Lines & Segments

Line primitives for connecting points and creating geometric constructions.

API Reference

geolet.primitives.lines.api.Segment

Segment(p1: PointT, p2: PointT, *, label: str = '', label_dir: str = 'N', label_pos: float = 0.5, color: str = 'black', style: str = 'solid', width: float = 1.0, marks: int = 0) -> SegmentT

Create a line segment between two points.

Parameters:

Name	Type	Description	Default
p1	PointT	First endpoint.	required
p2	PointT	Second endpoint.	required
label	str	Display label for the segment (empty string for no label).	''
label_dir	str	Direction for label placement (N, NE, E, SE, S, SW, W, NW).	'N'
label_pos	float	Relative position along path for label (0.0 = start, 1.0 = end).	0.5
color	str	Asymptote color name (e.g. 'black', 'red', 'blue').	'black'
style	str	Line style. One of: solid, dashed, dotted.	'solid'
width	float	Line width in Asymptote units.	1.0
marks	int	Number of tick marks to draw on segment (for congruence).	0

Returns:

Type	Description
SegmentT	A segment drawable satisfying SegmentT protocol.

---

geolet.primitives.lines.api.Line

Line(p1: PointT, p2: PointT, *, label: str = '', label_dir: str = 'N', label_pos: float = 0.0, color: str = 'black', style: str = 'solid', width: float = 1.0) -> LineT

Create an infinite line through two points.

Parameters:

Name	Type	Description	Default
p1	PointT	First point defining the line.	required
p2	PointT	Second point defining the line.	required
label	str	Display label for the line (empty string for no label).	''
label_dir	str	Direction for label placement (N, NE, E, SE, S, SW, W, NW).	'N'
label_pos	float	Relative position along path for label (0.0 = start, 1.0 = end).	0.0
color	str	Asymptote color name (e.g. 'black', 'red', 'blue').	'black'
style	str	Line style. One of: solid, dashed, dotted.	'solid'
width	float	Line width in Asymptote units.	1.0

Returns:

Type	Description
LineT	A line drawable satisfying LineT protocol.

---

geolet.primitives.lines.api.Triangle

Triangle(p1: PointT, p2: PointT, p3: PointT, *, color: str = 'black', style: str = 'solid', width: float = 1.0) -> TriangleT

Create a triangle defined by three vertices.

Automatically draws all three sides as segments. Provides methods to access triangle centers and circles.

Parameters:

Name	Type	Description	Default
p1	PointT	First vertex.	required
p2	PointT	Second vertex.	required
p3	PointT	Third vertex.	required
color	str	Asymptote color for all sides.	'black'
style	str	Line style for all sides. One of: solid, dashed, dotted.	'solid'
width	float	Line width for all sides.	1.0

Returns:

Type	Description
TriangleT	A triangle drawable satisfying TriangleT protocol.

---

geolet.primitives.lines.api.PerpendicularLine

PerpendicularLine(point: PointT, to: SegmentT | LineT, *, label: str = '', label_dir: str = 'N', label_pos: float = 0.0, color: str = 'black', style: str = 'solid', width: float = 1.0) -> LineT

Create a line perpendicular to a line or segment through a point.

Parameters:

Name	Type	Description	Default
point	PointT	Point the perpendicular line passes through.	required
to	SegmentT | LineT	The line or segment to be perpendicular to.	required
label	str	Display label for the line (empty string for no label).	''
label_dir	str	Direction for label placement (N, NE, E, SE, S, SW, W, NW).	'N'
label_pos	float	Relative position along path for label (0.0 = start, 1.0 = end).	0.0
color	str	Asymptote color name (e.g. 'black', 'red', 'blue').	'black'
style	str	Line style. One of: solid, dashed, dotted.	'solid'
width	float	Line width in Asymptote units.	1.0

Returns:

Type	Description
LineT	A perpendicular line drawable.

---

geolet.primitives.lines.api.ParallelLine

ParallelLine(point: PointT, to: SegmentT | LineT, *, label: str = '', label_dir: str = 'N', label_pos: float = 0.0, color: str = 'black', style: str = 'solid', width: float = 1.0) -> LineT

Create a line parallel to another line through a point.

