【色度学】HSP 色彩空间

由于HSL 和 HSV 的值并不能反应人眼看到的真实亮度（如下图），实际上人眼看青色会很亮， 但是在HSV模型中， 青色表现的亮度和蓝色一样， 为了解决这种亮度表示问题，所以引入了HSP色彩空间， 以反应人眼看到的真实的颜色；

image.png

HSP 的亮度公式定义为：

image.png

互转公式：

//如果是BT709 或 sRGB 色域参数如下， 不同的色域使用不同的Pr Pg Pb
#define  Pr  .299
#define  Pg  .587
#define  Pb  .114



//  public domain function by Darel Rex Finley, 2006
//
//  This function expects the passed-in values to be on a scale
//  of 0 to 1, and uses that same scale for the return values.
//
//  See description/examples at alienryderflex.com/hsp.html

void RGBtoHSP(
double  R, double  G, double  B,
double *H, double *S, double *P) {

  //  Calculate the Perceived brightness.
  *P=sqrt(R*R*Pr+G*G*Pg+B*B*Pb);

  //  Calculate the Hue and Saturation.  (This part works
  //  the same way as in the HSV/B and HSL systems???.)
  if      (R==G && R==B) {
    *H=0.; *S=0.; return; }
  if      (R>=G && R>=B) {   //  R is largest
    if    (B>=G) {
      *H=6./6.-1./6.*(B-G)/(R-G); *S=1.-G/R; }
    else         {
      *H=0./6.+1./6.*(G-B)/(R-B); *S=1.-B/R; }}
  else if (G>=R && G>=B) {   //  G is largest
    if    (R>=B) {
      *H=2./6.-1./6.*(R-B)/(G-B); *S=1.-B/G; }
    else         {
      *H=2./6.+1./6.*(B-R)/(G-R); *S=1.-R/G; }}
  else                   {   //  B is largest
    if    (G>=R) {
      *H=4./6.-1./6.*(G-R)/(B-R); *S=1.-R/B; }
    else         {
      *H=4./6.+1./6.*(R-G)/(B-G); *S=1.-G/B; }}}



//  public domain function by Darel Rex Finley, 2006
//
//  This function expects the passed-in values to be on a scale
//  of 0 to 1, and uses that same scale for the return values.
//
//  Note that some combinations of HSP, even if in the scale
//  0-1, may return RGB values that exceed a value of 1.  For
//  example, if you pass in the HSP color 0,1,1, the result
//  will be the RGB color 2.037,0,0.
//
//  See description/examples at alienryderflex.com/hsp.html

void HSPtoRGB(
double  H, double  S, double  P,
double *R, double *G, double *B) {

  double  part, minOverMax=1.-S ;

  if (minOverMax>0.) {
    if      ( H<1./6.) {   //  R>G>B
      H= 6.*( H-0./6.); part=1.+H*(1./minOverMax-1.);
      *B=P/sqrt(Pr/minOverMax/minOverMax+Pg*part*part+Pb);
      *R=(*B)/minOverMax; *G=(*B)+H*((*R)-(*B)); }
    else if ( H<2./6.) {   //  G>R>B
      H= 6.*(-H+2./6.); part=1.+H*(1./minOverMax-1.);
      *B=P/sqrt(Pg/minOverMax/minOverMax+Pr*part*part+Pb);
      *G=(*B)/minOverMax; *R=(*B)+H*((*G)-(*B)); }
    else if ( H<3./6.) {   //  G>B>R
      H= 6.*( H-2./6.); part=1.+H*(1./minOverMax-1.);
      *R=P/sqrt(Pg/minOverMax/minOverMax+Pb*part*part+Pr);
      *G=(*R)/minOverMax; *B=(*R)+H*((*G)-(*R)); }
    else if ( H<4./6.) {   //  B>G>R
      H= 6.*(-H+4./6.); part=1.+H*(1./minOverMax-1.);
      *R=P/sqrt(Pb/minOverMax/minOverMax+Pg*part*part+Pr);
      *B=(*R)/minOverMax; *G=(*R)+H*((*B)-(*R)); }
    else if ( H<5./6.) {   //  B>R>G
      H= 6.*( H-4./6.); part=1.+H*(1./minOverMax-1.);
      *G=P/sqrt(Pb/minOverMax/minOverMax+Pr*part*part+Pg);
      *B=(*G)/minOverMax; *R=(*G)+H*((*B)-(*G)); }
    else               {   //  R>B>G
      H= 6.*(-H+6./6.); part=1.+H*(1./minOverMax-1.);
      *G=P/sqrt(Pr/minOverMax/minOverMax+Pb*part*part+Pg);
      *R=(*G)/minOverMax; *B=(*G)+H*((*R)-(*G)); }}
  else {
    if      ( H<1./6.) {   //  R>G>B
      H= 6.*( H-0./6.); *R=sqrt(P*P/(Pr+Pg*H*H)); *G=(*R)*H; *B=0.; }
    else if ( H<2./6.) {   //  G>R>B
      H= 6.*(-H+2./6.); *G=sqrt(P*P/(Pg+Pr*H*H)); *R=(*G)*H; *B=0.; }
    else if ( H<3./6.) {   //  G>B>R
      H= 6.*( H-2./6.); *G=sqrt(P*P/(Pg+Pb*H*H)); *B=(*G)*H; *R=0.; }
    else if ( H<4./6.) {   //  B>G>R
      H= 6.*(-H+4./6.); *B=sqrt(P*P/(Pb+Pg*H*H)); *G=(*B)*H; *R=0.; }
    else if ( H<5./6.) {   //  B>R>G
      H= 6.*( H-4./6.); *B=sqrt(P*P/(Pb+Pr*H*H)); *R=(*B)*H; *G=0.; }
    else               {   //  R>B>G
      H= 6.*(-H+6./6.); *R=sqrt(P*P/(Pr+Pb*H*H)); *B=(*R)*H; *G=0.; }}}

参考资料：
http://alienryderflex.com/hsp.html