---
title: vDSP_polar
framework: accelerate
role: symbol
role_heading: Function
path: accelerate/vdsp_polar
---

# vDSP_polar

Converts single-precision rectangular coordinates to polar coordinates, using the specified stride.

## Declaration

```occ
extern void vDSP_polar(const float *__A, vDSP_Stride __IA, float *__C, vDSP_Stride __IC, vDSP_Length __N);
```

## Parameters

- `__A`: The input vector that contains adjacent pairs of coordinates.
- `__IA`: The distance between the adjacent coordinate pairs of elements in the input vector. This value must be an even number.
- `__C`: On output, the output vector that contains adjacent pairs of coordinates.
- `__IC`: The distance between the adjacent coordinate pairs of elements in the output vector. This value must be an even number.
- `__N`: The number of ordered pairs that the function processes.

## Discussion

Discussion The function uses the following calculation to convert rectangular coordinates to polar coordinates: for (n = 0; n < N; ++n) {     x = A[n*IA+0];     y = A[n*IA+1];     C[n*IC+0] = sqrt(x**2 + y**2);     C[n*IC+1] = atan2(y, x); } Vector A defines the input Cartesian (x, y) pairs. The function writes polar (rho, theta) pairs, where rho is the radius and theta is the angle in the range [-pi, pi] to output vector C. N specifies the number of coordinate pairs in A and C. Coordinate pairs are adjacent elements in the array, regardless of stride; stride is the distance from one coordinate pair to the next. The following code shows how to convert a single pair of rectangular coordinates to their polar equivalent.     let x = Float(5.0)     let y = Float(5.0)

let rectangularCoordinates = [x, y]

var polarCoordinates: [Float] = [0, 0]

let stride = vDSP_Stride(2)     let n = vDSP_Length(1)

vDSP_polar(rectangularCoordinates, stride,                 &polarCoordinates, stride,                 n)

let radius = polarCoordinates[0]     let angle = Measurement(value: Double(polarCoordinates[1]),                             unit: UnitAngle.radians)         .converted(to: UnitAngle.degrees)         .value On return, radius is 7.07, and angle is 45. This function performs the inverse operation of vDSP_rect, which converts polar to rectangular coordinates.

## See Also

### Converting rectangular coordinates to polar coordinates

- [vDSP_polarD](accelerate/vdsp_polard.md)