> ## Documentation Index
> Fetch the complete documentation index at: https://docs.ntop.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Surface Integral

<CardGroup cols={2}>
  <Card title="Implicit Body, Scalar Field, Scalar" href="#implicit-body-scalar-field-scalar" />

  <Card title="Implicit Body, Vector Field, Scalar" href="#implicit-body-vector-field-scalar" />
</CardGroup>

***

## About this Block

**What it does:** The **Surface Integral** block integrates the values of a scalar field over the domain of the surface of an implicit body. Decreasing the relative error input will increase the calculation’s accuracy, but will increase the calculation time.

**Common uses:**

* Computing the area of a surface

***

<h2 id="implicit-body-scalar-field-scalar">
  Implicit Body, Scalar Field, Scalar
</h2>

Integrate a function over the surface of an implicit body.

### Inputs

| Name           | Type                                                                 | Description                                                                       |
| -------------- | -------------------------------------------------------------------- | --------------------------------------------------------------------------------- |
| Body           | [Implicit Body](../../../../block-documentation/types/implicit-body) | The body defining the surface to integrate over.                                  |
| Integrand      | [Scalar Field](../../../../block-documentation/types/scalar-field)   | The function to integrate. Note that both scalar and vector fields are supported. |
| Relative error | [Scalar](../../../../block-documentation/types/scalar)               | The relative error used to determine algorithm convergence.                       |

### Outputs

| Type                                                   |
| ------------------------------------------------------ |
| [Scalar](../../../../block-documentation/types/scalar) |

***

<h2 id="implicit-body-vector-field-scalar">
  Implicit Body, Vector Field, Scalar
</h2>

Integrate a function over the surface of an implicit body.

### Inputs

| Name           | Type                                                                 | Description                                                                       |
| -------------- | -------------------------------------------------------------------- | --------------------------------------------------------------------------------- |
| Body           | [Implicit Body](../../../../block-documentation/types/implicit-body) | The body defining the surface to integrate over.                                  |
| Integrand      | [Vector Field](../../../../block-documentation/types/vector-field)   | The function to integrate. Note that both scalar and vector fields are supported. |
| Relative error | [Scalar](../../../../block-documentation/types/scalar)               | The relative error used to determine algorithm convergence.                       |

### Outputs

| Type                                                   |
| ------------------------------------------------------ |
| [Scalar](../../../../block-documentation/types/scalar) |