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Convert object space to tangent space?

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I''m doing dot3 bumpmapping. The directional light''s shadows do not change while the model do animation. I know I should use the tangent space,But: How to convert object space(The normalmap''s normal is stored in object space) to tangent(texture) space? How to build the tangent matrix?And do I need to multiply this matrix to every vertex of render object? thanks. We create world.

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I am not sure exactly of the dot3 bumpmapping method, but to convert a single normal to a tangent line, you will want the perpendicular vector of the normal the get that tangent.

So, if you have a vector N(x,y,z) which is the direction of the normal, you can see it as a direction starting from origin pointing towards x,y,z you want the perpendicular of that slope, to get the tangent slope.

Homepage: http://students.washington.edu/andrey

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