point
Constructs a 2D point. With three numbers, a 3D point: point(1, 2, 3).
x(number) --y(number) --
Coordinate Geometry
line
Constructs a 2D line in general form a*x + b*y + c = 0; line(P, Q) is the line through two points. In 3D, line(p, l, m, n) is the line through point p with direction ratios l, m, n, shown in symmetric form.
a(number) --b(number) --c(number) --
lineFromPoints
Constructs the line through two points. With two 3D points, the 3D line through them.
p(point2d) --q(point2d) --
lineFromSlope
Constructs the line y = m*x + k from a slope and y-intercept.
m(number) -- slopek(number) -- y-intercept
linePointSlope
Constructs the line through a point with a given slope.
p(point2d) --m(number) -- slope
lineFromAngle
Constructs an infinite line through a point at a direction in degrees. Positive angles are counter-clockwise from +x; negative angles clockwise.
p(point2d) -- point on the linedegrees(number) -- line direction in degrees
lineFromIntercepts
Constructs the line with given x- and y-intercepts.
xIntercept(number) --yIntercept(number) --
lineVertical
Constructs the vertical line x = k.
k(number) --
lineHorizontal
Constructs the horizontal line y = k.
k(number) --
circle
Constructs a circle from a centre point and radius.
centre(point2d) --r(number) --
ellipse
Constructs an axis-aligned ellipse from a centre point and horizontal/vertical semi-axis lengths. The value works with the conic-section functions: eccentricity, foci, vertices, tangentAt, normalAt, ...
centre(point2d) --rx(number) -- horizontal semi-axisry(number) -- vertical semi-axis
circleFromGeneral
Constructs a circle from its general-form coefficients (x^2 + y^2 + 2gx + 2fy + c = 0).
g(number) --f(number) --c(number) --
ratios
Constructs a 3D direction ratios value (l, m, n) -- unnormalized direction cosines.
a(number) --b(number) --c(number) --
midpoint
The midpoint of two points. Also works for two 3D points.
p(point2d) --q(point2d) --
sectionInternal
The point dividing segment pq internally in the ratio m:n. Also works for two 3D points.
p(point2d) --q(point2d) --m(number) --n(number) --
sectionExternal
The point dividing segment pq externally in the ratio m:n. Also works for two 3D points.
p(point2d) --q(point2d) --m(number) --n(number) --
collinear
True if three points lie on a common line. Also works for three 3D points.
p(point2d) --q(point2d) --r(point2d) --
distance
The distance between two values: point-point, point-line (either order), line-line (parallel only), or circle-circle (between centres). In 3D: point-point, point-line, point-plane, line-line (shortest distance) and between parallel planes.
a(point2d | line2d | circle2d) --b(point2d | line2d | circle2d) --
intersect
The intersection of two values: line-line (a point, or explanatory text if parallel/coincident) or line-circle (either order). Also for two planes: their line of intersection, or text if they are parallel. Also the intersection of two sets.
a(line2d | circle2d) --b(line2d | circle2d) --
positionOf
A point's position relative to a line ("above"/"on"/"below") or a circle ("inside"/"on"/"outside").
p(point2d) --x(line2d | circle2d) --
areParallel
True if two lines, or two direction ratios, are parallel. Also for two 3D lines or two planes.
a(line2d | ratios) --b(line2d | ratios) -- same kind as a
arePerpendicular
True if two lines, or two direction ratios, are perpendicular. Also for two 3D lines.
a(line2d | ratios) --b(line2d | ratios) -- same kind as a
angleBetweenLines
The angle, in radians, between two lines, or between two direction ratios. Also for two 3D lines (radians).
a(line2d | ratios) --b(line2d | ratios) -- same kind as a
slope
The slope of a line. Returns explanatory text for a vertical line.
l(line2d) --
yIntercept
A line's y-intercept. Returns explanatory text for a vertical line.
l(line2d) --
xIntercept
A line's x-intercept. Returns explanatory text for a horizontal line.
l(line2d) --
isVertical
True if a line is vertical.
