Computer-Aided Sketching: Incorporating the Locus to Improve the Three-Dimensional Geometric Design

José Ignacio Rojas-Sola,David Hernández-Díaz,Vicente Hernández-Abad,Francisco Hernández-Abad,Ricardo Villar-Ribera

doi:10.3390/sym12071181

José Ignacio Rojas-Sola, David Hernández-Díaz + Show 3 more

Open Access

https://doi.org/10.3390/sym12071181

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Abstract

This article presents evidence of the convenience of implementing the geometric places of the plane into commercial computer-aided design (CAD) software as auxiliary tools in the computer-aided sketching process. Additionally, the research considers the possibility of adding several intuitive spatial geometric places to improve the efficiency of the three-dimensional geometric design. For demonstrative purposes, four examples are presented. A two-dimensional figure positioned on the flat face of an object shows the significant improvement over tools currently available in commercial CAD software, both vector and parametric: it is more intuitive and does not require the designer to execute as many operations. Two more complex three-dimensional examples are presented to show how the use of spatial geometric places, implemented as CAD software functions, would be an effective and highly intuitive tool. Using these functions produces auxiliary curved surfaces with points whose notable features are a significant innovation. A final example provided solves a geometric place problem using own software designed for this purpose. The proposal to incorporate geometric places into CAD software would lead to a significant improvement in the field of computational geometry. Consequently, the incorporation of geometric places into CAD software could increase technical-design productivity by eliminating some intermediate operations, such as symmetry, among others, and improving the geometry training of less skilled users.

Highlights

Mathematics has been used to solve geometric problems throughout history, something that has proliferated with the possibility of establishing metric and geometric variables for analysis, or implementing such variables in the development of computer-aided design (CAD) software
Given that this article demonstrates the incorporation of geometric places into represents an improvement in design, the main objective of this research is to promote software represents an improvement in 3D CAD design, the main objective of this research isthe to functionality competitiveness achieved by taking the system to 3D
This article has presented the geometric places of the plane and the possibilities of improvement derived from their implementation in commercial CAD software as auxiliary tools in the Computer-Aided Sketching (CAS) process

Summary

Introduction

Mathematics has been used to solve geometric problems throughout history, something that has proliferated with the possibility of establishing metric (e.g., distances or angles) and geometric (e.g., parallelism or perpendicularity) variables for analysis, or implementing such variables in the development of computer-aided design (CAD) software. Such augmentations have become increasingly powerful, such that neither hand drawing—with either classical instruments or Euclidean tools (compass, set square, and bevel)—nor the need for in-depth knowledge of classical-geometry procedures are essential for designers anymore. Given a fixed point, a locus can be derived from the points that

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