Macros
#define	mindiffangle_int(a, b, modulo)
	Minimum Absolute Difference between Two Angles, Fix Point (Macro). More...

Functions
F32	Norm (point *a)
	Calculates the Euclidean Length of a Vector. More...

F32	AngleP (point *v)
	Calculates the Angle of a Vector. More...

F32	PointDistance (point a, point b)
	Calculates the Euclidean Distance between Two Points. More...

void	MidPoint (point a, point b, point *out)
	Calculates the Middle between Two Points. More...

void	VectorDifference (point a, point b, point *out)
	Calculates the Vector Difference of Two Points. More...

void	VectorScale (point a, F32 scalar, point out)
	Scales a Vector by a Value. More...

void	VectorSum (point a, point b, point *out)
	Calculates the Vector Sum of Two Points. More...

I32	LineIntersection (vcline a, vcline b, point *out)
	Calculates the Intersection Point of Two Lines. More...

F32	LineAngle (vcline a, vcline b)
	Calculates the Angle between Two Lines. More...

F32	LineAngle2 (vcline a, vcline b)
	Calculates the Angle between Two Lines. More...

F32	Angle (vcline *a)
	Calculates the Angle of a Line. More...

void	LineParallelD (F32 dist, vcline l, vcline out)
	Calculates the Line Parallel to `l` at Distance `dist`. More...

F32	PointLineDistance (point p, vcline l)
	Calculates the Distance beween a Point and a Line. More...

void	PointLineProjection (point p, vcline l, point *out)
	Maps Point to nearest Point on Line. More...

void	LinePerpendicular (point p, vcline l, vcline *out)
	Calculates a Line perpendicualar to a given One through a Point. More...

void	LineParallel (point p, vcline l, vcline *out)
	Calculates a Line parallel to a given One through a Point. More...

void	LineTranslate (point v, vcline l, vcline *out)
	Translates a Line parallel by a Vector. More...

void	LineParameters (point p1, point p2, vcline *out)
	Calculates the Line Parameters using Two Points. More...

void	LineParametersA (point p, F32 angle, vcline out)
	Calculates the Line Parameters using a point and an angle. More...

void	LineFromSlopeInterceptForm (F32 mx, F32 b, vcline *out)
	Calculates a vcline from Line Slope Intercept Form. More...

void	LineNormal (point p, F32 angle, vcline out)
	Calculates the line through the point `p` perpendicular to `angle`. More...

void	affine_point_map (point p, point target_p, F32 a[2][2], F32 t[2])
	Affine Transformation of a Point. More...

I32	IntersectionPointsN (image img, vcline ln, point p1, point p2)
	Calculates Two Intersection Points between a Line and the Boundaries of an Image Variable. More...

I32	IntersectionPoints (image a, F32 cx, F32 cy, F32 b, I32 X0, I32 Y0, I32 X1, I32 *Y1)
	Calculates Two Intersection Points between a Line and the Boundaries of an Image Variable. More...

I32	IntersectionPointsWithRect (F32 cx, F32 cy, F32 b, F32 xMin, F32 yMin, F32 xMax, F32 yMax, F32 X0, F32 Y0, F32 X1, F32 Y1)
	Calculates Two Intersection Points between a Line and a Boundary Rectangle. More...

Detailed Description

Macro Definition Documentation

◆ mindiffangle_int

#define mindiffangle_int	(	a,
		b,
		modulo
	)

Value:

( \
    ((a)-(b)<0)\
        ?( min( (modulo) + ((a)-(b)) % (modulo),             (((b)-(a)) % (modulo)) )) \
        :( min(            ((a)-(b)) % (modulo),  (modulo) + (((b)-(a)) % (modulo)) )) \
   )

The minimum absolute difference between the both given angles is returned modulo the given modulo parameter.

Note: All Parameters must be fix point. Floating point would not work!

Parameters

a,b	angles as integer values.
modulo	modulo as an integer value.

Function Documentation

◆ Norm()

F32 Norm ( point * a )

This function calculates the norm or length of a vector in point representation and returns the result as a float value. The result is given by out = sqrtf(( a->x)² + ( a->y)²).

Returns: the euclidean norm or distance

◆ AngleP()

F32 AngleP ( point * v )

This function calculates the angle between the horizontal x-axis and the vector v given in point coordinates and returns the result in radiants.

A value of 0 is output for a horizontal vector pointing right. The result increases for a clockwise rotation up to a value of 2π (360deg) and is always positive.

