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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).
- 06:11, 15 July 2023 Eric Lengyel talk contribs created page File:Point plane.svg
- 06:11, 15 July 2023 Eric Lengyel talk contribs uploaded File:Point plane.svg
- 06:11, 15 July 2023 Eric Lengyel talk contribs created page Projections (Created page with "Projections and antiprojections of one geometric object onto another can be accomplished using interior products as described below. The formulas on this page are general and do not require the geometric objects to be unitized. Most of them become simpler if unitization can be assumed. == Projection == The geometric projection of an object $$\mathbf x$$ onto an object $$\mathbf y$$ is given by the general formula $$(\mathbf y_\unicode{x25CB} \mathbin{\unicode{...")
- 06:10, 15 July 2023 Eric Lengyel talk contribs created page Euclidean distance (Created page with "The Euclidean distance between geometric objects can be measured by using commutators to calculate homogeneous magnitudes. The following table lists formulas for Euclidean distances between the main types of geometric objects in the 4D rigid geometric algebra $$\mathcal G_{3,0,1}$$. These formulas are general and do not require the geometric objects to be unitized. Most of them become simpler if unitization can be assumed. The points, lines, and p...")
- 06:10, 15 July 2023 Eric Lengyel talk contribs created page File:Distance line line.svg
- 06:10, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance line line.svg
- 06:10, 15 July 2023 Eric Lengyel talk contribs created page File:Distance point plane.svg
- 06:10, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance point plane.svg
- 06:09, 15 July 2023 Eric Lengyel talk contribs created page File:Distance point line.svg
- 06:09, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance point line.svg
- 06:09, 15 July 2023 Eric Lengyel talk contribs created page File:Distance point point.svg
- 06:09, 15 July 2023 Eric Lengyel talk contribs uploaded File:Distance point point.svg
- 06:06, 15 July 2023 Eric Lengyel talk contribs created page Flector (Created page with "400px|thumb|right|'''Figure 1.''' A flector represents an improper Euclidean isometry, which can always be regarded as a rotation about a line $$\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...")