An standard ADXL chipset will yield tilted axis along the X,Y and Z axis (taking gravity as the reference axis). I require to draw a rectangular plane on a 3d ViewPort . Using this X,Y and Z axis how can I draw a plane? What are the mathematical equations available where we can compute the new Plane using the X,Y and Z axis (Tilted)?
Since the X/Y/Z output represents the direction of gravity, it is also the normal vector of the horizon plane you intend to draw.
Conveniently assuming that the desired plane intersects the origin, you will of course get the scalar plane equation: x*X+y*Y+z*Z = 0, for any point (x,y,z) and the given normal vector (X,Y,Z).
Observing that planes are by definition infinite in extent, you now need to find a small rectangle that lies on the plane, ie. four suitable corner points (x,y,z). One approach could be to use +/-1 for x and y and solve for z to obtain the four corner points, which now have the simple solution {-1,-1,(-X-Y)/Z}, {-1,1,(-X+Y/Z}, {1,-1,(X-Y)/Z} and {1,1,(X+Y)/Z}. This will however only be useful for near horizontal orientations as the resulting z component will grow very large as Z goes towards zero. To account for this one can find the major axis first (ie. the maximum of X, Y and Z) and solve for that. This will always return rectangles that fit inside the unit box.
In other terms the chip already gives you three out of four components of the plane in Hesse normal form (HNF), which is { n_x, n_y, n_z, d } (n being the normalized normal of the plane i.e. direction of the gravity). d is the offset to the origin - so you can set this to zero and/or use the distance traveled by the chip, which i assume you can derive using the time between your measurements. To compute actual coordinates you can e.g. take four pairs (n_x,n_y) as your coordinates "on the ground" and compute n_z. If you need the planar piece rectangular, you need to start with one pair (n_x,n_y) and use the result together with cross product with (n_x,n_y,n_z) to find the other three points.
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