about geodesics

I am trying to check the degree of approximation of the geodesic component.
in theory at points of a geodesic curve match the surface normal and the principal normal to the curve. isn´t it?.

I tested on a cone and does not match,
in a sphere a major circle is a geodesic. analyzing the curve as section of a sphere (green curve) match both lines, surface normal and principal normal to curve, but if we draw a geodesic (magenta curve) do not match both lines.

i´m doing something wrong?

can anyone help me?

Attachments:

GEODESICAS_001.gh, 17 KB

Replies to This Discussion

Permalink Reply by Chris Tietjen on October 19, 2011 at 3:54pm

Checking the sphere I find reasonable agreement between the normals.

Chris

Attachments:

GeodesicNormals.gh, 13 KB

Permalink Reply by paco g on October 20, 2011 at 1:25am

thanks for your interest, chris.

if you check the cone the diference is greater.

i want to know the degree of approximation of this procedure to use it in a subsequent process.

deviation is really small, but in the case of the cone is visually noticeable.

paco

Attachments:

GeodesicNormals_cone.gh, 18 KB

Permalink Reply by Chris Tietjen on October 20, 2011 at 5:57am

In the case of the sphere you are comparing two geodesic curves generated by different methods. In the case of the cone you are comparing a base circle with a geodesic. How can these even be comparable? The problem with the cone example is that I see no way to draw a geodesic on the cone by any means other than using the geodesic component. Do you have a method of drawing a geodesic line on the cone (other than the trivial ruling line from the apex to the base circle in a plane of the height)?

Chris

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