Jump Flood Algorithms for Centroidal Voronoi Tessellation

Brief

Implemented both CPU and GPU version, you could consider this as the basic playground to implement the more advanced feature such as support arbitrary shape in 2D space, or by radix-sort to restore the analytic shape of each Voronoi region etc. Another interesting application of JFA is the problem of 2D/3D level set reinitialization.

n = 16

n = 64

CPU

/**
 * Copyright (c) 2014, Bo Zhou<Bo.Schwarzstein@gmail.com> and J CUBE Inc. Tokyo, Japan
 * All rights reserved.

 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    This product includes software developed by the <organization>.
 * 4. Neither the name of the <organization> nor the
 *    names of its contributors may be used to endorse or promote products
 *    derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY COPYRIGHT HOLDER AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL COPYRIGHT HOLDER BE LIABLE FOR ANY
 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#include <cmath>
#include <cstdlib>
#include <ctime>

#include <ImathColor.h>
#include <ImathVec.h>

#include <iostream>
#include <iterator>
#include <vector>

int main( int Argc , char ** Argv )
{
    -- Argc , ++ Argv ;
    if ( Argc !=  )
    {
        return EXIT_FAILURE ;
    }

    //
    int NumSites = atoi( Argv[] ) ;
    int Size     = atoi( Argv[] ) ;

    // 1) Generate the 2D sites and the fill color.
    //
    std::vector< Imath::V2f > SiteVec ;
    std::vector< int > SeedVecA( Size * Size , -  ) ;
    std::vector< Imath::C3c > RandomColorVec ;
    if ( NumSites >  )
    {
        srand( time(NULL) ) ;

        for ( int i =  ; i < NumSites ; ++ i )
        {
            float X = static_cast< float >( rand() ) / RAND_MAX * Size ;
            float Y = static_cast< float >( rand() ) / RAND_MAX * Size ;

            Imath::V2i Cell( static_cast< int >( floorf( X ) ) ,
                             static_cast< int >( floorf( Y ) ) ) ;
            SiteVec.push_back( Imath::V2f( Cell.x + 0.5f , Cell.y + 0.5f ) ) ;

            SeedVecA[Cell.x + Cell.y * Size] = i ;

            Imath::C3c C( static_cast< unsigned char >( static_cast< float >( rand() ) / RAND_MAX * 255.0f ) ,
                          static_cast< unsigned char >( static_cast< float >( rand() ) / RAND_MAX * 255.0f ) ,
                          static_cast< unsigned char >( static_cast< float >( rand() ) / RAND_MAX * 255.0f ) ) ;
            RandomColorVec.push_back( C ) ;
        }
    }
    else
    {
        NumSites =  ;

        SiteVec.push_back( Imath::V2f( 0.5f , 0.5f ) ) ;
        SeedVecA[] =  ;
        RandomColorVec.push_back( Imath::C3c(  ,  ,  ) ) ;
    }
    std::vector< int > SeedVecB( SeedVecA ) ;

    //
    const int SizeLowTwo = static_cast< int >( ceilf( logf( static_cast< float >( Size ) ) ) ) ;

    //
    static const Imath::V2i OffsetArray[] = { Imath::V2i( -  , -  ) ,
                                               Imath::V2i(    , -  ) ,
                                               Imath::V2i(    , -  ) ,
                                               Imath::V2i( -  ,    ) ,
                                               Imath::V2i(    ,    ) ,
                                               Imath::V2i( -  ,    ) ,
                                               Imath::V2i(    ,    ) ,
                                               Imath::V2i(    ,    ) } ;

    int * Ping = & SeedVecA[] ;
    int * Pong = & SeedVecB[] ;

    for ( int k = Size /  ; k >  ; k = k >>  )
    {
        fprintf( stdout , "k = %d\n" , k ) ;

        for ( int y =  ; y < Size ; ++ y )
        {
            for ( int x =  ; x < Size ; ++ x )
            {
                const int CellIdx = x + y * Size ;
                const int Seed = Ping[CellIdx] ;
                if ( Seed > -  )
                {
                    Imath::V2i Cell( x , y ) ;
                    for ( int i =  ; i <  ; ++ i )
                    {
                        const Imath::V2i & FillCell = Cell + k * OffsetArray[i] ;
                        if ( FillCell.x >=  && FillCell.x < Size && FillCell.y >=  && FillCell.y < Size )
                        {
                            const int FillCellIdx = FillCell.x + FillCell.y * Size ;
                            const int FillSeed = Pong[FillCellIdx] ;
                            if ( FillSeed <  )
                            {
                                Pong[FillCellIdx] = Seed ;
                            }
                            else
                            {
                                const Imath::V2f & FillP = Imath::V2f( FillCell.x + 0.5f , FillCell.y + 0.5f ) ;
                                if ( ( FillP - SiteVec[Seed] ).length() < ( FillP - SiteVec[FillSeed] ).length() )
                                {
                                    Pong[FillCellIdx] = Seed ;
                                }
                            }
                        }
                    }
                }
            }
        }

        std::copy( Pong , Pong + SeedVecA.size() , Ping ) ;
        std::swap( Ping , Pong ) ;
    }

