System for transforming coordinates

Claim 1

A system for transferring a polar to a rectangular coordinate system, comprising: a first input terminal to which a voltage G corresponding to the radius vector of a point in a polar coordinate system is applied; a second input terminal to which a voltage theta corresponding to the deflection angle of said point is applied; first circuit means for producing a sine wave output the amplitude of which is said voltage G; second circuit means for producing an output when said sine wave output passes a predetermined reference level; third circuit means receiving said voltage theta to detect a time corresponding to said deflection angle having been reached during the 2 pi period of said sine wave output; fourth circuit means for passing said sine wave output only during the time from said detected time till said second circuit means produces an output; fifth circuit means for detecting a time delayed by pi /2 from said time detected by said third circuit means; sixth circuit means for passing said sine wave output only during the time from said time detected by said fifth circuit means to when said second circuit means produces an output; seventh circuit means receiving the output from said fourth circuit means and said radius vector voltage G to produce a voltage corresponding to the X-axis component G cos theta of said point in said rectangular coordinate system; and eighth circuit means receiving the output from said sixth circuit means and said radius vector input G to produce an output voltage corresponding to the Y-axis component G sin theta of said point.

Claim 2

A system for transferring a polar to a rectangular coordinate system, comprising: a first input terminal to which a voltage G corresponding to the radius vector of a point in a polar coordinate system is applied; a second input terminal to which a voltage theta corresponding to the deflection angle of said point is applied; first circuit means for producing a sine wave output the amplitude of which is said voltage G; second circuit means for producing an output when said sine wave output passes a predetermined reference level; third circuit means receiving said voltage theta to detect a time corresponding to said deflection angle having been reached during the 2 pi period of said sine wave output; fourth circuit means for passing said sine wave output only during the time from said detected time till said second circuit means produces an output; fifth circuit means for detecting a time delayed by pi /2 from said time detected by said third circuit means; sixth circuit means for passing said sine wave output only during the time from said time detected by said fifth circuit means to when said second circuit means produces an output; seventh circuit means receiving the output from said fourth circuit means and said radius vector voltage G to produce a voltage corresponding to the X-axis component G cos theta of said point in said rectangular coordinate system; and eighth circuit means receiving the output from said sixth circuit means and said radius vector input G to produce an output voltage corresponding to the Y-axis component G sin theta of said point.

Claim 6

A system for transforming rectangular coordinates to polar coordinates, comprising: first circuit means receiving input voltages x and y corresponding to the X- and Y-axis components of a point in a rectanGular coordinate system to produce a sine wave output whose frequency is proportional to an angular velocity omega , whose amplitude is Square Root x2 + y2 and whose phase theta is tan 1(y/x), said first circuit means comprising a first and a second gate receiving said voltages x and y, respectively, as an input, means generating two-phase square wave pulses, said square wave pulses having a fundamental angular frequency omega and being 90* out of phase with respect to each other, means supplying said two-phase square wave pulses to both said first and said second gates as a gating signal, a first adder receiving the voltages that pass said gates while said gating signal is applied thereto so as to produce an output k corresponding to the sum of said voltages, a second adder for adding a voltage twice said output k and said voltages x and y, and a filter receiving the output from said second adder to pass the component of said fundamental angular frequency omega ; second circuit means receiving said sine wave output to produce an output corresponding to the amplitude thereof; third circuit means for producing a reference output signal when said sine wave output is at a reference voltage level; fourth circuit means for detecting said sine wave output having reached a voltage level corresponding to said phase theta to produce a detection signal; fifth circuit means for producing pulses whose width is equal to the time between the production of said reference signal and said detection signal; and sixth circuit means receiving said pulses produced by said fifth circuit means to produce an output voltage corresponding to said phase theta .

Claim 7

A system for transforming rectangular coordinates to polar coordinates, comprising: first circuit means receiving input voltages x and y corresponding to the X- and Y-axis components of a point in a rectanGular coordinate system to produce a sine wave output whose frequency is proportional to an angular velocity omega , whose amplitude is Square Root x2 + y2 and whose phase theta is tan 1(y/x), said first circuit means comprising a first and a second gate receiving said voltages x and y, respectively, as an input, means generating two-phase square wave pulses, said square wave pulses having a fundamental angular frequency omega and being 90* out of phase with respect to each other, means supplying said two-phase square wave pulses to both said first and said second gates as a gating signal, a first adder receiving the voltages that pass said gates while said gating signal is applied thereto so as to produce an output k corresponding to the sum of said voltages, a second adder for adding a voltage twice said output k and said voltages x and y, and a filter receiving the output from said second adder to pass the component of said fundamental angular frequency omega ; second circuit means receiving said sine wave output to produce an output corresponding to the amplitude thereof; third circuit means for producing a reference output signal when said sine wave output is at a reference voltage level; fourth circuit means for detecting said sine wave output having reached a voltage level corresponding to said phase theta to produce a detection signal; fifth circuit means for producing pulses whose width is equal to the time between the production of said reference signal and said detection signal; and sixth circuit means receiving said pulses produced by said fifth circuit means to produce an output voltage corresponding to said phase theta .