Chart.PackingScaleV;

			// Only need half pixel dilate for rects
			FAllocator2D::FRect	Rect;
			Rect.X = 0;
			Rect.Y = 0;
			Rect.W = FMath::CeilToInt( FMath::Abs( ChartSize.X ) + 1.0f );
			Rect.H = FMath::CeilToInt( FMath::Abs( ChartSize.Y ) + 1.0f );

			// Just in case lack of precision pushes it over
			Rect.W = FMath::Min( TextureResolution, Rect.W );
			Rect.H = FMath::Min( TextureResolution, Rect.H );

			const bool bRectPack = false;

			if( bRectPack )
			{
				if( LayoutRaster.Find( Rect ) )
				{
					// Is best?
					if( Rect.X + Rect.Y * TextureResolution < BestRect.X + BestRect.Y * TextureResolution )
					{
						BestOrientation = Orientation;
						BestRect = Rect;
					}
				}
				else
				{
					continue;
				}
			}
			else
			{
				uint32 BeginRasterize = FPlatformTime::Cycles();
				RasterizeChart( Chart, Rect.W, Rect.H );
				RasterizeCycles += FPlatformTime::Cycles() - BeginRasterize;

				uint32 BeginFind = FPlatformTime::Cycles();
				bool bFound = LayoutRaster.Find( Rect, ChartRaster );
				FindCycles += FPlatformTime::Cycles() - BeginFind;

				if( bFound )
				{
					// Is best?
					if( Rect.X + Rect.Y * TextureResolution < BestRect.X + BestRect.Y * TextureResolution )
					{
						BestOrientation = Orientation;
						BestRect = Rect;
					}
				}
				else
				{
					continue;
				}
			}
		}

		if( BestOrientation >= 0 )
		{
			// Add chart to layout
			OrientChart( Chart, BestOrientation );

			uint32 BeginRasterize = FPlatformTime::Cycles();
			RasterizeChart( Chart, BestRect.W, BestRect.H );
			RasterizeCycles += FPlatformTime::Cycles() - BeginRasterize;

			LayoutRaster.Alloc( BestRect, ChartRaster );

			Chart.PackingBias.X += BestRect.X;
			Chart.PackingBias.Y += BestRect.Y;
		}
		else
		{
			// Found no orientation that fit
			return false;
		}
	}

	double EndPackCharts = FPlatformTime::Seconds();

	UE_LOG(LogLayoutUV, Display, TEXT("PackCharts: %s"),	*FPlatformTime::PrettyTime(EndPackCharts - BeginPackCharts));
	UE_LOG(LogLayoutUV, Display, TEXT("  Rasterize: %u"),	RasterizeCycles);
	UE_LOG(LogLayoutUV, Display, TEXT("  Find: %u"),		FindCycles);

