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Combined display of all available logs of Conformal Geometric Algebra. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 02:34, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect circle.svg (Deleted old revision 20231023023447!Plane_connect_circle.svg)
- 02:34, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect circle.svg
- 02:34, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect circle.svg (Deleted old revision 20231023023428!Sphere_connect_circle.svg)
- 02:34, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect circle.svg
- 02:34, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect point.svg (Deleted old revision 20231023023412!Plane_connect_point.svg)
- 02:34, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect point.svg
- 02:33, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect point.svg (Deleted old revision 20231023023354!Sphere_connect_point.svg)
- 02:33, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect point.svg
- 02:33, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect dipole.svg (Deleted old revision 20231023023339!Plane_connect_dipole.svg)
- 02:33, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect dipole.svg
- 02:33, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect dipole.svg (Deleted old revision 20231023023321!Sphere_connect_dipole.svg)
- 02:33, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect dipole.svg
- 02:33, 23 October 2023 Eric Lengyel talk contribs deleted page File:Plane connect round.svg (Deleted old revision 20231023023306!Plane_connect_round.svg)
- 02:33, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Plane connect round.svg
- 02:31, 23 October 2023 Eric Lengyel talk contribs deleted page File:Sphere connect round.svg (Deleted old revision 20231023023140!Sphere_connect_round.svg)
- 02:31, 23 October 2023 Eric Lengyel talk contribs uploaded a new version of File:Sphere connect round.svg
- 22:54, 25 August 2023 Eric Lengyel talk contribs created page File:AntiwedgeProduct.svg
- 22:54, 25 August 2023 Eric Lengyel talk contribs uploaded File:AntiwedgeProduct.svg
- 22:54, 25 August 2023 Eric Lengyel talk contribs created page File:WedgeProduct.svg
- 22:54, 25 August 2023 Eric Lengyel talk contribs uploaded File:WedgeProduct.svg
- 03:58, 6 August 2023 Eric Lengyel talk contribs created page Spheres (Redirected page to Sphere) Tag: New redirect
- 03:58, 6 August 2023 Eric Lengyel talk contribs created page Circles (Redirected page to Circle) Tag: New redirect
- 03:58, 6 August 2023 Eric Lengyel talk contribs created page Dipoles (Redirected page to Dipole) Tag: New redirect
- 03:57, 6 August 2023 Eric Lengyel talk contribs created page Planes (Redirected page to Plane) Tag: New redirect
- 03:57, 6 August 2023 Eric Lengyel talk contribs created page Lines (Redirected page to Line) Tag: New redirect
- 03:57, 6 August 2023 Eric Lengyel talk contribs created page Flat points (Redirected page to Flat point) Tag: New redirect
- 03:57, 6 August 2023 Eric Lengyel talk contribs created page Round points (Redirected page to Round point) Tag: New redirect
- 03:26, 6 August 2023 Eric Lengyel talk contribs created page Exterior antiproduct (Redirected page to Exterior products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Geometric antiproduct (Redirected page to Geometric products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Geometric product (Redirected page to Geometric products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Antiwedge product (Redirected page to Exterior products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Wedge product (Redirected page to Exterior products) Tag: New redirect
- 03:25, 6 August 2023 Eric Lengyel talk contribs created page Projection (Redirected page to Projections) Tag: New redirect
- 03:24, 6 August 2023 Eric Lengyel talk contribs created page Dual (Redirected page to Duals) Tag: New redirect
- 03:24, 6 August 2023 Eric Lengyel talk contribs created page Anticarrier (Redirected page to Carriers) Tag: New redirect
- 03:24, 6 August 2023 Eric Lengyel talk contribs created page Carrier (Redirected page to Carriers) Tag: New redirect
- 03:23, 6 August 2023 Eric Lengyel talk contribs created page Partner (Redirected page to Partners) Tag: New redirect
- 03:23, 6 August 2023 Eric Lengyel talk contribs created page Container (Redirected page to Containers) Tag: New redirect
- 03:20, 6 August 2023 Eric Lengyel talk contribs created page Transversion (Created page with "__NOTOC__ A ''transversion'' is a reciprocal transformation performed by the operator :$$\mathfrak T = {\dfrac{\tau_{x\vphantom{y}}}{2} \mathbf e_{423} + \dfrac{\tau_y}{2} \mathbf e_{431} + \dfrac{\tau_z{\vphantom{y}}}{2} \mathbf e_{412} + \large\unicode{x1d7d9}}$$ . == Matrix Form == When a transversion $$\mathfrak T$$ is applied to a round point, it is equivalent to premultiplying the point by the $$5 \times 5$$ matrix :$$\begin{bmatrix} 1 & 0 & 0 & 0 & -\tau_x...")
- 03:20, 6 August 2023 Eric Lengyel talk contribs created page Dilation (Created page with "__NOTOC__ A ''dilation'' is a conformal transformation of Euclidean space performed by the operator :$$\mathbf D = \dfrac{1 - \sigma}{2} (c_x \mathbf e_{235} + c_y \mathbf e_{315} + c_z \mathbf e_{125} - \mathbf e_{321}) + \dfrac{1 + \sigma}{2} {\large\unicode{x1d7d9}}$$ . This operator scales an object $$\mathbf x$$ by the factor $$\sigma$$ about the center point $$\mathbf c = (c_x, c_y, c_z)$$ when used with the sandwich antiproduct $$\mathbf D \mathbin{\unicode{x27C...")
