The Centroid tool calculates the centroid and optionally the moment of inertia of objects that you click on with the tool. These objects may be rectangles, ellipses, circles, polygons, b-splines, splines, Bézier and groups containing these objects. Other types of objects (lines, text, arcs, etc) may be in the group but they are ignored. All objects must be closed shapes for the calculations to work properly, and the Centroid tool closes all open shapes prior to making a calculation.
Void objects are holes.
A group of objects may consist of 'solid' and 'void' objects. 'Solid' objects will be totalled in the calculation. 'Void' objects will be subtracted from the calculation and are intended as hollow shapes or holes in a cross-sectional shape.
The Centroid tool will calculate which objects are within other objects. Objects within 'void' objects are considered as solid objects. When objects overlap, the Centroid tool will show the results with the text in red, and with a warning that objects overlap. You can also confuse the Centroid tool by creating duplicate objects.
Multiple objects must be in a group to be considered as a single object.
A polygon which crosses over itself ('complex polygon') will result in completely inaccurate results.
The Centroid Tool calculates and reports the moment of inertia and other values about the X axis and optionally about the Y axis.
(Remember, moments of inertia are calculated about an axis -- not along an axis. For example, Ix indicates the moment of inertia about the X axis. This means that Ix is influenced by the parts of the area above and below the X axis, ie values in the Y-direction, and conversely Iy is influenced by the parts of the area to the left and right of the Y axis, ie in the X direction.)
The Centroid Tool also draws lines on the Principal Axis of the object for identification when any calculation of the moments of inertia are made. This makes it easy to rotate the object to align the Principal Axis to the X axis and then, after running the Centroid Tool again, you can obtain full report of values for the Principal Axis.
The Centroid tool uses the Area Units and Area Accuracy of the Drawing Setup/Units pane, except that acres and miles are reported at feet, and hectares and kilometers are reported as meters. Thus the units may be mm, cm, m, inches and feet.
The Centroid tool converts rounded rectangles, Béziers and B-splines to polygons to make all of the calculations for area and moments of inertia. The conversions of some shapes vary in extremely small amounts depending on the size of the object, so it's possible you may see some very small variations for the same shape comprised of Béziers and B-splines at different sizes and scales. The moments and areas of circles and ellipses are found by direct calculations.
In an effort to provide very precise areas, the Centroid tool bases its conversion of objects to polygon on the Area Accuracy of the Drawing Setup/Units pane up to six decimal places. It will be accurate up to six decimal places for square inches at 1:1 scale, which produces an area accurate to a millionth of a square inch. Setting the Area Accuracy to higher numbers will change the display, but the accuracy is never calculated higher than six decimal places for square inches.
To set the behavior of the tool:
You may select to calculate the moment of inertia, which will also calculate a number of additional things.
Select if you want the moment of inertia calculated about the X axis, or about both the X and Y axes.
You may select to have the moment of inertia to be calculate about the object's centroid or about the ruler origin.
Select Min/Max, Polar Moment of Intertia, Radius of Gyration and Section Modulus & Extreme Fiber if you want these to be reported.
To use the Centroid tool:
Click on the desired object.
The Centroid tool will place a centroid marker at the centroid of the selected objects. If you have selected the Moment of Inertia option, lines will be drawn to show the principal axis angle of the shape and a text will be placed in the drawing with a report on the characteristics of the shape.
If the Centroid tool encounters any open shapes, it will close them, and this will be reported in the text report and the report will be in red, since it may result in an inaccurate report.
Blue centerlines show the principal axis angle.
In this case, the moment of inertia is calculated about the drawing ruler origin.
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