Jarvis March Algorithm, also known as gift wrapping. Coding in Processing / Java and inspired by thecodingtrain.com computational geomentry.

JarvisMarch.pde

import java.util.*;

ArrayList<PVector> jarvisMarch(ArrayList<PVector> _input) throws InvalidJarvisInputException {

  if (_input.size() < 3) throw new InvalidJarvisInputException("Input must have at least 3 PVectors in the list.");

  ArrayList<PVector> output = new ArrayList<PVector>();

  ArrayList<PVector> input = deepCopyArrayListPVector(_input);
  Collections.sort(input, new leftSorter());

  output.add(input.get(0));

  int current = 0; // index into output
  int next = 1; // index into input
  while (true) {

    for (int i = 1; i < input.size(); i++) {
      PVector a = input.get(next).copy().sub(output.get(current));
      PVector b = input.get(i).copy().sub(output.get(current));
      PVector cross = a.cross(b);
      if ( cross.z < 0 || (cross.z == 0 && b.mag() > a.mag()) ) {
        next = i;
      }
    }

    if (next == 0) break;

    output.add(input.get(next));
    current++;
    input.remove(output.get(current));
    next = 0;

  }

  return output;

}

class InvalidJarvisInputException extends Exception {
  InvalidJarvisInputException(String message) {
    super("ERROR: Invalid Arguments for jarvisMarch(). " + message);
  }
}

class leftSorter implements Comparator<PVector> {
  int compare(PVector a, PVector b) {
    return round(a.x - b.x);
  }
}

ArrayList<PVector> deepCopyArrayListPVector(ArrayList<PVector> ls) {
  ArrayList<PVector> cp = new ArrayList<PVector>(ls.size());
  for (PVector v : ls) {
    cp.add(v.copy());
  }
  return cp;
}

Sketch.pde

int WIDTH = 600;
int HEIGHT = 600;

ArrayList<PVector> points = new ArrayList<PVector>();
ArrayList<PVector> hull;

void settings() {
  size(WIDTH, HEIGHT);
}

void setup() {

  int padding = width / 8;
  for (int i = 0; i < 25; i++) {
    points.add(new PVector(random(padding, width - padding), random(padding, height - padding)));
  }

  try {
    hull = jarvisMarch(points);
  } catch (Exception e) {
    e.printStackTrace();
    exit();
  }

}

void draw() {

  beginShape();
  for (int i = 0; i < hull.size(); i++) {
    vertex(hull.get(i).x, hull.get(i).y);
  }
  endShape(CLOSE);

  for (int i = 0; i < points.size(); i++) {
    circle(points.get(i).x, points.get(i).y, 3);
  }

  noLoop();
  
}