Geometric utilities for 2D points and segments. More...

Functions
const Geom_Number	area_of_parallelogram (const Point &a, const Point &b, const Point &c)
	Compute signed area of parallelogram formed by three points.

const Geom_Number	area_of_triangle (const Point &a, const Point &b, const Point &c)
	Compute area of triangle formed by three points.

const bool	points_are_colinear (const Point &a, const Point &b, const Point &c)
	Test if three points are collinear.

const bool	c_is_to_left_ (const Point &a, const Point &b, const Point &c)
	Test if point c is strictly left of line a→b.

const bool	is_clockwise (const Point &a, const Point &b, const Point &c)
	Test if points are in clockwise order.

const bool	left_on (const Point &a, const Point &b, const Point &c)
	Test if point c is left of or on line a→b.

const bool	proper_intersection (const Point &a, const Point &b, const Point &c, const Point &d)
	Test for proper segment intersection.

const bool	between (const Point &a, const Point &b, const Point &c)
	Test if point c is between points a and b.

const bool	intersect_improp (const Point &a, const Point &b, const Point &c, const Point &d)
	Test for improper (endpoint) segment intersection.

const bool	intersectp (const Point &a, const Point &b, const Point &c, const Point &d)
	Test if two segments intersect (proper or improper).

int	read_pixels (ifstream &in)
	Read integer from input stream (pixel coordinates).

Detailed Description

Geometric utilities for 2D points and segments.

This file provides functions for computational geometry operations including area calculations, collinearity tests, orientation tests, and segment intersection detection.

Functions

Function	Description
area_of_parallelogram	Signed area of parallelogram
area_of_triangle	Triangle area
points_are_colinear	Collinearity test
left_on	Left-of-line test
intersectp	Segment intersection

See also: point.H Point class; segment.H Segment class

Author: Leandro Rabindranath León

Definition in file point_utils.H.

Function Documentation

◆ area_of_parallelogram()

const Geom_Number area_of_parallelogram	(	const Point &	a,
		const Point &	b,
		const Point &	c
	)

inline

Compute signed area of parallelogram formed by three points.

Uses cross product to compute 2x the signed area of triangle abc. The sign indicates orientation:

Positive: a, b, c are counter-clockwise
Negative: a, b, c are clockwise
Zero: a, b, c are collinear

Parameters

a	First point
b	Second point
c	Third point

Returns: Signed area (2x triangle area)

Definition at line 74 of file point_utils.H.

References Point::get_x(), and Point::get_y().

Referenced by area_of_triangle(), and points_are_colinear().

◆ area_of_triangle()

const Geom_Number area_of_triangle	(	const Point &	a,
		const Point &	b,
		const Point &	c
	)

inline

Compute area of triangle formed by three points.

Parameters

a	First vertex
b	Second vertex
c	Third vertex

Returns: Unsigned area of triangle

Definition at line 90 of file point_utils.H.

References area_of_parallelogram().

◆ between()

const bool between	(	const Point &	a,
		const Point &	b,
		const Point &	c
	)

Test if point c is between points a and b.

Assumes a, b, c are collinear.

Parameters

a	First endpoint
b	Second endpoint
c	Point to test

Returns: true if c lies on segment ab

Definition at line 190 of file point_utils.H.

References Point::get_x(), and Point::get_y().

Referenced by intersect_improp(), and TEST_F().

◆ c_is_to_left_()

const bool c_is_to_left_	(	const Point &	a,
		const Point &	b,
		const Point &	c
	)

inline

Test if point c is strictly left of line a→b.

Parameters

a	First point of line
b	Second point of line
c	Point to test

Returns: true if c is strictly left of a→b

Definition at line 122 of file point_utils.H.

◆ intersect_improp()

const bool intersect_improp	(	const Point &	a,
		const Point &	b,
		const Point &	c,
		const Point &	d
	)

Test for improper (endpoint) segment intersection.

Segments intersect improperly if an endpoint of one lies on the other segment.

Parameters

a	First endpoint of segment 1
b	Second endpoint of segment 1
c	First endpoint of segment 2
d	Second endpoint of segment 2

Returns: true if segments intersect at an endpoint

Definition at line 217 of file point_utils.H.

References between().

Referenced by intersectp().

◆ intersectp()

const bool intersectp	(	const Point &	a,
		const Point &	b,
		const Point &	c,
		const Point &	d
	)

Test if two segments intersect (proper or improper).

Returns true if segments ab and cd intersect at any point.

Parameters

a	First endpoint of segment 1
b	Second endpoint of segment 1
c	First endpoint of segment 2
d	Second endpoint of segment 2

Returns: true if segments intersect

Definition at line 240 of file point_utils.H.

References intersect_improp().

◆ is_clockwise()

const bool is_clockwise	(	const Point &	a,
		const Point &	b,
		const Point &	c
	)

inline

Test if points are in clockwise order.

Parameters

a	First point
b	Second point
c	Third point

Returns: true if a, b, c are clockwise

Definition at line 135 of file point_utils.H.

◆ left_on()

const bool left_on	(	const Point &	a,
		const Point &	b,
		const Point &	c
	)

inline

Test if point c is left of or on line a→b.

Parameters

a	First point of line
b	Second point of line
c	Point to test

Returns: true if c is left of or on the line a→b

Definition at line 150 of file point_utils.H.

◆ points_are_colinear()

const bool points_are_colinear	(	const Point &	a,
		const Point &	b,
		const Point &	c
	)

inline

Test if three points are collinear.

Three points are collinear if they lie on the same line.

Parameters

a	First point
b	Second point
c	Third point

Returns: true if points are collinear

Definition at line 107 of file point_utils.H.

References area_of_parallelogram().

◆ proper_intersection()

const bool proper_intersection	(	const Point &	a,
		const Point &	b,
		const Point &	c,
		const Point &	d
	)

Test for proper segment intersection.

Two segments intersect properly if they cross each other's interior (not at endpoints).

Parameters

a	First endpoint of segment 1
b	Second endpoint of segment 1
c	First endpoint of segment 2
d	Second endpoint of segment 2

Returns: true if segments intersect properly

Definition at line 167 of file point_utils.H.

◆ read_pixels()

int read_pixels ( ifstream & in )

Read integer from input stream (pixel coordinates).

Helper function for reading image data.

Parameters

in	Input file stream

Returns: Integer value read

Definition at line 260 of file point_utils.H.