User contributions for Eric Lengyel

01:3601:36, 1 May 2024 diff hist +156‎ Symmetries in Projective Geometric Algebra ‎No edit summary current

01:5301:53, 29 April 2024 diff hist +476‎ Exercises ‎No edit summary current
01:4801:48, 29 April 2024 diff hist +918‎ N Exercises ‎ Created page with "These are exercises accompanying the book [https://www.amazon.com/dp/B0CXY8C72T/?tag=terathon-20 ''Projective Geometric Algebra Illuminated'']. == Exercises for Chapter 2 == '''1.''' Show that Equation (2.35) properly constructs a line containing two points $$\mathbf p$$ and $$\mathbf q$$ with non-unit weights by considering $$\mathbf p / p_w \wedge \mathbf q / q_w$$ and then scaling by $$p_wq_w$$. '''2.''' Let $$\mathbf u$$ be a basis element of the 4D projective alg..."

21:2821:28, 21 April 2024 diff hist +22‎ Main Page ‎ →‎Products and other binary operations current
21:2821:28, 21 April 2024 diff hist 0‎ Euclidean angle ‎No edit summary current
21:2721:27, 21 April 2024 diff hist +3,083‎ N Euclidean angle ‎ Created page with "The cosine of the Euclidean angle $$\cos \phi(\mathbf a, \mathbf b)$$ between two geometric objects '''a''' and '''b''' can be measured by the homogeneous magnitude given by :$$\cos \phi(\mathbf a, \mathbf b) = \left\Vert \mathbf a \vee \mathbf b^\unicode["segoe ui symbol"]{x2606}\right\Vert_\unicode{x25CF} + \left\Vert\mathbf a \right\Vert_\unicode{x25CB}\left\Vert\mathbf b \right\Vert_\unicode{x25CB}$$. In the case that the grades of $$\mathbf a$$ and $$\mathbf b..."
21:2721:27, 21 April 2024 diff hist 0‎ N File:Angle line line.svg ‎No edit summary current
21:2721:27, 21 April 2024 diff hist 0‎ N File:Angle plane line.svg ‎No edit summary current
21:2721:27, 21 April 2024 diff hist 0‎ N File:Angle plane plane.svg ‎No edit summary current
21:1521:15, 21 April 2024 diff hist +22‎ Euclidean distance ‎No edit summary current
21:1521:15, 21 April 2024 diff hist +287‎ Euclidean distance ‎No edit summary

