#include <heightfield.h>

Inheritance diagram for HeightFieldErosion:

Public Member Functions
	HeightFieldErosion (const HeightField &)
	Setup erosion using a heightfield.

void	HillSlope (double, double=1.0)
	Hillslope erosion.

void	DebrisSlope (double, double=1.0)
	Debris slope erosion.

void	StreamPowerErosion (double=0.0005, double=0.01, double=2., double=0.8, double=100.)
	Stream power erosion.

void	StreamPowerErosion (double, const ScalarField2 &, double=2., double=0.8, double=100.)
	Stream power erosion.

void	HillSlope (double, double, double, double)
	Hillslope erosion with constrained range.

void	DebrisSlope (double, double, double, double)
	Debris slope erosion with constrained range.

Public Member Functions inherited from HeightField
	HeightField ()
	Empty.

	HeightField (const ScalarField2 &)
	Create a heightfield from a scalar field.

	HeightField (const Box2 &, const QImage &, const double &=0.0, const double &=256.0 *256.0 - 1.0, bool=true)
	Create a heightfield from an image.

	HeightField (const Box2 &, int, int, const double &=0.0)
	Create a flat heightfield.

	HeightField (const Box2 &, int, int, const QVector< double > &)
	Create a heightfield.

	~HeightField ()
	Empty.

double	GetHeight (const Vector2 &) const
	Compute the height at a given position.

Vector	Vertex (const Vector2 &, bool=true) const
	Compute the vertex position on the terrain.

Vector	Vertex (int, int) const
	Compute the vertex corresponding to a given sample.

QVector< Vector >	ArrayVertexes (const QVector< QPoint > &) const
	Compute the coordinates of a set of points on the grid.

Vector	Normal (const Vector2 &, bool=true) const
	Compute the normal for a given position on the terrain.

Vector	Normal (int, int) const
	Compute the normal at a given sample.

double	Slope (int, int) const
	Compute the slope at a given integer point on the terrain.

double	Slope (const QPoint &, const QPoint &) const
	Compute the slope between two points.

double	AverageSlope (int, int) const
	Compute the average slope at a given integer point on the terrain.

double	Aspect (int, int) const
	Compute the aspect (face orientation) at a given integer point on the terrain.

double	K () const
	Compute the Lipschitz constant of the signed distance field defined as f(x,y,z)=z-h(x,y).

void	Subdivide (const double &, Random &=Random::R239)
	Refine the terrain.

ScalarField2	StreamArea (const double &=1.0) const
	Compute the stream area field of the terrain.

ScalarField2	StreamAreaSteepest () const
	Compute the stream area field of the terrain.

ScalarField2	StreamAreaLimited (const double &) const
	Compute the stream area field of the terrain using a limited flow propagation.

ScalarField2	StreamLength (bool=false) const
	Compute the stream length.

ScalarField2	StreamSourceElev (bool=false) const
	Return the maximum source elevation of the flows converging to each point in the height field.

VectorField2	FlowField (ScalarField2 &) const
	Compute the flow field of the terrain.

ScalarField2	AverageSlope () const
	Compute the average slope field of the terrain.

ScalarField2	Slope (bool=false) const
	Compute the maximum slope field of the terrain.

ScalarField2	Aspect () const
	Compute the aspect field (face orientation) of the terrain.

ScalarField2	WetnessIndex (const double &=1.0e-3, bool=false) const
	Compute the wetness index field of the terrain.

ScalarField2	StreamPower (bool=false) const
	Compute the stream power field of the terrain.

ScalarField2	StreamPower (double, double) const
	Compute the stream power field of the terrain.

ScalarField2	ReliefSteepness (const double &) const
	Compute the omni-directional relief and steepness.

ScalarField2	Jut (const double &) const
	Compute the Jut metric.

ScalarField2	Rut (const double &) const
	Compute the Rut metric.

ScalarField2	Peakedness (const double &) const
	Compute the peakedness of a terrain, defined as the percentage of cells in a disk that have lower or equal elevation than the center position.

ScalarField2	TopographicPositionIndex (const double &r) const
	Compute the TPI, an index that measures how much a cell rises with respect to the mean elevation of a given radius. It is very similar in spirit to Peakedness, but here we obtain a value in m instead of the % of cells below it.

ScalarField2	TopographicPositionIndex_SAT (const double &r) const
	Compute the TPI, an index that measures how much a cell rises with respect to the mean elevation of a given radius. It is very similar in spirit to Peakedness, but here we obtain a value in m instead of the % of cells below it.

