Algorithm (Workflow)

This function, CPLcopypatternTL, is designed to copy a Closed Polygon List (CPL) at positions defined by a Transformation List (TL). It is part of the SolidGeometry library.

Input Parameters

• CPL: A matrix (nx2) representing the Closed Polygon List to be copied.
• TL: An array of transformation matrices, typically obtained from the function TLofPL.
• dw: An optional parameter representing a turning angle or an array of turning angles (nx1). The default value is 0.

Output

• CPLN: The resulting Closed Polygon List after applying the transformations, represented as a matrix (nx2).

Algorithm Steps

1. Initialize dw to 0. If a third argument is provided and is not empty, set dw to this value.
2. Determine the number of transformations (np) from the third dimension of TL.
3. Calculate the number of points in CPL plus one (nc).
4. Initialize CPLN as a matrix of NaN values with dimensions (np*nc, 2).
5. If dw is a single value, replicate it to match the number of transformations.
6. Iterate over each transformation index i from 0 to np-1:
• If dw has more than one element, apply a rotation to CPL using PLtransR with the angle dw(i+1), then apply the transformation TL(i+1,:) using PLtransP.
• If dw is a single value, apply the transformation directly using PLtransT with TL(:,:,i+1).
• Append a row of [NaN NaN] to separate each transformed polygon.
7. Remove the last row of CPLN to clean up the output.
8. If no output is requested, plot the resulting CPLN using CPLplot with a red line style.

Example Usage

Two example calls to the function are provided:

• CPLcopypatternPL(PLcircle(1),20*rand(10,2)): Copies a circle with radius 1 at random positions.
• CPLcopypatternPL(PLcircle(1,4),20*rand(10,2),pi/10): Copies a circle with radius 1 and 4 segments at random positions with a turning angle of pi/10.