pol2cart — Transform polar or cylindrical coordinates to Cartesian coordinates.
[x,y] = pol2cart(theta,rho) converts polar coordinates to Cartesian coordinates. [x,y,z] = pol2cart(theta,rho,z) converts cylindrical coordinates and returns the elevation after MATLAB-style implicit expansion.
Syntax
[x, y] = pol2cart(theta, rho)
[x, y, z] = pol2cart(theta, rho, z)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
theta | Any | Yes | — | Polar or cylindrical angular coordinate in radians. |
rho | Any | Yes | — | Polar or cylindrical radial coordinate. |
z | Any | Yes | — | Cylindrical elevation coordinate. |
Returns
| Name | Type | Description |
|---|---|---|
x | NumericArray | Cartesian x coordinate. |
y | NumericArray | Cartesian y coordinate. |
z | NumericArray | Cartesian z coordinate. |
Returned values from pol2cart depend on how many outputs the caller requests.
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:pol2cart:InvalidInput | An input is not a supported real floating-point scalar or array. | pol2cart: invalid input |
RunMat:pol2cart:ComplexUnsupported | At least one input is complex. | pol2cart: complex inputs are not supported |
RunMat:pol2cart:SizeMismatch | Input arrays do not have compatible sizes for implicit expansion. | pol2cart: size mismatch |
RunMat:pol2cart:OutputCount | More outputs are requested than the selected syntax supports. | pol2cart: too many output arguments |
RunMat:pol2cart:Internal | Internal gather/conversion/allocation flow failed. | pol2cart: internal error |
How pol2cart works
- Typed-integer
theta,rho, orzinputs are independent RunMat-mode extensions and must be exactly representable in double before the coordinate transform. - Inputs must be real floating-point scalars, vectors, matrices, or N-D tensors.
theta,rho, and optionalzmust have the same size or compatible sizes for implicit expansion.xis computed asrho .* cos(theta)andyis computed asrho .* sin(theta).- For cylindrical coordinates, the output
zis the input elevation expanded to the same size asxandy. - Complex inputs are rejected, matching current MATLAB behavior.
- Integer, logical, string, char, cell, struct, and object inputs are rejected because MATLAB documents
pol2cartfor realsingleanddoubledata. - With no explicit multi-output context, RunMat returns the first output,
x, matching MATLAB's single-output assignment behavior.
Examples
Converting polar coordinates
theta = [0 pi/4 pi/2 pi];
rho = [5 5 10 10];
[x,y] = pol2cart(theta,rho)Expected output:
x = [5.0000 3.5355 0 -10.0000]
y = [0 3.5355 10.0000 0]Converting cylindrical coordinates
theta = [0 pi/2]';
rho = [1 2 3];
z = 7;
[x,y,z] = pol2cart(theta,rho,z)Expected output:
x =
1 2 3
0 0 0
y =
0 0 0
1 2 3
z =
7 7 7
7 7 7Using pol2cart with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how pol2cart changes the result.
Run a small pol2cart example, explain the result, then change one input and compare the output.
FAQ
What angle units does pol2cart use?⌄
theta is in radians, measured counterclockwise from the positive x-axis.
Can I request only two outputs with three inputs?⌄
Yes. [x,y] = pol2cart(theta,rho,z) computes the cylindrical transform but returns only x and y.
Does pol2cart accept complex inputs?⌄
No. Current MATLAB releases reject complex inputs, and RunMat does the same.
Does RunMat keep pol2cart on the GPU?⌄
Yes for real gpuArray inputs when the active provider supports the required sin, cos, and broadcasted multiply hooks. The returned x, y, and requested z outputs remain gpuArray values. Providers without those hooks fall back to host evaluation.
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Elementwise
abs · angle · bsxfun · complex · conj · double · erf · erfcinv · exp · expm1 · factorial · flintmax · gamma · gammaln · heaviside · hypot · idivide · imag · intmax · intmin · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · realmax · realmin · realsqrt · rescale · sign · single · sqrt · swapbytes · times · typecast · uint16 · uint32 · uint8
Reduction
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Structure
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Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how pol2cart is executed, line by line, in Rust.
- View the source for pol2cart in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
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