	return true;
}

void FLayoutUV::OrientChart( FMeshChart& Chart, int32 Orientation )
{
	switch( Orientation )
	{
	case 0:
		// 0 degrees
		Chart.PackingScaleU = FVector2D( Chart.UVScale.X, 0 );
		Chart.PackingScaleV = FVector2D( 0, Chart.UVScale.Y );
		Chart.PackingBias = -Chart.MinUV.X * Chart.PackingScaleU - Chart.MinUV.Y * Chart.PackingScaleV + 0.5f;
		break;
	case 1:
		// 0 degrees, flip x
		Chart.PackingScaleU = FVector2D( -Chart.UVScale.X, 0 );
		Chart.PackingScaleV = FVector2D( 0, Chart.UVScale.Y );
		Chart.PackingBias = -Chart.MaxUV.X * Chart.PackingScaleU - Chart.MinUV.Y * Chart.PackingScaleV + 0.5f;
		break;
	case 2:
		// 90 degrees
		Chart.PackingScaleU = FVector2D( 0, -Chart.UVScale.X );
		Chart.PackingScaleV = FVector2D( Chart.UVScale.Y, 0 );
		Chart.PackingBias = -Chart.MaxUV.X * Chart.PackingScaleU - Chart.MinUV.Y * Chart.PackingScaleV + 0.5f;
		break;
	case 3:
		// 90 degrees, flip x
		Chart.PackingScaleU = FVector2D( 0, Chart.UVScale.X );
		Chart.PackingScaleV = FVector2D( Chart.UVScale.Y, 0 );
		Chart.PackingBias = -Chart.MinUV.X * Chart.PackingScaleU - Chart.MinUV.Y * Chart.PackingScaleV + 0.5f;
		break;
	case 4:
		// 180 degrees
		Chart.PackingScaleU = FVector2D( -Chart.UVScale.X, 0 );
		Chart.PackingScaleV = FVector2D( 0, -Chart.UVScale.Y );
		Chart.PackingBias = -Chart.MaxUV.X * Chart.PackingScaleU - Chart.MaxUV.Y * Chart.PackingScaleV + 0.5f;
		break;
	case 5:
		// 180 degrees, flip x
		Chart.PackingScaleU = FVector2D( Chart.UVScale.X, 0 );
		Chart.PackingScaleV = FVector2D( 0, -Chart.UVScale.Y );
		Chart.PackingBias = -Chart.MinUV.X * Chart.PackingScaleU - Chart.MaxUV.Y * Chart.PackingScaleV + 0.5f;
		break;
	case 6:
		// 270 degrees
		Chart.PackingScaleU = FVector2D( 0, Chart.UVScale.X );
		Chart.PackingScaleV = FVector2D( -Chart.UVScale.Y, 0 );
		Chart.PackingBias = -Chart.MinUV.X * Chart.PackingScaleU - Chart.MaxUV.Y * Chart.PackingScaleV + 0.5f;
		break;
	case 7:
		// 270 degrees, flip x
		Chart.PackingScaleU = FVector2D( 0, -Chart.UVScale.X );
		Chart.PackingScaleV = FVector2D( -Chart.UVScale.Y, 0 );
		Chart.PackingBias = -Chart.MaxUV.X * Chart.PackingScaleU - Chart.MaxUV.Y * Chart.PackingScaleV + 0.5f;
		break;
	}
}

// Max of 2048x2048 due to precision
// Dilate in 28.4 fixed point. Half pixel dilation is conservative rasterization.
// Dilation same as Minkowski sum of triangle and square.
template< typename TShader, int32 Dilate >
void RasterizeTriangle( TShader& Shader, const FVector2D Points[3], int32 ScissorWidth, int32 ScissorHeight )
{
	const FVector2D HalfPixel( 0.5f, 0.5f );
	FVector2D p0 = Points[0] - HalfPixel;
	FVector2D p1 = Points[1] - HalfPixel;
	FVector2D p2 = Points[2] - HalfPixel;

	// Correct winding
	float Facing = ( p0.X - p1.X ) * ( p2.Y - p0.Y ) - ( p0.Y - p1.Y ) * ( p2.X - p0.X );
	if( Facing < 0.0f )
	{
		Swap( p0, p2 );
	}

	// 28.4 fixed point
	const int32 X0 = (int32)( 16.0f * p0.X + 0.5f );
	const int32 X1 = (int32)( 16.0f * p1.X + 0.5f );
	const int32 X2 = (int32)( 16.0f * p2.X + 0.5f );
	
	const int32 Y0 = (int32)( 16.0f * p0.Y + 0.5f );
	const int32 Y1 = (int32)( 16.0f * p1.Y + 0.5f );
	const int32 Y2 = (int32)( 16.0f * p2.Y + 0.5f );

	// Bounding rect
	int32 MinX = ( FMath::Min3( X0, X1, X2 ) - Dilate + 15 ) / 16;
	int32 MaxX = ( FMath::Max3( X0, X1, X2 ) + Dilate + 15 ) / 16;
	int32 MinY = ( FMath::Min3( Y0, Y1, Y2 ) - Dilate + 15 ) / 16;
	int32 MaxY = ( FMath::Max3( Y0, Y1, Y2 ) + Dilate + 15 ) / 16;

