Home > Circles & arcs

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Draw circles by center-and-point, by compass radius, or through three points, and sweep exact arcs.

Circles and arcs in Locus are exact - they stay true circular geometry all the way through, rather than being approximated by many short edges. That precision is what lets booleans, offsets, and export come out clean.

The most direct circle: click a center, then click a second point that sits on the circle. The distance between them is the radius. Because both are live points, dragging either one resizes or moves the circle, and anything built on it follows.

The compass circle sets its radius from a value rather than a point on the circle. Click a center, then supply the radius in one of two ways:

• Type a number.
• Pull the radius from an existing object: click a segment (its length becomes the radius) or another circle or arc (its radius becomes the radius).

When you pull the radius from another object, the link stays live: resize that source and every compass circle built from it resizes too. This is the way to keep a family of circles locked to a shared, editable size.

Click three points and Locus draws the one circle that passes through all of them - the circumcircle. Its center and radius are derived from the three points, so it stays live as you drag them. If the three points fall in a straight line there's no circle to draw, and that case is simply skipped.

Click three things and Locus draws a circle that touches or passes through all of them. A point is passed through; a line, segment, ray, circle or arc is touched. Each pick has to be a different object.

There is usually more than one answer. After the third click a ghost follows your cursor through them: move it until the one you want is showing, then click. The circle stays associative and keeps the solution you chose, not whichever is nearest later.

The name is Apollonius of Perga, the Greek geometer who around 200 BC asked for a circle touching three given points, lines or circles.

An arc is a partial circle. Click a center, then a start point, then wind the cursor to sweep the arc out to its end - the arc previews live as you move, and the click commits it. The radius comes from the center-to-start distance.

Winding is what gives you control over which way the arc goes. Sweep it the short way for the minor arc, or carry the cursor the long way around to commit the major arc. (When an arc is instead built from a fixed set of three points, it takes the short way between them.)

A whole circle (or ellipse) is a first-class fillable object - you don't have to wrap it in a region loop to give it a fill. Two ways to do it:

• Select the circle and use the Region tool, or
• Pick the Fill tool and click inside the circle.

Either way Locus fills the closed curve in place. Its Fill swatch then shows in the Layers style strip, its interior becomes click-selectable, and the fill exports to SVG (see Exporting SVG). When circles nest, clicking with the Fill tool fills the smallest one enclosing the click.

< Previous: Lines, rays & segments | Next: Ellipses >

• In the node graph: Circle: Center Point | Circle: Center Radius | Circle: 3 Points | Arc - build the same circles and arcs as nodes.