# Questions tagged [hemisphere]

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### Confusion about different sampling strategies in Monte Carlo Path Tracing

I am studying Monte Carlo Path Tracing from different sources. However, I have some confusion about the sampling part and dare to post here for experts' ...
• 135
1 vote
1 answer
91 views

### Has anyone found an analytic solution to the product of spherical gaussians from Xu et al?

In section 4.2 of this paper: http://cseweb.ucsd.edu/~ravir/274/15/papers/a209-xu.pdf Xu et al approximate the product of 2 anisotropic Gaussian distributions. I want to know if someone has found not ...
• 1,696
1 vote
2 answers
111 views

### If a 3D scene is rendered onto a hemispherical display, will there still be warping near the edges?

When a 3D scene is rendered to a 2D display, the image is distorted near the edges of the display. If a 3D scene is rendered onto a hemispherical display, will there still be warping?
2 votes
0 answers
320 views

### Exact Formula for Diffuse Hemisphere Lighting

The OpenGL Programming Guide states the formula for diffuse hemisphere lighting on a surface with normal vector $\vec{n}$ as \$L_o(\vec{n}) = L_i(\uparrow) (1-\frac{1}{2}\sin(\theta)) + L_i(\downarrow)...
• 121
4 votes
2 answers
876 views

### Why map Hammersley 2D set's (u,v) to sphere's (θ, φ) coordinates (and not to (φ, θ) )?

As explained in Holger Dammetz page Hammersley Points on the Hemisphere, the 2D coordinates (u,v) are usually mapped to the spherical coordinates (θ, φ). As a result, the coordinate "uniformly ...
• 1,851
12 votes
1 answer
962 views

### Convolution of Hemispherical Harmonics

Spherical Harmonics (SH) are a way to represent low-frequency spherical functions with only a handful of coefficients. They have some nice mathematical properties, e.g. a convolution with a kernel ...
• 2,293