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About F-rep

In F-rep (function representation), a geometric object is defined by a single real continuous function F(x1, x2, x3, …, xn) >= 0. Let's think why F(x1, x2, x3, …, xn) >= 0 can represent an object.

A geometric object in 3D space is described by: the inside, the surface, and the outside.

We assume that F(x1, x2, x3, …, xn) >= 0 is a rule which determines where a given point belongs, that is:

  F(x1, x2, x3, ..., xn) > 0 	: 	the inside of an object
  F(x1, x2, x3, ..., xn) = 0 	: 	the surface of an object
  F(x1, x2, x3, ..., xn) < 0 	: 	the outside an object

To make a mesh of triangles (polygonize) on the surface of an F-rep object, the function has to be sampled in space. The bounding box is used to limit a range of sampling in space, and it is divided into fixed-size grids. The function is sampled in each node of the grid; then polygons are generated based on the sampled values of the function. The high grid density makes a good approximation of an object, but the number of polygons increases. See F-Rep page for more details about F-rep.

HyperFun Polygonizer samples the specified function in 3D space to visualize an F-rep object described in HyperFun. The bounding box has a default size of 20, and the grid density is 30 along each axis. You can change the size of the bounding box and the grid density, when using HyperFun Polygonizer.

hyperfun/tut_about.txt · Last modified: 2020/12/31 10:49 (external edit)