Functions

Here are listed all of GeoScript's functions. Note that, the names are case-insensitive and ignore underscores. This means that functions perpendicular_through, perpendicularthrough, PERPendicularthrougH and P_erpendic_ular___Through_ are the same function. Overloads are listed in the order they are checked.

`acos`

acos(v: Number (no unit))

Return type: Number (angle)

Returns: Arccosine of this value.

`acot` (alias `actg`)

acot(v: Number (no unit))

Return type: Number (angle)

Returns: Arccotangent of this value.

`acsc`

acsc(v: Number (no unit))

Return type: Number (angle)

Returns: Arccosecant of this value.

`angle`

angle(ABC: 3-P)
angle(A: Point, B: Point, C: Point)

Return type: Number (angle)

Returns: measurement of the angle ABC

Displays: the angle's arms.

The function accepts additional properties in the form of:

#![allow(unused)]
fn main() {
struct Angle {
    display_arms: bool, // Default: true,
    arms_type: LineType, // Default: SEGMENT
}
}

display_arms decides whether the arms should be displayed and arms_type decides whether they should be segments, rays or lines. The assumed order for rays is B -> A and B -> C;

angle(k: Line, l: Line)

Return type: Number (angle)

Returns: measurement of the angle between k and l. Which angle, depends on the order of the lines. For predictable outcome, the point versions are strongly recommended.

`area`

area(A (Point), B (Point), C (Point), ...)
area(ABC... (Point collection))

Works for 3 or more points.

Return type: Number (distance^2)

Returns: the area of the given polygon.

`asec`

asec(v: Number (no unit))

Return type: Number (angle)

Returns: Arcsecant of this value.

`asin`

asin(v: Number (no unit))

Return type: Number (angle)

Returns: Arcsine of this value.

`atan` (alias `atg`)

atan(v: Number (no unit))

Return type: Number (angle)

Returns: Arctangent of this value.

`bisector`

bisector(AB: 2-P)
bisector(A: Point, B: Point)

Return type: Line

Returns: a bisector of the segment AB - a perpendicular line passing through its center.

bisector(ABC: 3-P)
bisector(A: Point, B: Point, C: Point)

Return type: Line

Returns: a bisector of the angle ABC - a line between lines AB and BC, where each point is in the same distance from both of these lines.

Displays: the angle's arms.

The function accepts additional properties in the form of:

#![allow(unused)]
fn main() {
struct Bisector {
    display_arms: bool, // Default: true,
    arms_type: LineType, // Default: SEGMENT
}
}

display_arms decides whether the arms should be displayed and arms_type decides whether they should be segments, rays or lines. The assumed order for rays is B -> A and B -> C;

angle(k: Line, l: Line)

`center` (alias `centre`)

center(circle: Circle)

**Return type: Point

`circle`

circle(center: Point, radius: Number (distance))
circle(radius: Number (distance), center: Point)

Return type: Circle

Returns: a circle with the given center and radius.

circle()

Return type: Circle

Returns: a circle with an adjusted (free point) center and an adjusted (free real) radius.

`circumcircle`

circumcircle(a: Point, b: Point, c: Point)
circumcircle(abc: 3-P)

Return type: Circle

Returns: the circle circumscribed on the three points given.

`circumcenter`

circumcenter(a: Point, b: Point, c: Point)
icircumcenter(abc: 3-P)

Return type: Point

Returns: the cetner of the circle circumscribed on the three points given.

`conjugate`

conjugate(v: Number (any unit))

Return type: Number (the same unit)

Returns: The conjugate of this number.

`convex` (alias `convexpolygon`, `convexpoly`)

convex(n: Number (literal, no unit))

Only works with a number literal.

Return type: PC-n

Returns: A convex polygon with n sides.

`cos`

cos(v: Number (angle))

Return type: Number (no unit)

Returns: Cosine of this angle.

`cot` (alias `ctg`)

cot(v: Number (angle))

Return type: Number (no unit)

Returns: Cotangent of this angle.

`csc`

csc(v: Number (angle))

Return type: Number (no unit)

Returns: Cosecant of this angle.

