#include <imesh_imls_surface.h>

Classes
struct	integral_data
	a data structure to hold the integral terms. More...
Public Member Functions
	imesh_imls_surface (const imesh_mesh &mesh, double eps=0.01, double lambda=0.1, bool enforce_bounded=false, const vcl_set< unsigned int > &no_normal_faces=vcl_set< unsigned int >())
	Constructor.
	imesh_imls_surface (const imesh_imls_surface &other)
	Copy Constructor.
double	operator() (const vgl_point_3d< double > &p) const
	evaluate the implicit surface at a point.
double	operator() (double x, double y, double z) const
	evaluate the implicit surface at a point.
double	w2 (double dist2) const
	evaluate the squared weighting function given a squared distance.
vgl_box_3d< double >	bounding_box () const
	return a bounding box for the original input mesh.
double	deriv (const vgl_point_3d< double > &p, vgl_vector_3d< double > &dp) const
	evaluate the function and its derivative (returned by reference).
double	deriv2 (const vgl_point_3d< double > &p, vgl_vector_3d< double > &dp, vnl_double_3x3 &ddp) const
	evaluate the function and its first and second derivatives (returned by reference).
void	set_epsilon (double eps)
	change the epsilon (smoothness) of the surface.
void	set_lambda (double lambda)
	change the lambda (accuracy parameter).
Static Public Member Functions
static void	line_integrals (double k1, double k2, double &I1, double &Ix)
	integrals of f(x)dx and x*f(x)dx over [0,1] where f(x)= 1/((x+k1)^2 + k2)^2.
static void	line_integrals (double k1, double k2, double &I1, double &Ix, double &dI1, double &dIx, double &dIx2)
	integrals of f(x)dx and x*f(x)dx over [0,1] where f(x)= 1/((x+k1)^2 + k2)^2.
static double	line_integral (const vgl_point_3d< double > &x, const vgl_point_3d< double > &p0, const vgl_point_3d< double > &p1, double v0, double v1, double eps)
	line integral of the squared weight function times a linear value on the line from p0 to p1.
static vgl_vector_3d< double >	line_integral_deriv (const vgl_point_3d< double > &x, const vgl_point_3d< double > &p0, const vgl_point_3d< double > &p1, double v0, double v1, double eps2)
	The derivative of the line integral with respect to x.
static vgl_vector_2d< double >	split_triangle_quadrature (const vgl_point_3d< double > &x, const vgl_point_3d< double > &m, const vgl_point_3d< double > &pp, const vgl_point_3d< double > &pm, double v0, double v1, double v2, double eps)
	area integral of the squared weight function times a linearly interpolated value.
template<class T , class F >
static T	triangle_quadrature (F quad_func, const vgl_point_3d< double > &x, const vgl_point_3d< double > &p0, const vgl_point_3d< double > &p1, const vgl_point_3d< double > &p2, const vgl_vector_3d< double > &n, double v0, double v1, double v2, double eps)
	area integral of the squared weight function times a linearly interpolated value.
static integral_data	split_triangle_quadrature_with_deriv (const vgl_point_3d< double > &x, const vgl_point_3d< double > &m, const vgl_point_3d< double > &pp, const vgl_point_3d< double > &pm, double v0, double v1, double v2, double eps)
	area integral of the squared weight function times a linearly interpolated value.
Private Member Functions
void	compute_centroids_rec (const vcl_auto_ptr< imesh_kd_tree_node > &node, const vcl_set< unsigned int > &no_normal_faces)
	recursively compute the area weighted centroids.
void	compute_unweighed_rec (const vcl_auto_ptr< imesh_kd_tree_node > &node)
	recursively compute the unweighted integrals.
void	compute_iso_level ()
	compute the iso value such that the mean value at the vertices is zero.
void	compute_enclosing_phi ()
	adjust the phi values until all vertices are within the iso surface.
Private Attributes
vcl_vector< vgl_point_3d < double > >	verts_
vcl_auto_ptr < imesh_regular_face_array< 3 > >	triangles_
vcl_auto_ptr< imesh_kd_tree_node >	kd_tree_
vcl_vector< double >	phi_
vcl_vector< double >	area_
vcl_vector< double >	unweighted_
vcl_vector< vgl_point_3d < double > >	centroid_
vcl_vector< vgl_vector_3d < double > >	normals_
vcl_vector< double >	normal_len_
double	eps2_
double	lambda_
double	iso_level_
bool	bounded_

Detailed Description

Definition at line 25 of file imesh_imls_surface.h.

