<p>Assuming that the classic Phong model is desired here, the dot product that goes into the specular calculation should be R·L, rather than N·H (which was introduced by Blinn). That is, Phong calculates specular using the angle between the reflected eye vector and the light vector.</p>

<p>In the diagram you posted, these vectors are shown and the angle is given as 15&deg;. So, R·L = cos(15&deg;) = 0.96 according to the table below the diagram.</p>

CC BY-SA 3.0
2016-03-29T17:20:31.733Z
2016-03-29T17:20:31.733Z
Nathan Reed
<p>I'm stuck on this question asking me to calculate the intensity of a pixel using Ray Tracing. It gives values such as $I_i$ but doesn't give any coordinates. </p>

<p>I know for the diffuse component, $I_ik_d(n,l)$ can be written as $I_ik_d(\cos\theta)$ but for the specular component $I_ik_s(h\cdot n)$ is there any other way to write it so that it doesn't require any vectors such as $h$ and $n$?</p>

<p>This is the question:</p>

<p><a href="https://i.sstatic.net/3s0AC.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3s0AC.png" alt="enter image description here"></a></p>

CC BY-SA 3.0
2016-03-27T06:01:07.813Z
Are you sure you want N·H, or do you want R·L i.e. reflection vector dotted with light source vector? The latter would be the classic Phong equation (N·H is Blinn), and the figure appears to mark the R·L angle: 15 degrees.
Nathan Reed
CC BY-SA 3.0
2016-03-27T10:17:51.400Z
Should the question not point out which Bidirectional Reflectance Distribution Function (BRDF) you need to use? You have Phong, Blinn-Phong, Modified Phong, Modified Blinn-Phong and a whole variety of physically-based ones.
Matthias
CC BY-SA 3.0
2016-03-27T13:28:42.073Z
@NathanReed how can i find R.L if i dont know the vectors? Do i just use 15 degrees?
user2976568
CC BY-SA 3.0
2016-03-27T17:24:35.710Z
@user2976568 The dot product is the cosine of the angle between the vectors (for unit vectors). Just as you remarked that N·L = cos(theta). :)
Nathan Reed
CC BY-SA 3.0
2016-03-29T08:07:37.823Z
@NathanReed sounds like the answer to me
joojaa
<raytracing><specular>
phong equation of illumination specular component
user2976568
# phong equation of illumination specular component

(Asked by: username_0 on 2016-03-26)

I'm stuck on this question asking me to calculate the intensity of a pixel using Ray Tracing. It gives values such as $I\_i$ but doesn't give any coordinates.

I know for the diffuse component, $I\_ik\_d(n,l)$ can be written as $I\_ik\_d(\cos\theta)$ but for the specular component $I\_ik\_s(h\cdot n)$ is there any other way to write it so that it doesn't require any vectors such as $h$ and $n$?

This is the question:

[![enter image description here](https://i.sstatic.net/3s0AC.png)](https://i.sstatic.net/3s0AC.png)

**Tags:** raytracing, specular

> **Comments:**
> **username_1**: Are you sure you want N·H, or do you want R·L i.e. reflection vector dotted with light source vector? The latter would be the classic Phong equation (N·H is Blinn), and the figure appears to mark the R·L angle: 15 degrees.  
> **username_2**: Should the question not point out which Bidirectional Reflectance Distribution Function (BRDF) you need to use? You have Phong, Blinn-Phong, Modified Phong, Modified Blinn-Phong and a whole variety of physically-based ones.  
> **username_0**: @username_1 how can i find R.L if i dont know the vectors? Do i just use 15 degrees?  
> **username_1**: @username_0 The dot product is the cosine of the angle between the vectors (for unit vectors). Just as you remarked that N·L = cos(theta). :)  
> **username_3**: @username_1 sounds like the answer to me  

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## 1 answers

### Answer by username_1 on 2016-03-29. Score: 5 | Accepted answer

Assuming that the classic Phong model is desired here, the dot product that goes into the specular calculation should be R·L, rather than N·H (which was introduced by Blinn). That is, Phong calculates specular using the angle between the reflected eye vector and the light vector.

In the diagram you posted, these vectors are shown and the angle is given as 15°. So, R·L = cos(15°) = 0.96 according to the table below the diagram.


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