`degrees` (alias `deg`)

degrees(value: Number (no unit))

Return type: Number (angle)

Returns: an angle with the given measurement in degrees. Related: radians

degrees(value: Number (angle))

Return type: Number (no unit)

Returns: the angle value in degrees. Related: radians

`dst` (alias `len`)

dst(AB: 2-P)
dst(A: Point, B: Point)

Return type: Number (distance)

Returns: the distance between points A and B.

Displays: the segment AB.

The function accepts additional properties in the form of:

#![allow(unused)]
fn main() {
struct Dst {
    display_segment: bool, // Default: true,
    style: Style, // Default: SOLID
}
}

display_segment decides whether the segment should be displayed and style decides how it should be displayed.

dst(P: Point, k: Line)
dst(k: Line, P: Point)

Return type: Number (distance)

Returns: the distance between point P and line k.

Displays: the segment between P and its perpendicular projection onto k.

The function accepts additional properties in the form of:

#![allow(unused)]
fn main() {
struct Dst {
    display_segment: bool, // Default: true,
    style: Style, // Default: DASHED
}
}

display_segment decides whether the segment should be displayed and style decides how it should be displayed.

dst(value: Number (no unit / distance))

Return type: Number (angle)

Returns: the value with a distance unit.

`equilateral` (alias `equilateral_triangle`)

equilateral()

Return type: Point collection (3)

Returns: an equilateral triangle.

`excircle`

excircle(a: Point, b: Point, c: Point)
excircle(abc: 3-P)

Return type: Circle

Returns: the circle excribed to the points given, with the center on the bisector of angle ABC.

`homothety`

homothety(origin: Point, scale: Number (no unit))
homothety(scale: Number (no unit), origin: Point)

Return type: TransformType

Returns: a homothety with an origin and scale.

`imaginary` (alias `im`)

imaginary(v: Number (any unit))

Return type: Number (the same unit)

Returns: The imaginary part of this number.

`incircle`

incircle(a: Point, b: Point, c: Point)
incircle(abc: 3-P)

Return type: Circle

Returns: the circle inscribed in the three points given.

`incenter`

incenter(a: Point, b: Point, c: Point)
incenter(abc: 3-P)

Return type: Point

Returns: the cetner of the circle inscribed in the three points given.

`intersection`

All overloads by default don't display the point dot. This can be changed with properties.

intersection(k: Line, l: Line)

Return type: Point

Returns: intersection of lines k and l.

intersection(k: Line, circle: Circle)
intersection(circle: Circle, k: Line)

Return type: Point

Returns: intersection of line k and circle circle.

intersection(o1: Circle, o2: Circle)

Return type: Point

Returns: intersection of circles o1 and o2.

Note: display_dot property is not currently supported.

`isosceles` (alias `isosceles_triangle`)

isosceles()

Return type: Point collection (3)

Returns: an isosceles triangle with AC = BC.

`line`

line(col: 2-PC)
line(P: Point, Q: Point)

Return type: Line

Returns: a line through two given points.

Displays: The created line.

`main_equilateral` (alias `main_equilateral_triangle`)

main_equilateral()

Return type: Point collection (3)

Returns: an equilateral triangle with C.y > A.y = B.y and A.x < B.x.

`main_isosceles` (alias `main_isosceles_triangle`)

main_isosceles()

Return type: Point collection (3)

Returns: an isosceles triangle with AC = BC, C.y > A.y = B.y and A.x < B.x.

`main_right` (alias `main_right_triangle`)

main_right()

Return type: Point collection (3)

Returns: a right triangle with angle(ACB) = deg(90), B.y > A.y = C.y and C.x < A.x.

`main_triangle` (alias `main_triangle`)

main_triangle()

Return type: Point collection (3)

Returns: a triangle with C.y > A.y = B.y and A.x < B.x.

`mid`

mid(col: 0-P)

Return Type: Point

Returns: The middle point of all points in the collection.

Note: The following functions allow any positive numbers of arguments.

mid(v_1: Number (any unit u), v_2 Number (the same unit u), ..., v_n: Number (the same unit u))

Return type: Number (the same unit u)

Returns: The average value of v_1, v_2, ... v_n.

mid(P_1: Point, P_2: Point, ..., P_n: Point)

Return type: Point

Returns: The middle point of P_1, P_2, ... P_n. Special cases: when n=2, the middle of a segment; When n=3, the centroid of a triangle.

