Recent content by GabrielCoriiu

Yes, the normal is always orthogonal to the tangent plane, where the gradient lies. However, there are infinitely many tangent spaces at every point (all the possible rotations of a plane around the normal axis). One of them could be defined by ## \vec z_t = \vec N, \vec y_t=\vec G, \vec x_t =...

I'm sure that integral curves can be applied to integral surfaces given that a surface is just a collection of curves, in the same way a curve is just a collection of points. As for the Morse theory, I'm not familiar with it, but as far as I understand it's mainly used for reconstructing a...

The vector field represents what the normal should be at any point so that a refracted ray of light focuses on a given point I've managed to integrate the gradient at a given depth within the field, which gives a height map Integration technique...

Hi, I'm trying to find all the valid surfaces that go through a vector field so that the normal of the surface at any point is equal with the vector from the vector field at the same point. The vector field is defined by the function: $$ \hat N(p) = \hat L(p) \cos \theta + \hat R(p)...

Hmmm, I've just realized that cos (θ1 - θ2) is I⋅R, supposedly they are unit vectors. I can now get θ1 and replace it in Snell's law and solve for θ1, which is exactly what I want :biggrin: Thanks BvU!

To rephrase the question, what should the surface orientation be, in order for the refracted ray to focus on a specific point, given the light direction and index of refraction.

Hi BvU, thank you for the warm welcome. I've changed the image in the original post, I hope this makes it more clear :)

I'm trying to reverse engineer refraction. So given I, R and k in the image, what is N so that sin(θ1)/sin(θ2) = k ?

Hey, I have a thought that has been bugging me for a while. I know that Einstein's theory about the universe says we are all living in a 4 dimensional universe (the space-time fabric), but what if every fundamental particle in the universe has its own space-time. As if there are as many...

Hey, I am Gabriel and I have a degree in computer science. I work in the video gaming industry, but this mysterious and amazing universe has always intrigued me.