[MATH]Project an axis to a plane

Question

how do i project the X axis to a plane if the plane is defined by three points? see pic here: http://129.25.16.135:2080/v6.5/books/usb/graphics/iconventions-local-surfaces.png

The default local 1-direction is the projection of the global x-axis onto the surface. If the global x-axis is within 0.1° of being normal to the surface, the local 1-direction is the projection of the global z-axis onto the surface.

let's suppose that these points are: t1 = [-0.362879991531372, 0.357021987438202, -0.373737007379532]

t2 = [-0.383525013923645, 0.371621012687683, -0.383549988269806]

t3 = [-0.383534014225006, 0.34629300236702, -0.38544899225235]

is the vector [0.78280971952246, -0.0307519963686645, 0.411184845614438] correct answer in this case? i've calculated the angle between the surf and x (1,0,0) is ~28°.

and can you give the entire procedure for the calculation, because i'm just puzzled.

Answer 1

Your diagram is a little unclear (for instance, it doesn't show t1, t2, t3), but it looks as if you want a vector tangent to the surface and in the XZ plane. If that's correct, then you have to calculate the partial derivative with respect to x (the slope in the x direction, which is easy if the surface really is a plane and you have three non-colinear points) and the y-component of your answer will be zero. If that's not correct, then please explain what "projection" you prefer.