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Points/On,C,N

N Equally Spaced Points on Circle

Creates N equally spaced points around a circle circumference — used for bolt-hole patterns and regular polygon construction.

What It Does

The Points/On,C,N operator creates N equally spaced points around the circumference of a circle, starting at a specified angle. This is the primary operator for bolt-hole patterns, regular polygon vertices, and circular arrays.

Syntax

Points/On, C, N, Angle, Z

Quick Input

C: [circle reference] Angle: [starting angle in degrees] N: [number of points] Z: 0

Direction Selector

No direction selector is required. The result is uniquely determined by the input geometry.

Worked Examples

Example 1 — 6-hole bolt pattern: C0 = Centre (0,0), radius 50 Points/On, C0, 6, 0, 0 → P0 = (50, 0) [at 0°] → P1 = (25, 43.301) [at 60°] → P2 = (-25, 43.301) [at 120°] → P3 = (-50, 0) [at 180°] → P4 = (-25, -43.301)[at 240°] → P5 = (25, -43.301) [at 300°] Example 2 — 4-hole pattern at 45° start: C0 = Centre (0,0), radius 30 Points/On, C0, 4, 45, 0 → P0 = (21.213, 21.213) [at 45°] → P1 = (-21.213, 21.213) [at 135°] → P2 = (-21.213, -21.213) [at 225°] → P3 = (21.213, -21.213) [at 315°]

Analytic Rule

Angular spacing = 360° / N Point i at angle: start_angle + i * (360/N) Coordinates: xi = cx + r * cos(start + i * 360/N) yi = cy + r * sin(start + i * 360/N) All N points created simultaneously. Each assigned an individual point reference identifier. Result: N exact analytic points.

FAQ

How do I create a bolt-hole pattern?

Use Points/On,C,N to create the hole centre points, then use Circle/Centre,R at each point to create the hole circles. The bolt circle radius is the pitch circle diameter / 2.

What is the starting angle?

The starting angle is measured from the positive X axis, counterclockwise. 0° places the first point at the rightmost position. 90° places it at the top.