Computing the Fractal Dimension

CAD drafting Computing the Fractal Dimension 0 Ribbon: 3DScan > Features > CAD software Computing the Fractal Dimension 1 Estimate the fractal dimension

CAD drawing Computing the Fractal Dimension 2 Menu: 3DScan > Features > CAD drafting Computing the Fractal Dimension 3 Estimate the fractal dimension

CAD software Computing the Fractal Dimension 4 Toolbar: Features 3DScan > CAD drawing Computing the Fractal Dimension 5 Estimate the fractal dimension

CAD drafting Computing the Fractal Dimension 6 Command line: PC_COMPUTE_FRACTAL_DIMS

Fractal (fractional) dimension is an indicator that helps describe complex objects such as coastlines, mountain reliefs, clouds, or snowflakes. These objects have a complex structure that becomes more detailed as the scale increases. Classical parameters, such as length or area, are insufficient to accurately describe such shapes.

The command estimates the fractal dimension of each individual point in the point cloud. The estimation method is box counting. This is a method for computing the fractal dimension applicable to any fractal objects, regardless of their shape. The method is especially convenient for objects that do not have a strict self-similar structure, such as point clouds.

For points in the cloud, the number of points within spheres of different radii, centered at the point being estimated, is calculated. A linear regression is constructed from the obtained data, and the slope of the calculated line is the fractal dimension.

The command parameters are set in the Properties bar.

CAD software Computing the Fractal Dimension 7

Parameters:

Computing points percentage	The percentage of cloud points participating in the computing.
Max Points	How many neighboring points should be taken to estimate the dimension of a point.
Clear	Whether to clear the neighborhoods of points specified in Max Points. This improves quality, but may reduce quality if the point density per geometry is low or scan lines are very pronounced. Cleaning the neighborhoods attempts to retain only those points that are true neighbors of the calculation point and discard points of other geometry that may accidentally fall within the neighborhood. For example, if several wires run in parallel, and you need to estimate the point size of a specific wire, the result will be poor if the estimate includes points from neighboring wires. Removing them will result in a correct estimate. However, for pronounced scan lines, this can reduce quality, since the estimate will then be based on the scan line, not the actual geometry.
Use interpolation	Enables the use of interpolation. For each previously uncalculated point, interpolation points are taken from the nearest calculated neighbors. The weight of each neighbor is determined as 1.0 for the closest and 0.1 for the furthest, with the others in the range between them. Based on the obtained weights, a weighted average of the fractal dimensions of the nearest interpolation points is found. Interpolation of the final result by points occurs after the calculation.
Points for interpolation	Number of interpolation points.