Line on a surface

LINE TRACED ON A SURFACE

Lines (or curves) traced on a surface can be classified into three categories:

- the geometric lines, that only depend on the geometry of the surface:

Line curvature asymptotic geodesic pseudogeodesic geodesic circle

Definition (see the notations) extreme normal curvature zero normal curvature - normal curvature = curvature of the curve
- minimal length normal curvature proportional to the curvature constant geodesic curvature

Differential condition or

- the topographic lines, based on a given vertical direction, supported by .

Line level slope helix crest, or thalweg

Definition Constant altitude Maximal slope Constant slope

Differential condition

- the gravitational lines, depending on a given gravitational field .

Line flow catenary brachistochrone

Definition line followed by a massive point. - shape assumed by a homogeneous wire placed on the surface
- homogeneous line the center of gravity of which has minimal altitude. - minimal travel time

Differential condition where

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Line	curvature	asymptotic	geodesic	pseudogeodesic	geodesic circle
Definition (see the notations)	extreme normal curvature	zero normal curvature	- normal curvature = curvature of the curve - minimal length	normal curvature proportional to the curvature	constant geodesic curvature
Differential condition		or

Line	level	slope	helix	crest, or thalweg
Definition	Constant altitude	Maximal slope	Constant slope
Differential condition

Line	flow	catenary	brachistochrone
Definition	line followed by a massive point.	- shape assumed by a homogeneous wire placed on the surface - homogeneous line the center of gravity of which has minimal altitude.	- minimal travel time
Differential condition			where