ScalarField2	TerrainRuggednessIndex (int=3, bool=false) const
	Compute the Terrain Ruggedness Index.

ScalarField2	LocalVariance (int=3) const
	Compute the local variance.

ScalarField2	LocalRange (int=3) const
	Compute the local range.

ScalarField2	AreaRatio (int=3) const
	Compute the surface to planar ratio of areas, a measure of terrain ruggedness.

ScalarField2	SurfaceRoughness (int=3) const
	Compute the surface roughness.

ScalarField2	HillslopeAsymmetry (double, double=0, double=45) const
	Compute the hillslope asymmetry map for a given direction.

ScalarField2	Accessibility (const double &, int=16) const
	Compute the accessibility.

ScalarField2	ClearSky (const double &r, int n) const
	Compute the clear sky.

ScalarField2	Light (const Vector &, bool=false) const
	Compute the direct lighting.

double	FractLaplacian (int x, int y, double s, int n) const
	Fractionnal Laplacian.

ScalarField2	FractLaplacian (double s, int n) const
	Fractionnal Laplacian.

int	FillDepressions ()
	Fills all pits and removes all digital dams from the HeightField.

int	FillDepressions (const double &)
	Modifies the HeightField to guarantee drainage.

int	FillDepressions (ScalarField2 &) const
	Fills all pits and removes all digital dams from the HeightField.

int	FillDepressions (const double &, ScalarField2 &) const
	Modifies the HeightField to guarantee drainage.

void	CompleteBreach ()
	Breach depressions.

bool	Intersect (const Ray &, double &, Vector &) const
	Compute the intersection between a ray and the surface of the terrain.

bool	Intersect (const Ray &, double &, Vector &, const Box &, const double &, const double &=1.0e8, const double &=1.0e-4) const
	Compute the intersection between a ray and the surface of the heightfield.

bool	Intersect (const Ray &, QVector< double > &, QVector< Vector > &, const Box &, const double &) const
	Compute the intersection between a ray and the surface of the heightfield.

bool	IntersectBox (const Ray &, double &, Vector &, Vector &, const Box &) const
	Compute the intersection between a ray and the surface border of the heightfield.

double	Shade (const Vector &, const QVector< Vector > &, const QVector< double > &, const double &) const
	Shade a vector of the terrain.

ScalarField2	Sun (const double &, int=5, int=1, int=0, int=12) const
	Compute the average direct lighting from the sun over a year.

ScalarField2	SelfShadow (const Vector &) const
	Compute the self shadowing map.

Array2I	Flow (bool=false) const
	Compute the flow topology.

Array2I	Geomorphons (const double &=0.02) const
	Compute the geomorphon index map.

Array2I	GeomorphonsTangent (double, double=0.02) const
	Compute the geomorphon index map.

Array2I	GeomorphonsAggregated (const double &=0.02) const
	Compute the aggregated geomorphon index map.

Box	GetBox () const
	Get the bounding box of the heightfield.

double	Signed (const Vector &) const
	Compute the signed distance do the heightfield.

void	Scale (const Vector &)
	Scale the height field.

void	Scale (const double &)
	Uniform scaling.

void	Unity ()
	Scale the heightfield so that the compact support should fit within unit box.

void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a heightfield.

QVector< QPoint >	Up (int, int) const
	Compute the cells that are uphill of input point.

QVector< QPoint >	Down (int, int) const
	Compute the cells that are downhill of input point.

int	CheckFlowSlope (const QPoint &, FlowStruct &, const double &=1.0) const
	Compute the flow directions at a given point, using an L² metric.

int	CheckFlowDirectionsAngle (const QPoint &, const double &, FlowStruct &) const
	Compute the flow directions at a given point.

Mesh	CreateMesh (bool=true, bool=false, const double &=0.0) const
	Create the geometry of the heightfield.

Mesh	CreateMeshSide (const double &=0.0) const
	Create the geometry of the border of the terrain.

void	CreateCubes (Box &, QVector< FrameScaled > &, const double &=-10.0) const
	Create a stack representation of the model.

void	Carve (const CubicCurve &, const double &, const double &)
	Carve the terrain using a cubic curve, whose elevation define the prescribed elevation along the curve.

void	Carve (const QuadricCurve &, const double &, const double &)
	Carve the terrain using a quadric curve, whose elevation define the prescribed elevation along the curve.

void	Carve (const CubicCurveSet &, const double &, const double &)
	Carve the terrain using a piecewise cubic curve, whose elevation define the prescribed elevation along the curve.

void	Carve (const QuadricCurveSet &, const double &, const double &)
	Carve the terrain using a piecewise quadric curve, whose elevation define the prescribed elevation along the curve.

void	Carve (const Segment &, const double &, const double &)
	Carve the terrain using a segment, whose elevation define the prescribed elevation along the curve.

void	Carve (const SmoothDisc2 &, const double &)
	Flatten the scalar field.

