VLFLspherecurvedPLEL
by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - VLFL/Surfaces
Introduced first in SolidGeometry 1.1, Creation date: 2013-08-13, Last change: 2025-09-14
returns VL and FL for a sphere-curved surface given by a point list and contour edge list
Description
This procedure is a combination of generating auxiliary points for the plane, the contour, for tesselation, and for transformation on a sphere surface.
Example Illustration
Syntax
[VL,FL,CEL]=VLFLspherecurvedPLEL(PL,CEL,R,d)
Input Parameter
PL: | | Point list 2D |
CEL: | | Contour edge list |
R: | | Radius [-R 0 0] |
d: | | maximum point distance of contour and grid (sofrd) |
Output Parameter
VL: | | Vertex list of surface |
FL: | | Facet list of surface |
CEL: | | Contour edge list |
Copyright 2013-2025 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 generate a vertex list (VL) and a facet list (FL) for a sphere-curved surface based on a given point list (PL) and contour edge list (CEL). The function is part of the VLFL-Library and was created by Tim Lueth in 2013.
Input Parameters
- PL: A 2D point list representing the initial set of points on a plane.
- CEL: A contour edge list that defines the edges connecting the points in PL.
- R: The radius of the sphere, with the center assumed to be at [-R, 0, 0].
- d: The maximum allowable distance between points on the contour and the grid.
Output Results
- VL: The vertex list of the sphere-curved surface.
- FL: The facet list of the sphere-curved surface.
- CEL: The updated contour edge list.
Algorithm Steps
- Set the maximum point distance for both x and y directions to the input parameter
d.
- Generate auxiliary grid points on a plane using the function
GPLauxgridpointsPLEL with inputs PL, CEL, dx, and dy. This function returns a grid point list GPL and a classification vector k.
- Add auxiliary contour points to the point list using the function
PLELaddauxpoints, which updates the contour edge list CEL and returns a revised list RL.
- Combine the revised list
RL with the grid points classified as part of the contour (where k == 1) to form a new grid point list GPL.
- Tessellate the grid and contour using the function
FLofPLEL to generate the facet list FL.
- Transform the 2D grid points into 3D coordinates on the sphere surface using spherical transformations:
z = R * cos(GPL(:,1)/R) * sin(GPL(:,2)/R)y = R * sin(GPL(:,1)/R)x = -R + R * cos(GPL(:,1)/R) * cos(GPL(:,2)/R)
- Combine the transformed coordinates into the vertex list
VL.
Algorithm explaination created using ChatGPT on 2025-08-19 06:52. (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