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I have a question regarding vectors. I am thinking ahead regarding an application that I am writing in OpenGL. Currently, four functions make up the vertex calculations, with one independent variable (w2center, w2normal, w2uv, uv2vector). A per-vertex center variable and per-vertex vector basis, calculated from w2normal, gives additional input uv2vector or the function which outputs the vertex. I would like to be able to animate surfaces rendered by adding two functions t2center and t2normal. Vector translation should be simple for t2center with an addition operation of w2center, yet I am unable to think or remember which operation I would use to combine normals, or directions of the surface, with the two two functions w2normal and t2normal. Would someone suggest an operation?

Below is an example image. The process involves relative centering with a surface hierarchy. Axii are drawn from surface centers, red is x or i, green is y or j, blue is z or k. The sphere has a single point center, yet the second surface has a parabolic line as its center, which is slightly able to be viewed by the black dots below the x or i axis. Taking for normal the first derivative of the parabola, I would like to be able to move center through another function, t2center, which would then change the "normal" or direction of the per-vertex basis. I think that addition is correct for centers, yet which operation would I use to combine the normals?

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# I Vector directions applied

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