Geometry by @futau

Namespase D2 for 2D objects

Located in headers/geom2d.h

D2::Point

D2::Point is a point in 2D, it has x and y coordinates.

You can create D2::Point by the following ways:

• by default: D2::Point() returns (0, 0) existen point,
• by two long double coordinates: D2::Point(long double x, long double y) returns (x, y) existen point,
• by one bool flag: D2::Point(bool exist) returns (0, 0) existen point if exist equals true and non-existen point otherwise,
• by two long double coordinates and one bool flag: D2::Point(long double x, long double y, bool exist) returns (x, y) existen point if exist equals true and non-existen point otherwise.

Let p to be D2::Point then you can do following:

• get coordinates: p.x or p.y and receive long double,
• get length: p.len() and receive long double,
• get lenght in square: p.len2() and receive long double,
• get unit vector: p.e() and receive D2::Point (same vector but length 1),
• get perpendicular vector: p.n() and receive D2::Point (the same length, but the turns may differ in different quarters of the plane),
• check for zero vector: p.isZero() and receive bool,
• check if it exists: p.exist() (recommended) or p.ex and receive bool (the cases where the point may not exist will be described below). If you try to use or output non-existen vector you catch std::logic_error("Error: Point does not exist in <...>").

Let p1 and p2 to be D2::Point then you can do following:

• get sum: p1 + p2 and receive D2::Point,
• get difference: p1 - p2 and receive D2::Point,
• get scalar product: p1 * p2 and receive long double,
• get vector product: p1 % p2 and receive long double,
• check for parallelism: p1 || p2 and receive bool,
• compare it:
  • p1 == p2,
  • p1 != p2,
  • p1 < p2,
  • p1 <= p2,
  • p1 > p2,
  • p1 >= p2 and receive bool,
• get rotation angle: p1.getAngle(p2) and receive float in radians included in (-pi; pi] (positive if counterclockwise rotation from p1 to p2).

Let a to be long double then you can do following:

• get multiplied vector: p * a and receive D2::Point,
• get divided vector: p / a and receive D2::Point,
• get rotated vector: p.rotate(a) (in degrees) or p.rotate_rad(a) (in radians) and receive D2::Point.

D2::Line

D2::Line is a line in 2D, it has a, b and c factors which describe an equation like a*x + b*y + c = 0.

You can create D2::Line by the following ways:

• by default: D2::Line() returns x - y = 0 line,
• by three long double factors: D2::Line(long double a, long double b, long double c) returns a*x + b*y + c = 0 line,
• by two D2::Point points: D2::Line(D2::Point p1, D2::Point p2) returns line which contains points given.

Let l to be D2::Line then you can do following:

• get perpendicular vector: l.n() and receive D2::Point (any length and any of two directions),
• get guide vector: l.guideVector() and receive D2::Point (any length and any of two directions),
• check if it exist: l.exist() or l.isZero() (true if a and b are zero so line does not exist) and receive bool.

Let l1 and l2 to be D2::Line then you can do following:

• compare it: l1 == l2 and receive bool,
• check for parallelism: l1 || l2 and receive bool.

There are Ox and Oy constant lines which correspond to the coordinate axes.

D2::Circle

D2::Circle is a circle in 2D, it has center and radius.

You can create D2::Circle by the following ways:

• by default: D2::Circle() returns circle with the center in (0, 0) point and the radius equals 1,
• by point and radius: D2::Circle(D2::Point center, long double radius) returns circle with the center in center point and the radius equals radius,
• by three numbers: D2::Circle(long double x, long double y, long double r) returns circle with the center in (x, y) point and the radius equals r.

D2::Segment

D2::Segment is a segment in 2D, it has p1 and p2 which are two endpoints.

You can create D2::Segment by the following ways:

• by default: D2::Segment() returns segment from (0, 0) point to (1, 1) point,
• by two endpoints: D2::Circle(D2::Point p1, D2::Point p1) returns segment from p1 point to p2 point.

Let s to be D2::Segment then you can do following:

• get length: s.len() and receive long double,
• check if it zero: s.isZero() and receive bool,
• get line containig the segment: s.getLine() and receive D2::Line,
• get vector: s.getVector() and receive D2::Point (any of two directions).

Function for 2D objects

D2::isCrossingLines

D2::isCrossingLines requires two D2::Line. Function checks if they intersect and returns bool (true if they intersect and false otherwise). It's worth nothing that false is always returned if the lines are equal.

D2::crossLines

D2::crossLines requires two D2::Line. Function finds the point of intersection and returns D2::Point. It returns non-existen point if there're not any intersection points or lines are equal.

D2::fromPointToLine

D2::fromPointToLine requires D2::Point and D2::Line. Function finds the shortest vector from the point to the line and returns D2::Point. It returns non-existen point if the line does not exist.

D2::isPointInCircle

D2::isPointInCircle requires D2::Point and D2::Circle. Function checks if the point is inside or on the border of the circle and returns bool (true if it is and false otherwise).

D2::isCrossingCircleAndLine

D2::isCrossingCircleAndLine requires D2::Circle and D2::Line. Function checks if they intersect and returns bool (true if they intersect and false otherwise).

D2::crossCircleAndLine

D2::crossCircleAndLine requires D2::Circle and D2::Line. Function finds the points where they intersect and returns std::pair<D2::Point, D2::Point>. It returns pair of two non-existen points if there're not any intersection points and returns pair of two equal points if there're only one intersection point.

D2::isCrossingCircles

D2::isCrossingCircles requires two D2::Circle. Function checks if they intersect and returns bool (true if they intersect and false otherwise).

D2::crossCircles

D2::crossCircles requires two D2::Circle. Function finds the points where they intersect and returns std::pair<D2::Point, D2::Point>. It returns pair of two non-existen points if there're not any intersection points and returns pair of two equal points if there're only one intersection point.

D2::isInSameSide

D2::isInSameSide requires D2::Line and two D2::Point. Function checks if the points are in the same side of the line including the line itself and returns bool (true if it is and false otherwise). It's worth nothing that true is always returned if at least one point is on the line itself.

D2::isInSameSideExcluding

D2::isInSameSideExcluding requires D2::Line and two D2::Point. Function checks if the points are in the same side of the line excluding the line itself and returns bool (true if it is and false otherwise). It's worth nothing that false is always returned if at least one point is on the line itself.

D2::isPointInSegment

D2::isPointInSegment requires D2::Segment and D2::Point. Function checks if the point is in the segment including endpoints and returns bool (true if it is and false otherwise).

D2::isCrossingSegments

D2::isCrossingSegments requires two D2::Segment. Function checks if they intersect including endpoints and returns bool (true if they intersect and false otherwise). It's worth nothing that false is always returned if there're more than one intersection points.

D2::crossSegments

D2::crossSegments requires two D2::Segment. Function finds the point of intersection including endpoints and returns D2::Point. It returns non-existen point if there're not any intersection points or there're more than one intersection points.

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