structure Geometry2D

Basic operations for 2-dimensional geometric data. Contains two substructures, Geometry.Vector and Geometry.Point.

Interface

type point = real * real

A point is a tuple (x,y).

val toString: point -> string

Conversion to a string. For example toString (1.0, 2.0) = "(1.0,2.0)".

val distance: point * point -> real

Standard euclidean distance between two points.

structure Geometry2D.Vector

type t = real * real

A vector is a tuple (x,y).

val toString: t -> string

Convert to a string.

val add: t * t -> t
val sub: t * t -> t
val dot: t * t -> t
val cross: t * t -> t

Some basic operations on vectors.

val length: t -> real

Euclidean length (magnitude) of a vector.

val angle: t * t -> real

angle (u, v) is the rotation (in radians) of v with respect to u. This is a value between -π and π. Positive rotation is counter-clockwise, negative is clockwise.

For example, angle ((1.0,0.0),(0.0,1.0)) is approximately π/2, and angle ((1.0,0.0),(~1.0,~1.0)) is approximately -3π/4

val scaleBy: real -> t -> t

Multiply the length (magnitude) of a vector by some scalar.

structure Geometry2D.Point

type t = point

A point is a tuple (x,y).

val add: t * t -> t
val sub: t * t -> t

Basic operations on points.

val minCoords: t * t -> t
val maxCoords: t * t -> t

minCoords computes the lower-left point of the bounding box of two points. Similarly, maxCoords computes the upper-right point of the bounding box.

val triArea: t * t * t -> t

The (signed) area of a triangle between three points. The orientation of the triangle determines the sign: from left to right, if the points are in counter-clockwise order, the area is positive. If they are in clockwise order, the area is negative.

val counterClockwise: t * t * t -> bool

Test if the three points are in counter-clockwise order, from left to right.

val triAngle: t * t * t -> real

triAngle (a,b,c) is the angle (in radians) of the triangle inside vertex b.

val inCircle: t * t * t -> t -> bool

inCircle (a,b,c) x tests whether or not the point x is within the circumcircle of the triangle (a,b,c).