<p>According to <a href="https://en.wikipedia.org/wiki/Phong_reflection_model" rel="nofollow noreferrer">Phong's reflection model</a>, there are different reflection constants (<strong>k</strong>) and different intensities of the light source (<strong>i</strong>) for ambient, diffuse, and specular terms:</p>
<p><span class="math-container">$I_p=k_ai_a+\sum_{m \in lights} \left(k_d(\hat{L}_m \cdot \hat{N})i_{m,d} + k_s(\hat{R}_m \cdot \hat{V})^\alpha i_{m,s} \right)$</span></p>
<p>I had some questions about this model:</p>
<ol>
<li><p>When a pixel is under shadow (umbra), does the equation become this way:
<span class="math-container">$I_p=k_ai_a$</span> ?</p>
</li>
<li><p>Suppose we only have one major light source. So the equation can be something like this: <span class="math-container">$I_p \approx k_ai_a+ k_d(\hat{L} \cdot \hat{N})i_{d} + k_s(\hat{R} \cdot \hat{V})^\alpha i_{s} $</span></p>
<p>Can the ambient portion of pixels (<span class="math-container">$k_ai_a$</span>) become larger than the rest (even with no specular reflection)?</p>
<p>Basically, can this happen: <span class="math-container">$k_ai_a \stackrel{?}{\geq} k_d(\hat{L} \cdot \hat{N})i_{d}$</span></p>
</li>
<li><p>Is there any relationship between <span class="math-container">$k_a, k_d, k_s$</span> and <span class="math-container">$i_a, i_d, i_s$</span> of one point in a scene?</p>
</li>
</ol>

CC BY-SA 4.0
2020-11-05T17:58:54.117Z
There's no relationship between those. The ambient term is a heuristic anyways that's there to substitute for the lack of indirect illumination - not that it does a good job at that.
lightxbulb
CC BY-SA 4.0
2020-11-06T13:06:52.047Z
@lightxbulb so for example on a sunny day outdoors, can the skylight (ambient) be larger than sunlight (diffuse)? I feel like there should be some kind of relationship between diffuse and ambient reflection when there is only one light source in a scene.
Hadi GhahremanNezhad
CC BY-SA 4.0
2020-11-06T17:54:27.350Z
There is actually no such thing as the ambient term. It's an outdated model and is just an approximation. When you get into pathtracing this ambient term gets replaced by indirect illumination which is again based on either diffuse or specular terms or any other term depending on the BRDF of the surface.
gallickgunner
CC BY-SA 4.0
2020-11-06T20:50:13.740Z
@gallickgunnerThank you for the clear explanation. Do you know any reflection models that are most recent? Also, if there is only one light source in a scene, shouldn't **indirect illumination** (e.g. shadows) always be less than **(total illumination - indirect illumination)**? (assuming total illumination = direct + indirect)
Hadi GhahremanNezhad
CC BY-SA 4.0
2020-11-07T06:12:50.770Z
Microfacet models are used commonly. More complex materials require a layered approach. As for the other question, the answer is not neccessarily. Think of a scenario where an object is lit by sun directly and it's again lit by placing a mirror or a magnifying glass at a specific angle so all the light converges or reflects in the same direction and arrives at our said object. This way light coming indirectly either by refraction through the glass or reflection illuminates the object more and creates a blinding whiteness. Reason why u see caustics.
gallickgunner
CC BY-SA 4.0
2020-11-07T19:11:09.420Z
@gallickgunner Ok I see what you are saying. The caustic was a good example (although, I think for the most part it should be **intensity = sun + indirect** and **sun >= indirect**) but not always. And thank you for mentioning Microfacet models. I was searching a lot.
Hadi GhahremanNezhad
CC BY-SA 4.0
2020-11-09T07:19:37.933Z
Phongs reflection model is a pure guess it makes nontrue assumptions. But its simple, by design, so thats why it gets used.
joojaa
CC BY-SA 4.0
2020-11-11T18:27:42.443Z
@joojaa Thank you, that wasn't mentioned anywhere I looked. Do you know where I can find the most recent models? Is there a type of papers published working on this?
Hadi GhahremanNezhad
<rendering><lighting><pixels>
Can ambient light reflection of a surface be larger than diffuse reflection?
Hadi GhahremanNezhad
# Can ambient light reflection of a surface be larger than diffuse reflection?

(Asked by: username_0 on 2020-11-05)

According to [Phong's reflection model](https://en.wikipedia.org/wiki/Phong_reflection_model), there are different reflection constants (**k**) and different intensities of the light source (**i**) for ambient, diffuse, and specular terms:

$I\_p=k\_ai\_a+\sum\_{m \in lights} \left(k\_d(\hat{L}\_m \cdot \hat{N})i\_{m,d} + k\_s(\hat{R}\_m \cdot \hat{V})^\alpha i\_{m,s} \right)$

I had some questions about this model:

1. When a pixel is under shadow (umbra), does the equation become this way:
   $I\_p=k\_ai\_a$ ?
2. Suppose we only have one major light source. So the equation can be something like this: $I\_p \approx k\_ai\_a+ k\_d(\hat{L} \cdot \hat{N})i\_{d} + k\_s(\hat{R} \cdot \hat{V})^\alpha i\_{s} $

   Can the ambient portion of pixels ($k\_ai\_a$) become larger than the rest (even with no specular reflection)?

   Basically, can this happen: $k\_ai\_a \stackrel{?}{\geq} k\_d(\hat{L} \cdot \hat{N})i\_{d}$
3. Is there any relationship between $k\_a, k\_d, k\_s$ and $i\_a, i\_d, i\_s$ of one point in a scene?

**Tags:** rendering, lighting, pixels

> **Comments:**
> **username_1**: There's no relationship between those. The ambient term is a heuristic anyways that's there to substitute for the lack of indirect illumination - not that it does a good job at that.  
> **username_0**: @username_1 so for example on a sunny day outdoors, can the skylight (ambient) be larger than sunlight (diffuse)? I feel like there should be some kind of relationship between diffuse and ambient reflection when there is only one light source in a scene.  
> **username_2**: There is actually no such thing as the ambient term. It's an outdated model and is just an approximation. When you get into pathtracing this ambient term gets replaced by indirect illumination which is again based on either diffuse or specular terms or any other term depending on the BRDF of the surface.  
> **username_0**: @gallickgunnerThank you for the clear explanation. Do you know any reflection models that are most recent? Also, if there is only one light source in a scene, shouldn't **indirect illumination** (e.g. shadows) always be less than **(total illumination - indirect illumination)**? (assuming total illumination = direct + indirect)  
> **username_2**: Microfacet models are used commonly. More complex materials require a layered approach. As for the other question, the answer is not neccessarily. Think of a scenario where an object is lit by sun directly and it's again lit by placing a mirror or a magnifying glass at a specific angle so all the light converges or reflects in the same direction and arrives at our said object. This way light coming indirectly either by refraction through the glass or reflection illuminates the object more and creates a blinding whiteness. Reason why u see caustics.  
> **username_0**: @username_2 Ok I see what you are saying. The caustic was a good example (although, I think for the most part it should be **intensity = sun + indirect** and **sun >= indirect**) but not always. And thank you for mentioning Microfacet models. I was searching a lot.  
> **username_3**: Phongs reflection model is a pure guess it makes nontrue assumptions. But its simple, by design, so thats why it gets used.  
> **username_0**: @username_3 Thank you, that wasn't mentioned anywhere I looked. Do you know where I can find the most recent models? Is there a type of papers published working on this?  

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## 0 answers

