#include <opennurbs_point.h>

Public Member Functions
const ON_SurfaceCurvature	FlipSurfaceOrientation () const
	The sign of the principal curvatures are with respect to a choice of surface orientation. This function returns the principal curvatures of the surface with opposite choice of orientation. More...

double	GaussianCurvature () const
	The Gaussian curvature is k1*k2. More...

bool	IsNan () const
	Returns True if either of k1 or k2 is a nan. More...

bool	IsSet () const
	Returns True if k1 and k2 are both valid finite values. More...

bool	IsUnset () const
	Returns True if either of k1 or k2 is not a valid finite value. More...

bool	IsZero () const
	Returns True if k1 and k2 are both zero. More...

double	KappaValue (ON::curvature_style kappa_style) const
	Calculate one of the four typical curvature values associated with the two principal curvatures and frequently used in false color curvature analysis. More...

double	MaximumPrincipalCurvature () const

double	MaximumRadius () const
	If a principal curvature value is zero or the principal curvatures have opposite signs, then the maximum radius of curvature is infinite and ON_SurfaceCurvature::InfinteRadius is returned. Otherwise the maximum radius of curvature is 1/min(fabs(k1),fabs(k2)). More...

double	MeanCurvature () const
	The mean curvature is (k1+k2)/2. More...

double	MinimumPrincipalCurvature () const

double	MinimumRadius () const
	The minimum radius of curvature is 1/max(fabs(k1),fabs(k2)). Infinte radius values are returned as ON_SurfaceCurvature::InfinteRadius. More...

Static Public Member Functions
static int	Compare (const ON_SurfaceCurvature &lhs, const ON_SurfaceCurvature &rhs)
	Dictionary compare k1 and k2. Values with nans sort last. More...

static int	CompareGaussianCurvature (const ON_SurfaceCurvature &lhs, const ON_SurfaceCurvature &rhs)
	Compare lhs.GaussianCurvature() and rhs.GaussianCurvature(). Values with nans sort last. More...

static int	CompareMaximumAndMinimumPrincipalCurvatures (const ON_SurfaceCurvature &lhs, const ON_SurfaceCurvature &rhs)
	Dictionary compare lhs.MaximumPrincipalCurvature() and rhs.MaximumPrincipalCurvature(). Values with nans sort last. More...

static int	CompareMaximumPrincipalCurvature (const ON_SurfaceCurvature &lhs, const ON_SurfaceCurvature &rhs)
	Compare lhs.MaximumPrincipalCurvature() and rhs.MaximumPrincipalCurvature(). Values with nans sort last. More...

static int	CompareMaximumRadius (const ON_SurfaceCurvature &lhs, const ON_SurfaceCurvature &rhs)
	Compare lhs.MaximumRadius() and rhs.MaximumRadius(). Values with nans sort last. More...

static int	CompareMeanCurvature (const ON_SurfaceCurvature &lhs, const ON_SurfaceCurvature &rhs)
	Compare lhs.MeanCurvature() and rhs.MeanCurvature(). Values with nans sort last. More...

static int	CompareMinimumPrincipalCurvature (const ON_SurfaceCurvature &lhs, const ON_SurfaceCurvature &rhs)
	Compare lhs.MinimumPrincipalCurvature() and rhs.MinimumPrincipalCurvature(). Values with nans sort last. More...

static int	CompareMinimumRadius (const ON_SurfaceCurvature &lhs, const ON_SurfaceCurvature &rhs)
	Compare lhs.MinimumRadius() and rhs.MinimumRadius(). Values with nans sort last. More...

static const ON_SurfaceCurvature	CreateFromGaussianAndMeanCurvatures (double gaussian_curvature, double mean_curvature)
	Create an ON_SurfaceCurvature from a gaussian and mean curvature values using the relationsip between the principal curvatures, gaussian and mean. k1 = mean + sqrt(meanmean - gaussian) k2 = mean - sqrt(meanmean - gaussian) If the radicand is negative, we assume we're dealing with a bit of numerical noise or estimates and set the principal curvatures k1 = k2 = sign(mean)*sqrt(gaussian) More...

static const ON_SurfaceCurvature	CreateFromPrincipalCurvatures (double k1, double k2)
	Create an ON_SurfaceCurvature from the principal curvature values. The principal curvature values are the most fundamental curvature properties of a surface. Other curvatures are calculated from them. For example gaussian curvature = k1 * k2 and mean curvature = (k1 + k2)/2. More...

Public Attributes
double	k1

double	k2
	principal curvatures More...

Static Public Attributes
static const double	InfinteRadius
	Value used to indicate a radius of curvature is infinite (1e300). More...

static const ON_SurfaceCurvature	Nan
	k1 = k2 = ON_DBL_QNAN More...

static const ON_SurfaceCurvature	Zero
	k1 = k2 = 0 More...

