Computational Geometry


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Nearest Neighbor Search (最近傍点探索)

  • Locality Sensitive Hashing (LSH)
    • P. Indyk and R. Motwani (1998) "Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality,” In Proceedings of the 30th ACM Symposium on Theory of Computing (STOC’98), pp.604-613.

Triagnle

Area(2D)

Area(3D)

Circumscribed Circle

Inscribed Circle

Equilateral triangle


Tetrahedra

Volume

 V = 1/6 \begin {vmatrix} a_x & a_y  & a_z & 1 \\ b_x & b_y  & b_z & 1 \\ c_x & c_y  & c_z & 1 \\ d_x & d_y  & d_z & 1 \end{vmatrix}

The volume is positive if points a,b,c are ordered as counterclockwise when viewed from the point d, and negative if they are ordered as clcockwise.

Circumscribed Sphere

Inscribed Sphere

Equilateral Tetrahedra


Transform

Translate

x2 = x1 + tx
y2 = y1 + ty
z2 = z1 + tz

Scale

x2 = x1 * sx
y2 = y1 * sy
z2 = z1 * sx

Rotate(2D)

x2 = x1 * cos(v) - y1 * sin(v)
y2 = x1 * sin(v) + y1 * cos(v)

Rotate(3D)

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