Geometry & modeling
Surface continuity
Definition
Surface continuity describes how smoothly adjacent curves or surface patches meet. G0 continuity joins them at the same position, G1 also aligns their tangent direction, and G2 additionally matches curvature so the rate of bending flows across the boundary.
Also known as: geometric continuity
Updated
G0, G1, and G2#
Autodesk Fusion Help exposes three matching levels for T-spline edges:
- G0, or positional continuity, makes the boundaries meet.
- G1, or tangent continuity, also aligns their tangent directions.
- G2, or curvature continuity, also aligns how curvature changes through the join.
A deliberate corner may need only G0. A normal mechanical blend often needs G1. A glossy product surface may need G2 so reflections do not reveal an abrupt curvature change.
How it is inspected#
Autodesk Fusion Help documents zebra, curvature-map, and environment-map analysis for checking surface quality and curvature. CAD systems also use curvature combs and cross-sections to expose pinches and changes that can disappear in ordinary shaded display.
Continuity is a local condition at a join. A G2 boundary does not guarantee that the rest of either patch has good shape, suitable draft, or enough wall thickness after the surfaces become a solid.
Relation to NURBS#
NURBS surfaces are controlled by mathematical curves and control points, so the CAD system can evaluate position, tangent direction, and curvature along a shared edge. The chosen continuity level constrains how neighbouring surfaces behave at that edge; it does not make unrelated patches globally smooth.
Sources
Related terms
Surface modeling
Surface modeling creates and edits zero-thickness faces that define the outer boundary of a shape without enclosing material or volume. It is used for complex curvature, product styling, face repair, and hybrid workflows where surfaces are later stitched, knit, or thickened into a solid.
NURBS
NURBS are mathematical curves and surfaces that can represent both simple shapes, such as lines, arcs, and circles, and complex freeform surfaces exactly. CAD kernels use them for the faces and edges of B-Rep solids that are not simple planes or cylinders.
B-Rep
B-Rep is the way professional CAD kernels describe a solid: by its boundary, made of exact surfaces (faces), the curves where they meet (edges), and the points where edges end (vertices). Because the geometry is exact and the topology is explicit, B-Rep models can be measured, filleted, dimensioned, and manufactured precisely.