Returns: angle between x-axis and vector

◆ PointDistance()

F32 PointDistance	(	point *	a,
		point *	b
	)

The function calculates the Euclidean distance between two points and returns the result.

◆ MidPoint()

void MidPoint	(	point *	a,
		point *	b,
		point *	out
	)

The function uses 2 points a and b to calculate the arithmetic middle right inbetween the points and outputs the result in point out.

It is possible to use this function in place, i.e. the pointer out may be identical to either a or b.

◆ VectorDifference()

void VectorDifference	(	point *	a,
		point *	b,
		point *	out
	)

The function calculates the vector difference of two points and returns the result out = a - b.

It is possible to use this function in place, i.e. the pointer out may be identical to either a or b.

◆ VectorScale()

void VectorScale	(	point *	a,
		F32	scale,
		point *	out
	)

The function calculates the vector scaled by a given value and returns the result out = a * scale.

It is possible to use this function in place, i.e. the pointer out may be identical to in.

◆ VectorSum()

void VectorSum	(	point *	a,
		point *	b,
		point *	out
	)

The function calculates the vector sum of two points and returns the result out = a + b.

It is possible to use this function in place, i.e. the pointer out may be identical to either a or b.

◆ LineIntersection()

I32 LineIntersection	(	vcline *	a,
		vcline *	b,
		point *	out
	)

This function finds the intersection point of 2 lines given in the standard normal form $ cx * x + cy * y - b = 0 $ .

Return values

ERR_SINGULAR	If Lines are Parallel.
ERR_NONE	On Success.

◆ LineAngle()

F32 LineAngle	(	vcline *	a,
		vcline *	b
	)

This function calculates the angle between two lines a and b given in vector normal form and returns the result in radiants: A value of 0 is output if both lines are parallel. In all other cases, the result is the angle that line a must be rotated clockwise to be parallel to b. The result increases for a clockwise rotation up to a value of π (180deg) and is always positive.

Returns: angle between line a and line b

◆ LineAngle2()

F32 LineAngle2	(	vcline *	a,
		vcline *	b
	)

This function calculates the angle between two lines a and b and returns the result in radiants. A value of 0 is output if both lines are parallel. In all other cases, the result is the angle that line a must be rotated clockwise to be parallel to b. In contrast to function LineAngle(), the result covers a full range from -π (-180deg) to +π (180deg) and assumes that the lines are oriented.

◆ Angle()

F32 Angle ( vcline * a )

This function calculates the angle between the horizontal x-axis and line a given in vector normal form and returns the result in radiants. A value of 0 is output for a horizontal line. The result increases for a clockwise rotation up to a value of π (180deg) and is always positive.

Returns: angle between x-axis and line

◆ LineParallelD()

void LineParallelD	(	F32	dist,
		vcline *	l,
		vcline *	out
	)

calculates the line parallel to l at distance dist larger dist means that the line is more distant to the origin.

It is possible to use this function in place, i.e. the pointer l may be identical to out.

Parameters

dist	distance for parallel line
l	reference line
out	result line

◆ PointLineDistance()

F32 PointLineDistance	(	point *	p,
		vcline *	l
	)

This function calculates the distance beween a point and a line and returns the result.

◆ PointLineProjection()

void PointLineProjection	(	point *	p,
		vcline *	l,
		point *	out
	)

This function maps a point to a nearest point on a line. Nearest means: The euclidean distance between the points is minimal.

◆ LinePerpendicular()

void LinePerpendicular	(	point *	p,
		vcline *	l,
		vcline *	out
	)

This function calculates a line perpendicualar to a given one through a point. The result is stored in out.

It is possible to use this function in place, i.e. the pointer l may be identical to out.

◆ LineParallel()

void LineParallel	(	point *	p,
		vcline *	l,
		vcline *	out
	)

This function calculates a line parallel to a given one through a point. The result is stored as out.

It is possible to use this function in place, i.e. the pointer l may be identical to out.

◆ LineTranslate()

void LineTranslate	(	point *	v,
		vcline *	l,
		vcline *	out
	)

This function translates a line by a vector given. The result is stored as out.

The line parameters cx and cy must form a vector of norm 1 for this function to work properly.

It is possible to use this function in place, i.e. the pointer l may be identical to out.

◆ LineParameters()

void LineParameters	(	point *	p1,
		point *	p2,
		vcline *	out
	)

This function calculates the line parameters for a line running through the two points p1 and p2. If the two points are too close together, (distance < 5.0e-7), all line parameters will be set to 0.0.

