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Combined display of all available logs of Rigid Geometric Algebra. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 06:09, 15 July 2023 Eric Lengyel talk contribs created page File:Distance point line.svg
- 06:09, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance point line.svg
- 06:09, 15 July 2023 Eric Lengyel talk contribs created page File:Distance point point.svg
- 06:09, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance point point.svg
- 06:06, 15 July 2023 Eric Lengyel talk contribs created page Flector (Created page with "400px|thumb|right|'''Figure 1.''' A flector represents an improper Euclidean isometry, which can always be regarded as a rotation about a line $$\boldsymbol l$$ and a reflection across a plane perpendicular to the same line. A ''flector'' is an operator that performs an improper isometry in Euclidean space. Such isometries encompass all possible combinations of an odd number of reflections, inversions, transflections, and rotorefle...")
- 06:06, 15 July 2023 Eric Lengyel talk contribs created page File:Improper isom.svg
- 06:06, 15 July 2023 Eric Lengyel talk contribs uploaded File:Improper isom.svg
- 06:04, 15 July 2023 Eric Lengyel talk contribs created page File:Complements.svg
- 06:04, 15 July 2023 Eric Lengyel talk contribs uploaded File:Complements.svg
- 06:04, 15 July 2023 Eric Lengyel talk contribs created page Complements (Created page with "''Complements'' are unary operations in geometric algebra that perform a specific type of dualization. Every basis element $$\mathbf x$$ has a ''right complement'', which we denote by $$\overline{\mathbf x}$$, that satisfies the equation :$$\mathbf x \wedge \overline{\mathbf x} = {\large\unicode{x1D7D9}}$$ . There is also a ''left complement'', which we denote by $$\underline{\mathbf x}$$, that satisfies the equation :$$\underline{\mathbf x} \wedge \mathbf x = {\larg...")
- 06:03, 15 July 2023 Eric Lengyel talk contribs created page Geometric property (Created page with "An element $$\mathbf x$$ of a geometric algebra possesses the ''geometric property'' if and only if the geometric product between $$\mathbf x$$ and its own reverse is a scalar, which is given by the dot product, and the geometric antiproduct between $$\mathbf x$$ and its own antireverse is an antiscalar, which is given by the antidot product. That is, :$$\mathbf x \mathbin{\unicode{x27D1}} \mathbf{\tilde x} = \mathbf x \mathbin{\unicode{x25CF}} \mathbf{\...")
- 06:03, 15 July 2023 Eric Lengyel talk contribs created page Unitization (Created page with "''Unitization'' is the process of scaling an element of a projective geometric algebra so that its weight norm becomes the antiscalar $$\large\unicode{x1D7D9}$$. An element that has a weight norm of $$\large\unicode{x1D7D9}$$ is said to be ''unitized''. An element $$\mathbf x$$ is unitized by calculating :$$\mathbf{\hat x} = \dfrac{\mathbf x}{\left\Vert\mathbf x\right\Vert_\unicode{x25CB}} = \dfrac{\mathbf x}{\sqrt{\mathbf x \mathbin{\unicode{x25CB}} \smash{\ma...")
- 06:02, 15 July 2023 Eric Lengyel talk contribs created page Geometric norm (Created page with "The ''geometric norm'' is a measure of the magnitude of an element. It has two components called the bulk norm and the weight norm. For points, lines, and planes, the geometric norm is equal to the shortest Euclidean distance between the geometry and the origin. For motors and flectors, the geometric norm is equal to half the distance that the origin is moved by the isometry operator. == Bulk Norm == The ''bulk norm'' of an element $$\mathbf x$$, d...")
- 05:59, 15 July 2023 Eric Lengyel talk contribs created page Dual rotation (Created page with "A ''dual rotation'' is a proper isometry of dual Euclidean space. For a bulk normalized line $$\boldsymbol l$$, the specific kind of dual motor :$$\mathbf R = \boldsymbol l\sin\phi + \mathbf 1\cos\phi$$ , performs a dual rotation of an object $$\mathbf x$$ by twice the angle $$\phi$$ with the sandwich product $$\mathbf R \mathbin{\unicode{x27D1}} \mathbf x \mathbin{\unicode{x27D1}} \mathbf{\tilde R}$$. The line $$\boldsymbol l$$ and its bulk complement...")
- 05:59, 15 July 2023 Eric Lengyel talk contribs created page File:DualRotation.svg
- 05:59, 15 July 2023 Eric Lengyel talk contribs uploaded File:DualRotation.svg
- 05:59, 15 July 2023 Eric Lengyel talk contribs created page File:Rotation.svg
- 05:59, 15 July 2023 Eric Lengyel talk contribs uploaded File:Rotation.svg
- 05:59, 15 July 2023 Eric Lengyel talk contribs created page Dual translation (Created page with "__NOTOC__ A ''dual translation'' is a proper isometry of dual Euclidean space. The specific kind of dual motor :$$\mathbf T = t_x \mathbf e_{41} + t_y \mathbf e_{42} + t_z \mathbf e_{43} + \mathbf 1$$ performs a perspective projection in the direction of $$\mathbf t = (t_x, t_y, t_z)$$ with the focal length given by :$$g = \dfrac{1}{2\Vert \mathbf t \Vert}$$ . == Example == The left image below shows the flow field in the ''x''-''z'' plane for the translation $...")
- 05:58, 15 July 2023 Eric Lengyel talk contribs created page File:DualTranslation.svg