    //
    FILE * Output = fopen( Argv[] , "wb" ) ;
    fprintf( Output , "P6\n%d %d\n255\n" , Size , Size ) ;

    std::vector< Imath::C3c > Pixels( Size * Size , Imath::C3c(  ) ) ;
    for ( int y =  ; y < Size ; ++ y )
    {
        for ( int x =  ; x < Size ; ++ x )
        {
            const int Seed = Pong[x + y * Size] ;
            if ( Seed != -  )
            {
                Pixels[x + y * Size] = RandomColorVec[Seed] ;
            }
        }
    }

    for( std::vector< Imath::V2f >::const_iterator itr = SiteVec.begin() ; itr != SiteVec.end() ; ++ itr )
    {
        const int x = static_cast< int >( floorf( itr->x ) ) ;
        const int y = static_cast< int >( floorf( itr->y ) ) ;
        Pixels[x + y * Size] = Imath::C3c(  ,  ,  ) ;
    }

    fwrite( & Pixels[].x ,  , Pixels.size() , Output ) ;
    fclose( Output ) ;

    return EXIT_SUCCESS ;
}

JFA CPU

GPU

/**
 * Copyright (c) 2014, Bo Zhou<Bo.Schwarzstein@gmail.com> and J CUBE Inc. Tokyo, Japan
 * All rights reserved.

 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    This product includes software developed by the <organization>.
 * 4. Neither the name of the <organization> nor the
 *    names of its contributors may be used to endorse or promote products
 *    derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY COPYRIGHT HOLDER AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL COPYRIGHT HOLDER BE LIABLE FOR ANY
 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <ctime>

#include <cuda_runtime.h>
#include <cuda_runtime_api.h>

#include <iostream>
#include <iterator>
#include <vector>

__global__ void Kernel( int SizeX , int SizeY , const float2 * SiteArray , const int * Ping , int * Pong , int k , int * Mutex )
{
    //
    const int CellX = threadIdx.x + blockIdx.x * blockDim.x ;
    const int CellY = threadIdx.y + blockIdx.y * blockDim.y ;

    const int CellIdx = CellX + CellY * SizeX ;
    const int Seed = Ping[CellIdx] ;
    if ( Seed <  )
    {
        return ;
    }

    //
    const int2 OffsetArray[] = { { -  , -  } ,
                                  {    , -  } ,
                                  {    , -  } ,
                                  { -  ,    } ,
                                  {    ,    } ,
                                  { -  ,    } ,
                                  {    ,    } ,
                                  {    ,    } } ;

    for ( int i =  ; i <  ; ++ i )
    {
        const int FillCellX = CellX + k * OffsetArray[i].x ;
        const int FillCellY = CellY + k * OffsetArray[i].y ;
        if ( FillCellX >=  && FillCellX < SizeX && FillCellY >=  && FillCellY < SizeY )
        {
            //
            const int FillCellIdx = FillCellX + FillCellY * SizeX ;

            // Lock
            //
            while ( atomicCAS( Mutex , -  , FillCellIdx ) == FillCellIdx )
            {
            }

            const int FillSeed = Pong[FillCellIdx] ;

            if ( FillSeed <  )
            {
                Pong[FillCellIdx] = Seed ;
            }
            else
            {
                float2 P = make_float2( FillCellX + 0.5f , FillCellY + 0.5f ) ;

                float2 A = SiteArray[Seed] ;
                float2 PA = make_float2( A.x - P.x , A.y - P.y ) ;
                float PALength = PA.x * PA.x + PA.y * PA.y ;

                const float2 B = SiteArray[FillSeed] ;
                float2 PB = make_float2( B.x - P.x , B.y - P.y ) ;
                float PBLength = PB.x * PB.x + PB.y * PB.y ;

                if ( PALength < PBLength )
                {
                    Pong[FillCellIdx] = Seed ;
                }
            }

            // Release
            //
            atomicExch( Mutex , -  ) ;
        }
    }
}

int main( int Argc , char * Argv[] )
{
    -- Argc , ++ Argv ;
    if ( Argc !=  )
    {
        return EXIT_FAILURE ;
    }

