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.

# Category Archives: Maths

# Tangent space matrix (TBN)

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).

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# Bézier curves

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.

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