# RTP_R¶

 Syntax RTP_R (imag, real) Location PTRRTP

The function RTP_R takes a given rectangular co-ordinate and returns the so-called module (ie. the radius in polar co-ordinates). The result of RTP_R is always strictly positive and is not affected by the sign of the imag and real parameters, because of the symmetries of a circle.

Example 1

Draw a rectangular pattern in green and the corresponding polar pattern again displayed as rectangular co-ordinates in white:

```100 SCALE 10,-5,-5: PAPER 0: CLS
110 FOR x = -3 TO 3 STEP .4
120   FOR y = -3 TO 3 STEP 5E-2
130     INK 4: POINT x, y
140     INK 7: POINT RTP_R(x,y), RTP_T(x,y)
150   END FOR y
160 END FOR x
```

Example 2

The same as the above example but the polar co-ordinates are treated even more unusually. If you correct the program and exchange a and b in line 140 then the two patterns will match exactly - this reveals what the RTP_… functions are actually doing:

```100 SCALE 10,-5,-5: PAPER 0: CLS
110   FOR x = -3 TO 3 STEP .4
120   FOR y = -3 TO 3 STEP 2E-2
130     INK 4: POINT x, y
140     a = RTP_R(x,y): b = RTP_T(x,y)
145     INK 7: POINT b * COS(a), b * SIN(a)
150   END FOR y
160 END FOR x
```

CROSS-REFERENCE

Polar co-ordinates also need an angle, this is calculated with RTP_T. The PTR_X and PTR_Y pair of functions are complementary to RTP_R and RTP_T.