Importing tabular data as a parametric plane

When you import tabular data from a text file into a table field, the software can transform the spatial portion of the tabular data from physical coordinates to parametric (u,v) coordinates if the data points conform to the following requirements:

• The tabular data contains values for two spatial independent variables only.

• The data points define the bounds and are located at the corners of a four-sided surface.

• Equal numbers of data points are on opposing edges of the four-sided surface.

• The locations of all the data points have an inherent row-column structure.The sequences of data points that form the rows or columns do not necessarily have to lie on a straight line. They can form curves.

• The tabular data is in listed in the text file to reflect the inherent row-column structure of the data.

For example, the row-column structure graph shows a set of data points that conform to these requirements.

Row-column structure graph

To use this capability, when you create the table field, you must select one of the following independent domains: XY Plane, YZ Plane, ZX Plane.

When you import the tabular data, in the Table Data Import dialog box, select the Imported Data is in Structured Data Format check box. In the Format group, in the Number of Structured Data Rows spin box, specify the number of points that lie on the +v-axis. In the Number of Structured Data Columns spin box, specify the number of points that lie on the +u-axis. Then select the Create Spatial Map check box.

Creating a structured-format text file

Suppose that the tabular data in the data point table corresponds to the geometry in the row-column structure graph.

Note:

The values for pressure are shown as constant along each row of data points in the row-column structure graph. However, this is not a requirement and has only been done to help you visualize how to organize the data points in the text file.

Data point table

Data point	x	y	Pressure
1	2.00	2.00	500
2	3.85	2.40	500
3	5.25	2.45	500
4	6.75	2.25	500
5	2.70	3.10	750
6	4.10	3.25	750
7	5.25	3.35	750
8	6.50	3.25	750
9	3.15	4.15	1250
10	4.25	4.15	1250
11	5.30	4.10	1250
12	6.40	4.00	1250
13	3.30	5.30	1750
14	4.40	5.20	1750
15	5.35	4.95	1750
16	6.30	4.75	1750
17	3.25	6.25	2500
18	4.40	6.15	2500
19	5.40	5.85	2500
20	6.25	5.50	2500

How you organize the data points in the text file determines the origin of the parametric coordinate system and which edge of the four-sided surface that passes through the origin of the parametric coordinate system corresponds to the +u-axis of the parametric coordinate system.

• The first data point listed in the text file defines the origin of the parametric coordinate system. This data point must correspond to a corner on the four-sided surface.For example, in the row-column structure graph, points 1, 4, 17, and 20 are all valid choices for the first data point to list in the text file.

• The next N data points listed in the text file define the edge that corresponds to the +u-axis of the parametric coordinate system, where N is the number specified in the Number of Structured Data Columns spin box minus one. These data points must lie on an edge of the four-sided surface that passes through the origin of the parametric coordinate system and be listed in the order they occur along the +u-axis.For example, in the row-column structure graph, if you enter 4 in the Number of Structured Data Columns spin box and list point 1 as the first data point, the second data point in the text file is point 2, the third is point 3, and the forth is point 4.

• The sequence of data points listed in the text file repeats itself for the remaining rows of data points.

Text file examples

The following examples refer to the points shown in the row-column structure graph and the corresponding tabular data in the data point table.

Suppose that you want to place the origin of the parametric coordinate system at point 1, and you want to have the +u-axis of the parametric coordinate system correspond to the edge with points 1, 2, 3, and 4. In the Number of Structured Data Columns box, type 4 and organize the tabular data in the text file as follows:

2.00,2.00,500 3.85,2.40,500 5.25,2.45,500 6.75,2.25,500 2.70,3.10,750 4.10,3.25,750 5.25,3.35,750 6.50,3.25,750 3.15,4.15,1250 4.25,4.15,1250 5.30,4.10,1250 6.40,4.00,1250 3.30,5.30,1750 4.40,5.20,1750 5.35,4.95,1750 6.30,4.75,1750 3.25,6.25,2500 4.40,6.15,2500 5.40,5.85,2500 6.25,5.50,2500Text file to define origin at point 1 and u-axis along bottom edge	Parametric coordinate system with origin at point 1 and u-axis along bottom edge