l(line2d) --
isHorizontal
True if a line is horizontal.
l(line2d) --
areCoincident
True if two lines are the same line. Also for two planes.
l1(line2d) --l2(line2d) --
footOfPerpendicular
The foot of the perpendicular from a point to a line. In 3D: from a point to a 3D line or to a plane.
p(point2d) --l(line2d) --
imageOfPoint
The mirror image of a point reflected across a line. In 3D: the mirror image of a point in a plane.
p(point2d) --l(line2d) --
familyThroughIntersection
A line in the family l1 + lambda*l2 passing through the intersection of two lines.
l1(line2d) --l2(line2d) --lambda(number) --
parallelThrough
The line through a point, parallel to a given line.
p(point2d) --l(line2d) --
perpendicularThrough
The line through a point, perpendicular to a given line.
p(point2d) --l(line2d) --
sameSide
True if two points lie on the same side of a line.
p(point2d) --q(point2d) --l(line2d) --
circleArea
The area of a circle.
c(circle2d) --
circumference
The circumference of a circle.
c(circle2d) --
diameter
The diameter of a circle.
c(circle2d) --
radiusSq
The square of a circle's radius.
c(circle2d) --
tangentAt
The tangent line to a circle at a point on it. Also for a parabola, ellipse or hyperbola and a point on it.
c(circle2d) --p(point2d) -- a point on the circle
radicalAxis
The radical axis of two circles.
c1(circle2d) --c2(circle2d) --
relativePosition
How two circles relate to each other (e.g. "intersecting", "concentric", "one inside the other").
c1(circle2d) --c2(circle2d) --
triangleArea
The area of the triangle formed by three points.
p(point2d) --q(point2d) --r(point2d) --
triangleAreaSigned
The signed area of the triangle formed by three points -- positive for counterclockwise winding, negative for clockwise.
p(point2d) --q(point2d) --r(point2d) --
isDegenerate
True if three points are collinear (form a degenerate triangle with zero area). With one conic() value: true if the conic is degenerate (a pair of lines, a point, ...).
p(point2d) --q(point2d) --r(point2d) --
classify
Classifies a triangle formed by three points (e.g. "equilateral", "isosceles", "right-angled").
p(point2d) --q(point2d) --r(point2d) --
perimeter
The perimeter of the triangle formed by three points.
p(point2d) --q(point2d) --r(point2d) --
centroid
The centroid of the triangle formed by three points. Also works for three or four 3D points.
p(point2d) --q(point2d) --r(point2d) --
incentre
The incentre of the triangle formed by three points.
p(point2d) --q(point2d) --r(point2d) --
circumcentre
The circumcentre of the triangle formed by three points. Returns explanatory text for a degenerate triangle.
p(point2d) --q(point2d) --r(point2d) --
orthocentre
The orthocentre of the triangle formed by three points. Returns explanatory text for a degenerate triangle.
p(point2d) --q(point2d) --r(point2d) --
eulerLine
The Euler line of the triangle formed by three points (through the centroid, orthocentre, and circumcentre). Returns explanatory text for a degenerate triangle.
p(point2d) --q(point2d) --r(point2d) --
ninePointCentre
The nine-point centre of the triangle formed by three points. Returns explanatory text for a degenerate triangle.
p(point2d) --q(point2d) --r(point2d) --
sideA
The length of side a (opposite p) of the triangle formed by three points.
p(point2d) --q(point2d) --r(point2d) --
sideB
The length of side b (opposite q) of the triangle formed by three points.
p(point2d) --q(point2d) --r(point2d) --
sideC
The length of side c (opposite r) of the triangle formed by three points.
p(point2d) --q(point2d) --r(point2d) --
toCosines
Converts direction ratios to direction cosines, as a 3-element array.
r(ratios) --
ratioDot
The dot product of two direction ratios.
r1(ratios) --r2(ratios) --
ratioMagSq
The squared magnitude of a direction ratios value.
r(ratios) --
generalForm
g, f, c of a circle written as x^2 + y^2 + 2gx + 2fy + c = 0.
c(circle2d) --