Warren Thom wrote: .... > Two questions: > > In the main procedure > > (1) If x=x3*g/z3 y=y3*g/z3 are replaced by > x=x3 y=y3*g/z3 would this give a trace for a > cylinder? That is, curve the > paper into a half circle, with > the gnomon at the center of the > circle (cylinder). > > (2) Would x=x3*g/z3 and y=y3 give a cylinder in the other direction? > > Thank you, Fer. > > Warren Thom
Warren, I didn't write in my pages in details about the coordinate systems x0, y0, z0 and so on. These are based on a sphere with radius 1. x*x + y*y + z*z = 1 x and y are in a plane, z is perpendicular to that plane. System 0 lies in the equatorial plane with z to the northpole. System 1 lies in the horizontal plane with z to the zenith. System 2 also lies in the horizontal plane, but x,y rotated with angle d. z still points to the zenith. System 3 lies in the plane of the sundial with z to the endpoint of the gnomon. In this way you have the sun's position in x,y,z relative to a plane. In system 0 the x-axis points to the west, the y-axis points upwards. In system 1 the x-axis points to the west, the y-axis to the south. In system 3 the x and y have opposite direction of the coordinatesystem for the shadowpoint. With the values of x1, y1, z1 you are able to calculate the sun's height and azimuth. h = arcsin ( z1 ) : no test of quadrant is needed. az = arctan ( x1/y1) : test for quadrant is needed. As you now see the use of the coordinates x0,y0,z0 and so on, you will see that you may not change the mainprocedure as you proposed to calculate a cylindrical sundial. Fer.
