13 2d and 3d geometry with fastmath.vector - DRAFT 🛠
authors: Nedeljko Radovanovic, Epidiah Ravachol, Daniel Slutsky
(ns noj-book.fastmath-vector-geom2d3d
(:require [fastmath.vector :as vec]
[clojure.math :as math]
[emmy.mafs :as mafs]
[scicloj.kindly.v4.kind :as kind]))13.1 a few operations
13.1.1 rounding
(-> (vec/vec2 1/3 2/3)
(vec/approx 5))[0.33333 0.66667]13.1.2 addition
(vec/add (vec/vec2 -2 -1)
(vec/vec2 1 4))[-1.0 3.0]13.1.3 rotation
Pi radians = 180 degress
(-> (vec/vec2 1 0)
(vec/rotate math/PI))[-1.0 1.224646799076922E-16](-> (vec/vec2 1 0)
(vec/rotate math/PI)
(vec/approx 5))[-1.0 0.0]rotating by Pi ratians (90 degrees) around the z axis:
(-> (vec/vec3 1 0 1)
(vec/rotate 0 0 (/ math/PI 2))
(vec/approx 5))[0.0 1.0 1.0]13.2 visualizing 2d addition
(the parallelogram rule)
(mafs/mafs
{:viewBox {:x [-5 5 ]
:y [-5 5]}}
(mafs/cartesian)
(mafs/vector [-2 -1] {:color :blue})
(mafs/vector [1 4] {:color :blue})
(mafs/vector (vec
(vec/add (vec/vec2 -2 -1)
(vec/vec2 1 4)))
{:color :red}))13.3 visualizing 2d rotation
(mafs/mafs
{:viewBox {:x [-5 5 ]
:y [-5 5]}}
(mafs/cartesian)
(mafs/vector (vec (vec/vec2 -2 -1))
{:color :blue})
(mafs/vector (vec (vec/rotate
(vec/vec2 -2 -1)
(/ math/PI 2)))
{:color :red}))13.4 visualizing 3d rotation
(defn vec3d->plotly-coords [v]
{:x [0 (v 0)]
:y [0 (v 1)]
:z [0 (v 2)]
:type :scatter3d
:mode :lines+markers
:line {:width 10}
:marker {:size 4}})(let [orig-v (vec/vec3 1 0 0)]
(kind/plotly
{:data [(vec3d->plotly-coords orig-v)
(vec3d->plotly-coords (vec/rotate orig-v
0
(/ math/PI 10)
0))]}))(def random-shape
(repeatedly 6
(fn []
(vec/vec3 (+ 1 (rand))
(+ 2 (rand))
0))))(defn shape->plotly-coords [shape]
{:x (mapv #(% 0) shape)
:y (mapv #(% 1) shape)
:z (mapv #(% 2) shape)
:type :scatter3d
:mode :markers+lines
:line {:width 10}
:marker {:size 4}})(kind/plotly
{:data [(shape->plotly-coords random-shape)
(shape->plotly-coords
(map #(vec/rotate %
0
0
Math/PI)
random-shape))
(shape->plotly-coords [[0 0 0]])]})