# [Ipopt] (no subject)

Nuno Silva pg17455 at alunos.uminho.pt
Sat Sep 1 15:35:08 EDT 2012

```Greetings

I'm a researcher enrolled in a project that requires fitting measured
data into known functions.
The measured data is the color variation of a point on a material, as
the camera and light source moves around the object.

A simplistic model is the Lambertian BRDF model that simply says that
the color value is the dot product of the normal at that point with
the incident light direction.

The incident lighting direction and the camera direction are known,
they are a discrete set of directions expressed in polar coordinates w
:= (theta, phi)

The objective is to find the best parameters of the BRDF model so that
it is most correlated with the measured data, this is, to minimize the
difference between the measured data and the estimated values.

I came up with this:

/** This class implements the following NLP.
*
* Lambert BRDF model
* min f(T, N, wi, wo) = T - dot(wi, N)
* s.t.
* f(T, N, wi, wo) >= 0, (non-negativity)
* f(T, N, wi, wo) = f(T, N, wo, wi) <=> f(T, N, wi, wo) - f(T,
N, wo, wi) = 0, (Helmholtz reciprocity)
* S(f(T, N, wi, wo)cos(theta_o)) <= 1, (conservation of energy)
* ||N||2 = 1, (normal is normalized)
* Nz >= 0, (normal is on the upper hemisphere)
* note:
* T -> measured texel value
* N -> Normal: {Nx, Ny, Nz}
* wi -> incomming direction (light): {theta_i, phi_i}
* wo -> outgoing direction (camera): {theta_o, phi_o}
*/

But I do not know how to supply IPOPT with the discrete set of
directions of measurement.
Can someone assist me on this?

Regards
Nuno Silva
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