VLFLspherecurvedCL
by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - Analytical Geometry
Introduced first in SolidGeometry 1.1, Creation date: 2013-08-11, Last change: 2025-09-14
returns VL and FL for a sphere curved surface given by a 2D contour point 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,CVL,CL]=VLFLspherecurvedCL(CL,R)
Input Parameter
CL: | | Points list of 2D contour |
R: | | Radius [-R 0 0] |
Output Parameter
VL: | | Vertex list of surface |
FL: | | Facet list of surface |
CVL: | | Contour Vertex list |
CL: | | Contour list (incl. auxiliary points) |
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 function, VLFLspherecurvedCL, is designed to generate a vertex list (VL) and a facet list (FL) for a surface that is curved like a sphere, based on a given 2D contour point list (CL) and a specified radius (R).
Input Parameters
- CL: A list of 2D points that define the contour of the surface.
- R: The radius of the sphere, specified as a vector [-R 0 0].
- varargin: Optional parameter to specify a different radius for the y-dimension (Ry). If not provided, Ry defaults to Rx.
Output Results
- VL: The vertex list of the generated surface.
- FL: The facet list of the generated surface.
- CVL: The contour vertex list.
- CL: The contour list, including any auxiliary points added during processing.
Algorithm Steps
- Set Ry to Rx unless a different value is provided in varargin.
- Calculate the grid spacing (dx, dy) using the function
sofrd with the minimum of Rx and Ry.
- Generate auxiliary grid points using
GPLauxgridpointsCL with the contour list (CL) and grid spacing (dx, dy).
- Add auxiliary points to the contour list using
RLaddauxpoints.
- Determine the number of points (n) in the updated contour list (RL).
- Create a connectivity list (CEL) for the contour points.
- Combine the contour points and auxiliary grid points into a single list (GPL).
- Perform Delaunay triangulation on the combined point list (GPL) and connectivity list (CEL) to generate the facet list (FL).
- Determine the in/out status of the points to identify contour points.
- Calculate the 3D coordinates (x, y, z) for each point on the sphere surface using spherical transformations.
- Construct the vertex list (VL) using the calculated 3D coordinates.
- Update the facet list (FL) to include only the triangles that are part of the surface.
- Extract the contour vertex list (CVL) from the vertex list (VL).
- If no output arguments are specified, plot the surface using
VLFLplot.
Algorithm explaination created using ChatGPT on 2025-08-19 01:42. (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