Rodrigo Braga Pinheiro. What is it?. It is a point-based rendering, i.e., the 3D models are represented by points (point cloud) and not by triangles, as they are commonly represented.
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It is a point-based rendering, i.e., the 3D models are represented by points (point cloud) and not by triangles, as they are commonly represented.
Point cloud - Set of vertices in a 3D coordinate system. These vertices are usually defined by X, Y, and Z coordinates, and typically are intended to be representative of the external surface of an object.
Triangulation-based 3D scanners ﬁnd the positions of points on a surface by computing corresponding pixels from two viewpoints. The correspondence deﬁnes a pair of rays in space, and the intersection of the rays determines a 3D position.
Consider a D-dimensional sphere with radius R, centered at the origin (C), and constrained to include all the points in P. Spherical flipping reflects a point ϵP with respect to the sphere (spherical mirror) by applying the following equation:
= point inside the sphere
R = radius of sphere
Intuitively, spherical flipping reflects every point internal to the sphere along the ray from C to toits image outside the sphere.
Figure 2 - Spherical flipping (in red) of a 2D curve (in blue) using a sphere (in green) centered at the view point (in magenta).
The convex hull of a set Q of points is the smallest convex polygon P for which each point Q is either on the boundary of P or in its interior.
Result of spherical flipping
The shape of L for different values of β(in degrees), where = (10;0), R = 30.
from through and from through , is the largest possible empty region.
From “L Equation”, it can be deduced that the largest region corresponds to the smallest β. This means that βj and βk that correspond to the largest possible empty region, are the smallest possible for . Note that βjand βk can be extracted from “L Equation”. For to be visible, the sum of βjand βk should satisfy βj + βk = const (i.e., a large empty region is associated with )
The empty gray region between Lj and Lk, as defined by the values of βj + βk.