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"

Functions
template<typename point_type , typename space_type >
space_type	get_analytic_sdf_sphere (const point_type coords, const space_type radius, const space_type center_x=0, const space_type center_y=0, const space_type center_z=0)
	Computes the analytical signed distance function of a sphere for a given point in space. More...

template<typename point_type , typename space_type >
space_type	get_analytic_sdf_sphere (const point_type coords, const space_type radius, const space_type center[point_type::dims])
	Based on coordinates, radius and center, returns signed distance function of a sphere. More...

template<size_t SDF_exact, typename grid_type , typename space_type >
void	init_analytic_sdf_sphere (grid_type &grid, const space_type radius, const space_type center_x=0, const space_type center_y=0, const space_type center_z=0)
	Initializes the exact solution of the signed distance function of a sphere on an OpenFPM grid. More...

template<size_t SDF_exact, typename grid_type , typename space_type >
void	init_analytic_sdf_sphere (grid_type &grid, const space_type radius, const space_type center[grid_type::dims])
	Computes the analytical signed distance function of a sphere for a given point in space. More...

template<typename point_type , typename space_type >
space_type	get_analytic_sdf_circle (point_type coords, const space_type radius, const space_type center_x=0, const space_type center_y=0)
	Computes the analytical signed distance function of a circle for a given point in space. More...

template<typename point_type , typename space_type >
space_type	get_analytic_sdf_circle (const point_type coords, const space_type radius, const space_type center[point_type::dims])
	Based on coordinates, radius and center, returns signed distance function of a disk. More...

template<size_t SDF_exact, typename grid_type , typename space_type >
void	init_analytic_sdf_circle (grid_type &grid, const space_type radius, const space_type center_x=0, const space_type center_y=0)
	Initializes the exact solution of the signed distance function of a circle on an OpenFPM grid. More...

template<size_t SDF_exact, typename grid_type , typename space_type >
void	init_analytic_sdf_circle (grid_type &grid, const space_type radius, const space_type center[grid_type::dims])
	Computes the analytical signed distance function of a disk for a given point in space. 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() [1/2]

template<typename point_type , typename space_type >

space_type get_analytic_sdf_circle	(	const point_type	coords,
		const space_type	radius,
		const space_type	center[point_type::dims]
	)

Based on coordinates, radius and center, returns signed distance function of a disk.

Template Parameters

point_type	Template type of input coordinates.
space_type	Template type of space.

Parameters

coords	Input coordinates of type point_type.
radius	Radius of type space_type.
center	Center array of type space_type[2].

Returns: Value of signed distance function.

Definition at line 206 of file AnalyticalSDF.hpp.

◆ get_analytic_sdf_circle() [2/2]

template<typename point_type , typename space_type >

space_type get_analytic_sdf_circle	(	point_type	coords,
		const space_type	radius,
		const space_type	center_x = `0`,
		const 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) is thus:

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

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 disk.
center_x	Space_type x-coordinate of disk center.
center_y	Space_type y-coordinate of disk center.

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

Definition at line 181 of file AnalyticalSDF.hpp.

◆ get_analytic_sdf_sphere() [1/2]

template<typename point_type , typename space_type >

space_type get_analytic_sdf_sphere	(	const point_type	coords,
		const space_type	radius,
		const space_type	center[point_type::dims]
	)

Based on coordinates, radius and center, returns signed distance function of a sphere.

Template Parameters

point_type	Template type of input coordinates.
space_type	Template type of space.

Parameters

coords	Input coordinates of type point_type.
radius	Radius of type space_type.
center	Center array of type space_type[3].

Returns: Value of signed distance function.

Definition at line 72 of file AnalyticalSDF.hpp.

◆ get_analytic_sdf_sphere() [2/2]

template<typename point_type , typename space_type >

space_type get_analytic_sdf_sphere	(	const point_type	coords,
		const space_type	radius,
		const space_type	center_x = `0`,
		const space_type	center_y = `0`,
		const 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() [1/2]

template<size_t SDF_exact, typename grid_type , typename space_type >

void init_analytic_sdf_circle	(	grid_type &	grid,
		const space_type	radius,
		const space_type	center[grid_type::dims]
	)

Computes the analytical signed distance function of a disk 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) is thus:

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

Template Parameters

SDF_exact	Size_t index of property to which analytical SDF of circle will be saved.
grid_type	Template type of input grid.
space_type	Template type of space.

Parameters

grid	Input grid of type grid_type.
radius	Radius of type space_type.
center	Array containing 2 elements for center coordinate in x and y.

Definition at line 268 of file AnalyticalSDF.hpp.

◆ init_analytic_sdf_circle() [2/2]

template<size_t SDF_exact, typename grid_type , typename space_type >

void init_analytic_sdf_circle	(	grid_type &	grid,
		const space_type	radius,
		const space_type	center_x = `0`,
		const 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 234 of file AnalyticalSDF.hpp.

◆ init_analytic_sdf_sphere() [1/2]

template<size_t SDF_exact, typename grid_type , typename space_type >

void init_analytic_sdf_sphere	(	grid_type &	grid,
		const space_type	radius,
		const space_type	center[grid_type::dims]
	)

Computes the analytical signed distance function of a sphere 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

SDF_exact	Size_t index of property to which analytical SDF of sphere will be saved.
grid_type	Template type of input grid.
space_type	Template type of space.

Parameters

grid	Input grid of type grid_type.
radius	Radius of type space_type.
center	Array containing 3 elements for center coordinate in x, y and z.

Definition at line 138 of file AnalyticalSDF.hpp.

◆ init_analytic_sdf_sphere() [2/2]

template<size_t SDF_exact, typename grid_type , typename space_type >

void init_analytic_sdf_sphere	(	grid_type &	grid,
		const space_type	radius,
		const space_type	center_x = `0`,
		const space_type	center_y = `0`,
		const 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 102 of file AnalyticalSDF.hpp.

Functions

Detailed Description

Function Documentation

◆ get_analytic_sdf_circle() [1/2]

◆ get_analytic_sdf_circle() [2/2]

◆ get_analytic_sdf_sphere() [1/2]

◆ get_analytic_sdf_sphere() [2/2]

◆ init_analytic_sdf_circle() [1/2]

◆ init_analytic_sdf_circle() [2/2]

◆ init_analytic_sdf_sphere() [1/2]

◆ init_analytic_sdf_sphere() [2/2]