Affine Combination

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An affine combination of points ${\mathbf{p}}_0,{\mathbf{p}}_1,\dots ,{\mathbf{p}}_{\mathbf{n}}\in E^3$ is a point $\mathbf{p}\in E^3$:

$$\mathbf{p}=\sum _{i=0}^n{a}_i{\mathbf{p}}_{\mathbf{i}}$$

Where $a_0,a_1,\dots ,a_n\in \mathbb{R}$ are affine coordinates of $\mathbf{p}$ w.r.t ${\mathbf{p}}_0,{\mathbf{p}}_1,\dots ,{\mathbf{p}}_{\mathbf{n}}$, where ${\sum }_{i=0}^n{a}_i=1$.

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Further, if this holds to further criterias, it can be defined as a Convex Affine Combination

Examples: Line segments, convex polygons, triangles, tetrahedra → The building blocks of our models.