2D curve functions

Export of 2D curve functions. More...

Data Structures
struct	CVFAlignment2DResult
struct	CVFAlignmentConfiguration

Functions
cvbres_t	CVFAlignCurves2D (const CVIPointD *Curve, cvbdim_t CurveLength, const CVIPointD *CurveToBeAligned, cvbdim_t CurveToBeAlignedLength, const CVFAlignmentConfiguration &Config, CVFAlignment2DResult &Result)
	Aligns two 2D curves via an iterative closest point method considering consensus correspondence for better shape alignment. More...
cvbres_t	CVFCalculateEnclosedArea (const CVIPointD *Curve, cvbdim_t CurveLength, double *EnclosedArea)
	Calculates the enclosed area of the given curve. More...
cvbres_t	CVFCalculateQuadraticDifferencesToClosestPoint (const CVIPointD *Curve, cvbdim_t CurveLength, const CVIPointD *Points, cvbdim_t PointsLength, double *Differences)
	Calculates the quadratic distance of Points to closest point of given Curve (Points of Curve - Points). More...
cvbres_t	CVFCalculateSignedDifferences (const CVIPointD *Curve, cvbdim_t CurveLength, const CVIPointD *Points, cvbdim_t PointsLength, double *SignedDifferences)
	Calculates signed differences along the y axis of given points to curve (Curve - Points). More...
cvbres_t	CVFIntersectCurve2DWithLine (const CVIPointD *Curve, cvbdim_t CurveLength, CVIPointD Normal, double DistanceToOrigin, cvbdim_t IntersectionPointsLength, CVIPointD *IntersectionPoints, cvbdim_t &IntersectionPointsCalculatedLength)
	Intersects a 2D curve with a line. More...
cvbres_t	CVFMerge2Curves (const CVIPointD *CurveLHS, cvbdim_t CurveLengthLHS, const CVIPointD *CurveRHS, cvbdim_t CurveLengthRHS, cvbbool_t sort, cvbdim_t CurveOutAllocatedLength, CVIPointD *CurveOut, cvbdim_t &CurveOutLength)
	Merges two curves into one curve with interpolation. More...
cvbres_t	CVFResampleCurve2D (const CVIPointD *Curve, cvbdim_t CurveLength, cvbdim_t ResampledCurveLength, CVIPointD *ResampledCurve)
	Resamples a 2-dimensional curve via linear interpolation assuming that the "speed" of the time mapping is constant. More...

Detailed Description

Export of 2D curve functions.

Function Documentation

CVFAlignCurves2D()

cvbres_t CVFAlignCurves2D	(	const CVIPointD *	Curve,
		cvbdim_t	CurveLength,
		const CVIPointD *	CurveToBeAligned,
		cvbdim_t	CurveToBeAlignedLength,
		const CVFAlignmentConfiguration &	Config,
		CVFAlignment2DResult &	Result
	)

Aligns two 2D curves via an iterative closest point method considering consensus correspondence for better shape alignment.

The method used here is a version of the ICP (iterative closest point) method. It uses a consensus metric to find the correspondence between points to stabilize the iterations needed in the alignment method. It supports only rigid transformations for the alignment. If not enough points within a given consens are found a classical ICP step is performed by finding correspondences solely based on nearest neighbours without any feasibility check.

Attention

Memory of size CurveLength*sizeof(CVIPointD) bytes has to be allocated by the caller for Curve! Same for CurveToBeAligned and CurveToBeAlignedLength.

Parameters

[in]	Curve	Reference curve.
[in]	CurveLength	Length of Curve.
[in]	CurveToBeAligned	Curve to be aligned to Curve.
[in]	CurveToBeAlignedLength	Length of CurveToBeAligned.
[in]	Config	Configuration of alignment.
[out]	Result	Alignment result.

Returns

• CVC_ERROR(CVC_E_OK) on success
• CVC_ERROR(CVC_E_INVALIDDIMENSION) if CurveLength and/or CurveToBeAlignedLength is invalid

CVFCalculateEnclosedArea()

cvbres_t CVFCalculateEnclosedArea	(	const CVIPointD *	Curve,
		cvbdim_t	CurveLength,
		double *	EnclosedArea
	)

Calculates the enclosed area of the given curve.

