In order to draw, for instance, roads or walls, we know how to calculate a miter join on 2 connecting lines, resulting in something like this
But is there an algorithm to efficiently calculate points for a nice join when 3 or more lines connect to the same point, like this
The input is a list of segments
NB: The ultimate goal is to triangulate this
Let's say your segments (in red) join in the origin of your cartesian coordinates system. Identify your segments by their angle from an axis of your choice, let's say the x axis. Draw the walls (in black) around the segment, let's say they have both different width from the red segment, t₁ and t₂.
Now the idea is to find the coordinates of your intersection vector. As you can see, a rhombus immediatly emerges from this geometry. Doing a bit of vector calculation gets you easily to the answer.
Here is a little Python script for illustration, using MatPlotLib:
import matplotlib.pyplot as plt
import math
angles = [1.0, 2.0, 2.5, 3.0, 5.0] # list of angles corresponding to your red segments (middle of your walls)
wall_len = [0.05, 0.1, 0.02, 0.08, 0.1] # list of half-width of your walls
nb_walls = len(angles)
for a in angles:
plt.plot((0, math.cos(a)), (0, math.sin(a)), "r", linewidth=3) # plotting the red segments
for i in range(0, len(angles)):
j = (i + 1)%nb_walls
angle_n = angles[i] # get angle Θ_n
angle_np = angles[j] # get the angle Θ_n+1 (do not forget to loop to the first angle when you get to the last angle in the list)
wall_n = wall_len[i] # get the thickness of the n-th wall t_n
wall_np = wall_len[j] # get the thickness of the n+1-th wall t_n+1
dif_angle = angle_np - angle_n # ΔΘ
t1 = wall_n/math.sin(dif_angle) # width of the rhombus
t2 = wall_np/math.sin(dif_angle) # height of the rhombus
x = t2*math.cos(angle_n) + t1*math.cos(angle_np) # x coordinates of the intersection point
y = t2*math.sin(angle_n) + t1*math.sin(angle_np) # y coordinates of the intersection point
wall_n = [math.cos(angle_n), math.sin(angle_n)] # for plotting n-th wall
wall_np = [math.cos(angle_np), math.sin(angle_np)] # for plotting n+1-th wall
plt.plot((x, wall_n[0] + x), (y, wall_n[1] + y), "k") # plotting the n wall
plt.plot((x, wall_np[0] + x), (y, wall_np[1] + y), "k") # plotting the n+1 wall
plt.show()
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