lambdaisland.witchcraft.matrix — com.lambdaisland/witchcraft 0.31.300

Vector/Matrix math

A vector in this context can be anything that implements [[lambdaisland.witchcraft/with-xyz]]: a Clojure vector ([x y z]), a Clojure map ({:x .. :y .. :z ..}), or a Glowstone Location or Vector. You get the type back that you put in.

A matrix is a vector of vectors (regular Clojure vectors) and can be 3x3 (linear) or 4x4 (affine/homogenous).

This code is not optimized for speed, it is fine for generating and manipulating minecraft structures, not for heavy number crunching.

center clj

(center coll)

The center point of a collection of points, simply takes the average in each dimension.

chebyshev clj

(chebyshev x y)

Chebyshev (maximum metric) distance

cross-product clj

(cross-product a b)

dot-product clj

(dot-product a b)

Vector dot product

Arguments can be Clojure maps (:x/:y/:z), vectors, or Glowstone Location or Vector instances. Returns a number.

extrude clj

(extrude coll dir steps)

Extrude a shape in a given direction, takes a collection of locations/blocks, a direction vector, and a number of times to apply the direction vector.

identity-matrix clj

(identity-matrix degree)

Return a degree x degree matrix with all elements on the diagonal 1 and all others 0

m* clj

(m* m s)

Multiply a matrix with a scalar

m*m clj

(m*m m1 m2)

(m*m m1 m2 & rest)

Multiply matrices

m*v clj

(m*v m v)

Multiply a matrix (vector of vectors) with a vector

m is a Clojure vector of vectors, 3x3 (linear) or 4x4 (affine). v can be a Clojure map (:x/:y/:z), vector ([x y z]), or Glowstone Location or Vector instance. Returns the same type as v.

manhatten clj

(manhatten x y)

Manhatten distance

mirror-matrix clj

(mirror-matrix mappings)

Matrix which mirrors points, mappings is a map of one or more of :x/:y/:z to :x/:-x/:y/:-y/:z/:-z. E.g. a mapping of {:x :-x} means that the x value gets flipped, in other words it's a mirroring around the z=0 plane. {:x :z, :z :x} means that the x and z values get swapped, i.e. a mirroring around the x=z plane.

rotate clj

(rotate rad dim1 dim2 coll)

Rotate a shape around its center (average of all block locations), given an angle in radians, and the two dimensions (as keywords, :x/:y/:z) that form the plane within which to rotate.

rotation-matrix clj

(rotation-matrix rad dim1 dim2)

Matrix which rotates around the origin, takes the rotation in radians, and the dimensions that form the plane in which the rotation is performed, e.g. (rotation-matrix Math/PI :x :z)

transform clj

(transform coll m)

(transform coll m & rest)

Transform a collection by applying a matrix to each element

translation-matrix clj

(translation-matrix v)

Returns an affine transformation matrix that moves a location by a fixed amount in each dimension.

transpose clj

(transpose m)

Transpose a matrix

v* clj

(v* v s)

Multiply a vector with a scalar

v can be a Clojure map (:x/:y/:z), vector ([x y z]), or Glowstone Location or Vector instance. Returns the same type as v.

v+ clj

(v+ a b)

Vector addition

Arguments can be Clojure maps (:x/:y/:z), vectors, or Glowstone Location or Vector instances. The return type is the type of a.

v- clj

(v- a)

(v- a b)

Vector subtraction

Arguments can be Clojure maps (:x/:y/:z), vectors, or Glowstone Location or Vector instances. The return type is the type of a.

vlength clj

(vlength v)

Vector length

vnorm clj

(vnorm v)

Normalize a vector to be length=1

with-origin clj

(with-origin matrix origin)

Takes an affine transformation matrix, and an origin coordinate, and returns a matrix which performs the same trasnformation, but around the new origin. Use this to change the "anchor" around which e.g. a rotation happens, which by default is otherwise the [0 0 0] origin coordinate.