AnalyticalSDF.hpp File Reference

Header file containing functions that compute the analytical solution of the signed distance function (SDF) for a 3D sphere and a 2D disk of defined radius on a grid. More...

#include <iostream>
#include "Vector/vector_dist.hpp"
#include "Grid/grid_dist_id.hpp"

Go to the source code of this file.

Functions
template<typename point_type , typename space_type >
space_type	get_analytic_sdf_sphere (point_type coords, space_type radius, space_type center_x=0, space_type center_y=0, space_type center_z=0)
	Computes the analytical signed distance function of a sphere for a given point in space. More...
template<size_t SDF_exact, typename grid_type , typename space_type >
void	init_analytic_sdf_sphere (grid_type &grid, space_type radius, space_type center_x=0, space_type center_y=0, space_type center_z=0)
	Initializes the exact solution of the signed distance function of a sphere on an OpenFPM grid. More...
template<typename point_type , typename space_type >
space_type	get_analytic_sdf_circle (point_type coords, space_type radius, space_type center_x=0, space_type center_y=0)
	Computes the analytical signed distance function of a circle for a given point in space. More...
template<size_t SDF_exact, typename grid_type , typename space_type >
void	init_analytic_sdf_circle (grid_type &grid, space_type radius, space_type center_x=0, space_type center_y=0)
	Initializes the exact solution of the signed distance function of a circle on an OpenFPM grid. More...

Detailed Description

Header file containing functions that compute the analytical solution of the signed distance function (SDF) for a 3D sphere and a 2D disk of defined radius on a grid.

Author

Justina Stark

Date

October 2020

Definition in file AnalyticalSDF.hpp.

Function Documentation

get_analytic_sdf_circle()

template<typename point_type , typename space_type >

space_type get_analytic_sdf_circle	(	point_type	coords,
		space_type	radius,
		space_type	center_x = 0,
		space_type	center_y = 0
	)

Computes the analytical signed distance function of a circle for a given point in space.

At the center of the circle, φ_SDF_analytic = Radius. Moving outwards from the center on, the value for the SDF decreases steadily, eventually becomes 0 at the circle surface and negative beyond the surface. The analytic SDF for a circle of radius R and center (a, b, c) is thus:

\[ \phi_{SDF}(x, y, z) = R - \sqrt{((x-a)^2 + (y-b)^2 + (z-c)^2)} \]

Template Parameters

point_type	Template type of OpenFPM Point<dimension, type>.
space_type	Template type of radius.

Parameters

coords	Point_type coordinates of point.
radius	Space_type radius of the sphere.
center_x	Space_type x-coordinate of sphere center.
center_y	Space_type y-coordinate of sphere center.
center_z	Space_type z-coordinate of sphere center.

Returns

Space_type variable that contains the exact solution for the signed distance function of a given point in a sphere of given radius, where the SDF has positive values inside and negative values outside the sphere.

Definition at line 116 of file AnalyticalSDF.hpp.

get_analytic_sdf_sphere()

template<typename point_type , typename space_type >

space_type get_analytic_sdf_sphere	(	point_type	coords,
		space_type	radius,
		space_type	center_x = 0,
		space_type	center_y = 0,
		space_type	center_z = 0
	)

Computes the analytical signed distance function of a sphere for a given point in space.

At the center of the sphere, φ_SDF_analytic = Radius. Moving outwards from the center on, the value for the SDF decreases steadily, eventually becomes 0 at the sphere surface and negative beyond the surface. The analytic SDF for a sphere of radius R and center (a, b, c) is thus:

\[ \phi_{SDF}(x, y, z) = R - \sqrt{((x-a)^2 + (y-b)^2 + (z-c)^2)} \]

Template Parameters

point_type	Template type of OpenFPM Point<dimension, type>.
space_type	Template type of radius.

Parameters

coords	Point_type coordinates of point.
radius	Space_type radius of the sphere.
center_x	Space_type x-coordinate of sphere center.
center_y	Space_type y-coordinate of sphere center.
center_z	Space_type z-coordinate of sphere center.

Returns

Space_type variable that contains the exact solution for the signed distance function of a given point in a sphere of given radius, where the SDF has positive values inside and negative values outside the sphere.

Definition at line 46 of file AnalyticalSDF.hpp.

init_analytic_sdf_circle()

template<size_t SDF_exact, typename grid_type , typename space_type >

void init_analytic_sdf_circle	(	grid_type &	grid,
		space_type	radius,
		space_type	center_x = 0,
		space_type	center_y = 0
	)

Initializes the exact solution of the signed distance function of a circle on an OpenFPM grid.

Solves the exact SDF for each grid nodes and writes the solution to a given property.

Template Parameters

SDF_exact	Index of property where the anaytical solution for the SDF should be written to.
grid_type	Template type of the input grid.
space_type	Template type of radius and center coordinates.

Parameters

grid	Input OpenFPM grid.
radius	Radius of the filled circle.
center_x	X-coordinate of the circle center.
center_y	Y-coordinate of the circle center.

Definition at line 144 of file AnalyticalSDF.hpp.

init_analytic_sdf_sphere()

template<size_t SDF_exact, typename grid_type , typename space_type >

void init_analytic_sdf_sphere	(	grid_type &	grid,
		space_type	radius,
		space_type	center_x = 0,
		space_type	center_y = 0,
		space_type	center_z = 0
	)

Initializes the exact solution of the signed distance function of a sphere on an OpenFPM grid.

Solves the exact SDF for each grid nodes and writes the solution to a given property.

Template Parameters

SDF_exact	Index of property where the anaytical solution for the SDF should be written to.
grid_type	Template type of the input grid.
space_type	Template type of radius the sphere is supposed to have.

Parameters

grid	Input OpenFPM grid.
radius	Radius of the filled sphere.
center_x	Space_type x-coordinate of sphere center.
center_y	Space_type y-coordinate of sphere center.
center_z	Space_type z-coordinate of sphere center.

Definition at line 77 of file AnalyticalSDF.hpp.