Title: Draw stars inside polygons with Python and tkinter

[This program connects the vertices on polygons in various ways to draw stars.]

This example shows how to draw stars inside a polygon by connecting every M-th vertex as it draws. If the polygon has N sides and N and M are relatively prime (have no common factors except 1), then the lines visit every vertex and the result is a star. If M is 1, then the lines draw the polygon.

The draw method loops for i in range(num_points), drawing each star in the center of the program's canvas. It also draws each star near the i-th vertex.

The following code shows the draw method that arranges the star drawing.

def draw(self): # Delete any previous drawing objects. self.canvas.delete(tk.ALL) try: num_points = int(self.num_points_var.get()) if num_points < 3: messagebox.showinfo('Invalid # Points', 'The polygon must have at least 3 points.') return # Get the polygon radii. width = self.canvas.winfo_width() height = self.canvas.winfo_height() r3 = min(width, height) / 2 r1 = r3 / 2 r2 = r3 / 4 r3 = r1 + r2 # Position variables. cx = width / 2 cy = height / 2 # Position the original points. pts1 = [] pts2 = [] theta = -math.pi / 2 dtheta = 2 * math.pi / num_points for i in range(num_points): pts1.append((r1 * math.cos(theta), r1 * math.sin(theta))) pts2.append((r2 * math.cos(theta), r2 * math.sin(theta))) theta += dtheta # Draw stars. for skip in range(1, num_points): # Draw the big version of the star. self.draw_star(num_points, cx, cy, pts1, skip) # Draw the smaller version. theta = -math.pi / 2 + skip * 2 * math.pi / num_points x = int(cx + r3 * math.cos(theta)) y = int(cy + r3 * math.sin(theta)) self.draw_star(num_points, x, y, pts2, skip) except Exception as ex: messagebox.showinfo('Drawing Error', ex)

The draw method starts by making arrays holding points to draw the central and outer stars. These points would draw a polygon centered at the origin if they were drawn as they are in the arrays.

Next the code starts a for loop to draw the smaller polygons. The program calls the draw_star method to draw the central star. It then calculates where the smaller polygon should be drawn and calls draw_star again to draw it there.

The draw_star method shown in the following code draws the lines connecting a polygon's vertices.

def draw_star(self, num_points, x, y, orig_pts, skip): '''Draw a star centered at (x, y) using this skip value.''' # Make a PointF array with the points in the proper order. pts = [] for i in range(num_points): pt = orig_pts[(i * skip) % num_points] pts.append((pt[0] + x, pt[1] + y)) # Draw the star. self.canvas.create_polygon(pts, fill='', outline='red')

This code makes a pts list to hold points. It loops through the vertex numbers. It calculates (i * skip) % num_points for each so it skips some vertices each time. It gets the appropriate vertex, adds the x and y values to center the star at the correct location, and adds the translated point to the pts list.

After building the pts list, the code uses it to create a polygon that draws the star.

Download the example to see all of the details.