Constructor & Destructor Documentation

imesh_imls_surface::imesh_imls_surface	(	const imesh_mesh &	mesh,
		double	eps = `0.01`,
		double	lambda = `0.1`,
		bool	enforce_bounded = `false`,
		const vcl_set< unsigned int > &	no_normal_faces = `vcl_set<unsigned int>()`
	)

Constructor.

Definition at line 19 of file imesh_imls_surface.cxx.

imesh_imls_surface::imesh_imls_surface ( const imesh_imls_surface & other )

Copy Constructor.

Definition at line 94 of file imesh_imls_surface.cxx.

Member Function Documentation

vgl_box_3d< double > imesh_imls_surface::bounding_box ( ) const

return a bounding box for the original input mesh.

Definition at line 231 of file imesh_imls_surface.cxx.

void imesh_imls_surface::compute_centroids_rec	(	const vcl_auto_ptr< imesh_kd_tree_node > &	node,
		const vcl_set< unsigned int > &	no_normal_faces
	)		`[private]`

recursively compute the area weighted centroids.

Definition at line 165 of file imesh_imls_surface.cxx.

void imesh_imls_surface::compute_enclosing_phi ( ) [private]

adjust the phi values until all vertices are within the iso surface.

Also computes the iso level

Definition at line 127 of file imesh_imls_surface.cxx.

void imesh_imls_surface::compute_iso_level ( ) [private]

compute the iso value such that the mean value at the vertices is zero.

Definition at line 116 of file imesh_imls_surface.cxx.

void imesh_imls_surface::compute_unweighed_rec ( const vcl_auto_ptr< imesh_kd_tree_node > & node ) [private]

recursively compute the unweighted integrals.

Definition at line 209 of file imesh_imls_surface.cxx.

double imesh_imls_surface::deriv	(	const vgl_point_3d< double > &	p,
		vgl_vector_3d< double > &	dp
	)		const

evaluate the function and its derivative (returned by reference).

Definition at line 368 of file imesh_imls_surface.cxx.

double imesh_imls_surface::deriv2	(	const vgl_point_3d< double > &	p,
		vgl_vector_3d< double > &	dp,
		vnl_double_3x3 &	ddp
	)		const

evaluate the function and its first and second derivatives (returned by reference).

Definition at line 467 of file imesh_imls_surface.cxx.

double imesh_imls_surface::line_integral	(	const vgl_point_3d< double > &	x,
		const vgl_point_3d< double > &	p0,
		const vgl_point_3d< double > &	p1,
		double	v0,
		double	v1,
		double	eps2
	)		`[static]`

line integral of the squared weight function times a linear value on the line from p0 to p1.

(value at p0 is v0 and at p1 is v1) eps2 is epsilon^2

Definition at line 563 of file imesh_imls_surface.cxx.

vgl_vector_3d< double > imesh_imls_surface::line_integral_deriv	(	const vgl_point_3d< double > &	x,
		const vgl_point_3d< double > &	p0,
		const vgl_point_3d< double > &	p1,
		double	v0,
		double	v1,
		double	eps2
	)		`[static]`

The derivative of the line integral with respect to x.

Definition at line 581 of file imesh_imls_surface.cxx.

void imesh_imls_surface::line_integrals	(	double	k1,
		double	k2,
		double &	I1,
		double &	Ix
	)		`[static]`

integrals of f(x)dx and x*f(x)dx over [0,1] where f(x)= 1/((x+k1)^2 + k2)^2.

These equations are wrong in the paper, they should be (for a=1): Beta = atan( k1/sqrt(k2) ) - atan( (k1+1)/sqrt(k2) ) I1 = -Beta * 1/(2*k2^(3/2)) + (k2 - k1*(k1+1)) / (2*k2*(k1^2+k2)*((k1+1)^2+k2)) Ix = Beta * k1/(2*k2^(3/2)) + (k1 + 1) / (2*k2*((k1+1)^2+k2))

Definition at line 496 of file imesh_imls_surface.cxx.

void imesh_imls_surface::line_integrals	(	double	k1,
		double	k2,
		double &	I1,
		double &	Ix,
		double &	dI1,
		double &	dIx,
		double &	dIx2
	)		`[static]`

integrals of f(x)dx and x*f(x)dx over [0,1] where f(x)= 1/((x+k1)^2 + k2)^2.

