In this sketch I make use of the cross product of two 2D vectors, to determine whether 3 points are collinear (*NB: you cannot do this with PVector, because it returns the cross product of two 3D vectors, so is flawed*). Here is the sketch:-

```
import py5
from vector.vec2d import Vec2D
from circle.t_points import TrianglePoints
from circle.circumcircle import Circumcircle
def settings():
py5.size(800, 600, py5.P2D)
def setup():
global points
sketch_title('Circumcircle')
py5.ellipse_mode(py5.RADIUS)
py5.scale(1, -1)
py5.translate(0, -py5.height)
points = TrianglePoints()
def draw():
global points
py5.background(0)
py5.no_stroke()
pts = points.positions()
for pt in pts:
py5.fill(255, 255, 0)
py5.ellipse(pt.x, pt.y, 5, 5)
py5.fill(250)
py5.text(str(pt), pt.x - 30, pt.y - 20)
py5.no_fill()
py5.stroke(200, 0, 0)
if points.full():
py5.triangle(pts[0].x, pts[0].y, pts[1].x, pts[1].y, pts[2].x, pts[2].y)
draw_circle()
def mouse_pressed():
global points
points.append(Vec2D(py5.mouse_x, py5.mouse_y))
def draw_circle():
global points
circumcircle = Circumcircle(points.positions())
if points.full():
circumcircle.calculate()
center_point = circumcircle.center
radius = circumcircle.radius
py5.no_fill()
py5.stroke(255)
if points.collinear():
return
py5.ellipse(center_point.x, center_point.y, radius, radius)
def sketch_title(name):
py5.get_surface().set_title(name)
py5.run_sketch()
```

For full code see github repo here. Here is snippet using matrix from numpy to calculate center and radius of circumcircle:-

```
import numpy as np
from vector.vec2d import Vec2D
# Circumcircle from 3 points
class Circumcircle:
def __init__(self, points):
self.points = points
def calculate(self):
vec = self.points[2]
self.center = Vec2D(-(self.bx() / self.am()), -(self.by() / self.am()))
self.radius = self.center.dist(vec) # points[2] = c
# Matrix math see matrix_math.md and in detail
# http://mathworld.wolfram.com/Circumcircle.html
def am(self):
pts = self.points
a = [pts[0].x, pts[0].y, 1.0]
b = [pts[1].x, pts[1].y, 1.0]
c = [pts[2].x, pts[2].y, 1.0]
matrix = np.array([a, b, c])
return 2 * np.linalg.det(matrix)
def bx(self):
pts = self.points
a = [pts[0].x**2 + pts[0].y**2, pts[0].y, 1.0]
b = [pts[1].x**2 + pts[1].y**2, pts[1].y, 1.0]
c = [pts[2].x**2 + pts[2].y**2, pts[2].y, 1.0]
matrix = np.array([a, b, c])
return -np.linalg.det(matrix)
def by(self):
pts = self.points
a = [pts[0].x**2 + pts[0].y**2, pts[0].x, 1.0]
b = [pts[1].x**2 + pts[1].y**2, pts[1].x, 1.0]
c = [pts[2].x**2 + pts[2].y**2, pts[2].x, 1.0]
matrix = np.array([a, b, c])
return np.linalg.det(matrix)
```