Lines and arcs

planex2d has three exact edge types: lines, circular arcs and full circles. Each constructor returns a wire of one edge, so the result can go straight into a face, a Boolean operation or an export, and wire.edges[0] gives the edge itself. Smooth curves through points are described in Splines.

import math
import planex as px

Lines and arcs

A line runs between two points. An arc runs from its start to its end around a center, counterclockwise unless reverse=True is given. Figure 1 shows a line from (0, 0) to (30, 40) (a), a quarter circle of radius 10 from (10, 0) to (0, 10) (b), and the other three quarters between the same points, drawn clockwise (c). The ends are marked.

line = px.Line((0, 0), (30, 40))
quarter = px.Arc((10, 0), (0, 10), center=(0, 0))
rest = px.Arc((10, 0), (0, 10), center=(0, 0), reverse=True)

(a) A line

(b) Counterclockwise: a quarter

(c) reverse=True: three quarters

Figure 1: A line and two arcs between the same points

The lengths are 50, 5π and 15π, the last one up to the rounding of its final digit:

print("line:", line.mass)
print("quarter / π:", quarter.mass / math.pi)
print("three quarters / π:", rest.mass / math.pi)

line: 50.0
quarter / π: 5.0
three quarters / π: 14.999999999999998

Full circles

px.Circle(center, r) makes a full circle. It is one exact edge with no vertices. Nothing splits it into arcs until another edge crosses or touches it, and a face with a circular hole keeps the hole as one edge.

ring = px.Circle((0, 0), 10)
edge = ring.edges[0]
print(len(ring.edges), "edge,", len(ring.vertices), "vertices")
print("center", tuple(edge.center), "radius", edge.edge.radius)
print("length / π:", ring.mass / math.pi)

1 edge, 0 vertices
center (0.0, 0.0) radius 10.0
length / π: 20.0

What an edge knows

Every edge provides its start, its end and its midpoint. An arc also provides its center, its radius and its sweep in degrees. The sweep is negative when the arc runs clockwise. Figure 2 shows these points for both arcs.

e = quarter.edges[0]
print("start", tuple(e.start), "end", tuple(e.end), "midpoint", tuple(e.midpoint))
print("center", tuple(e.center), "radius", e.edge.radius, "sweep", e.edge.sweep)
print("sweep of the three quarters:", rest.edges[0].edge.sweep)

start (10.0, 0.0) end (0.0, 10.0) midpoint (7.0710678118654755, 7.071067811865475)
center (0.0, 0.0) radius 10.0 sweep 90.0
sweep of the three quarters: -270.0

(a) The quarter

(b) The three quarters

Figure 2: The points every arc provides

The edge data that belongs to the edge’s geometry, such as the radius and the sweep, sits on e.edge. The points, the length and the properties sit on e itself.