Fig 8 -

<p>A point cloud image consist of a set of points in 3D coordinate system with geometric coordinates stored in <i>N</i> × 3 matrix (i) Top-row left image (5184×3) and its squared image on right. (ii) Bottom-row left image (20402 × 3) represents two spheres of radius <i>r</...

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Bibliographic Details
Main Author:	Pushpendra Singh (185150) (author)
Other Authors:	Anubha Gupta (6019520) (author), Shiv Dutt Joshi (3835129) (author)
Published:	2024
Subjects:	Biophysics Biochemistry Cell Biology Pharmacology Developmental Biology Space Science Mathematical Sciences not elsewhere classified subsequent investigations revealed paramount mathematical objective hamilton discovered quaternions established superposition paradigm commutative division algebra associative division algebra >- periodic functions >&# 960 ;</ four division algebras complex number systems specified quantum states traditional complex numbers div >< p unified multiplication operation existing multiplication structures normed division algebras finite dimensions represents new hypercomplex numbers complex numbers hypercomplex numbers associated algebras two new quantum state finite dimensions existing real addition operation numbers constitutes spherical multiplication proposed multiplication viable alternative vectors within thereby offering study transcends study presents space formed simultaneously preserving shedding light real three proposed methodology practical applications potential complement higher dimensions geometric properties foundational discipline extended spaces euler identity dimensions forms dimensions 1 comprehensive generalization abelian group
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Fig 8 -

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