interpolation - Color scaling function

Question

I am trying to visualize some values on a form. They range from 0 to 200 and I would like the ones around 0 be green and turn bright red as they go to 200.

Basically the function should return color based on the value inputted. Any ideas ?

Answer 1

Basically, the general method for smooth transition between two values is the following function:

function transition(value, maximum, start_point, end_point):
    return start_point + (end_point - start_point)*value/maximum

That given, you define a function that does the transition for triplets (RGB, HSV etc).

function transition3(value, maximum, (s1, s2, s3), (e1, e2, e3)):
    r1= transition(value, maximum, s1, e1)
    r2= transition(value, maximum, s2, e2)
    r3= transition(value, maximum, s3, e3)
    return (r1, r2, r3)

Assuming you have RGB colours for the s and e triplets, you can use the transition3 function as-is. However, going through the HSV colour space produces more "natural" transitions. So, given the conversion functions (stolen shamelessly from the Python colorsys module and converted to pseudocode :):

function rgb_to_hsv(r, g, b):
    maxc= max(r, g, b)
    minc= min(r, g, b)
    v= maxc
    if minc == maxc then return (0, 0, v)
    diff= maxc - minc
    s= diff / maxc
    rc= (maxc - r) / diff
    gc= (maxc - g) / diff
    bc= (maxc - b) / diff
    if r == maxc then
        h= bc - gc
    else if g == maxc then
        h= 2.0 + rc - bc
    else
        h = 4.0 + gc - rc
    h = (h / 6.0) % 1.0 //comment: this calculates only the fractional part of h/6
    return (h, s, v)

function hsv_to_rgb(h, s, v):
    if s == 0.0 then return (v, v, v)
    i= int(floor(h*6.0)) //comment: floor() should drop the fractional part
    f= (h*6.0) - i
    p= v*(1.0 - s)
    q= v*(1.0 - s*f)
    t= v*(1.0 - s*(1.0 - f))
    if i mod 6 == 0 then return v, t, p
    if i == 1 then return q, v, p
    if i == 2 then return p, v, t
    if i == 3 then return p, q, v
    if i == 4 then return t, p, v
    if i == 5 then return v, p, q
    //comment: 0 <= i <= 6, so we never come here

, you can have code as following:

start_triplet= rgb_to_hsv(0, 255, 0) //comment: green converted to HSV
end_triplet= rgb_to_hsv(255, 0, 0) //comment: accordingly for red

maximum= 200

… //comment: value is defined somewhere here

rgb_triplet_to_display= hsv_to_rgb(transition3(value, maximum, start_triplet, end_triplet))