Geometry

A Point object defines a point in the plane

A LabeledPoint carries a "label" (i.e. any additional information such as a text tag, or any other data structure), in addition to position information. Data points on a plot are LabeledPoints.

Given a labelling function and a Point p, returned a LabeledPoint containing p and the computed label

Apply a function to the label

A frame, i.e. a bounding box for objects

The unit square (0, 0) - (1, 1)

Create a Frame from a container of Points P, i.e. construct two points p1 and p2 such that :

p1 := inf(x,y) P

p2 := sup(x,y) P

Build a frame rooted at the origin (0, 0)

The width is the extent in the x direction and height is the extent in the y direction

The width is the extent in the x direction and height is the extent in the y direction

Frame corner coordinates

Frame corner coordinates

Frame corner coordinates

Frame corner coordinates

V2 is a vector in R^2

Build a Point p from a V2 v (i.e. assuming v points from the origin (0,0) to p)

A Mat2 can be seen as a linear operator that acts on points in the plane

Diagonal matrices in R2 behave as scaling transformations

Create a diagonal matrix

The origin of the axes, point (0, 0)

The (1, 1) point

X-aligned unit vector

Y-aligned unit vector

Euclidean (L^2) norm

Normalize a V2 w.r.t. its Euclidean norm

Create a V2 v from two endpoints p1, p2. That is v can be seen as pointing from p1 to p2

Build a V2 v from a Point p (i.e. assuming v points from the origin (0,0) to p)

Move a point along a vector

Move a LabeledPoint along a vector

Create a V2 v from two endpoints p1, p2. That is v can be seen as pointing from p1 to p2

`pointRange n p q` returns a list of equi-spaced Points between p and q.

Given two frames F1 and F2, returns a function f that maps an arbitrary vector v contained within F1 onto one contained within F2.

This function is composed of three affine maps :

1. map v into a vector v01 that points within the unit square,
2. map v01 onto v01'. This transformation serves to e.g. flip the dataset along the y axis (since the origin of the SVG canvas is the top-left corner of the screen). If this is not needed one can just supply the identity matrix and the zero vector,
3. map v01' onto the target frame F2.

NB: we do not check that v is actually contained within the F1, nor that v01' is still contained within [0,1] x [0, 1]. This has to be supplied correctly by the user.

Map function values across frames

Additive group :

v ^+^ zero == zero ^+^ v == v

v ^-^ v == zero

Vector space : multiplication by a scalar quantity

Hermitian space : inner product

Linear maps, i.e. linear transformations of vectors

Multiplicative matrix semigroup ("multiplying" two matrices together)

The class of invertible linear transformations

Numerical equality

A list of nx by ny points in the plane arranged on the vertices of a rectangular mesh.

NB: Only the minimum x, y coordinate point is included in the output mesh. This is intentional, since the output from this can be used as an input to functions that use a corner rather than the center point as refernce (e.g. rect)

Interpolation

Safe