All public logs

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).

• 03:16, 6 August 2023 Eric Lengyel talk contribs created page Partners (Created page with "The ''partner'' of a round object (a round point, dipole, circle, or sphere) is the round object having the same center, same carrier, and same absolute size, but having a squared radius of the opposite sign. The partner of an object $$\mathbf x$$ is denoted by $$\operatorname{par}(\mathbf x)$$, and it is given by the meet of the carrier of $$\mathbf x$$ with the container of $$\mathbf x^*$$: :$$\operatorname{par}(\mathbf x) = \operatorna...")
• 03:16, 6 August 2023 Eric Lengyel talk contribs created page Carriers (Created page with "== Carrier == The ''carrier'' of a round object (a round point, dipole, circle, or sphere) is the lowest dimensional flat object (a flat point, line, or plane) that contains it. The carrier of an object $$\mathbf x$$ is denoted by $$\operatorname{car}(\mathbf x)$$, and it is calculated by simply multiplying $$\mathbf x$$ by $$\mathbf e_5$$ with the wedge product to extract the round part of $$\mathbf x$$ as a flat geometry: :$$\operatorn...")
• 03:16, 6 August 2023 Eric Lengyel talk contribs created page Centers (Created page with "The ''center'' of a round object (a round point, dipole, circle, or sphere) is the round point having the same center and radius. The center of an object $$\mathbf x$$ is denoted by $$\operatorname{cen}(\mathbf x)$$, and it is given by the meet of $$\mathbf x$$ and its own anticarrier: :$$\operatorname{cen}(\mathbf x) = -\operatorname{car}(\mathbf x^*) \vee \mathbf x$$ . (The negative sign is not strictly necessary, but is included so the fu...")
• 03:15, 6 August 2023 Eric Lengyel talk contribs created page Containers (Created page with "The ''container'' of a round object (a round point, dipole, circle, or sphere) is the smallest sphere that contains it. The container of an object $$\mathbf x$$ is denoted by $$\operatorname{con}(\mathbf x)$$, and it is given by the connect of $$\mathbf x$$ with its own carrier: :$$\operatorname{con}(\mathbf x) = \operatorname{car}(\mathbf x)^* \wedge \mathbf x$$ . The squared radius of an object's container has the same sign as the squared radi...")
• 03:15, 6 August 2023 Eric Lengyel talk contribs created page Center (Created page with "The ''center'' of a round object (a round point, dipole, circle, or sphere) is the round point having the same center and radius. The center of an object $$\mathbf x$$ is denoted by $$\operatorname{cen}(\mathbf x)$$, and it is given by the meet of $$\mathbf x$$ and its own anticarrier: :$$\operatorname{cen}(\mathbf x) = -\operatorname{car}(\mathbf x^*) \vee \mathbf x$$ . (The negative sign is not strictly necessary, but is included so the fu...")
• 03:15, 6 August 2023 Eric Lengyel talk contribs created page Sphere (Created page with "__NOTOC__ In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''sphere'' $$\mathbf s$$ is a quadrivector having the general form :$$\mathbf s = s_u \mathbf e_{1234} + s_x \mathbf e_{4235} + s_y \mathbf e_{4315} + s_z \mathbf e_{4125} + s_w \mathbf e_{3215}$$ . If the $$s_u$$ component is zero, then the sphere contains the point at infinity, and it is thus a flat plane. Given a center $$\mathbf p = (p_x, p_y, p_z)$$ and a radius $$r$$, a sphere can be...")
• 03:15, 6 August 2023 Eric Lengyel talk contribs created page Circle (Created page with "__NOTOC__ In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''circle'' $$\mathbf c$$ is a trivector with ten components having the general form :$$\mathbf c = c_{gx} \mathbf e_{423} + c_{gy} \mathbf e_{431} + c_{gz} \mathbf e_{412} + c_{gw} \mathbf e_{321} + c_{vx} \mathbf e_{415} + c_{vy} \mathbf e_{425} + c_{vz} \mathbf e_{435} + c_{mx} \mathbf e_{235} + c_{my} \mathbf e_{315} + c_{mz} \mathbf e_{125}$$ . If the $$gx$$, $$gy$$, $$gz$$, and $$gw$$ componen...")
