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- 01:50, 28 August 2024 Dot products (hist | edit) [2,177 bytes] Eric Lengyel (talk | contribs) (Created page with "The dot products between two unitized objects of the same type are listed in the following table. The vector $$\mathbf v$$ is the difference between their center positions, and the scalars $$r_1$$ and $$r_2$$ are their radii. In the case of dipoles and circles, the vectors $$\mathbf n_1$$ and $$\mathbf n_2$$ correspond to the directions of the carrier lines or the normals of the carrier planes. {| class="wikitable" ! Type || Dot Product |- | style="padding: 12px;" | Rou...")
- 02:01, 13 April 2024 Metrics (hist | edit) [839 bytes] Eric Lengyel (talk | contribs) (Created page with "The ''metric'' used in the 5D conformal geometric algebra over 3D Euclidean space is the $$5 \times 5$$ matrix $$\mathfrak g$$ given by :$$\mathfrak g = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 \\ 0 & 0 & 0 & -1 & 0\\\end{bmatrix}$$ . The ''metric exomorphism matrix'' $$\mathbf G$$, often just called the "metric" itself, corresponding to the metric $$\mathfrak g$$ is the $$32 \times 32$$ matrix shown below. Im...")