Curve Continuity and the Curvature Comb
A curve can pass through a node without a visible corner and still have an uneven transition. Continuity describes what the adjoining segments share at that point: position, direction, curvature, and the way curvature changes.
Use these distinctions to diagnose a particular shape. A higher continuity level is useful only where it supports the design.
The Curvature Comb
Choose View > Contours > Curvature to show the curvature comb. The Toolbar, View panel, and Measurements widget also provide curvature controls. FontLab draws a fringe of short lines perpendicular to the outline. Each line represents the amount of bending at that position.
Longer bristles indicate tighter curvature; shorter bristles indicate gentler curvature. A straight segment has zero curvature. The comb's scale and appearance can be adjusted in Preferences > Glyph Window, so compare adjoining curves under the same display settings.
Inspect one join
- Open a curved glyph and make it current.
- Enable Curvature and zoom to a node that should join smoothly.
- Follow the comb toward the node from both sides.
- Compare the direction, height, and progression of the bristles across the join.
- Hide the comb or use Quick Preview to judge whether the feature is visible in the filled letter.
A gap or angular separation at the join can indicate a change in tangent direction. If the combs meet in direction but their heights jump, the curvature differs on the two sides. Curve tension, introduced with curve construction, changes how curvature develops along a segment; the comb lets you inspect that result. The comb envelope is the boundary traced by the tips of the bristles. Even when bristle heights match at the join, an abrupt change in that boundary’s slope can reveal a mismatch in how curvature develops.
Inspect the whole segment as well as its endpoints. A bump in the middle can reveal an unwanted change in bending even when the joins look regular. Near an inflection, curvature approaches zero and changes sign; that can be a deliberate feature rather than a defect.
The comb is a readout. Turning it on does not smooth a curve or constrain a node. It helps you decide which point or handle needs attention. Tunni controls and ordinary point editing can change the shape while the comb reports the result.
Use the comb to assess structure
An extra node may divide what could be one clean curve into two awkward segments. If the join is difficult to regularize, try removing the node on a copy and compare the result. Conversely, a complex intended curvature progression may need another segment.
A quiet-looking comb is not proof that a node is redundant, and a changing comb is not automatically bad. The outline's intended shape remains the test. Very small numerical differences can also become exaggerated by a large comb scale.
Continuity Levels: G0–G3
The geometric continuity levels form a hierarchy: each higher level includes the lower ones.
| Level | What matches at the join | Typical diagnostic |
|---|---|---|
| G0 | Position: the segments meet | A corner is possible because direction need not match |
| G1 | Tangent direction as well as position | No directional break, but comb height can jump |
| G2 | Curvature as well as tangent direction | Comb heights match across the join |
| G3 | Rate of change of curvature as well | The comb envelope progresses through the join without an abrupt slope change |
Position and direction
G0 means that the segments connect. It does not require a corner, and a corner-node property does not prove that the actual geometry has a kink. It permits independent directions; the resulting positions determine whether those directions happen to align.
An ordinary smooth node maintains the aligned handle relationship needed for G1 on a regular curve join. A tangent node maintains the directional relationship between a line and a curve. These constraints prevent an abrupt direction change, but do not necessarily match curvature.
Curvature
At G2, the curvature agrees on both sides of the join. This is different from saying that the curve has constant curvature everywhere. Curvature can vary along both segments while meeting at the same value at the node.
A line has zero curvature. A curve joining it with G2 continuity therefore needs curvature approaching zero at the join. Merely aligning the curve handle to the line gives the directional condition, not necessarily that curvature condition.
Change of curvature
G3 adds agreement in how rapidly curvature changes along the path. It can help a long, rounded transition feel even, but is a stronger constraint on the geometry. Forcing it onto an intentionally taut or angular shape can change the design substantially.
The comb is a visual diagnostic of these relationships, not a numerical certificate. Rounding, very short handles, and extreme magnification can complicate its appearance. Judge the join in context and inspect the intended output.
Use G0 where a corner is intended, G1 where direction alone needs to flow, and higher continuity where the shape benefits from it. The objective is a controlled curve, including any deliberate discontinuities.