Uses the shoelace algorithm to calculate the enclosed area of the given curve. All points are assumed to be in order, clockwise or anticlockwise will not affect the outcome. This algorithm can only handle not self intersecting curves, e.g. a figure eight curve will not work with this algorithm.

For numerical stabilization all points are shifted to be centered around the origin.

If the curve is not closed, i.e. the first and last point in the given point set don't match, the curve is closed automatically by connecting the first and last point.

Note

The points on the curve are evaluated in the order in which they are listed. We assume an ordered point set (not ordered by axis, but ordered according to the curve).

Parameters

[in]	Curve	Curve.
[in]	CurveLength	Length of Curve.
[out]	EnclosedArea	The enclosed of the given Curve as double.

Returns

• CVC_ERROR(CVC_E_OK) on success
• CVC_ERROR(CVC_E_NOTENOUGHDATA) if Curve contains less than 2 points.

CVFCalculateQuadraticDifferencesToClosestPoint()

cvbres_t CVFCalculateQuadraticDifferencesToClosestPoint	(	const CVIPointD *	Curve,
		cvbdim_t	CurveLength,
		const CVIPointD *	Points,
		cvbdim_t	PointsLength,
		double *	Differences
	)

Calculates the quadratic distance of Points to closest point of given Curve (Points of Curve - Points).

Note

The points have to be ordered by time, i.e. two consecutive points must adjoin another on the curve.

For the calculation of the signed differences the curve is assumed to be infinite. It is extended at the starting and endpoint.

Attention

Memory of size PointsLength*sizeof(double) bytes has to be allocated by the caller for Differences!

Parameters

[in]	Curve	Curve.
[in]	CurveLength	Length of Curve.
[in]	Points	Points.
[in]	PointsLength	Length of Points.
[out]	Differences	Array of length PointsLength to receive differences.

Returns

• CVC_ERROR(CVC_E_OK) on success
• CVC_ERROR(CVC_E_NOTENOUGHDATA) if Curve contains less than 2 points.

CVFCalculateSignedDifferences()

cvbres_t CVFCalculateSignedDifferences	(	const CVIPointD *	Curve,
		cvbdim_t	CurveLength,
		const CVIPointD *	Points,
		cvbdim_t	PointsLength,
		double *	SignedDifferences
	)

Calculates signed differences along the y axis of given points to curve (Curve - Points).

Note

The points have to be ordered by time, i.e. two consecutive points must adjoin another on the curve.

For the calculation of the signed differences the curve is assumed to be infinite. It is extended at the starting and endpoint.

Attention

Memory of size PointsLength*sizeof(double) bytes has to be allocated by the caller for SignedDifferences!

Parameters

[in]	Curve	Curve.
[in]	CurveLength	Length of Curve.
[in]	Points	Points.
[in]	PointsLength	Length of Points.
[out]	SignedDifferences	Array of length PointsLength to receive signed differences.

Returns

• CVC_ERROR(CVC_E_OK) on success
• CVC_ERROR(CVC_E_NOTENOUGHDATA) if Curve contains less than 2 points.

CVFIntersectCurve2DWithLine()

cvbres_t CVFIntersectCurve2DWithLine	(	const CVIPointD *	Curve,
		cvbdim_t	CurveLength,
		CVIPointD	Normal,
		double	DistanceToOrigin,
		cvbdim_t	IntersectionPointsLength,
		CVIPointD *	IntersectionPoints,
		cvbdim_t &	IntersectionPointsCalculatedLength
	)

Intersects a 2D curve with a line.

The line is defined by the hessian normal form:

normal* x = d, with | Normal | = 1 and d > 0.

Note

The points have to be ordered by time, i.e. two consecutive points must adjoin another on the curve.

The curve is finite. It starts and ends at the first and last point respectively.

Attention

Memory of size CurveLength*sizeof(CVIPointD) bytes has to be allocated by the caller for IntersectionPoints. The number of intersection points IntersectionPointsLength will be calculated with this function and will be lower than CurveLength.