Detailed Description

ON_SurfaceCurvature

Member Function Documentation

◆ Compare()

static int ON_SurfaceCurvature::Compare	(	const ON_SurfaceCurvature &	lhs,
		const ON_SurfaceCurvature &	rhs
	)

static

Dictionary compare k1 and k2. Values with nans sort last.

Parameters

lhs
rhs

Returns: -1, 0 or +1.

◆ CompareGaussianCurvature()

static int ON_SurfaceCurvature::CompareGaussianCurvature	(	const ON_SurfaceCurvature &	lhs,
		const ON_SurfaceCurvature &	rhs
	)

static

Compare lhs.GaussianCurvature() and rhs.GaussianCurvature(). Values with nans sort last.

Parameters

lhs
rhs

Returns: -1, 0 or +1.

◆ CompareMaximumAndMinimumPrincipalCurvatures()

static int ON_SurfaceCurvature::CompareMaximumAndMinimumPrincipalCurvatures	(	const ON_SurfaceCurvature &	lhs,
		const ON_SurfaceCurvature &	rhs
	)

static

Dictionary compare lhs.MaximumPrincipalCurvature() and rhs.MaximumPrincipalCurvature(). Values with nans sort last.

Parameters

lhs
rhs

Returns: -1, 0 or +1.

◆ CompareMaximumPrincipalCurvature()

static int ON_SurfaceCurvature::CompareMaximumPrincipalCurvature	(	const ON_SurfaceCurvature &	lhs,
		const ON_SurfaceCurvature &	rhs
	)

static

Compare lhs.MaximumPrincipalCurvature() and rhs.MaximumPrincipalCurvature(). Values with nans sort last.

Parameters

lhs
rhs

Returns: -1, 0 or +1.

◆ CompareMaximumRadius()

static int ON_SurfaceCurvature::CompareMaximumRadius	(	const ON_SurfaceCurvature &	lhs,
		const ON_SurfaceCurvature &	rhs
	)

static

Compare lhs.MaximumRadius() and rhs.MaximumRadius(). Values with nans sort last.

Parameters

lhs
rhs

Returns: -1, 0 or +1.

◆ CompareMeanCurvature()

static int ON_SurfaceCurvature::CompareMeanCurvature	(	const ON_SurfaceCurvature &	lhs,
		const ON_SurfaceCurvature &	rhs
	)

static

Compare lhs.MeanCurvature() and rhs.MeanCurvature(). Values with nans sort last.

Parameters

lhs
rhs

Returns: -1, 0 or +1.

◆ CompareMinimumPrincipalCurvature()

static int ON_SurfaceCurvature::CompareMinimumPrincipalCurvature	(	const ON_SurfaceCurvature &	lhs,
		const ON_SurfaceCurvature &	rhs
	)

static

Compare lhs.MinimumPrincipalCurvature() and rhs.MinimumPrincipalCurvature(). Values with nans sort last.

Parameters

lhs
rhs

Returns: -1, 0 or +1.

◆ CompareMinimumRadius()

static int ON_SurfaceCurvature::CompareMinimumRadius	(	const ON_SurfaceCurvature &	lhs,
		const ON_SurfaceCurvature &	rhs
	)

static

Compare lhs.MinimumRadius() and rhs.MinimumRadius(). Values with nans sort last.

Parameters

lhs
rhs

Returns: -1, 0 or +1.

◆ CreateFromGaussianAndMeanCurvatures()

static const ON_SurfaceCurvature ON_SurfaceCurvature::CreateFromGaussianAndMeanCurvatures	(	double	gaussian_curvature,
		double	mean_curvature
	)

static

Create an ON_SurfaceCurvature from a gaussian and mean curvature values using the relationsip between the principal curvatures, gaussian and mean. k1 = mean + sqrt(mean*mean - gaussian) k2 = mean - sqrt(mean*mean - gaussian) If the radicand is negative, we assume we're dealing with a bit of numerical noise or estimates and set the principal curvatures k1 = k2 = sign(mean)*sqrt(gaussian)

Parameters

gaussian_curvature

Gaussian curvature = k1*k2 (product of principal curvatures).

Parameters

mean_curvature Mean curvature = (k1+k2)/2 (average of principal curvatures).

Returns: A surface curvature with GaussianCurvature() = gaussian_curvature and MeanCurvature() = gaussian_curvature.

◆ CreateFromPrincipalCurvatures()

static const ON_SurfaceCurvature ON_SurfaceCurvature::CreateFromPrincipalCurvatures	(	double	k1,
		double	k2
	)

static

Create an ON_SurfaceCurvature from the principal curvature values. The principal curvature values are the most fundamental curvature properties of a surface. Other curvatures are calculated from them. For example gaussian curvature = k1 * k2 and mean curvature = (k1 + k2)/2.

Parameters

k1
k2

Returns: An ON_SurfaceCurvature with the specified principal curvatures.

◆ FlipSurfaceOrientation()

const ON_SurfaceCurvature ON_SurfaceCurvature::FlipSurfaceOrientation ( ) const

The sign of the principal curvatures are with respect to a choice of surface orientation. This function returns the principal curvatures of the surface with opposite choice of orientation.

