lsegment

by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - Auxiliary function
Introduced first in SolidGeometry 1.0, Creation date: 2012-07-15, Last change: 2025-09-14

returns all supporting points of a line/edge including start and end point, separated

Example Illustration

Syntax

[OVEL,UVEL,AEL]=lsegment(p1,p2,t)

Input Parameter

`p1`:		Starting point of an edge
`p2`:		End point of an edge
`t`:		list of points: [p=p1+t*(p2-p1) , direction]

Output Parameter

`OVEL`:		Edge list of an outer contour
`UVEL`:		Edge list of an inner contour
`AEL`:		Complete contour line

Copyright 2012-2025 Tim C. Lueth. All rights reserved. The code is the property of Tim C. Lueth and may not be redistributed or modified without explicit written permission. This software may be used free of charge for academic research and teaching purposes only. Commercial use, redistribution, modification, or reverse engineering is strictly prohibited. Access to source code is restricted and granted only under specific agreements. For licensing inquiries or commercial use, please contact: Tim C. Lueth

Algorithm (Workflow)

This algorithm is designed to compute all supporting points of a line segment, including the start and end points, based on a given list of parameterized points. The function is named lsegment and is part of the SG-Library, specifically categorized under auxiliary procedures.

Input Parameters

p1: The starting point of the line segment.
p2: The ending point of the line segment.
t: A list of parameterized points, where each point is defined as p = p1 + t * (p2 - p1) and includes a direction component.

Output Results

AVEL: The complete contour line, which includes all supporting points of the line segment.

Algorithm Steps

Remove duplicate rows from t using unique(t, 'rows').
Determine the number of points nt in t.
If the last point in t has an infinite parameter, remove it and decrement nt.
If nt is zero, initialize t with default points [0 0; 1 0] and set nt to 2.
Ensure the last point in t has a parameter of 1. If not, append [1 0] to t and increment nt.
Ensure the first point in t has a parameter of 0. If not, prepend [0 0] to t and increment nt.
Initialize an empty array AVEL to store the contour line points.
Iterate over the points in t in steps of 2:

If the current index i is less than or equal to nt-1, compute the supporting points for the segment between t(i) and t(i+1) and append them to AVEL.
If the current index i is less than or equal to nt-2, compute the supporting points for the segment between t(i+1) and t(i+2) and append them to AVEL.

Algorithm explaination created using ChatGPT on 2025-08-18 23:17. (Please note: No guarantee for the correctness of this explanation)

Last html export of this page out of FM database by TL: 2025-09-21