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I'm a professional programmer with a mathematical disposition.


Sep
20
comment Curvature of the image of a curve projected onto a surface
It's not clear to me that the construction as you describe it gives the correct curve. Can you justify the idea that there is a locally aligned parametrization that has the second derivative projection properties? Unfortunately I have to award the bounty soon, so please answer quickly. I'll give it some further thought myself.
Sep
18
comment Curvature of the image of a curve projected onto a surface
@alex: the surface will generally be a NURBS surface, so there is no hope of an implicit form. Thanks for the suggestion.
Sep
14
revised Curvature of the image of a curve projected onto a surface
edited tags
Sep
14
awarded  Promoter
Sep
14
revised Curvature of the image of a curve projected onto a surface
added 66 characters in body
Sep
13
answered Archimedes and center of gravity of an triangle
Aug
31
comment “Mathematical Induction”
ODEs do it for me every time!
Aug
31
awarded  Teacher
Aug
31
revised “Mathematical Induction”
added 141 characters in body
Aug
31
answered “Mathematical Induction”
Aug
25
comment Curvature of the image of a curve projected onto a surface
@anon: Thanks for this. I intend to see if I can get it to work in Mathematica, but I haven't gotten to it yet.
Aug
18
awarded  Supporter
Aug
18
comment Curvature of the image of a curve projected onto a surface
I modified the question to avoid references to derivatives in $C_S$.
Aug
18
awarded  Editor
Aug
18
revised Curvature of the image of a curve projected onto a surface
Removed methion of derivatives for C_S
Aug
18
comment Curvature of the image of a curve projected onto a surface
@Jesse: Hmmm, that didn't come out very nice, did it. I guess you can't use html in comments? How did you get your subscripts?
Aug
18
comment Curvature of the image of a curve projected onto a surface
@Jesse: Actually I was a bit sloppy on my wording. <em>C<sub>S</sub></em>'(<em>t<sub>0</sub></em>) is proportional to <em>C<sub>S</sub></em>'(<em>t<sub>0</sub></em>), which is all I need in my case. This problem comes from my desire to walk along the surface tracing out the projection from an initial point. I intend to do this by estimating a step with derivative information, and then correcting by iteration. The approach of walking along the curve projecting points is flawed because the projection is one-to-many.
Aug
18
awarded  Student
Aug
18
asked Curvature of the image of a curve projected onto a surface