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1

$begingroup$

I am trying to simulate the saturation for a colour.
I know there might be a good proper way but I'm only doing it to better understand some concepts.

The saturation is one value while a colour can be represented as a three dimensional vector with minimum value $(0,0,0)$ and maximum value $(1,1,1)$.

I did some experimentation and figured that the three norm for such a vector would give me a value between $0$ and $1$, the way I wanted it.

What this means is:

$f(x,y,z) = sqrt[3]x^3 + y^3 + z^3$

I wish to visualise this function.

I am guessing that a transformation is the way to go.

Also, the 2 norm has the name "Euclidean norm" (for good reason), is there a name for the 3 norm as well?

multivariable-calculus vectors

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asked yesterday

Rahul ChhabraRahul Chhabra

83

New contributor

Rahul Chhabra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It probably depends on the extent to which you want to visualize this. As-is it would require a four-dimensional visualization - obviously not useful. You could probably, alternatively, look at the level surfaces in 3D (where $f$ is constant) for various constants.
  $endgroup$
  – Eevee Trainer
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That seems like a good idea. Thanks!
  $endgroup$
  – Rahul Chhabra
  yesterday
  

  
  
  
  

add a comment | 

1

$begingroup$

I am trying to simulate the saturation for a colour.
I know there might be a good proper way but I'm only doing it to better understand some concepts.

The saturation is one value while a colour can be represented as a three dimensional vector with minimum value $(0,0,0)$ and maximum value $(1,1,1)$.

I did some experimentation and figured that the three norm for such a vector would give me a value between $0$ and $1$, the way I wanted it.

What this means is:

$f(x,y,z) = sqrt[3]x^3 + y^3 + z^3$

I wish to visualise this function.

I am guessing that a transformation is the way to go.

Also, the 2 norm has the name "Euclidean norm" (for good reason), is there a name for the 3 norm as well?

multivariable-calculus vectors

share|cite|improve this question

asked yesterday

Rahul ChhabraRahul Chhabra

83

New contributor

Rahul Chhabra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It probably depends on the extent to which you want to visualize this. As-is it would require a four-dimensional visualization - obviously not useful. You could probably, alternatively, look at the level surfaces in 3D (where $f$ is constant) for various constants.
  $endgroup$
  – Eevee Trainer
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That seems like a good idea. Thanks!
  $endgroup$
  – Rahul Chhabra
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

I am trying to simulate the saturation for a colour.
I know there might be a good proper way but I'm only doing it to better understand some concepts.

The saturation is one value while a colour can be represented as a three dimensional vector with minimum value $(0,0,0)$ and maximum value $(1,1,1)$.

I did some experimentation and figured that the three norm for such a vector would give me a value between $0$ and $1$, the way I wanted it.

What this means is:

$f(x,y,z) = sqrt[3]x^3 + y^3 + z^3$

I wish to visualise this function.

I am guessing that a transformation is the way to go.

Also, the 2 norm has the name "Euclidean norm" (for good reason), is there a name for the 3 norm as well?

multivariable-calculus vectors

share|cite|improve this question

asked yesterday

Rahul ChhabraRahul Chhabra

83

New contributor

Rahul Chhabra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

asked yesterday

Rahul ChhabraRahul Chhabra

83

New contributor

Rahul Chhabra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

asked yesterday

Rahul ChhabraRahul Chhabra

83

New contributor

Rahul Chhabra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked yesterday

Rahul ChhabraRahul Chhabra

83

New contributor

Rahul Chhabra is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked yesterday

Rahul ChhabraRahul Chhabra

83