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Feb
13
awarded  Popular Question
Oct
18
awarded  Yearling
Jan
22
awarded  Custodian
Jan
22
reviewed Approve suggested edit on About calculating Integrals
Jan
22
comment About calculating Integrals
@ThiesHeidecke That is not what I wanted. Of course you can try to approximate the specular highlight by sampling a single point on the ray, but that was not the Intention
Jan
22
comment About calculating Integrals
@swish oic. Too bad this is impossible. I will continue testing and try to find a solution, I will come back to this later.
Jan
22
comment About calculating Integrals
@swish you said it would Integrate... I dont believe so. Mathematica does not find a Integral for $e^{-cos^{-1}(u^2)}$, The resulting function would be way more complicated...
Jan
22
awarded  Commentator
Jan
22
comment About calculating Integrals
I will post this to Math.SE in the original form in order to get further assistance. This question is less Mathematica-oriented I fear
Jan
22
comment About calculating Integrals
@swish In fact, I have already made such an optimization to get only the third coordinate of H to change. Originally, $H(u)=\overrightarrow{a}+(\overrightarrow{b}-\overrightarrow{a})*u-\overrightarr‌​ow{x} + \overrightarrow{v}$. We modified the coordinate system in a way that made $\overrightarrow{b}-\overrightarrow{a}={0,0,v}$. If we were to change the coordinate system to make $H(u)={0,0,u*v}$, we would have to inversely transform x,l,n,v in every "step" of integration, which would be almost impossible I fear.
Jan
22
comment About calculating Integrals
@DanielLichtblau I will try this. However it will make integrating way harder, as there will be a few new variables? That makes simplifying not easier...
Jan
22
revised About calculating Integrals
added 4 characters in body
Jan
22
comment About calculating Integrals
@swish I am absolutely sure. This is an integral over specular lighting (Gauss Specular lighting) along a part of the z-axis. The formula is $e^{-\angle(H,L)^2}$ - I just realized I forgot the ^2 >_<
Jan
22
asked About calculating Integrals
Dec
25
accepted Preventing Numerical value from being evaluated
Dec
24
comment Solving an Integral equation
I found my typo in the third try (I thought that would not work, because it instantly threw dozens of errors at me) How do I improve the precision? AccuracyGoal and PrecisionGoal do not change the output?
Dec
24
accepted Solving an Integral equation
Dec
24
revised Solving an Integral equation
added 214 characters in body
Dec
24
comment Solving an Integral equation
Oh I tried something similar aswell... I got a bunch of Infinite Expression errors however? I will add that to the OP
Dec
24
asked Solving an Integral equation