# Tag Info

Accepted

• 8,447

### Vertices of a regular polygon given the incircle radius

what is the relation between radius of the in-circle and circum-circle of a polygon? That is $cos ( \frac{2\pi}{n}*\frac{1}{2} ) = cos ( \frac{\pi}{n})$ The triangle with edges from the center to ...
• 6,010
Accepted

### Radiative Transfer Equation for Photorealistic Rendering

I suspect the answer to (a) is simply performance. Full volumetric path tracing / photon mapping based on the RTE can certainly be done (and I'm sure it sometimes is), but it's very expensive and ...
• 25.2k
Accepted

### Calculating the gradient of a triangular mesh

A function $f$ on your triangulated surface is an assignment of real numbers on the vertices of the triangulation and therefore $f \in \mathbb{R}^{|\mathcal{V}|}$. According to the continuous theory, ...
• 221
Accepted

### Calculate normals from vertices

You are not too far off with your second averaging approach. The problem is, that the area is the wrong weighting factor for what you want to achieve. You want each of the 3 sides of the cube to ...
• 1,251
There are 2 ways to go about intersecting the triangle. Let the vertices of the triangle have positions $v_1, v_2, v_3$. Let the ray have origin $o$ and direction $d$. Let the model (4x4) matrix be $M$...