Center of cylinder

isabella

i am looking for a way to find the coordinate of the center of a circle in a sheared cylinder. the base of the cylinder has a center (x,y,z), the angle of tilt of the cylinder is theta.so i need a formula which allows me to get the center of any circle in the cylinder.however i can't seem to get the right formula.i've attached a file with the drawing of the sheared cylinder.(although the cylinder is sheared, it still have a circular cross-section)

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HallsofIvy

Homework Helper
Although they are not shown in the picture, can we assume that you are given the radius and height (measured along the axis) of the cylinder? Also, since this is a 3D problem, we would need to know in which direction the cylinder is tilted (over the x-axis, y-axis, or z-axis?). If you know those, this is a simple trig problem.

In order not to confuse it with general coordinates, I'm going to call the given point (x0,y0,z0).

Assuming that the height of the cylinder, measured along the axis is h and that the axis lies above the x-axis, we get immediately that the coordinates of the "top" of the cylinder (the other end of the axis) are x1= x0+ h sin &theta;, y1= y0, and z1= z0+ h cos &theta;. You can get the coordinates of the center point, a, and point b (1/3 of the way from (x0,y0,z0) to (x1,y1,z1)?) from those.

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