ScalarField2	GradientDistance (const HeightField &) const
	Compute the gradient distance between two heightfields.

ScalarField2	Sea (const double &=0.0) const
	Compute the water elevation in every cell according to a uniform sea level.

QVector< double >	Cross (const Vector2 &, const Vector2 &, int) const
	Compute the elevation along a segment.

void	SmoothBreachMultiScale (const QVector< int > &)
	Smooth breaching with a given input series.

void	SmoothBreachGeometric (double, double)
	Smooth breaching with a geometric series.

void	SmoothBreachLinear (double)
	Smooth breaching process.

void	LowErosionMultiScale (const QVector< double > &, const QVector< double > &)
	Preparametered multi-scale medium scale erosion. Similar capacity limited erosion/deposition to Mei [2007], but with drainage-like flow routing instead of shallow water.

void	LowErosionGeometric (double, double, double, double)
	Preparametered multi-scale medium scale erosion. Similar capacity limited erosion/deposition to Mei [2007], but with drainage-like flow routing instead of shallow water.

void	StabilizeSlope (double, double, int max_iter=200)
	Apply a parralelizable version of a thermal erosion (aka slope stabilization).

QString	EncodeSize () const
	Code the size and range parameters of the heightfield into a string.

Additional Inherited Members
Static Public Member Functions inherited from HeightField
static Box	Size (const QString &)
	Compute the box of the heightfield from a string.

Static Public Attributes inherited from HeightField
static const double	flat = 1.0e-8
	Small negative epsilon value used in breaching and flow algorithms.

Detailed Description

Erosion.

Constructor & Destructor Documentation

◆ HeightFieldErosion()

HeightFieldErosion::HeightFieldErosion ( const HeightField & h )

explicit

Setup erosion using a heightfield.

Parameters

h	Heightfield

Member Function Documentation

◆ DebrisSlope() [1/2]

void HeightFieldErosion::DebrisSlope	(	double	k,
		double	t,
		double	a,
		double	b )

Debris slope erosion with constrained range.

Parameters

k	Erosion coefficient.
t	Time step.
a,b	Slope range for cropping values.

◆ DebrisSlope() [2/2]

void HeightFieldErosion::DebrisSlope	(	double	k,
		double	t = 1.0 )

Debris slope erosion.

Compute debris slope erosion using \( h=h- k t \Nabla h \).

Parameters

k	Erosion coefficient.
t	Time step.

◆ HillSlope() [1/2]

void HeightFieldErosion::HillSlope	(	double	k,
		double	t,
		double	a,
		double	b )

Hillslope erosion with constrained range.

Parameters

k	Erosion coefficient.
t	Time step.
a,b	Laplacian range for cropping values.

◆ HillSlope() [2/2]

void HeightFieldErosion::HillSlope	(	double	k,
		double	t = 1.0 )

Hillslope erosion.

Compute hill slope erosion using \( h=h- k t \Delta h \).

Parameters

k	Erosion coefficient.
t	Time step.

◆ StreamPowerErosion() [1/2]

void HeightFieldErosion::StreamPowerErosion	(	double	k,
		const ScalarField2 &	u,
		double	p_sl = 2.,
		double	p_sa = 0.8,
		double	t = 100. )

Stream power erosion.

Parameters

k	Erosion coefficient.
u	Uplift map.
p_sl,p_sa	Slope and area exponents in the Stream Power computation.
t	Time step.

◆ StreamPowerErosion() [2/2]

void HeightFieldErosion::StreamPowerErosion	(	double	k = 0.0005,
		double	u = 0.01,
		double	p_sl = 2.,
		double	p_sa = 0.8,
		double	t = 100. )

Stream power erosion.

Parameters

k	Erosion coefficient.
u	Uplift constant value.
p_sl,p_sa	Slope and area exponents in the Stream Power computation.
t	Time step.

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ HeightFieldErosion()

Member Function Documentation

◆ DebrisSlope() [1/2]

◆ DebrisSlope() [2/2]

◆ HillSlope() [1/2]

◆ HillSlope() [2/2]

◆ StreamPowerErosion() [1/2]

◆ StreamPowerErosion() [2/2]