The HSV-RGB
Transform Pair
The following routines are written in C (with C++ comments). See the closely related
HWB-RGB Transform
Pair.
#define RETURN_HSV(h, s, v) {HSV.H = h; HSV.S = s; HSV.V = v; return HSV;}
#define RETURN_RGB(r, g, b) {RGB.R = r; RGB.G = g; RGB.B = b; return RGB;}
#define UNDEFINED -1
// Theoretically, hue 0 (pure red) is identical to hue 6 in these transforms. Pure
// red always maps to 6 in this implementation. Therefore UNDEFINED can be
// defined as 0 in situations where only unsigned numbers are desired.
typedef struct {float R, G, B;} RGBType;
typedef struct {float H, S, V;} HSVType;
HSVType
RGB_to_HSV( RGBType RGB ) {
| // RGB are each on [0, 1]. S and V are returned on [0, 1] and H is | |
| // returned on [0, 6]. Exception: H is returned UNDEFINED if S==0. | |
| float R = RGB.R, G = RGB.G, B = RGB.B, v, x, f; | |
| int i; | |
| HSVType HSV; | |
| x = min(R, G, B); | |
| v = max(R, G, B); | |
| if(v == x) RETURN_HSV(UNDEFINED, 0, v); | |
| f = (R == x) ? G - B : ((G == x) ? B - R : R - G); | |
| i = (R == x) ? 3 : ((G == x) ? 5 : 1); | |
| RETURN_HSV(i - f /(v - x), (v - x)/v, v); |
}
Note: The algorithm above for hue is essentially
H = (R==x)? 3+(g-b) : (G==x)? 5+(b-r) : 1+(r-g),
where r = (v-R)/(v-x) etc. Mr Yu Chun Fang of the Chinese Academy of Sciences noticed, in an email to me of 10 Nov 2000, that this is the same as
H = (R==v)? 0+(b-g) : (G==v)? 2+(r-b) : 4+(g-r).
He had seen my algorithm published in an unnamed Chinese book in this form. The forms are, indeed, equivalent.
RGBType
HSV_to_RGB( HSVType HSV ) {
| // H is given on [0, 6] or UNDEFINED. S and V are given on [0, 1]. | ||
| // RGB are each returned on [0, 1]. | ||
| float h = HSV.H, s = HSV.S, v = HSV.V, m, n, f; | ||
| int i; | ||
| RGBType RGB; | ||
| if (h == UNDEFINED) RETURN_RGB(v, v, v); | ||
| i = floor(h); | ||
| f = h - i; | ||
| if ( !(i&1) ) f = 1 - f; // if i is even | ||
| m = v * (1 - s); | ||
| n = v * (1 - s * f); | ||
| switch (i) { | ||
| case 6: | ||
| case 0: RETURN_RGB(v, n, m); | ||
| case 1: RETURN_RGB(n, v, m); | ||
| case 2: RETURN_RGB(m, v, n) | ||
| case 3: RETURN_RGB(m, n, v); | ||
| case 4: RETURN_RGB(n, m, v); | ||
| case 5: RETURN_RGB(v, m, n); | ||
| } | ||
}