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Awesome job so far everyone! Please give us your feedback on how our article efforts are going. We still need more finished articles for our May contest theme: Remake the Classics

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#ActualTsus

Posted 14 September 2012 - 06:41 AM

Hi CryZe!

Alright, let me show you how I got to my equations. I’m still convinced that they are correct. Posted Image

The intensity is the flux per solid angle: $I = \frac{\Phi}{\omega}[/formula]The solid angle is area of a cone cap divided by squared distance: [formula]\omega=\frac{A}{r^2}[/formula]Now, I assume the solid angle’s top sits at the point light position and opens up toward the viewed receiver area. The viewed receiver area is the receiver area *viewed* from the light’s view. Therefore, the *viewed* receiver area is the receiver area times the cosine of the enclosed angle between normal and direction to light. (That’s what makes the difference to your equation. You forgot in your second line about using only the *viewed* part.)[formula]I=\frac{\Phi}{A \cdot cos(\theta)/r ^2}[/formula]Now, using that the irradiance is the flux per receiver area: [formula]E=\frac{\Phi}{A}[/formula]gives: [formula]I=\frac{E \cdot r^2}{cos(\theta)}[/formula].Rearranging leads to: [formula]E=\frac{I \cdot cos(\theta)}{r^2}[/formula], which is my line from before.Your first line is slightly wrong, too. From the definition of the radiance: [formula]L=\frac{\Phi}{A \cdot cos(\theta) \cdot \omega}[/formula] and the definition of intensity:[formula]I=\frac{\Phi}{ \omega}[/formula] we get: [formula]L=\frac{I}{ A \cdot cos(\theta)}[/formula]Rearranging and using [formula]A=r_0^2\pi[/formula] gives: [formula]I=L \cdot r_0^2\pi \cdot cos(\theta)[/formula]��(Your first line misses the cosine.)You pulled the cosine in later in the third line (which is therefore wrong, too). Note that a BRDF is [formula]fr = L_i/E_i[/formula]. The cosine isn’t here as well.Eventually, you get the correct result in the end, since your mistakes in line one and three cancelled each other out. Summarizing, your cosine should move from line three to line one and everything is fine.As for the thing about Pi, I usually just compute the irradiance for a light like that:[formula]E=\frac{I \cdot cos(\theta)}{r^2}[/formula]and than just use [formula]L=fr \cdot E[/formula] to get the radiance for that light.I don’t explicitly compute the incoming radiance ([formula]L_i$ ), therefore my Pi in the BRDF doesn’t cancel out.

Best regards!

#2Tsus

Posted 14 September 2012 - 06:39 AM

Hi CryZe!

Alright, let me show you how I got to my equations. I’m still convinced that they are correct. Posted Image

The intensity is the flux per solid angle: $I = \frac{\Phi}{\omega}[/formula]The solid angle is area of a cone cap divided by squared distance: [formula]\omega=\frac{A}{r^2}[/formula]Now, I assume the solid angle’s top sits at the point light position and opens up toward the viewed receiver area. The viewed receiver area is the receiver area *viewed* from the light’s view. Therefore, the *viewed* receiver area is the receiver area times the cosine of the enclosed angle between normal and direction to light. (That’s what makes the difference to your equation. You forgot in your second line about using only the *viewed* part.)[formula]I=\frac{\Phi}{A \cdot cos( heta)/r ^2}[/formula]Now, using that the irradiance is the flux per receiver area: [formula]E=\frac{\Phi}{A}[/formula]gives: [formula]I=\frac{E \cdot r^2}{cos( heta)}[/formula].Rearranging leads to: [formula]E=\frac{I \cdot cos( heta)}{r^2}[/formula], which is my line from before.Your first line is slightly wrong, too. From the definition of the radiance: [formula]L=\frac{\Phi}{A \cdot cos( heta) \cdot \omega}[/formula] and the definition of intensity:[formula]I=\frac{\Phi}{ \omega}[/formula] we get: [formula]L=\frac{I}{ A \cdot cos( heta)}[/formula]Rearranging and using [formula]A=r_0^2\pi[/formula] gives: [formula]I=L \cdot r_0^2\pi \cdot cos( heta)[/formula]��(Your first line misses the cosine.)You pulled the cosine in later in the third line (which is therefore wrong, too). Note that a BRDF is [formula]fr = L_i/E_i[/formula]. The cosine isn’t here as well.Eventually, you get the correct result in the end, since your mistakes in line one and three cancelled each other out. Summarizing, your cosine should move from line three to line one and everything is fine.As for the thing about Pi, I usually just compute the irradiance for a light like that:[formula]E=\frac{I \cdot cos( heta)}{r^2}[/formula]and than just use [formula]L=fr \cdot E[/formula] to get the radiance for that light.I don’t explicitly compute the incoming radiance ([formula]L_i$ ), therefore my Pi in the BRDF doesn’t cancel out.

Best regards!

#1Tsus

Posted 14 September 2012 - 06:34 AM

Hi CryZe!

Alright, let me show you how I got to my equations. I’m still convinced that they are correct. Posted Image

The intensity is the flux per solid angle: $I = \frac{\Phi}{\omega}[/formula]The solid angle is area of a cone cap divided by squared distance: [formula]\omega=\frac{A}{r^2}[/formula]Now, I assume the solid angle’s top sits at the point light position and opens up toward the viewed receiver area. The viewed receiver area is the receiver area *viewed* from the light’s view. Therefore, the *viewed* receiver area is the receiver area times the cosine of the enclosed angle between normal and direction to light. (That’s what makes the difference to your equation. You forgot in your second line about using only the *viewed* part.)[formula]I=\frac{\Phi}{A \cdot cos(\theta)/r ^2}[/formula]Now, using that the irradiance is the flux per receiver area: [formula]E=\frac{\Phi}{A}[/formula]gives: [formula]I=\frac{E \cdot r^2}{cos(\theta)}[/formula].Rearranging leads to: [formula]E=\frac{I \cdot cos(\theta)}{r^2}[/formula], which is my line from before.Your first line is slightly wrong, too. From the definition of the radiance: [formula]L=\frac{\Phi}{A \cdot cos(\theta) \cdot \omega}[/formula] and the definition of intensity:[formula]I=\frac{\Phi}{ \omega}[/formula] we get: [formula]L=\frac{I}{ A \cdot cos(\theta)}[/formula]Rearranging and using [formula]A=r_0^2\pi[/formula] gives: [formula]I=L \cdot r_0^2\pi \cdot cos(\theta)[/formula]��(Your first line misses the cosine.)You pulled the cosine in later in the third line (which is therefore wrong, too). Note that a BRDF is [formula]fr = L_i/E_i[/formula]. The cosine isn’t here as well.Eventually, you get the correct result in the end, since your mistakes in line one and three cancelled each other out. Summarizing, your cosine should move from line three to line one and everything is fine.As for the thing about Pi, I usually just compute the irradiance for a light like that:[formula]E=\frac{I \cdot cos(\theta)}{r^2}[/formula]and than just use [formula]L=fr \cdot E[/formula] to get the radiance for that light.I don’t explicitly compute the incoming radiance ([formula]L_i$ ), therefore my Pi in the BRDF doesn’t cancel out.

Never mind about the slight mistakes. Usually it’s me who’s wrong. Posted Image

Best regards!

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