2.8.18 marea(Pro)

1 Menu Information
2 Brief Information
3 Additional Information
4 Command Line Usage
5 X-Function Execution Options
6 Variables
7 Description
8 Examples
9 Algorithm
10 Related X-Functions

Menu Information

Analysis: Mathematics: Matrix Surface Area

Brief Information

Calculate matrix surface area

Additional Information

This feature is for OriginPro only, 8.1 SR0 or later versions.

Command Line Usage

marea im:=[mbook1] missing:=1 area:=area;

X-Function Execution Options

Please refer to the page for additional option switches when accessing the x-function from script

Variables

Display
Name

Variable
Name

I/O
and
Type

Default
Value

Description

Input Matrix

Input

MatrixObject

Specify the input matrix.

Interpolate for Missing Value

missing

Input

int

If this parameter is true, Origin will do interpolation for missing value.

Area

area

Output

double

Area result output destination. Default is Results Log window.

Description

This X-Function is used to calculate the area of the matrix surface. You can specify a variable for the result area as well as whether or not to interpolate for the missing value. Also, the result area will be always put to the Results Log Window automatically.

Examples

This example is going to calculate the area of the active matrix.

Create a new project and import data <Origin Program Directory>\Samples\Matrix Conversion and Gridding\3D XYZ.dat.
Highlight Column C, Change the type of Column C to be Z by selecting the right-click menu Set As: Z. Then select main menu Worksheet: Convert to Matrix: XYZ Gridding.
In the XYZ Gridding: Convert Worksheet to Matrix dialog, keep the default settings and click the OK button to convert the worksheet to a matrix.
Activate the matrix, then run xyzarea -d; in Command Window to bring up the marea dialog box.
Check the check box behind the Interpolate for Missing Value.
Click the OK button, then the area of the matrix is put to Results Log Window.

Algorithm

In three dimensions Cartesian space, the area of a general triangle $A = (x_A, y_A, z_A), B = (x_B, y_B, z_B), C = (x_C, y_C, z_C)$ is

$S=\frac{1}{2} \sqrt{ \left( \det\begin{pmatrix} x_A & x_B & x_C \\ y_A & y_B & y_C \\ 1 & 1 & 1 \end{pmatrix} \right)^2 + \left( \det\begin{pmatrix} y_A & y_B & y_C \\ z_A & z_B & z_C \\ 1 & 1 & 1 \end{pmatrix} \right)^2 + \left( \det\begin{pmatrix} z_A & z_B & z_C \\ x_A & x_B & x_C \\ 1 & 1 & 1 \end{pmatrix} \right)^2 }$ .

To calculate the area of a matrix surface, the matrix surface is divided into many sub-triangles like below. The the area of the matrix surface is the sum of all the area of its sub-triangles.