23:5223:52, 13 April 2024 diff hist +76‎ Transformation groups ‎No edit summary current
23:5123:51, 13 April 2024 diff hist +92‎ Flector ‎No edit summary current
23:5123:51, 13 April 2024 diff hist +86‎ Motor ‎No edit summary current
23:5023:50, 13 April 2024 diff hist +73‎ Plane ‎No edit summary current
23:5023:50, 13 April 2024 diff hist +71‎ Line ‎No edit summary current
23:4923:49, 13 April 2024 diff hist +73‎ Point ‎No edit summary current
23:3323:33, 13 April 2024 diff hist 0‎ Duality ‎No edit summary current
23:3323:33, 13 April 2024 diff hist 0‎ Unitization ‎No edit summary current
23:3323:33, 13 April 2024 diff hist 0‎ Geometric constraint ‎No edit summary current
23:3223:32, 13 April 2024 diff hist 0‎ Geometric norm ‎No edit summary current
23:3223:32, 13 April 2024 diff hist 0‎ Reverses ‎No edit summary current
23:3223:32, 13 April 2024 diff hist 0‎ Duals ‎No edit summary current
23:3223:32, 13 April 2024 diff hist 0‎ Bulk and weight ‎No edit summary current
23:3123:31, 13 April 2024 diff hist 0‎ Metrics ‎No edit summary current
23:3123:31, 13 April 2024 diff hist 0‎ Complements ‎No edit summary current
23:3123:31, 13 April 2024 diff hist 0‎ Grade and antigrade ‎No edit summary current
23:3023:30, 13 April 2024 diff hist −40‎ Euclidean distance ‎No edit summary
23:2823:28, 13 April 2024 diff hist +68‎ Projections ‎No edit summary current
23:2723:27, 13 April 2024 diff hist +102‎ Interior products ‎No edit summary current
23:2723:27, 13 April 2024 diff hist +19‎ N Weight dual ‎ Redirected page to Duals current Tag: New redirect
23:2723:27, 13 April 2024 diff hist +19‎ N Bulk dual ‎ Redirected page to Duals current Tag: New redirect
23:2623:26, 13 April 2024 diff hist +89‎ Dot products ‎No edit summary current
23:2523:25, 13 April 2024 diff hist −202‎ Geometric products ‎No edit summary current
23:2423:24, 13 April 2024 diff hist −153‎ Exterior products ‎No edit summary current
05:1605:16, 13 April 2024 diff hist +70‎ Duality ‎No edit summary
05:1505:15, 13 April 2024 diff hist +66‎ Unitization ‎No edit summary
05:1405:14, 13 April 2024 diff hist +78‎ Geometric constraint ‎No edit summary
05:1405:14, 13 April 2024 diff hist +71‎ Geometric norm ‎No edit summary
05:1305:13, 13 April 2024 diff hist +66‎ Attitude ‎No edit summary current
05:1105:11, 13 April 2024 diff hist +79‎ Reverses ‎No edit summary
05:1005:10, 13 April 2024 diff hist +75‎ Grade and antigrade ‎No edit summary
05:0805:08, 13 April 2024 diff hist +13‎ Metrics ‎ →‎In the Book
05:0805:08, 13 April 2024 diff hist +71‎ Bulk and weight ‎No edit summary
05:0705:07, 13 April 2024 diff hist +79‎ Metrics ‎No edit summary
05:0605:06, 13 April 2024 diff hist +65‎ Complements ‎No edit summary
05:0505:05, 13 April 2024 diff hist +1,145‎ Duals ‎No edit summary
01:5401:54, 13 April 2024 diff hist +8‎ Duals ‎No edit summary
01:5401:54, 13 April 2024 diff hist +7‎ Bulk and weight ‎No edit summary
01:5401:54, 13 April 2024 diff hist +21‎ N Metric antiexomorphism matrix ‎ Redirected page to Metrics current Tag: New redirect
01:5301:53, 13 April 2024 diff hist +21‎ N Metric exomorphism matrix ‎ Redirected page to Metrics current Tag: New redirect
01:5301:53, 13 April 2024 diff hist +8‎ Dot products ‎No edit summary
01:5301:53, 13 April 2024 diff hist +486‎ Metrics ‎No edit summary
01:4801:48, 13 April 2024 diff hist +674‎ N Metrics ‎ Created page with "The ''metric'' used in the 4D rigid geometric algebra over 3D Euclidean space is the $$4 \times 4$$ matrix $$\mathfrak g$$ given by :$$\mathfrak g = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\\end{bmatrix}$$ . The ''metric exomorphism matrix'' $$\mathbf G$$, often just called the "metric" itself, corresponding to the metric $$\mathfrak g$$ is the $$16 \times 16$$ matrix shown below. 420px The ''metri..."
01:4801:48, 13 April 2024 diff hist 0‎ N File:Antimetric-rga-3d.svg ‎No edit summary current
01:4501:45, 13 April 2024 diff hist 0‎ N File:Metric-rga-3d.svg ‎No edit summary current
01:4001:40, 13 April 2024 diff hist +14‎ Main Page ‎ →‎Various properties and unary operations
01:3601:36, 13 April 2024 diff hist +40‎ Duals ‎No edit summary

20:3920:39, 12 April 2024 diff hist +247‎ Complements ‎No edit summary
06:2706:27, 12 April 2024 diff hist +12‎ Bulk and weight ‎ →‎See Also
06:2606:26, 12 April 2024 diff hist +12‎ Complements ‎ →‎See Also
06:2606:26, 12 April 2024 diff hist 0‎ Duals ‎ →‎See Also
06:2606:26, 12 April 2024 diff hist +669‎ Duals ‎No edit summary
06:1806:18, 12 April 2024 diff hist +486‎ Duals ‎No edit summary
06:1606:16, 12 April 2024 diff hist +19‎ N Dual ‎ Redirected page to Duals current Tag: New redirect
06:1506:15, 12 April 2024 diff hist +560‎ N Duals ‎ Created page with "The ''metric dual'' or just "dual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2605}$$ and defined as :$$\mathbf u^\unicode["segoe ui symbol"]{x2605} = \overline{\mathbf{Gu}}$$ , where $$\mathbf G$$ is the extended metric tensor. The ''metric antidual'' or just "antidual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2606}$$ and defined as :$$\mathbf u^\unicode["segoe ui symbol"]{x2606} = \over..."
06:0906:09, 12 April 2024 diff hist +12‎ Main Page ‎ →‎Various properties and unary operations