• 03:14, 6 August 2023 Eric Lengyel talk contribs created page Dipole (Created page with "__NOTOC__ In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''dipole'' $$\mathbf d$$ is a bivector with ten components having the general form :$$\mathbf d = d_{vx} \mathbf e_{41} + d_{vy} \mathbf e_{42} + d_{vz} \mathbf e_{43} + d_{mx} \mathbf e_{23} + d_{my} \mathbf e_{31} + d_{mz} \mathbf e_{12} + d_{px} \mathbf e_{15} + d_{py} \mathbf e_{25} + d_{pz} \mathbf e_{35} + d_{pw} \mathbf e_{45}$$ . If the $$vx$$, $$vy$$, $$vz$$, $$mx$$, $$my$$, and $$mz$$ com...")
• 03:14, 6 August 2023 Eric Lengyel talk contribs created page Round point (Created page with "__NOTOC__ In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''round point'' $$\mathbf a$$ is a vector having the general form :$$\mathbf a = a_x \mathbf e_1 + a_y \mathbf e_2 + a_z \mathbf e_3 + a_w \mathbf e_4 + a_u \mathbf e_5$$ . Given a position $$\mathbf p = (p_x, p_y, p_z)$$ and a radius $$r$$, a round point can be formulated as :$$\mathbf a = p_x \mathbf e_1 + p_y \mathbf e_2 + p_z \mathbf e_3 + \mathbf e_4 + \dfrac{p^2 + r^2}{2} \mathbf e_5$$ . Th...")
• 03:14, 6 August 2023 Eric Lengyel talk contribs created page Plane (Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a plane. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''plane'' $$\mathbf g$$ is a quadrivector having the general form :$$\mathbf g = g_x \mathbf e_{4235} + g_y \mathbf e_{4315} + g_z \mathbf e_{4125} + g_w \mathbf e_{3215}$$ . A plane can be viewed as an infinitely large sphere containing the point at infinity. A plane in conformal geometric algebra is the precise...")
• 03:14, 6 August 2023 Eric Lengyel talk contribs created page Line (Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a line. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''line'' $$\boldsymbol l$$ is a trivector having the general form :$$\boldsymbol l = v_x \mathbf e_{415} + v_y \mathbf e_{425} + v_z \mathbf e_{435} + m_x \mathbf e_{235} + m_y \mathbf e_{315} + m_z \mathbf e_{125}$$ . A line can be viewed as an infinitely large circle that contains the point at infinity. A line in...")
• 03:13, 6 August 2023 Eric Lengyel talk contribs created page Flat point (Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a flat point. In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a ''flat point'' $$\mathbf p$$ is a bivector having the general form :$$\mathbf p = p_x \mathbf e_{15} + p_y \mathbf e_{25} + p_z \mathbf e_{35} + p_w \mathbf e_{45}$$ . A flat point can be viewed as a dipole that has one end at the point at infinity. A flat point in conformal geometric algebra is the precise...")
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Wedge product.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Wedge product.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet sphere.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet sphere.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet point.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet point.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet plane.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet plane.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet line.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet line.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet dipole.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet dipole.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere meet circle.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere meet circle.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect point.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect point.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect line.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect line.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect dipole.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect dipole.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Sphere connect circle.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Sphere connect circle.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Round join round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Round join round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Point join round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Point join round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Point.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Point.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Point connect round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Point connect round.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs created page File:Plane meet plane.svg (Uploaded with SimpleBatchUpload)
• 03:12, 6 August 2023 Eric Lengyel talk contribs uploaded File:Plane meet plane.svg (Uploaded with SimpleBatchUpload)