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Finite segments, infinite lines, and half-line rays, plus the constructions built on them - parallels, perpendiculars, bisectors, and tangents.
Locus keeps three straight-edge objects strictly distinct, because they behave differently the moment you intersect anything with them.
A segment is finite - the edge between two points, and nothing beyond. A line is fully infinite, running forever in both directions. A ray is a half-line: it starts at a point and shoots infinitely through a second one.
The distinction is not cosmetic. It decides where crossings count:
- A segment crosses another object only between its two endpoints: where it's actually drawn.
- A line crosses along its whole infinite extent.
- A ray crosses only on the forward half, ahead of its start point, never behind it.
So if you want two short edges to register a crossing out past their ends, build a line through those points instead of a segment. All three carry editable defining points, so you can retarget their ends later and everything built on them updates live.
Give the parallel tool a base line (or segment) and a point, and it draws the infinite line through that point running parallel to the base. The perpendicular tool does the same at a right angle to the base. Both stay live - move the base or the point and the result re-orients.
The perpendicular bisector is the line at a right angle to a segment through its midpoint - the set of points equidistant from both ends. Build it from two points, or from a single segment.
Like the midpoint, it's a dual-form construction: it can be defined either by two loose points or by a segment, and you can redefine it between the two later by double-clicking its reference row and picking the other kind. Built from a segment, it remembers that segment and follows its endpoints as they move.
The angle bisector splits the angle between two arms. Each arm can be a point or an object (a segment, ray, or line), and you can mix them:
- Two point arms bisect the angle at a chosen vertex.
- Two object arms bisect the angle at the point where those two objects cross: the vertex is found for you.
- One of each bisects between the point's direction and the object's direction at the vertex.
By default the result is an infinite line. Turn on Only Ray and you get a half-line instead, starting at the vertex and heading out along the bisector direction - useful when you only want the bisector going one way.
The tangent tool draws a line from an outside point that just touches a circle (or arc). There are always two such tangents, one on each side. When you draw it, click the external point and then the circle, and Locus drops a draggable tangent point on the circle - drag it to flip which of the two tangents you get, following your cursor and snapping to the exact touch point when you release. A point inside the circle has no tangent, so those are skipped.
Any line object carries a small LINE / RAY toggle in its row in the Layers panel. Click it to switch that object between drawing as a full infinite line and drawing as a half-line from its anchor. This is the panel-side equivalent of the angle bisector's Only Ray option - the same per-object choice, exposed as a control you can flip whenever you like.
Tip
For where these objects register crossings with circles and ellipses, see Circles & arcs and Ellipses.
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