Multi-primary-color　display　technology　has　been　an　important　technical　route　to　achieve　color　gamut　expansion,　which　improves　display　brightness　and　energy　efficiency　by　adding　white　sub-pixels.　To　drive　Red-Green-Blue-White　(RGBW)　displays,　color　gamut　mapping　is　required.　In　order　to　make　the　color　saturation　theoretically　consistent　before　and　after　color　gamut　mapping,　the　white　sub-pixel　grayscale　value　is　usually　deducted　from　values　of　chromatic　sub-pixels　in　traditional　algorithms,　which　greatly　reduces　the　contribution　of　chromatic　sub-pixels　to　brightness　enhancement,　resulting　in　a　less　overall　brightness　increase.　In　addition,　there　is　currently　few　objective　and　intuitive　evaluation　index　to　evaluate　the　performance　of　algorithms.　A　mathematical　model　of　color　gamut　mapping　transformation　was　established　by　combining　the　general　method　of　color　gamut　mapping　in　this　paper.　Two　key　parameters　of　the　mapping　rate-of-change　function　and　the　white　sub-pixel　driving　function　are　proposed.　According　to　the　characteristics　of　RGBW　color　gamut　mapping　algorithm,　a　four-in-one　evaluation　index　system　was　proposed,　it　includes　the　Average　Brightness　Magnification　(ABM),　the　Average　Chromatic　Sub-Pixels　Magnification　(ACSM),　the　Average　White　Sub-pixel　Ratio　(AWSR),　and　the　Average　Saturation　Ratio　(ASR).　Based　on　the　evaluation　index　system,　the　Mapping　Rate-of-Change　Function　and　the　White　Sub-Pixel　Driving　Function　were　determined.　A　linear　algorithm　function　was　constructed　based　on　evaluation　index　system,　which　was　continuously　adjusted　to　a　quadratic　function　to　reach　the　best　effect,　and　a　more　efficient　and　simplified　new　color　gamut　mapping　algorithm　was　realized.　The　proposed　algorithm　is　designed　to　increase　the　contribution　of　chromatic　sub-pixels　to　the　brightness　improvement　of　the　image　without　deducting　the　white　component　and　with　maximizing　the　chromatic　sub-pixels　grayscale　values,　and　it　can　also　balance　the　AWSR　and　the　ASR　by　adjusting　the　weight　factor.　Simulation　images　processed　by　the　proposed　algorithm　is　displayed　on　an　RGB　Flat　Panel　Display　(FPD)　to　simulate　algorithms　effect.　Furthermore,　the　physical　verification　is　carried　out　on　a　projector　that　supports　RGBW　projection,　and　the　imaging　brightness　under　two　platforms　is　measured　respectively　by　using　an　image　luminance　colorimeter.　The　results　show　that　the　brightness　of　the　proposed　algorithm　can　be　increased　by　2.26　times　and　2.59　times　on　flat　panel　display　and　projector　platforms　respectively.　In　terms　of　evaluation　indices,　the　ABM　of　the　proposed　algorithm　reached　2.304,　the　ACSM　reached　1.677,　the　ABM　reached　2.3　times　that　of　traditional　algorithms,　and　the　contribution　of　the　chromatic　sub-pixels　grayscale　values　to　the　brightness　improvement　reached　1.67　times　that　of　traditional　algorithms.　The　AWSR　was　0.261,　and　the　ASR　was　0.733,　which　better　balanced　the　overall　brightness　enhancement　and　saturation　decrease　of　images.　Simulation　rendering　pictures　of　each　algorithm　on　an　RGB　flat　panel　display　were　also　taken　in　the　experiment,　as　well　as　actual　pictures　projected　by　an　RGBW　projector.　Judging　from　these　pictures,　the　proposed　algorithm　can　significantly　enhance　the　display　brightness　and　have　a　good　performance　of　color　retention.　The　calculation　results　of　evaluation　indices,　measurement　results　and　simulation　verification　results　are　basically　consistent,　so　the　evaluation　index　system　can　better　show　the　performance　of　the　RGBW　color　gamut　mapping　algorithm.　This　study　provides　a　reference　for　evaluation　performance　of　RGBW　algorithms　and　construction　of　new　algorithms　in　the　future,　and　providing　new　directions　for　color　gamut　mapping　in　multi-primary-color　displays.　©　2025,　Chinese　Optical　Society.　All　rights　reserved.