Parameters

[in]	Curve	Curve to be intersected.
[in]	CurveLength	Length of Curve.
[in]	Normal	Normal of line (Hessian normal form).
[in]	DistanceToOrigin	Distance of line to origin (Hessian normal form).
[in]	IntersectionPointsLength	Length of IntersetionPoints allocated by the caller.
[out]	IntersectionPoints	Array which receives calculated intersection points.
[out]	IntersectionPointsCalculatedLength	Number of calculated intersection points.

Returns

• CVC_ERROR(CVC_E_OK) on success
• CVC_ERROR(CVC_E_INVALIDDIMENSION) if not enough memory was allocated for intersection points
• CVC_ERROR(CVC_E_NOTENOUGHDATA) if Curve contains less than 2 points

CVFMerge2Curves()

cvbres_t CVFMerge2Curves	(	const CVIPointD *	CurveLHS,
		cvbdim_t	CurveLengthLHS,
		const CVIPointD *	CurveRHS,
		cvbdim_t	CurveLengthRHS,
		cvbbool_t	sort,
		cvbdim_t	CurveOutAllocatedLength,
		CVIPointD *	CurveOut,
		cvbdim_t &	CurveOutLength
	)

Merges two curves into one curve with interpolation.

Takes two curves and merges them into one combined curve. If they overlap, an interpolation method is used to find a suitable approximation. This interpolation is done when switching between the two curves while the points are interleaved. The order in which the points are interleaved is defined by the closest neighbour for each point from CurveRHS to CurveLHS.

This method works with curves in 2D.

If sort is set true, then the best starting point of the two possible starting points (each of the given curve statrint points is a valid choice). This means, the algorithm checks which starting point from the two staring points is the best starting point for the merged curve. To make this decision the distance from each possible starting point to the other given curve is calculated and the point with the highest distance is taken as the overall starting point for the new generated merged curve. This method does work well for regular curves (not self intercepting curves). It can be switched off to save computation time if the caller is sure about the correct order.

Note

The points on the curve are evaluated in the order in which they are listed. We assume an ordered point set (not ordered by axis, but ordered according to the curve).

Parameters

[in]	CurveLHS	Left hand side curve. This curve is assumed starting point if sort is false.
[in]	CurveLengthLHS	Length of CurveLHS.
[in]	CurveRHS	right hand side curve
[in]	CurveLengthRHS	Length of CurveRHS
[in]	sort	Boolean to decide if left and right order of the two curves is to be found by the algorithm.
[in]	CurveOutAllocatedLength	Length of CurveOut allocated by the caller. The maximum possible length of a merged curve is the sum of lengths of both input curves, the minimum length is the maximum length of both input curves.
[out]	CurveOut	Merged curve
[out]	CurveOutLength	length of the merged curve

Returns

• CVC_ERROR(CVC_E_OK) on success
• CVC_ERROR(CVC_E_INVALIDDIMENSION) if any input curve Curve contains less than 1 point or the allocated space for output curve was too small.
• CVC_ERROR(CVC_E_PARAMETER) if any of the input curves or the output is a nullptr.

CVFResampleCurve2D()

cvbres_t CVFResampleCurve2D	(	const CVIPointD *	Curve,
		cvbdim_t	CurveLength,
		cvbdim_t	ResampledCurveLength,
		CVIPointD *	ResampledCurve
	)

Resamples a 2-dimensional curve via linear interpolation assuming that the "speed" of the time mapping is constant.

Note

The points have to be ordered by time, i.e. two consecutive points must adjoin another on the curve.

Attention

Memory of size ResampledCurveLength*sizeof(CVIPointD) bytes has to be allocated by the caller for ResampledCurve!

Parameters

[in]	Curve	Curve to be resampled.
[in]	CurveLength	Length of Curve.
[in]	ResampledCurveLength	Length of ResampledCurve.
[out]	ResampledCurve	Array of length ResampledCurveLength to receive resampled curve.

Returns

• CVC_ERROR(CVC_E_OK) on success
• CVC_ERROR(CVC_E_INVALIDDIMENSION) if CurveLength and/or ResampledCurveLength is invalid