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

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## Abstract

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## 1. Introduction

#### Background

## 2. Methods: A Novel Focus of Locus

#### 2.1. Plane Example

#### 2.2. Spatial Example 1

#### 2.3. Spatial Example 2

#### 2.4. Locus Example Solved with Developed Tool

## 3. Reflections

## 4. Conclusions

- An analytical and graphical study of the most relevant spatial geometric places to take advantage of current calculation capacities; we also propose the creation of new initiatives promoting spatial geometric places in technical design;
- Communication with 3D CAD software developers about the convenience of incorporating the most relevant plane geometric places, including those currently deemed ineffectual due to being curved lines not generated by circumferential arcs;
- An investigation into the best approach to introducing loci functions within CAD programs to users, and insight into situations where these functions are able to solve a geometric problem, especially in more complex loci cases.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Conical curves as loci: (

**A**) ellipse; (

**B**) parabola; (

**C**) hyperbola; (

**D**,

**E**) equidistance between a straight line and a circumference; (

**F**,

**G**) hyperbola: locus formed by points equidistant between a circle and a point.

**Figure 2.**Conical curves as loci: (

**A**) locus of points with a distance to a fixed point double the distance of another; (

**B**) arc capable: angle α; (

**C**) locus of the points of the plane that observe a circumference from the same angle; (

**D**) lines of a given length that are tangential to a circle; (

**E**) construction of a triangle from a segment on a given surface.

**Figure 5.**This is an example of a part with a nerve whose placement would be much easier if based on the bisecting plane concept.

**Figure 6.**(

**a**) Pyramidal structure with a quadrangular base and a mechanical arm; (

**b**) Mechanical arm.

**Figure 7.**Locus2 (

**a**) initial data; (

**b**) transparent solid model; (

**c**) opaque wireframe model; (

**d**) top view.

**Figure 8.**Transparent solid models of the geometric places: (

**a**) Locus2 and Locus3; (

**b**) Locus1, Locus2 and Locus3.

**Figure 10.**Screenshots: (

**a**) given entities represented in blue and locus curve solution in green; (

**b**) In black, some circumferences that corroborate the solution.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rojas-Sola, J.I.; Hernández-Díaz, D.; Villar-Ribera, R.; Hernández-Abad, V.; Hernández-Abad, F.
Computer-Aided Sketching: Incorporating the Locus to Improve the Three-Dimensional Geometric Design. *Symmetry* **2020**, *12*, 1181.
https://doi.org/10.3390/sym12071181

**AMA Style**

Rojas-Sola JI, Hernández-Díaz D, Villar-Ribera R, Hernández-Abad V, Hernández-Abad F.
Computer-Aided Sketching: Incorporating the Locus to Improve the Three-Dimensional Geometric Design. *Symmetry*. 2020; 12(7):1181.
https://doi.org/10.3390/sym12071181

**Chicago/Turabian Style**

Rojas-Sola, José Ignacio, David Hernández-Díaz, Ricardo Villar-Ribera, Vicente Hernández-Abad, and Francisco Hernández-Abad.
2020. "Computer-Aided Sketching: Incorporating the Locus to Improve the Three-Dimensional Geometric Design" *Symmetry* 12, no. 7: 1181.
https://doi.org/10.3390/sym12071181