- 03:19, 6 August 2023 Eric Lengyel talk contribs created page Rotation (Created page with "__NOTOC__ A ''rotation'' is a proper isometry of Euclidean space performed by the operator :$$\mathbf R = \boldsymbol l\sin\dfrac{\phi}{2} + {\large\unicode{x1d7d9}}\cos\dfrac{\phi}{2}$$ , where $$\boldsymbol l$$ is a unitized line corresponding to the axis of rotation. This operator is identical to the [http://rigidgeometricalgebra.org/wiki/index.php?title=Rotation rotation operator in rigid geometric algebra] but with the extra factor of $$\mathbf e_5$$. It rotat...")
- 03:19, 6 August 2023 Eric Lengyel talk contribs created page Translation (Created page with "__NOTOC__ A ''translation'' is a proper isometry of Euclidean space performed by the operator :$$\mathbf T = {\dfrac{\tau_{x\vphantom{y}}}{2} \mathbf e_{235} + \dfrac{\tau_y}{2} \mathbf e_{315} + \dfrac{\tau_z{\vphantom{y}}}{2} \mathbf e_{125} + \large\unicode{x1d7d9}}$$ . This operator is identical to the [http://rigidgeometricalgebra.org/wiki/index.php?title=Translation translation operator in rigid geometric algebra] but with the extra factor of $$\mathbf e_5$$. It...")
- 03:19, 6 August 2023 Eric Lengyel talk contribs created page Projections (Created page with "Any geometric object $$\mathbf x$$ can be projected onto another geometric object $$\mathbf y$$ of higher grade by first calculating the connect of $$\mathbf x$$ with $$\mathbf y$$ and then using the meet operation to intersect the result with $$\mathbf y$$. That is, the projection of $$\mathbf x$$ onto $$\mathbf y$$ is given by :$$(\mathbf y^* \wedge \mathbf x) \vee \mathbf y$$ . This formula is general and works for flat points, lines, planes, r...")
- 03:19, 6 August 2023 Eric Lengyel talk contribs created page Connect (Created page with "The ''connect'' operation is performed by taking the wedge product between the dual of an object ''A'' and another object ''B'' with lower grade. The result is an object ''C'' that is orthogonal to ''A'' and contains ''B'', allowing a projection of ''B'' onto ''A'' through a simple intersection of ''A'' and ''C''. The flat points, lines, planes, round points, dipoles, circles, and spheres appearing in the following tables are defined...")
- 03:18, 6 August 2023 Eric Lengyel talk contribs created page Join and meet (Created page with "The ''join'' is a binary operation that calculates the higher-dimensional geometry containing its two operands, similar to a union. The ''meet'' is another binary operation that calculates the lower-dimensional geometry shared by its two operands, similar to an intersection. The flat points, lines, planes, round points, dipoles, circles, and spheres appearing in the following tables are defined as follows: :$$\mathbf p = p_x \mathbf e_{15} +...")
- 03:18, 6 August 2023 Eric Lengyel talk contribs created page Exterior products (Created page with "The ''exterior product'' is the fundamental product of Grassmann Algebra, and it forms part of the geometric product in geometric algebra. There are two products with symmetric properties called the exterior product and exterior antiproduct. == Exterior Product == The following Cayley table shows the exterior products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. 1440px == Exterior Anti...")
- 03:17, 6 August 2023 Eric Lengyel talk contribs created page Wedge products (Created page with "The ''exterior product'' is the fundamental product of Grassmann Algebra, and it forms part of the geometric product in geometric algebra. There are two products with symmetric properties called the exterior product and exterior antiproduct. == Exterior Product == The following Cayley table shows the exterior products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. 1440px == Exterior Anti...")
- 03:17, 6 August 2023 Eric Lengyel talk contribs created page Geometric products (Created page with "The ''geometric product'' is the fundamental product of geometric algebra. There are two products with symmetric properties called the geometric product and geometric antiproduct. == Geometric Product == The following Cayley table shows the geometric products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric product is the scalar basis element $$\mathbf 1$$. Cells colored yellow correspond...")
- 03:16, 6 August 2023 Eric Lengyel talk contribs created page Duals (Created page with "The ''dual'' of an object $$\mathbf x$$, denoted by $$\mathbf x^*$$, is given by :$$\mathbf x^* = \mathbf{\tilde x} \mathbin{\unicode{x27D1}} {\large\unicode{x1d7d9}}$$ . The following table lists the duals for the geometric objects in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. {| class="wikitable" ! Type !! Definition !! Dual |- | style="padding: 12px;" | Flat point | style="padding: 12px;" | $$\mathbf p = p_x \mathbf e_{15} + p_y \mathbf e_{25} + p...")
- 03:16, 6 August 2023 Eric Lengyel talk contribs created page Attitude (Created page with "The ''attitude'' function, denoted by $$\operatorname{att}$$, extracts the attitude of a geometry and returns a purely directional object. The attitude function is defined as :$$\operatorname{att}(\mathbf x) = \mathbf x \vee \overline{\mathbf e_4}$$ . The following table lists the attitude for the geometric objects in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. {| class="wikitable" ! Type !! Definition !! Attitude |- | style="padding: 12px;" | Flat poin...")