	// Clip to image
	MinX = FMath::Clamp( MinX, 0, ScissorWidth );
	MaxX = FMath::Clamp( MaxX, 0, ScissorWidth );
	MinY = FMath::Clamp( MinY, 0, ScissorHeight );
	MaxY = FMath::Clamp( MaxY, 0, ScissorHeight );

	// Deltas
	const int32 DX01 = X0 - X1;
	const int32 DX12 = X1 - X2;
	const int32 DX20 = X2 - X0;

	const int32 DY01 = Y0 - Y1;
	const int32 DY12 = Y1 - Y2;
	const int32 DY20 = Y2 - Y0;

	// Half-edge constants
	int32 C0 = DY01 * X0 - DX01 * Y0;
	int32 C1 = DY12 * X1 - DX12 * Y1;
	int32 C2 = DY20 * X2 - DX20 * Y2;

	// Correct for fill convention
	C0 += ( DY01 < 0 || ( DY01 == 0 && DX01 > 0 ) ) ? 0 : -1;
	C1 += ( DY12 < 0 || ( DY12 == 0 && DX12 > 0 ) ) ? 0 : -1;
	C2 += ( DY20 < 0 || ( DY20 == 0 && DX20 > 0 ) ) ? 0 : -1;

	// Dilate edges
	C0 += ( abs(DX01) + abs(DY01) ) * Dilate;
	C1 += ( abs(DX12) + abs(DY12) ) * Dilate;
	C2 += ( abs(DX20) + abs(DY20) ) * Dilate;

	for( int32 y = MinY; y < MaxY; y++ )
	{
		for( int32 x = MinX; x < MaxX; x++ )
		{
			// same as Edge1 >= 0 && Edge2 >= 0 && Edge3 >= 0
			int32 IsInside;
			IsInside  = C0 + (DX01 * y - DY01 * x) * 16;
			IsInside |= C1 + (DX12 * y - DY12 * x) * 16;
			IsInside |= C2 + (DX20 * y - DY20 * x) * 16;

			if( IsInside >= 0 )
			{
				Shader.Process( x, y );
			}
		}
	}
}

void FLayoutUV::RasterizeChart( const FMeshChart& Chart, uint32 RectW, uint32 RectH )
{
	// Bilinear footprint is -1 to 1 pixels. If packed geometrically, only a half pixel dilation
	// would be needed to guarantee all charts were at least 1 pixel away, safe for bilinear filtering.
	// Unfortunately, with pixel packing a full 1 pixel dilation is required unless chart edges exactly
	// align with pixel centers.

	ChartRaster.Clear();

	for( uint32 Tri = Chart.FirstTri; Tri < Chart.LastTri; Tri++ )
	{
		FVector2D Points[3];
		for( int k = 0; k < 3; k++ )
		{
			const FVector2D& UV = TexCoords[ 3 * SortedTris[ Tri ] + k ];
			Points[k] = UV.X * Chart.PackingScaleU + UV.Y * Chart.PackingScaleV + Chart.PackingBias;
		}

		RasterizeTriangle< FAllocator2DShader, 16 >( ChartShader, Points, RectW, RectH );
	}
}

void FLayoutUV::CommitPackedUVs()
{
	// Alloc new UV channel
	RawMesh->WedgeTexCoords[ DstChannel ].SetNumUninitialized( TexCoords.Num() );

	// Commit chart UVs
	for( int32 i = 0; i < Charts.Num(); i++ )
	{
		FMeshChart& Chart = Charts[i];

		Chart.PackingScaleU /= TextureResolution;
		Chart.PackingScaleV /= TextureResolution;
		Chart.PackingBias /= TextureResolution;

		for( uint32 Tri = Chart.FirstTri; Tri < Chart.LastTri; Tri++ )
		{
			for( int k = 0; k < 3; k++ )
			{
				uint32 Index = 3 * SortedTris[ Tri ] + k;
				const FVector2D& UV = TexCoords[ Index ];
				RawMesh->WedgeTexCoords[ DstChannel ][ Index ] = UV.X * Chart.PackingScaleU + UV.Y * Chart.PackingScaleV + Chart.PackingBias;
			}
		}
	}
}