◆ LineParametersA()

void LineParametersA	(	point *	p,
		F32	angle,
		vcline *	out
	)

This function calculates the line through the point p with angle angle

Parameters

p	point for line calculation
angle	angle for line calculation, in degree
out	result line

◆ LineFromSlopeInterceptForm()

void LineFromSlopeInterceptForm	(	F32	mx,
		F32	b,
		vcline *	out
	)

The function transforms a line representation in slope intercept form known as: y = mx * x + b to the more universial representation used by vcline: out->cx * x + out->cy * y - out->b = 0.

Parameters

mx,b	Slope Intercept Representation of Line.
out	Line in Normal Form.

◆ LineNormal()

void LineNormal	(	point *	p,
		F32	angle,
		vcline *	out
	)

This function calculates the line through the point p NORMAL, i.e. perpendicular to angle

Parameters

p	point for line calculation
angle	angle for line calculation, in degree
out	result line

◆ affine_point_map()

void affine_point_map	(	point *	p,
		point *	target_p,
		F32	a[2][2],
		F32	t[2]
	)

Parameters

p	Point in Original Image (x, y).
target_p	(Result) Target Point of `p` After Affine Transformation.
a	2D Transformation Matrix.
t	2D Translation Vector.

◆ IntersectionPointsN()

I32 IntersectionPointsN	(	image *	img,
		vcline *	ln,
		point *	p1,
		point *	p2
	)

This function calculates two intersection points between a line and the boundaries of an image variable given. The intersection points are calculated in the following order: Left, Right, Top, Bottom. The line is parameterized as vcline struct.

Parameters

img	Pointer to Image Variable.
ln	Line.
p1	Coordinates of First Intersection Point.
p2	Coordinates of Second Intersection Point.

See also: IntersectionPoints().

Return values

ERR_PARAM	If Less than 2 Points Found.
ERR_NONE	On Success.

◆ IntersectionPoints()

I32 IntersectionPoints	(	image *	a,
		float	cx,
		float	cy,
		float	b,
		I32 *	X0,
		I32 *	Y0,
		I32 *	X1,
		I32 *	Y1
	)

This function calculates two intersection points between a line and the boundaries of an image variable given. The intersection points are calculated in the following order: Left, Right, Top, Bottom. The line is parameterized in a normalized vector form as: (cx * x) + (cy * y) - b = 0.

Parameters

a	Pointer to Image Variable.
cx,cy,b	Line Parameters.
X0,Y0	Coordinates of First Intersection Point.
X1,Y1	Coordinates of Second Intersection Point.

See also: IntersectionPointsN(), IntersectionPointsWithRect().

Return values

ERR_PARAM	If Less than 2 Points Found.
ERR_NONE	On Success.

◆ IntersectionPointsWithRect()

I32 IntersectionPointsWithRect	(	float	cx,
		float	cy,
		float	b,
		F32	xMin,
		F32	yMin,
		F32	xMax,
		F32	yMax,
		F32 *	X0,
		F32 *	Y0,
		F32 *	X1,
		F32 *	Y1
	)

This function calculates two intersection points between a line and a boundary rectangle. The intersection points are calculated in the following order: Left, Right, Top, Bottom. The line is parameterized in a normalized vector form as: (cx * x) + (cy * y) - b = 0.

Parameters

xMin,yMin,xMax,yMax	Boundary rectangle.
cx,cy,b	Line Parameters.
X0,Y0	Coordinates of First Intersection Point.
X1,Y1	Coordinates of Second Intersection Point.

See also: IntersectionPoints(), IntersectionPointsN().

Return values

ERR_PARAM	If Less than 2 Points Found.
ERR_NONE	On Success.

Geometry Functions

Macros

Functions

Detailed Description

Macro Definition Documentation

◆ mindiffangle_int

Function Documentation

◆ Norm()

◆ AngleP()

◆ PointDistance()

◆ MidPoint()

◆ VectorDifference()

◆ VectorScale()

◆ VectorSum()

◆ LineIntersection()

◆ LineAngle()

◆ LineAngle2()

◆ Angle()

◆ LineParallelD()

◆ PointLineDistance()

◆ PointLineProjection()

◆ LinePerpendicular()

◆ LineParallel()

◆ LineTranslate()

◆ LineParameters()

◆ LineParametersA()

◆ LineFromSlopeInterceptForm()

◆ LineNormal()

◆ affine_point_map()

◆ IntersectionPointsN()

◆ IntersectionPoints()

◆ IntersectionPointsWithRect()