math - Polar to linear movement of a yoke -


i writing algorithm convert polar movement of mechanical yoke (pan , tilt) , linear movement between 2 points. i.e. know start , end pan & tilt values want ensure end result straight line , not arc. picture this, application light , circle of light projected wants move in straight line.

i have worked out if tilt not change between start , end points light pans across arc tilt needs deflect down towards 0 half way through movement , original value again end of movement. tilt v light pans.

the amount of maximum deflection given by:

delta = tilt_angle - ( tilt_angle x cos(half_angle_of_pan) )

my question in case of end tilt being different start? adding delta changing value tilt give same end result or calculation more complicated?

martin


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