A cross platform library for exact extended complex numbers, geometry and transform.
lein replusing a test runner in test/complex/test-runner.cljc which can work from either clojure or clojurescript
(require 'complex.test-runner)
(complex.test-runner/runner)or
lein test- see dev/node-repl.clj to start a node repl from a clojure repl
run cljs test using nodejs
lein nodetestan alias, which does a build:
lein cljsbuild once node-devand runs the built target from nodejs:
node resources/run.jswhich calls the -main function in test/complex/node_test_runner.cljs
git clone git@github.com:wbabic/complex.git
cd complex
lein installcomplex number addition, multiplication, one, zero, infinity subtraction, multiplication identity and inverse length angle conjugate point line triangle circle geometric transformations translation, dilation reflection - in a line or a circle reciprocation
transforms using + - * / bar circle preserving transformations orientation preserving and reversing
transformable - able to be transformed renderable - able to be rendered
protocols Complex Transform Transformable Renderable
geometric types: point line circle triangle style combined in a sequence, rendered to the canvas or, eventually, to svg and webgl
- Number types Complex number with algebraic operations of addition and multiplication
- Transform types Mobius transformations that can be composed and conjugated and have inverses preserving generalized circles
- Pencils of circles and their orthogonal compliments and their images illustrating a particular transform, associated with that transfrom
able to be generated and validated passed over the wire, using transit saved in a database or a file as edn
entries a b c d determinant trace inverse fixed points
of a mobius transformation with translation, rotation, scaling
in vector.cljc algebraic operations for vectors and matrices
sum product scal-mul dot len len-sq angle midpoint mvmult mmmult mat-inverse
in number.cljc
represented as a vector of two rational numbers [x y] or [r a] with the possibility of being infinity where 1/zero = infinity and 1/infinity = zero and zero/zero = infinity/infinity = undefined
complex numbers can be added, multiplied and conjugated they have a length and an angle
linear fractional transformation in trasnform.cljc
represented as a vector of four complex numbers [a b c d] that can be normalized so that ad - bc = 1 has a determinant, trace, inverse can be composed and conjugated
translation rotation scaling inversion all represented as 4-vectors of complex number
composition of transformation implemented as matrix multipliation of 2x2 complex matrices
inverse of a transformation as inverse of a 2x2 matrix conjugation by a conjugataing map as composition of three matrices
image of a generalized circle in geometry.cljc
Grandma’s recipe and project 3.7 in Indra’s Pearls
my idea: image of a line line represented by two points look at image of the two points and of their midpoint they are either collieanr, in which case the image of the line is a line or they form a triangle, in which case the image of the line is a circle, the circumcircle of the triangle
so what is the circumcircle of a triangle? the circumcenter is the intesection of the perpendicualr bisectors the radius is the distance from the circumcenter to one of the vertices of the triangle see illuminated triangle
todo: look at method from geometry of complex numbers where a generalized circle is repsesented as a Hermitian matrix
extend a line segment between two points to a whole line
given two points, p1 p2, there are three parts: the finite segment p1 to p2 the infinite segments from infinity to p1 and from p2 to infinity
the image of the three parts can also be distinguished
given three points the circumcircle of a triangle, if not collinear or a line, a circle passing through infinity, if collinear
z = (at + b)/(ct + d) generalized equation z*zbar + a*z + abar*zbar + b = 0 center = -abar radius = a*abar - b
example: z = (1 + it)/(1 - it) z1 z0 z_infinity
constructed and calibrated
passing through three given points, p q and r at t = 0, 1 and infinity, respectively see Deaux
Introduction to Geometry Coxeter
Indra’s Pearls The vision of Felix Klein Mumford, Series, Wright
Visual Complex Analysis Tristan Needham
Geometry of Complex Numbers Hans Schwerdttfeger
Introduction to the Geometry of Complex Numbers Roland Deaux
clojurescript testing https://github.com/clojure/clojurescript/wiki/Testing
generative tests https://github.com/clojure/test.check
for documentation and testing
blog: http://blog.getprismatic.com/schema-for-clojurescript-data-shape-declaration-and-validation/ docs: http://prismatic.github.io/schema/
github: https://github.com/Prismatic/schema
https://github.com/jessitron/contracts-as-types-examples/blob/master/test/contractypes/report_example_test.clj https://github.com/jessitron/contracts-as-types-examples https://github.com/jessitron/schematron
Philly ETE 2015 #4 Contracts & Clojure: The Best-Yet Compromise of Types and Tests Jessica Kerr https://www.youtube.com/watch?v=GFQqyXoL0YQ http://www.slideshare.net/jessitron/contracts-inclojurepete
david mcneil extending prismatic schema to higher order http://david-mcneil.com/post/114783282473/extending-prismatic-schema-to-higher-order https://gist.github.com/david-mcneil/a46b091c05a91adb8336
(def Point [s/Num])
(def Circle "a schema for circles" {:center Point :radius s/Num})
(s/check Circle {:center [0 0] :radius 1})
(s/validate Circle {:center [0 0] :radius 1})
(def circle [(s/one s/Keyword "tag") (s/one Circle "data")])
(s/check circle [:circle {:center [0 0] :radius 1}])how to describe [:triangle p1 p2 p3]
for instance a point is a single complex number a line, two complex numbers a triangle made up of three complex numbers, if not collinear, has a circumcircle - a circumcenter and a radius a transform can be applied to a point a line or a triangle and consists of complex addition and multiplication along with subtraction and division with refelction and inversion using the complex conjugate