How to interpolate colors around the spectrum of hues?

Question

I wanted to generate a 7 segment display whose color brightness varies with time, this can be done by just using linear relationship.

Color activeColour2 = new Color(1, DateTime.Now.Millisecond*0.001f, DateTime.Now.Millisecond*0.001f);

So in 1 complete second, it produce color in the range of (1,0,0) to (1,1,1) as in the code below:

using System;
using UnityEngine;

public class ClockDigit2 : MonoBehaviour
{    
    static readonly bool[,] SEGMENT_IS_ACTIVE = new bool[,] {

        {true,  true,  true,  true,  true,  true,  false}, // 0
        {false, true,  true,  false, false, false, false}, // 1
        {true,  true,  false, true,  true,  false, true }, // 2
        {true,  true,  true,  true,  false, false, true }, // 3
        {false, true,  true,  false, false, true,  true }, // 4
        {true,  false, true,  true,  false, true,  true }, // 5
        {true,  false, true,  true,  true,  true,  true }, // 6
        {true,  true,  true,  false, false, false, false}, // 7
        {true,  true,  true,  true,  true,  true,  true }, // 8
        {true,  true,  true,  true,  false, true,  true }  // 9
    };

    
    public Color32 inactiveColour = Color.black;  


    public SpriteRenderer[] segments = new SpriteRenderer[7];
   

    public void Display(int number)
    {   
        Color activeColour2 = new Color(1, DateTime.Now.Millisecond*0.001f, DateTime.Now.Millisecond*0.001f);
        var digit = number % 10;
        if (digit < 0) digit *= -1;   

        for (int i = 0; i < 7; i++)
        {
            if (SEGMENT_IS_ACTIVE[digit, i])
            {
                segments[i].color = activeColour2;
            }
            else
            {
                segments[i].color = inactiveColour;
            }
        }  

    }    

    void Update()
    {    
        Display(DateTime.Now.Second);    
    }    
}

However, now I want to interpolate through all the colors in the circle above over 1 second.

I don't know how to express this as a formula for R, G, and B. The RGB value is not linear relationship: as you spin the selected color in the chart, you can notice the RGBA components vary together in a nonlinear form.

I considered using Lagrangian interpolation. However, this will not be accurate or might fail greatly because if you take a reference point at the circle and assume in 1sec, it made a complete revolution, you will notice there is a certain period of time where the RGB value is constant along the path: either 0 and 1.

So is there any method to get a formula that perfectly fits the color chart with respect to time?

Answer 1

I'm not aware of the Color.HSVToRGB method in Unity. using Color activeColour2 = Color.HSVToRGB(DateTime.Now.Millisecond*0.001f,1,1) give the desired result since the conversion is a linear relationship with respect to time.