Convex Hull with Rhino Python
This Rhino Python code calculates the cross-product determinant used to determine the orientation of three points (current, next_point, and point) to see if they form a left turn or a right turn. This is a well-known technique in computational geometry to check the relative orientation of points. In this script, the direction is the cross-product determinant that determines the relative orientation of the points. If the result is negative, the point is to the right of the line from current to next_point, indicating a clockwise turn. On the other hand, if the result is positive, this means they are counter-clockwise. If the result is zero, this means the points are collinear. Therefore, the algorithm correctly identifies the points that form the convex hull by wrapping around the set of points.
The Convex Hull Generator for Rhino is a tool designed to create convex hulls from selected point clouds. It uses the gift-wrapping algorithm (Jarvis March). Thus, users can select points within Rhino, and the script will calculate and draw the convex boundary by connecting the outermost points. It is educational for those who want to understand the cross-product.
import rhinoscriptsyntax as rs
def convex_hull(points):
start = min(points, key=lambda p: p[0])
hull = [start]
current = start
while True:
next_point = points[0]
for point in points:
if point == current:
continue
direction = (next_point[0] - current[0]) * (point[1] - current[1]) - (next_point[1] - current[1]) * (point[0] - current[0])
if direction < 0 or next_point == current:
next_point = point
if next_point == start:
break
else:
hull.append(next_point)
current = next_point
return hull
points = rs.GetPointCoordinates("Select points")
if points:
hull = convex_hull(points)
for i in range(len(hull)):
rs.AddLine(hull[i], hull[(i + 1) % len(hull)])
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