Some useful formulas when dealing with octrees. Remember that an octree of height h equal to zero means that it is composed by a single root node with no children.
The tangent space matrix of a vertex on a surface (also called TBN matrix, due to its components), is a matrix that converts from coordinates expressed in tangent space to coordinates expressed in object space (being the later, the base in which all vertex coordinates are expressed).
Bézier curves are widely used in computer graphics to generate animation paths, smooth interpolations between values, modeling of shapes and so on. Below, a general way to compute Bézier curves of arbitrary degree is shown in Casteljau’s algorithm, and after that, the explicit equations for solving Bézier curves of degree 1, 2 and 3 are given.