Suppose that you want to place the origin of the parametric coordinate system at point 4, and you want to have the +u-axis of the parametric coordinate system correspond to the edge with points 4, 8, 12, 16, and 20. In the Number of Structured Data Columns box, type 5 and organize the tabular data in the text file as follows:

6.75,2.25,500 6.50,3.25,750 6.40,4.00,1250 6.30,4.75,1750 6.25,5.50,2500 5.25,2.45,500 5.25,3.35,750 5.30,4.10,1250 5.35,4.95,1750 5.40,5.85,2500 3.85,2.40,500 4.10,3.25,750 4.25,4.15,1250 4.40,5.20,1750 4.40,6.15,2500 2.00,2.00,500 2.70,3.10,750 3.15,4.15,1250 3.30,5.30,1750 3.25,6.25,2500Text file to define origin at point 4 and u-axis along right edge	Parametric coordinate system with origin at point 4 and u-axis along right edge

Tip:

To view the parametric coordinate system as shown in Figures 2 and 3, in the Table Field dialog box, in the Surface Validation group, select the Preview check box.

Calculating parametric coordinates of intermediate points

When the software calculates the parametric coordinates of intermediate points, it fits a low-order spline through the sequence of points that form each row or column. It then calculates the parametric coordinate for a point as the ratio of the distance along the row or column to the point to the total length of the curve.

For example, suppose that point 1 is the origin and the +u-axis extends through points 2, 3, and 4. Because all of these points lie on the u-axis, their v-coordinate is known to be 0. Furthermore, the u-coordinate of points 1 and 4 are known to be 0 and 1, respectively. The software calculates the parametric u-coordinate for points 2 and 3 by computing the ratio of their distance along the edge from point 1 to the total length along the edge between points 1 and 4.

Approximating the low-order spline with lines between points, you can calculate the distances between points 1 and 2, 2 and 3, and 3 and 4 as follows:

{u_{12}} = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{({y_2} - {y_1})}^2}} = \sqrt {{{\left( {3.85 - 2.00} \right)}^2} + {{(2.40 - 2.00)}^2}} = 1.892.....

{u_{23}} = \sqrt {{{\left( {{x_3} - {x_2}} \right)}^2} + {{({y_3} - {y_2})}^2}} = \sqrt {{{\left( {5.25 - 3.85} \right)}^2} + {{(2.45 - 2.40)}^2}} = 1.400.....

{u_{34}} = \sqrt {{{\left( {{x_4} - {x_3}} \right)}^2} + {{({y_4} - {y_3})}^2}} = \sqrt {{{\left( {6.75 - 5.25} \right)}^2} + {{(2.25 - 2.45)}^2}} = 1.513.....

The total distance is:

S = {s_{12}} + {s_{23}} + {s_{34}} = 4.806.....

The u-coordinates for points 2 and 3 are:

{u_2} = \frac{{{s_{12}}}}{S} = \frac{{1.892.....}}{{4.806.....}} = 0.3937.....

{u_3} = \frac{{{s_{12}} + {s_{23}}}}{S} = \frac{{1.892..... + 1.400.....}}{{4.806.....}} = 0.6851.....

The software calculates all of the other unknown parametric coordinates for intermediate points similarly.

Where do I find it?

Application	Pre/Post
Prerequisites	A text file with row-column structure tabular data
Simulation Navigator	Right-click the Fields node→New Field→Table
Location in dialog box	Table Field dialog box:Domain group→Independent list and Dependent listData Points group→Import from Text File Table Data Import dialog box→Imported Data is in Structured Data Format

Learn more

Importing ordered or structured tabular data from a text file

Importing tabular data as a parametric line

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Importing tabular data as a parametric plane, Simcenter 3D 2021.1 Series

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