<p>I don't think having a equation for flat shading is meaningful as such. Mainly because the formula for flat shading is same as the formula for the model the flat shading is emulating. The difference is that flat shading is operating per primitive rather than per point or per vertex.</p>

<p>So there can in fact exist multiple formulas that work differently but are still all flat shading.</p>

CC BY-SA 3.0
2017-03-17T09:19:17.510Z
2017-03-17T09:19:17.510Z
joojaa
<p>Is there an equation for flat shading?</p>

<p>To my understanding, it is this:</p>

<p>$$I = I_a \times K_a + F_{att} \times  I_l \times  (K_d \times  (N \times  L))$$</p>

<p>Final intensity = ambient reflection x ambient reflection coefficient + (attenuation x incident light intensity x (diffusive reflection coefficient x (surface normal x Light intensity))</p>

<p>However, I have only found one source for this equation (my lecture slides).</p>

<p>Are there any other sources to confirm this is the equation for flat shading? I can't find one.</p>

CC BY-SA 3.0
2017-03-17T07:56:16.103Z
The (surface normal x Light intensity) / diffuse part, shouldn't that be N.L * lightColour * diffuseColour ?
PaulHK
CC BY-SA 3.0
2017-03-17T08:33:59.497Z
I didn't add a divide anywhere in the equation. It is lightIntensity*(diffusive reflection coefficient * (N.L))
S.A
CC BY-SA 3.0
2017-03-17T08:56:44.863Z
@PaulHK Is it possible you could give a reference to where you found the equation for flat shading?
S.A
CC BY-SA 3.0
2017-03-17T09:33:54.467Z
OpenGL's fixed function pipeline, I found a decent reference here > http://www.cs.cmu.edu/afs/cs/academic/class/15462-s09/www/lec/02/lec02b.pdf
PaulHK
CC BY-SA 3.0
2017-03-17T09:34:51.223Z
This equation doesn't consider flat or smooth shading, that is down to you to use either a fixed normal per triangle or interpolated vertex normals.
PaulHK
<rendering>
What is the equation for flat shading?
S.A
# What is the equation for flat shading?

(Asked by: username_0 on 2017-03-17)

Is there an equation for flat shading?

To my understanding, it is this:

$$I = I\_a \times K\_a + F\_{att} \times I\_l \times (K\_d \times (N \times L))$$

Final intensity = ambient reflection x ambient reflection coefficient + (attenuation x incident light intensity x (diffusive reflection coefficient x (surface normal x Light intensity))

However, I have only found one source for this equation (my lecture slides).

Are there any other sources to confirm this is the equation for flat shading? I can't find one.

**Tags:** rendering

> **Comments:**
> **username_1**: The (surface normal x Light intensity) / diffuse part, shouldn't that be N.L * lightColour * diffuseColour ?  
> **username_0**: I didn't add a divide anywhere in the equation. It is lightIntensity*(diffusive reflection coefficient * (N.L))  
> **username_0**: @username_1 Is it possible you could give a reference to where you found the equation for flat shading?  
> **username_1**: OpenGL's fixed function pipeline, I found a decent reference here > http://www.cs.cmu.edu/afs/cs/academic/class/15462-s09/www/lec/02/lec02b.pdf  
> **username_1**: This equation doesn't consider flat or smooth shading, that is down to you to use either a fixed normal per triangle or interpolated vertex normals.  

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## 1 answers

### Answer by username_2 on 2017-03-17. Score: 3 | Accepted answer

I don't think having a equation for flat shading is meaningful as such. Mainly because the formula for flat shading is same as the formula for the model the flat shading is emulating. The difference is that flat shading is operating per primitive rather than per point or per vertex.

So there can in fact exist multiple formulas that work differently but are still all flat shading.


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