Intersections

Find intersection points between geometric objects.

API Reference

geolet.primitives.intersections.api.Intersection

Intersection(obj1: Intersectable, obj2: Intersectable, *, label: str = '', index: int = 0, label_dir: str = 'NE', color: str = 'black') -> IntersectionPoint

Create an intersection point between two AsyPath objects.

Parameters:

Name	Type	Description	Default
obj1	Intersectable	First geometric object (Segment, Circle, Line, etc.).	required
obj2	Intersectable	Second geometric object (Segment, Circle, Line, etc.).	required
label	str	Display name for the intersection point. Omit for hidden.	''
index	int	Which intersection point (0 or 1) when multiple exist.	0
label_dir	str	Direction to place label relative to point.	'NE'
color	str	Asymptote color name.	'black'

Returns:

Type	Description
IntersectionPoint	An intersection point drawable.

---

geolet.primitives.intersections.api.TangentPoint

TangentPoint(point: PointT, circle: CircleT, *, index: int = 0, label: str = '', label_dir: str = 'NE', color: str = 'black') -> IntersectionPoint

Create the point where a tangent line touches a circle.

This is a composition of Tangent and Intersection - it creates a tangent line from the point to the circle, then finds where that tangent touches the circle.

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 point (0 or 1) when two exist.	0
label	str	Display name for the tangent point. Omit for hidden.	''
label_dir	str	Direction to place label relative to point.	'NE'
color	str	Asymptote color name.	'black'

Returns:

Type	Description
IntersectionPoint	The point of tangency as an intersection point.

Example

O = Point("O", 0, 0) c = CircleWithRadius(O, 2) P = Point("P", 4, 0) T1 = TangentPoint(P, c, index=0, label="T_1") T2 = TangentPoint(P, c, index=1, label="T_2")

Examples

Line-Line Intersection

from geolet import Point, Line, Intersection, autofigure


@autofigure
def line_intersection():
    A = Point("A", 0, 0, label_dir="SW")
    B = Point("B", 4, 2, label_dir="NE")
    C = Point("C", 0, 2, label_dir="NW")
    D = Point("D", 4, 0, label_dir="SE")

    line1 = Line(A, B, color="blue")
    line2 = Line(C, D, color="red")

    Intersection(line1, line2, label="P", color="purple")

Circle-Line Intersection

from geolet import Point, Line, CircleWithRadius, Intersection, autofigure


@autofigure
def circle_line_intersection():
    O = Point("O", 0, 0, label_dir="SW")
    c = CircleWithRadius(O, 2, color="blue")

    A = Point("A", -3, -1, label_dir="W")
    B = Point("B", 3, 1, label_dir="E")
    line = Line(A, B, color="red")

    # Two intersection points
    Intersection(c, line, index=0, label="P", label_dir="NE")
    Intersection(c, line, index=1, label="Q", label_dir="SW")

Circle-Circle Intersection

from geolet import Point, CircleWithRadius, Intersection, autofigure


@autofigure
def circle_circle_intersection():
    O1 = Point("O_1", 0, 0, label_dir="SW")
    O2 = Point("O_2", 2, 0, label_dir="SE")

    c1 = CircleWithRadius(O1, 2, color="blue")
    c2 = CircleWithRadius(O2, 2, color="red")

    Intersection(c1, c2, index=0, label="P", label_dir="N")
    Intersection(c1, c2, index=1, label="Q", label_dir="S")

Tangent Points

from geolet import Point, CircleWithRadius, TangentPoint, Tangent, autofigure


@autofigure
def tangent_points():
    O = Point("O", 0, 0, label_dir="SW")
    c = CircleWithRadius(O, 2, color="blue")

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

    # Tangent lines
    Tangent(P, c, index=0, color="gray", style="dashed")
    Tangent(P, c, index=1, color="gray", style="dashed")

    # Points of tangency
    TangentPoint(P, c, index=0, label="T_1", color="red")
    TangentPoint(P, c, index=1, label="T_2", color="red")