Returns: ON_SurfaceCurvature::CreateFromPrincipalCurvatures(-this->k2, -this->k1);

◆ GaussianCurvature()

double ON_SurfaceCurvature::GaussianCurvature ( ) const

The Gaussian curvature is k1*k2.

Returns: If this is set, the Gausian curvature is returned. Otherwise ON_DBL_QNAN is returned.

◆ IsNan()

bool ON_SurfaceCurvature::IsNan ( ) const

Returns: True if either of k1 or k2 is a nan.

◆ IsSet()

bool ON_SurfaceCurvature::IsSet ( ) const

Returns: True if k1 and k2 are both valid finite values.

◆ IsUnset()

bool ON_SurfaceCurvature::IsUnset ( ) const

Returns: True if either of k1 or k2 is not a valid finite value.

◆ IsZero()

bool ON_SurfaceCurvature::IsZero ( ) const

Returns: True if k1 and k2 are both zero.

◆ KappaValue()

double ON_SurfaceCurvature::KappaValue ( ON::curvature_style kappa_style ) const

Calculate one of the four typical curvature values associated with the two principal curvatures and frequently used in false color curvature analysis.

Parameters

kappa_style Specifies which type curvature (Gaussian, mean, ...) value to calculate from the principal curvatures. The Gausian curvature can be positive or negative. The other curvatures are are >= 0. In particular, ON::curvature_style::mean_curvature return fabs(this->MeanCurvature()).

Returns: If kappa_style and the principal curvatures are valid, the specified type of curvature value is returned. Infinte radii are returned as ON_SurfaceCurvature::InfinteRadius. Otherwise ON_DBL_QNAN is returned.

◆ MaximumPrincipalCurvature()

double ON_SurfaceCurvature::MaximumPrincipalCurvature ( ) const

Returns: If this is set, the maximum of k1 and k2 is returned. Otherwise ON_DBL_QNAN is returned.

◆ MaximumRadius()

double ON_SurfaceCurvature::MaximumRadius ( ) const

If a principal curvature value is zero or the principal curvatures have opposite signs, then the maximum radius of curvature is infinite and ON_SurfaceCurvature::InfinteRadius is returned. Otherwise the maximum radius of curvature is 1/min(fabs(k1),fabs(k2)).

Returns: IF k1 and k2 are valid, the maximum radius of curvature is returned. Otherwise ON_DBL_QNAN is returned.

◆ MeanCurvature()

double ON_SurfaceCurvature::MeanCurvature ( ) const

The mean curvature is (k1+k2)/2.

Returns: If this is set, the signed mean curvature is returned. Otherwise ON_DBL_QNAN is returned.

◆ MinimumPrincipalCurvature()

double ON_SurfaceCurvature::MinimumPrincipalCurvature ( ) const

Returns: If this is set, the minimum of k1 and k2. Otherwise ON_DBL_QNAN is returned.

◆ MinimumRadius()

double ON_SurfaceCurvature::MinimumRadius ( ) const

The minimum radius of curvature is 1/max(fabs(k1),fabs(k2)). Infinte radius values are returned as ON_SurfaceCurvature::InfinteRadius.

Returns: Minimum radius of curvature up to a maximum of 1e300. If both k1 and k2 are zero, then 1e300 is returned.

Member Data Documentation

◆ InfinteRadius

const double ON_SurfaceCurvature::InfinteRadius

static

Value used to indicate a radius of curvature is infinite (1e300).

◆ k1

double ON_SurfaceCurvature::k1

◆ k2

double ON_SurfaceCurvature::k2

principal curvatures

◆ Nan

const ON_SurfaceCurvature ON_SurfaceCurvature::Nan

static

k1 = k2 = ON_DBL_QNAN

◆ Zero

const ON_SurfaceCurvature ON_SurfaceCurvature::Zero

static

k1 = k2 = 0

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Function Documentation

◆ Compare()

◆ CompareGaussianCurvature()

◆ CompareMaximumAndMinimumPrincipalCurvatures()

◆ CompareMaximumPrincipalCurvature()

◆ CompareMaximumRadius()

◆ CompareMeanCurvature()

◆ CompareMinimumPrincipalCurvature()

◆ CompareMinimumRadius()

◆ CreateFromGaussianAndMeanCurvatures()

◆ CreateFromPrincipalCurvatures()

◆ FlipSurfaceOrientation()

◆ GaussianCurvature()

◆ IsNan()

◆ IsSet()

◆ IsUnset()

◆ IsZero()

◆ KappaValue()

◆ MaximumPrincipalCurvature()

◆ MaximumRadius()

◆ MeanCurvature()

◆ MinimumPrincipalCurvature()

◆ MinimumRadius()

Member Data Documentation

◆ InfinteRadius

◆ k1

◆ k2

◆ Nan

◆ Zero