isedgar

function ray_casting(point, polygon){
    var n=polygon.length,
        is_in=false,
        x=point[0],
        y=point[1],
        x1,x2,y1,y2;

    for(var i=0; i < n-1; ++i){
        x1=polygon[i][0];
        x2=polygon[i+1][0];

isedgar

var polygon={
    area: function(points){
        var sum=0, n=points.length;

        if(points[0][0] != points[n-1][0] || points[0][1] != points[n-1][1]){
            sum += (points[n-1][0]*points[0][1] - points[0][0]*points[n-1][1]);
        }

        for(var i=0; i < n-1; ++i){
            sum += (points[i][0]*points[i+1][1] - points[i+1][0]*points[i][1]);

isedgar

function inner_angle(a,b,c){ // inner angle at point b in degrees
    var v1=[a[0] - b[0], a[1] - b[1]],
        v2=[c[0] - b[0], c[1] - b[1]];
        
    return Math.acos(math.inner(v1, v2) / (math.norm(v1) * math.norm(v2))) * 180 / Math.PI;
}

var math={
    norm: function(v){
        var s=0, n=v.length;

isedgar

var app={
    angle: function(a,b,c){ // angle at point b
        var v1=[b[0] - a[0], b[1] - a[1]],
            v2=[b[0] - c[0], b[1] - c[1]];
            
        return Math.acos(this.inner(v1, v2) / (this.norm(v1) * this.norm(v2)));
    },
    is_clockwise: function(a,b,c){
        return ((b[0]-a[0]) * (c[1]-a[1]) - (c[0]-a[0]) * (b[1]-a[1])) < 0 ? true : false;
    },

isedgar

def ray_casting(point, polygon):
    intersections = 0
    x, y = point

    for k in range(len(polygon)-1):
        x1, y1 = polygon[k]
        x2, y2 = polygon[k+1]

        if (y < y1) != (y < y2) and\
        x < (x2-x1)*(y-y1)/(y2-y1)+x1:

isedgar

Voronoi diagram in the Cartesian plane

INPUT:

sites := {(x₀, y₀), (x₁, y₁), ..., (x_n-1, y_n-1)}

pad := padding (some number)

---

ALGORITHM:

n := number of sites

isedgar

Voronoi diagram in the Cartesian plane

INPUT:

S := {(x₀, y₀), (x₁, y₁), ..., (x_n-1, y_n-1)}

pad := padding (some number)

---

ALGORITHM:

x_l := minimum x-coordinate in S (left)

isedgar

// Naive code to create 2D Voronoi cells (Cartesian plane)

var voronoi = {
    compute: function(sites, pad){ // pad: box padding
        var boundary = this.points_boundary(sites);

        var x_left = boundary[0] - pad;   // min x
        var y_bottom = boundary[1] - pad; // min y
        var x_right = boundary[2] + pad;  // max x
        var y_top = boundary[3] + pad;    // max y

isedgar

samples = [[1,2], [2,0], [3,1], [2,2]]
labels = [1,1,-1,-1]

def dot(a, b):
    return sum([a[j]*b[j] for j in range(len(a))])

w, b = [0,0], 0

for n in range(100):
    n_updates = 0

isedgar

import numpy as np
from sklearn.preprocessing import normalize
from sklearn.multiclass import OneVsOneClassifier as ovo
from sklearn.linear_model import Perceptron

X = np.array([[-1,0,0,0,0,0,0,0],[-1,-1,0,0,0,1,0,0],[-1,0,-1,0,0,1,0,0],[-1,-1,-1,0,0,1,0,1],[-1,0,-1,-1,0,1,0,1],[-1,0,-1,0,-1,1,0,1],[-1,0,-1,0,0,1,-1,1],[-1,0,0,-1,0,1,0,0],[-1,0,0,0,-1,1,0,0],[-1,0,0,0,0,1,-1,0],[-1,0,0,0,0,1,0,-1],[0,-1,0,0,0,0,0,0],[-1,-1,0,0,0,1,0,0],[0,-1,-1,0,0,1,0,0],[-1,-1,-1,0,0,1,0,1],[0,-1,-1,-1,0,1,0,1],[0,-1,-1,0,-1,1,0,1],[0,-1,-1,0,0,1,-1,1],[0,-1,0,-1,0,1,0,0],[0,-1,0,0,-1,1,0,0],[0,-1,0,0,0,1,-1,0],[0,-1,0,0,0,1,0,-1],[0,0,-1,0,0,0,0,0],[-1,1,-1,0,0,0,0,0],[-1,1,-1,1,-1,0,0,0],[-1,1,-1,1,0,-1,0,0],[-1,1,-1,1,0,0,-1,0],[-1,1,-1,1,0,0,0,-1],[0,1,-1,-1,0,0,0,0],[0,1,-1,0,-1,0,0,0],[0,1,-1,0,0,-1,0,0],[0,1,-1,0,0,0,-1,0],[0,1,-1,0,0,0,0,-1],[0,0,0,-1,0,0,0,0],[1,-1,0,-1,0,0,0,0],[1,-1,-1,-1,0,1,0,0],[1,-1,-1,-1,1,1,-1,0],[1,-1,-1,-1,1,1,0,-1],[1,-1,0,-1,-1,1,0,0],[1,-1,0,-1,0,1,-1,0],[1,-1,0,-1,0,1,0,-1],[1,0,-1,-