    //
    int NumSites = atoi( Argv[] ) ;
    int Size     = atoi( Argv[] ) ;

    //
    int NumCudaDevice =  ;
    cudaGetDeviceCount( & NumCudaDevice ) ;
    if ( ! NumCudaDevice )
    {
        return EXIT_FAILURE ;
    }

    //
    //
    std::vector< float2 > SiteVec ;
    std::vector< int >    SeedVec( Size * Size , -  ) ;
    std::vector< uchar3 > RandomColorVec ;
    for ( int i =  ; i < NumSites ; ++ i )
    {
        float X = static_cast< float >( rand() ) / RAND_MAX * Size ;
        float Y = static_cast< float >( rand() ) / RAND_MAX * Size ;
        int CellX = static_cast< int >( floorf( X ) ) ;
        int CellY = static_cast< int >( floorf( Y ) ) ;

        SiteVec.push_back( make_float2( CellX + 0.5f , CellY + 0.5f ) ) ;
        SeedVec[CellX + CellY * Size] = i ;

        RandomColorVec.push_back( make_uchar3( static_cast< unsigned char >( static_cast< float >( rand() ) / RAND_MAX * 255.0f ) ,
                                               static_cast< unsigned char >( static_cast< float >( rand() ) / RAND_MAX * 255.0f ) ,
                                               static_cast< unsigned char >( static_cast< float >( rand() ) / RAND_MAX * 255.0f ) ) ) ;
    }

    //
    size_t SiteSize = NumSites * sizeof( float2 ) ;

    float2 * SiteArray = NULL ;
    cudaMalloc( & SiteArray , SiteSize ) ;
    cudaMemcpy( SiteArray , & SiteVec[] , SiteSize , cudaMemcpyHostToDevice ) ;

    //
    size_t BufferSize = Size * Size * sizeof( int ) ;

    int * Ping = NULL , * Pong = NULL ;
    cudaMalloc( & Ping , BufferSize ) , cudaMemcpy( Ping , & SeedVec[] , BufferSize , cudaMemcpyHostToDevice ) ;
    cudaMalloc( & Pong , BufferSize ) , cudaMemcpy( Pong , Ping , BufferSize , cudaMemcpyDeviceToDevice ) ;

    //
    int * Mutex = NULL ;
    cudaMalloc( & Mutex , sizeof( int ) ) , cudaMemset( Mutex , -  , sizeof( int ) ) ;

    //
    //
    cudaDeviceProp CudaDeviceProperty ;
    cudaGetDeviceProperties( & CudaDeviceProperty ,  ) ;

    dim3 BlockDim( CudaDeviceProperty.warpSize , CudaDeviceProperty.warpSize ) ;
    dim3 GridDim( ( Size + BlockDim.x -  ) / BlockDim.x ,
                  ( Size + BlockDim.y -  ) / BlockDim.y ) ;

    for ( int k = Size /  ; k >  ; k = k >>  )
    {
        Kernel<<< GridDim , BlockDim >>>( Size , Size , SiteArray , Ping , Pong , k , Mutex ) ;
        cudaDeviceSynchronize() ;

        cudaMemcpy( Ping , Pong , BufferSize , cudaMemcpyDeviceToDevice ) ;
        std::swap( Ping , Pong ) ;
    }
    cudaMemcpy( & SeedVec[] , Pong , BufferSize , cudaMemcpyDeviceToHost ) ;

    //
    cudaFree( SiteArray ) ;
    cudaFree( Ping ) ;
    cudaFree( Pong ) ;
    cudaFree( Mutex ) ;

    //
    //
    FILE * Output = fopen( Argv[] , "wb" ) ;
    fprintf( Output , "P6\n%d %d\n255\n" , Size , Size ) ;

    std::vector< uchar3 > Pixels( Size * Size ) ;
    for ( int y =  ; y < Size ; ++ y )
    {
        for ( int x =  ; x < Size ; ++ x )
        {
            const int Seed = SeedVec[x + y * Size] ;
            if ( Seed != -  )
            {
                Pixels[x + y * Size] = RandomColorVec[Seed] ;
            }
        }
    }

    for( std::vector< float2 >::const_iterator itr = SiteVec.begin() ; itr != SiteVec.end() ; ++ itr )
    {
        const int x = static_cast< int >( floorf( itr->x ) ) ;
        const int y = static_cast< int >( floorf( itr->y ) ) ;
        Pixels[x + y * Size] = make_uchar3(  ,  ,  ) ;
    }

    fwrite( & Pixels[].x ,  , Pixels.size() , Output ) ;
    fclose( Output ) ;

    return EXIT_SUCCESS ;
}

JFA CUDA