hobz Posted February 5, 2010 Share Posted February 5, 2010 I have a flashlight angled at [math]\phi[/math] from zenith (the z-axis). the flashlight can be rotated around the z-axis so the beam forms a cone (angled at [math]\phi[/math] from zenith). Moreover, the bulb in the flashlight can also be angled [math]\phi[/math], so the resulting angle from zenith can vary from [math]0[/math] to [math]2\phi[/math] degrees. The question is, how do I transform a cartesian coordinate representation in space, into the two axes? So, for instance, [math](x,y,z)[/math] becomes [math](r,\theta_1,\theta_2)[/math] where [math]\theta_1[/math] is the angle of the flashlight itself. and [math]\theta_2[/math] the angle of the bulb. [math]r[/math] is the radial distance which is probably [math]\sqrt{x^2+y^2+z^2}[/math]. Merged post follows: Consecutive posts mergedI just realized that there are several solutions to the cartesian coordinates. Perhaps it is better to define [math]\theta_2[/math] as the difference between the bulb and the flashlight. Thus [math]\theta_2 = 0[/math] when the resulting beam angle from zenith is [math]2\phi[/math]. In that case, what would the transform then look like? Link to comment Share on other sites More sharing options...
hobz Posted February 11, 2010 Author Share Posted February 11, 2010 No-one an expert on coordinate transforms? Link to comment Share on other sites More sharing options...
Dave Posted February 12, 2010 Share Posted February 12, 2010 You're looking for something like spherical polar co-ordinates. Link to comment Share on other sites More sharing options...
hobz Posted February 12, 2010 Author Share Posted February 12, 2010 Yes I know. However, it's with a twist because the actual position is a combination of the angles. Link to comment Share on other sites More sharing options...
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