`orthocenter` (alias `orthocentre`)

orthocenter(A: Point, B: Point, C: Point)
orthocenter(ABC: 3-P)

Return type: Point

Returns: The intersection of the triangles altitudes.

`parallel_through` (alias `parallel`)

parallel_through(P: Point, k: Line)
parallel_through(k: Line, P: Point)

Return type: Line

Returns: a line parallel to k, passing through P.

`perpendicular_through` (alias `perpendicular`)

perpendicular_through(P: Point, k: Line)
perpendicular_through(k: Line, P: Point)

Return type: Line

Returns: a line perpendicular to k, passing through P.

`point`

point()

Return type: Point

Returns: an adjusted (free) point.

`polygon` (alias `poly`)

polygon(n: Number (literal, no unit))

Only works with a number literal.

Return type: PC-n

Returns: A polygon with n sides. Possibly concave, possibly self-intersecting.

`radians` (alias `rad`)

radians(value: Number (no unit))

Return type: Number (angle)

Returns: an angle with the given measurement in radians. Related: degrees

radians(value: Number (angle))

Return type: Number (no unit)

Returns: the value of the angle in radians. Related: degrees

`radius`

radius(circle: Circle)

Return type: Number (distance)

Returns: the radius of the given circle.

`real` (alias `re`)

real(v: Number (any unit))

Return type: Number (the same unit)

Returns: The real part of this number.

real()

Return type: Number (no unit)

Returns: A free, adjustable real number.

`reflect` (alias `reflection`)

reflect(line: Line)

Return type: TransformType

Returns: A reflection about a line.

`rotate` (alias `rotation`)

rotate(origin: Point, angle: Number (angle), scale: Number (unitless))
rotate(origin: Point, scale: Number (unitless), angle: Number (angle))
rotate(angle: Number (angle), origin: Point, scale: Number (unitless))
rotate(angle: Number (angle), scale: Number (unitless), origin: Point)
rotate(scale: Number (unitless), origin: Point, angle: Number (angle))
rotate(scale: Number (unitless), angle: Number (angle), origin: Point)
rotate(angle: Number (angle), origin: Point)
rotate(origin: Point, angle: Number (angle))

Return type: TransformType

Returns: A rotation around an origin by an angle (possibly negative), along with an optional homothety at the same point.

`right` (alias `right_triangle`)

right()

Return type: Point collection (3)

Returns: a right triangle with angle(ACB) = deg(90).

`sec`

sec(v: Number (angle))

Return type: Number (no unit)

Returns: Secant of this angle.

`segment`

segment(AB: 2-P)
segment(A: Point, B: Point)

Return type: Segment

Returns: the segment AB.

Displays: the segment AB.

The function accepts additional properties in the form of:

#![allow(unused)]
fn main() {
struct Segment {
    display_segment: bool, // Default: true,
    style: Style, // Default: SOLID
}
}

display_segment decides whether the segment should be displayed and style decides how it should be displayed.

`signedarea`

signedarea(A (Point), B (Point), C (Point), ...)
signedarea(ABC... (Point collection))

Works for 3 or more points.

Return type: Number (distance^2)

Returns: the signed area of the given polygon.

`sin`

sin(v: Number (angle))

Return type: Number (no unit)

Returns: Sine of this angle.

`tan` (alias `tg`)

tan(v: Number (angle))

Return type: Number (no unit)

Returns: Tangent of this angle.

`to_complex`

to_complex(A: Point)

Return type: Number (distance)

Returns: the point as a complex number.

`to_point`

to_point(v: Number (distance))

Return type: Point

Returns: the complex number as a point.

`transform`

transform(t: TransformType, object: Any)

Return type: Depends on the transformationi and input.

Returns: The object transformed using the transformation. Is type isn't supported, a compile error will be raised.

`translate` (alias `translation`)

translate(vector: Distance)

Return type: TransformType

Returns: A translation by a vector.

`triagngle` (alias `triangle`)

triangle()

Return type: Point collection (3)

Returns: a triangle.

`x`

x(P: Point)

Return type: Number (distance)

Returns: The x coordinate of the point.

`y`

y(P: Point)

Return type: Number (distance)

Returns: The y coordinate of the point.

The Geo-AID Book