Parameters:

Name	Type	Description	Default
point	PointT	Point the parallel line passes through.	required
to	SegmentT | LineT	The line to be parallel to (Line or Segment).	required
label	str	Display label for the line (empty string for no label).	''
label_dir	str	Direction for label placement (N, NE, E, SE, S, SW, W, NW).	'N'
label_pos	float	Relative position along path for label (0.0 = start, 1.0 = end).	0.0
color	str	Asymptote color name (e.g. 'black', 'red', 'blue').	'black'
style	str	Line style. One of: solid, dashed, dotted.	'solid'
width	float	Line width in Asymptote units.	1.0

Returns:

Type	Description
LineT	A parallel line drawable.

---

geolet.primitives.lines.api.AngleBisector

AngleBisector(vertex: PointT, p1: PointT, p2: PointT, *, label: str = '', label_dir: str = 'N', label_pos: float = 0.0, color: str = 'black', style: str = 'solid', width: float = 1.0) -> LineT

Create the angle bisector at a vertex between two rays.

Creates the bisector of the angle formed at vertex by rays to p1 and p2.

Parameters:

Name	Type	Description	Default
vertex	PointT	The vertex of the angle.	required
p1	PointT	Point defining the first ray from vertex.	required
p2	PointT	Point defining the second ray from vertex.	required
label	str	Display label for the line (empty string for no label).	''
label_dir	str	Direction for label placement (N, NE, E, SE, S, SW, W, NW).	'N'
label_pos	float	Relative position along path for label (0.0 = start, 1.0 = end).	0.0
color	str	Asymptote color name (e.g. 'black', 'red', 'blue').	'black'
style	str	Line style. One of: solid, dashed, dotted.	'solid'
width	float	Line width in Asymptote units.	1.0

Returns:

Type	Description
LineT	An angle bisector line drawable.

---

geolet.primitives.lines.api.Tangent

Tangent(point: PointT, circle: CircleT, *, index: int = 0, label: str = '', label_dir: str = 'N', label_pos: float = 0.0, color: str = 'black', style: str = 'solid', width: float = 1.0) -> LineT

Create a tangent line from an external point to a circle.

When the point is external to the circle, two tangent lines exist. Use index=0 for the first tangent and index=1 for the second.

Parameters:

Name	Type	Description	Default
point	PointT	External point from which tangent is drawn.	required
circle	CircleT	The circle to draw tangent to.	required
index	int	Which tangent line (0 or 1) when two exist.	0
label	str	Display label for the line (empty string for no label).	''
label_dir	str	Direction for label placement (N, NE, E, SE, S, SW, W, NW).	'N'
label_pos	float	Relative position along path for label (0.0 = start, 1.0 = end).	0.0
color	str	Asymptote color name (e.g. 'black', 'red', 'blue').	'black'
style	str	Line style. One of: solid, dashed, dotted.	'solid'
width	float	Line width in Asymptote units.	1.0

Returns:

Type	Description
LineT	A tangent line drawable.

Example

O = Point("O", 0, 0) c = CircleWithRadius(O, 2) P = Point("P", 4, 0) t1 = Tangent(P, c, index=0, color="blue") t2 = Tangent(P, c, index=1, color="red")

Examples

Basic Segment

from geolet import Point, Segment, autofigure


@autofigure
def segment_example():
    A = Point("A", 0, 0, label_dir="SW")
    B = Point("B", 4, 0, label_dir="SE")

    Segment(A, B, label="c")

Triangle with Methods

from geolet import Point, Triangle, autofigure


@autofigure
def triangle_example():
    A = Point("A", 0, 0, label_dir="SW")
    B = Point("B", 6, 0, label_dir="SE")
    C = Point("C", 2, 4, label_dir="N")

    T = Triangle(A, B, C)

    # Access triangle centers via methods
    G = T.centroid(label="G", color="blue")
    H = T.orthocenter(label="H", color="red")

Perpendicular Line

from geolet import Point, Segment, PerpendicularLine, autofigure


@autofigure
def perpendicular_example():
    A = Point("A", 0, 0, label_dir="SW")
    B = Point("B", 4, 0, label_dir="SE")
    P = Point("P", 2, 2, label_dir="N")

    seg = Segment(A, B)
    PerpendicularLine(P, seg, style="dashed", color="blue")

Tangent Lines

from geolet import Point, CircleWithRadius, Tangent, autofigure


@autofigure
def tangent_example():
    O = Point("O", 0, 0)
    c = CircleWithRadius(O, 2)

    P = Point("P", 4, 0, label_dir="E")

    # Two tangent lines from external point
    Tangent(P, c, index=0, color="blue")
    Tangent(P, c, index=1, color="red")