User jeremy - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T21:53:03Z http://mathoverflow.net/feeds/user/17345 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/73538/surface-fitting-with-convexity-requirement Surface fitting with convexity requirement Jeremy 2011-08-24T02:58:58Z 2012-08-09T21:15:27Z <p>Hi all,</p> <p>Consider a cloud of points in 3D space (x,y,z). The data is well-behaved, once plotted the surface looks like some sort of spheroid. I assumed a form for the fitting function f(x,y,z) = c1 x^2 + c2 y^2 + c3 z^2 + c4 x^2y^2 + ..etc</p> <p>The coefficients were obtained using a least squares approximation. My only problem is that the surface has some concave portions. Does anyone know how to express a constraint that would generate the coefficients (c1,c2, ...) but ensure convexity at all points?</p> <p>Thanks a lot!</p> <p>J</p> http://mathoverflow.net/questions/73453/directional-distortion-of-a-surface/73515#73515 Answer by Jeremy for Directional Distortion of a Surface Jeremy 2011-08-23T17:49:28Z 2012-02-24T19:07:02Z <p>EDIT (David White): This is really a comment to Gerhard's answer, not an answer in and of itself.</p> <p>Thank you for your input Gerhard. A small clarification: what is desired is not two surfaces \$f_3\$ and \$f_4\$, but just one function that would undergo directional distortion and that would be some interpolation of \$f_1\$ and \$f_2\$ (to ensure tangentiality as \$f_1\$ grows closer to \$f_2\$).</p> <p>Regarding the straw model. Are you using some discrete description (particles)? Where each point would undergo a different displacement \$u\$? If so, we can generate a surface \$f_3\$ but we loose the closed-form formula for it, am I correct?</p> <p>Thanks again,</p> http://mathoverflow.net/questions/73453/directional-distortion-of-a-surface/73515#73515 Comment by Jeremy Jeremy 2011-08-24T02:51:12Z 2011-08-24T02:51:12Z Thanks for your help Gerhard