Also compute the integrals when f(x)=1/((x+k1)^2 + k2)^3 (for use in derivatives)

Beta = atan( k1/sqrt(k2) ) - atan( (k1+1)/sqrt(k2) ) I1 = -Beta * 1/(2*k2^(3/2)) + (k2 - k1*(k1+1)) / (2*k2*(k1^2+k2)*((k1+1)^2+k2)) Ix = Beta * k1/(2*k2^(3/2)) + (k1 + 1) / (2*k2*((k1+1)^2+k2)) dI1 = 1/8 * ( -Beta*3/k2^(5/2) + (5*k2^3 - (k1*(k1+1)-3)*k2^2 - k1*(k1+1)*(9*k1*(k1+1)+5)*k2 - 3*k1^3*(k1+1)^3) / (k2^2*(k1^2+k2)^2*((k1+1)^2+k2)^2) ) dIx = 1/8 * ( Beta*3*k1/k2^(5/2) + ((k1^2+k2)*((3*(k1+1)+1)*k2^2 + (k1+1)*(6*k1^2+3*k1+2)*k2 + 3*k1^2*(k1+1)^3)) /(k2^2*(k1^2+k2)^2*((k1+1)^2+k2)^2) ) dIx2 = 1/8 * ( -Beta*(3*k1^2+k2)/k2^(5/2) - ((k1^2+k2)^2*(k2^2 + (k1+1)*(4*k1-1)*k2 + 3*k1*(k1+1)^3)) /(k2^2*(k1^2+k2)^2*((k1+1)^2+k2)^2) )

Definition at line 526 of file imesh_imls_surface.cxx.

double imesh_imls_surface::operator() ( const vgl_point_3d< double > & p ) const

evaluate the implicit surface at a point.

Definition at line 288 of file imesh_imls_surface.cxx.

double imesh_imls_surface::operator()	(	double	x,
		double	y,
		double	z
	)		const `[inline]`

evaluate the implicit surface at a point.

Definition at line 41 of file imesh_imls_surface.h.

void imesh_imls_surface::set_epsilon ( double eps )

change the epsilon (smoothness) of the surface.

Definition at line 238 of file imesh_imls_surface.cxx.

void imesh_imls_surface::set_lambda ( double lambda ) [inline]

change the lambda (accuracy parameter).

Definition at line 67 of file imesh_imls_surface.h.

vgl_vector_2d< double > imesh_imls_surface::split_triangle_quadrature	(	const vgl_point_3d< double > &	x,
		const vgl_point_3d< double > &	pm,
		const vgl_point_3d< double > &	p1,
		const vgl_point_3d< double > &	p2,
		double	vm,
		double	v1,
		double	v2,
		double	eps
	)		`[static]`

area integral of the squared weight function times a linearly interpolated value.

m is the point closest point on the triangle to sample point x pp is second closest vertex and pm is the furthest call triangle_quadrature to first split an arbitrary triangle eps2 is epsilon^2

m is the point closest point on the triangle to sample point x p0 and p1 are the other vertices call triangle_quadrature to first split an arbitrary triangle eps2 is epsilon^2

Definition at line 606 of file imesh_imls_surface.cxx.

imesh_imls_surface::integral_data imesh_imls_surface::split_triangle_quadrature_with_deriv	(	const vgl_point_3d< double > &	x,
		const vgl_point_3d< double > &	pm,
		const vgl_point_3d< double > &	p1,
		const vgl_point_3d< double > &	p2,
		double	vm,
		double	v1,
		double	v2,
		double	eps
	)		`[static]`

area integral of the squared weight function times a linearly interpolated value.

Also computes vector term used in the derivative m is the point closest point on the triangle to sample point x pp is second closest vertex and pm is the furthest call triangle_quadrature to first split an arbitrary triangle eps2 is epsilon^2

Also computes vector term used in the derivative m is the point closest point on the triangle to sample point x p0 and p1 are the other vertices call triangle_quadrature to first split an arbitrary triangle eps2 is epsilon^2

Definition at line 690 of file imesh_imls_surface.cxx.

template<class T , class F >

T imesh_imls_surface::triangle_quadrature	(	F	quad_func,
		const vgl_point_3d< double > &	x,
		const vgl_point_3d< double > &	p0,
		const vgl_point_3d< double > &	p1,
		const vgl_point_3d< double > &	p2,
		const vgl_vector_3d< double > &	n,
		double	v0,
		double	v1,
		double	v2,
		double	eps
	)		`[static]`