toryrailu'a

valsi

toryrailu'a

type

lujvo

creator

krtisfranks

time entered

Thu Jan 14 19:05:47 2021  

English

Definition #72363 - Preferred

 

definition

x₁ is the geodesic path from x₂ to x₃ via or through points including/on connected manifold component/in connected graph component x₄, with distance being measured by standard/metric/weighting x₅.

notes

x₁ and x₂ must belong to the same connected component (which includes/encompasses x₄). The overall 'distance' travelled must be the minimal option under the orientation (from x₂ to x₃; this is not always symmetric) and path weighting/the specified metric such that the points x₄ are included in the path or the path is in/on connected manifold/graph component x₄ (as appropriate). In other words, x₁ includes a geodesic from x₂ to x₃ through/on/along/in points or space x₄. If the notion of distance is well-formed, then the triangle inequality should be satisfied and, therefore, x₁ should be composed of certain of geodesic subpaths between points in x₄ U Set(x₂, x₃). If x₄ is oriented or is an ordered list of points, then the path must connect them in that order (or a permitted order if there are multiple options).

gloss words

• geodesic
• geodesic path

created by

krtisfranks

vote information

1

time

Thu Jul 22 14:47:41 2021

Examples

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