# Reflexively-Fused Cylinders

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## Abstract

**:**

## 1. Introduction

## 2. Introductory Example

## 3. Reflective Fusion

- Condition 1.
- Neither $a\left(t\right)$ nor $b\left(t\right)$ has self-intersections,
- Condition 2.
- $a\left(0\right)=b\left(0\right)$, $a\left(1\right)=b\left(1\right)$ and ${a}_{y}\left(0\right)={a}_{y}\left(1\right)=0$,
- Condition 3.
- $a\left(t\right)\ne b\left({t}^{\prime}\right)$ for any $t,{t}^{\prime}\in (0,1)$,
- Condition 4.
- ${a}_{x}\left(t\right)={b}_{x}\left(t\right)$ for any $t\in [0,1]$.

## 4. Conditions for Realizability

## 5. Examples

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Reflexively-fused object “Card Suits”: (

**a**) object on a mat surface; (

**b**) the same object on a plane mirror.

**Figure 2.**Situation seen from a general viewpoint: (

**a**) another view of the object in Figure 1; (

**b**) spatial configuration of the input.

**Figure 4.**Computation of space curve $c\left(t\right)$ from the pair of planar curves $a\left(t\right)$ and $b\left(t\right)$ on the $xy$ plane.

**Figure 6.**Bat. (

**a**) a target shape; (

**b**) the resulting cylinder on a mat surface; (

**c**) the same object on the mirror; (

**d**) the same object as observed from a general viewpoint.

**Figure 7.**Flower and pot. (

**a**) a target shape; (

**b**) the resulting cylinder on a mat surface; (

**c**) the same object on the mirror; (

**d**) the same object as observed from a general viewpoint.

**Figure 8.**Man and woman. (

**a**) target shapes; (

**b**) the resulting cylinders on a mat surface; (

**c**) the same objects on the mirror; (

**d**) the same objects as observed from a general viewpoint.

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**MDPI and ACS Style**

Sugihara, K.; Moriguchi, M.
Reflexively-Fused Cylinders. *Symmetry* **2018**, *10*, 275.
https://doi.org/10.3390/sym10070275

**AMA Style**

Sugihara K, Moriguchi M.
Reflexively-Fused Cylinders. *Symmetry*. 2018; 10(7):275.
https://doi.org/10.3390/sym10070275

**Chicago/Turabian Style**

Sugihara, Kokichi, and Masaki Moriguchi.
2018. "Reflexively-Fused Cylinders" *Symmetry* 10, no. 7: 275.
https://doi.org/10.3390/sym10070275