Algorithm (Workflow)

This function, VLULplot, is designed to visualize the union list of an object, face by face. It is part of the SolidGeometry library and was introduced by Tim Lueth in 2012. The function takes in several parameters to control the visualization process.

Input Parameters

• VL: The vertex list of the object. It contains the coordinates of the vertices that define the object.
• UL: The union list of the object. This list defines how the vertices are connected to form the faces of the object.
• c: (Optional) The color of the unions. Default is 'm' (magenta).
• Amin: (Optional) The minimal size of the area to plot. Default is 3.9.
• p: (Optional) The delay between plotting each union. A value of -1 means the user must press a key to proceed to the next union.

Algorithm Steps

1. Initialize default values for color (c), minimal area (Amin), and delay (p) if they are not provided.
2. Determine the number of unions (n) and the number of faces (k) from the union list (UL).
3. Check if Amin is a matrix. If so, set kl to Amin and adjust k accordingly. Otherwise, set kl to 1 through k.
4. If p is -1 and Amin is not provided, call VLFLplot to plot the entire object and return.
5. Initialize variables for timing and control of the plotting loop.
6. Loop through each union (i from 1 to k):
• Call FLofUL to get the face list (FL), normal vector (v), and area (A) for the current union.
• If the area (A) is less than or equal to Amin, break the loop.
• Call VLFLplot to plot the current face list (FL) with the specified color (c).
• Adjust the plot axes to be auto-scaled and equal.
• Display the author's name using PRplot.
• If p is non-negative, pause for p seconds. Otherwise, wait for a key press.
• Update timing and control variables to estimate remaining time and adjust the plotting speed.
7. If the loop is exited early (i < k), print a message indicating that the plotting was aborted due to the area being smaller than Amin, and note the number of unions not plotted.